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Course Description: Review of basic algebra, second-degree grade of C or higher in MATH 001.
Thinking Skills: The students will engage in the process of inquiry and problem solving that involves both critical and creative thinking. They shall usereasoned standards in solving problems and presenting arguments.
Life Value Skills: The students will analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems. 1)
Communication Skills: The students will communicate orally and in writing in an appropriate manner both personally and professionally. They are expected to read comprehension and the ability to analyze and evaluate. They shall listen with an open mind and respond with respect.
Cultural Skills: The students will understand their own and other cultural traditions and respect the diversity of the human experience.
COURSE OBJECTIVES
Thinking Skills: Students will:
Briefly study the basic ideas of a first algebra course.
Solve quadratic equations by factoring, completing the square, and by use of the quadratic formula.
Improve the ability to read and solve application problems by means of constructing appropriate algebraic models and then applying algebraic techniques to find a solution.
Explore exponential and logarithmic functions, including application problems, and the efficient and appropriate use of logarithms and their properties.
Learn the techniques of solving systems of equations and appropriately apply these processes to word problems.
Communication Skills: Students will:
Communicate both in writing and orally throughout the course; particular attention will be paid to the accurate and appropriate use of the language of algebra.
Use calculators to solve problems, communicate solutions and explore options.
Life Value Skills: Students will
Appreciate the intellectual honesty of deductive reasoning; a mathematician's work must stand up to the scrutiny of logic, and it is unethical to try to pass off invalid work.
Do their own work, honestly challenging themselves to master the material.
Cultural Skills: Students will
Read, write and manipulate mathematical notation.
Experience mathematics as a culture of its own, with its own language and modes of thinkingFURTHER COURSE NOTES: This course is designed to give students the algebraic tools required in subsequent courses, specifically MATH 180 (Elementary Functions), MATH 230 (Elements of Statistics), or MATH 270 (Managerial Mathematics). "Tools" here means both symbol manipulation and the logical and problem-solving skills - in short, how to "do" algebra and "what to do with it".
There are those who view College Algebra as a remedial or review course, since it covers the same material as does high school's Algebra II. It is nevertheless a college course, and I will reguard it as such. I am far more interested in your real understanding of the material than I am in your "loading and dumping" huge lists of definitions and formulas. We will cover the material at about three times the pace of the typical high school version, and much more will be expected of you outside the classroom. The rule of thumb, "2 hours outside of class for each hour in class", is probably appropriate here. You need to see yourself as an active learner, to take responsibility for your own learning, to avail yourself of the aids in place (tutors, the teacher, study groups, computer software, web sites) but to make sure that you honestly learn how to do what is required of you – you can only rely on others up to a point!
Mathematics can be very deceptive, you may understand exactly what is presented in class and, if you are shown how to do a problem, see where each step came from. THIS DOES NOT MEAN YOU CAN DO IT. Think about listening in on a conversation in some other language; you may understand what the people in the conversation are saying, but this does not mean you can join in the conversation very easily. Think of listening to some music that you particularly enjoy. Can you sit down and play it? This takes practice, and the same is true of Math. If you need help with a question, and you have been shown how to do it, try to do one just like it later that day when you are alone. Try a day later. Try again a week later. If you can still do it a week later, you are on your way to owning that particular skill.
You should be capable of success, as long as you apply yourself sufficiently. You are here because your ACT score, your placement exam, or your grades in previous courses, or some combination of these, indicate that this is the appropriate level for you – you are ready for this material, but not yet ready to move on to the course beyond this one. This does not mean this course will be "easy" for you, but that you should be able to handle it.
You must believe that "Mathematics is not a spectator sport". You are the LEARNER and you must engage in the learning process. The purpose of the course is not for me to convince you that I know algebra, but for you to learn it. Again, it comes down to your accepting responsibility for your learning.
Technology You will find the course much easier if you have some sort of graphing calculator. If you have anything other than a TI machine and need some help using it, it will take me a little while to research how your machine works. At the very least, you should have a scientific calculator for some of the work later in the semester.
Please note that the assigned homeworks are odd numbered questions and that the answers to these are at the back of the book. This is so that you can check your work as you go. It does, however, bring up a couple of points 1) SIMPLY COPYING DOWN THE ANSWERS FROM THE BACK OF THE BOOK DOES NOT CONSTITUTE DOING HOMEWORK and 2) your correct answer may not match the correct answer at the back of the book – this should be viewed as a learning experience (how do the two answers match up?)
Examinations 700 pts
There will be sevenCumulative Final Examination 200 pts
Total 1050 pts
Attendance Policy:
You can afford to miss no more than the equivalent of one week of class. Any more absences are a dangerous loss of classtime percentage. Once you have had 4 unexcused absences, every unexcused absence from that point onward will incur a penalty of 10 pts from your participation and attendance score.RESOURCES: Tutoring is available in the Learning Center - third floor, Murphy Center. I also want you to consider coming to see me if you have a problem with some material. Sometimes we can resolve in a few minutes a difficulty that can cause problems for weeks. I don't resent your coming – it's part of my job! I want your success as much as you do.
FINAL COMMENTS: You, as the student, are the learner, andAMERICANS WITH DISABILITY ACT |
Synopses & Reviews
Publisher Comments:
Merchandising math is a multifaceted topic that involves many levels of the retail process, including assortment planning; vendor analysis; markup and pricing; and terms of sale. A Practical Approach to Merchandising Mathematics, Revised 1st Edition, brings each of these areas together into one comprehensive text to meet the needs of students who will be involved with the activities of merchandising and buying at the retail level. Students will learn how to use typical merchandising forms; become familiar with the application of computers and computerized forms in retailing; and recognize the basic factors of buying and selling that affect profit |
Math 131: Precalculus I
PLEASE NOTE
Beginning Summer 2009, this course will be known as Math 141; only the course number will change.
Course Description
Math 131 is the first course in a two-quarter precalculus sequence that also includes Math 132. Math 131 focuses on the general nature of functions. Topics include: linear, quadratic, exponential, and logarithmic functions; and applications.
Who should take this course?
Generally, students seeking to take the 151–152–153 calculus sequence take the 131–132 precalculus sequence first. Some students in programs like business take this course (in place of Math 140) and then take Math 150 instead of Math 132. You should consult the planning sheet for your program and consult an advisor to determine if this sequence is appropriate for you.
Who is eligible to take this course?
The prerequisite for this course is Math 90 with a grade of 2.0 or higher. Students new to EdCC with an appropriately high Accuplacer score may also consider taking Math 131.
Is this course transferable?
This course transfers to the University of Washington as UW Math 120 if both Math 131 and Math 132 are taken; consult an advisor or see the Transfer Center to determine transferability to other institutions.
What textbook is used for this course?
The first edition of Precalculus Concepts and Functions: A Unit Circle Approach by Michael Sullivan and Michael Sullivan III; a lower-priced custom version comprising Chapters 1–7 and 9 is available through the EdCC Bookstore. Beginning Winter 2007, the same textbook will be used for Math 132.
What else is required for this course?
Students are required to have a graphing calculator; the TI-83 Plus or TI-84 Plus is recommended. |
Mathematics
Need to figure out how many overtime hours you must work to make up the lost wages from an unexpected sick day? Want to alter grandma's lasagna recipe to serve 10 instead of 8? Is Pi Day your favorite holiday? If so, then you might want to figure math into your education equation. Mathematics is the science of numbers. Mathematicians use patterns and symbols to formulate and test theories.
As a BYU undergrad, you will have access to top-notch facilities and equipment. Not only is our gear great, but our staff and faculty are as well. In the Math Lab, you can ask skilled student employees for help in any of your mathematics courses. Professors and TAs will be available every step of the way to help guide you on your quest to become a mathMathematics is the search for truth and understanding. It is painting a picture of reality with symbols."
Riding Mathematical Waves
Options for Retailers
Undergraduate research makes classroom learning come alive and can help propel you into a professional career. You will have the opportunity to put your book knowledge into practice by working on real research projects. The Math Department has several special labs and resources available to students including Interdisciplinary Mentoring Program in Analysis, Computation and Theory (IMPACT), Summer Research Experience for Undergraduates (REU), and Center for Mentoring Undergraduate Research in Mathematics (CURM). We teach students technical and research skills that will prepare them areas include making and breaking codes, creating techniques to model sound waves, and using math to explore the many dimensions of the universe.
• Algebraic Geometry
Students study curves, surfaces, and other shapes defined by systems of algebraic equations. This combination of algebra and geometry has many areas of application including computer graphics, cryptography, and mathematical physics.
• Applied Mathematics & Mathematical Physics
Applied mathematics students research mathematical methods that are used in science, engineering, business, and industry. It describes the professional specialty in which mathematicians solve practical problems.
Mathematical physics students study the development of mathematical methods that are applied to physics. It develops methods suitable for the formulation of physical theories.
• Combinatorics & Matrix Theory
Combinatorics students study finite structures. Aspects include counting the structures, deciding when criteria can be met, and constructing and analyzing objects meeting certain criteria.
Matrix theory students study matrices; rectangular arrays of numbers, symbols, or expressions. Matrices are used in most scientific fields including physics, computer graphics, and quantum mechanics.
• Differential Equations & Dynamical Systems
Students research systems that evolve in time, with a particular focus on how short-term rates of change affect long-term outcomes. This theory is applied to the study of many things including the motion of the solar system, the growth of populations, and the spread of disease.
• Geometric Topology & Geometric Group Theory
Geometric topology students research settings which mathematicians call a space. This branch of math emphasizes aspects that are most closely allied to classical geometry like distances, polyhedral objects that generalize intervals and triangles; manifolds that generalize planes, surfaces, and Euclidean spaces.
Geometric group theory students research models of symmetries and rigid motions. It is applied when objects such as a molecule or a space exhibits symmetries or admits motions. The group of symmetries or motions reflects the geometry of the object or space on which it acts.
• Mathematical Biology
Students focus on the mathematical representation, treatment, and modeling of biological processes. This branch of math has a variety of applications ranging from predicting how populations change over time, how infectious diseases spread, and how do cells move.
Students study equations involving unknown functions and several independent variables and their partial derivatives. These equations are used to solve problems such as the propagation of sound, heat, or elasticity.
• Stochastic Differential Equations
Students research equations in which one or more of the terms is a stochastic process. SDE are used to model various phenomena from fluctuating stock prices to thermal fluctuations.
Many of our students go on to get advanced degrees and additional experience that broaden their career opportunities. BYU Mathematics alumni have found jobs in government, academia, and numerous business positions including working at:
"Math is used all over the place—in finances, insurance, engineering, physics, and several other industries. Taking math classes will help you think more analytically and help you to be more diverse in life."
–Darrell Johnson, Symetra Financial
Eric Murphy Lecture
Hear the confessions of a recovering English major and unrepentant math nerd.
Hands On: Riding Mathematical Waves
Join the Hands On team and the Department of Mathematics as they figure out how waves work.
Options for Retailers
See how a BYU student developed options for retailers to help protect against risks.
We Use Math
Discover the opportunities and success you can have by studying math.
Why Mathematicians Play with Bubbles
See math students determine what shape of bubble has the least surface area. |
Lanham Seabrook, MD AlgebraMATLAB is used in the course to some extent. MATLAB stands for Matrix Laboratory and involves the formulation of a problem in matrix terms. Matlab can handle vast amounts of input data and manipulate the data in accordance with the instructions that the user provides |
Mathematics For Elementary Teachers - 05 edition
Summary: The goal of this text is to provide prospective elementary teachers with a deep understanding of the mathematics they will be called on to teach. Through a careful, mathematically precise development of concepts, this text asks that students go beyond simply knowing how to carry out mathematical procedures. Students must also be able to explain why mathematics works the way it does. Being able to explain why is a vital skill for teachers. Through activities, examples...show more and applications, the author expects students to write and solve problems, make sense of the mathematics, and write clear, logical explanations of the mathematical concepts. The accompanying Activities Manual promotes engagement, exploration, and discussion of the material, rather than passive absorption. Both students and instructors should find this material fun, interesting, and rewarding |
Additional product details
Fundamentals of Precalculus is designed to review the fundamental topics that are necessary for success in calculus. Containing only five chapters, this text contains the rigor essential for building a strong foundation of mathematical skills and concepts, and at the same time supports students' mathematical needs with a number of tools newly developed for this revision. A student who is well acquainted with the material in this text will have the necessary skills, understanding, and insights required to succeed in calculus. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book. |
Contents on this page
Staffing
Examiner: David Martin Moderator:
Other requisites
It is recommended that students undertake this course prior to EDX1280 and/or EDX3280.
Rationale
Mathematics is a fascinating and indispensable discipline in modern society. It gives the opportunity for students to develop their logic and reasoning skills that can be applied to many other areas of interest. To face future challenges in producing a highly skilled Australian workforce, pre-service primary and middle school teachers must have a broad understanding up to, and including, Year 7 mathematics. Additionally, in view of the rollout of the National Curriculum and the introduction of external pre-registration testing, it is imperative that all pre-service teachers have practical knowledge of mathematics. It is a pre-requisite understanding that pre-service teachers possess a satisfactory level of mathematical content knowledge to demonstrate satisfactory levels of achievement on the external test and possess the skills and knowledge to adapt to the new curriculum and suitably engage in the mathematics education courses within the Faculty of Education. This course aims to facilitate these needs by providing the opportunity for pre-service teachers to revise relevant mathematics content knowledge while adapting to the Australian Curriculum. It may also give pre-service teachers an opportunity to re-visit the discipline after an extended lapse or simply revise the material.
Synopsis
This course focuses on the mathematical content knowledge required by teachers from Prep to Year7. It will cover the content from the Australian Curriculum strands appropriate for this age range namely: Number; Algebra; Measurement; Geometry; and Probability & Statistics. NOTE: Minimum enrolment numbers apply to this offeringdescribe and apply appropriate higher order thinking and problem solving in the content areas listed in #1 above (Assignment 2)
develop age appropriate mathematical challenges in the years of learning P-7 (Assignment 2)
work confidently with current mathematics syllabus documentation in Years P-7 (Assignment 2)
Topics
Description
Weighting(%)
1.
Number: involves the operations on numbers, fractions, and place value and where each of the topics are represented in the Australian Curriculum from Years P-7. This strand has strong links with all other stands, including Geometry and spatial sense.
20.00
2.
Patterning and algebra: involves patterns of numbers, relationships between numbers and the use of symbols to denote unknowns or variables and where each of the topics are represented in the Australian Curriculum from Years P-7.
20.00
3.
Geometry: this strand involves the properties of 2-dimensional and 3-dimensional space and shapes, location and transformation, and geometric reasoning and where each of the topics are represented in the Australian Curriculum from Years P-7.
20.00
4.
Probability and Statistics: involves chance, mathematical treatment of data and interpretation of the data and where each of the topics are represented in the Australian Curriculum from Years P-7.
20.00
5.
Measurement: this strand involves properties of the real-world that can be measured, the units used to measure them and the process of measurement and where each of the topics are represented in the Australian Curriculum from Years P-7.
20.00
Text and materials required to be purchased or accessed
ALL textbooks and materials available to be purchased can be sourced from USQ's Online Bookshop (unless otherwise stated). (
Assessment details
Examination date(s) will be advised via UConnect when the official examination timetable is released.Closed Examination: Candidates are allowed to bring only writing and drawing instruments into the closed examination.
Examination period when Deferred/Supplementary examinations will be held:
Any Deferred or Supplementary examination for this course will be held during the next examination period |
The author presents a book based on an algorithmic view of mathematics. The reason is algorithmic considerations of mathematical problems, having been more important in the past, are nowadays of minor importance in presenting and teaching mathematical techniques and solution schemes. Two reasons might be responsible for the development: first, the increasing importance of engineering in the development of software, and secondly, the shortened base courses at universities due to the so called Bologna process. Therefore, the author is interested in teaching and introducing a broad range of mathematical fields to stimulate interest in one or the other field, including algorithmic mathematics. After a brief introduction the book starts with a presentation of elementary counting problems and discrete probability theory. Chapter three contains graphs and the application of graphs, followed by chapter four on trees and matchings. Numerical problems and linear algebra are presented in chapter five, including eigenvalues, eigenvectors, and the Cholesky decomposition. Chapters six and seven deal with non-linear optimization, which is used as an application of algorithms in the field of analysis. More detailed, in chapter six the author discusses the necessary and sufficient conditions for extreme values, using graphical tools to show visually the content and meaning of the sentence of implicit defined functions. The graphical approach is also used in the following chapter which discusses numerical procedures as a solution strategy for nonlinear optimization problems. The chapter eight gives an introduction into linear optimization based on the Kuhn-Tucker conditions. In addition, the author presents the Simplex algorithm from a geometrical point of view. Furthermore, the author shows how geometric ideas can be efficiently translated into the tableau scheme of the Simplex algorithm. The final chapter nine contains solutions for the exercises given in the previous chapters. The textbook can be considered as a useful extension of mathematical knowledge beyond elementary standards and is suitable for applied scientists and mathematicians as well.
Reviewer:
Herbert S. Buscher (Halle, Saale) |
Real-World Problem Solving
The GED Mathematics Test concentrates on real-world problem solving. For about half of the items, it uses graphic-based material, such as charts, tables, graphs, and diagrams. Students can expect to see most problems presented in a practical context that may address more than one concept. The GED Mathematics Test also measures analytical and reasoning skills.
Think for a moment about the steps that you use to solve any problem, not just a math problem. When solving a problem, you probably:
Sort through the information.
Pull together the information that you need.
Discard unnecessary information.
Put the information together in a manner that works for you.
Decide on the best approach for solving the problem.
Solve the problem using that approach.
If the approach you selected worked, then you have solved your problem. If it didn't work, then you go back to the drawing board to see if there is another approach that you can use.
The same thing works in math. Students must learn how to analyze, approach, and solve problems if they are to be successful on the GED Mathematics Test. |
Apart from understanding the statements of
abstract theorems (see Formulating mathematics), you should
become used to proving them rigorously. The most
important theorems will be proved in books and
lectures, but you may be asked to reproduce the proofs
in examinations. Moreover, you will frequently be set
problems which require you to prove abstract statements
which you have not seen before. In all cases, the aim
will be to write out accurate and efficient proofs.
There are three basic skills concerning proofs: |
Textbook: Colin Adams and Robert Franzosa,
Introduction to Topology: Pure and
Applied, Prentice Hall. ISBN-13:
978-0131848696. There is a list of corrections and clarifications to the book on-line.
Course Philosophy
Topology is concerned with geometrical properties that are
preserved under continuous deformations of objects. These properties are
determined only by positioning of points with respect to each other and not by
the distances between them (topology's maiden name is Analysis Situs, which means analysis of
place). One of the first problems that could be called topological is the
Euler's Koenigsberg bridges problem. Topology may
become very abstract; in this course the emphasis will be on the geometric and
visual underpinnings of topological concepts and results, and on mathematical
rigor. One of the goals of the course is helping students to refine their capacities of reading
abstract mathematical texts and develop a basic view of topology and its
applicationsHomework: There will be
weekly homework assignments that will be collected and graded. As a rule,
homework assignments will be due on Tuesday.
Tests:
There will be two tests and a final.
Grading:
Homework 35%, Tests 40%, Final 25%
Tentative Course Outline
I expect to cover the core material of the first seven
chapters of the textbook. The really interesting stuff starts after the core chapters;
beyond the basics I plan to discuss one of the three topics listed at the
bottom the list of the key topics:
1.Topological
spaces, bases.
2.Interior,
closure, and boundary.
3.Subspaces,
product spaces, quotient spaces.
4.Continuity
and homeomorphisms.
5.Metric
spaces.
6.Connected
spaces.
7.Compactness
through coverings and limit points; compactifications.
8.Homotopy
and degree of mappings; the Brouwer fixed point
theorem.
9.Knots.
10.Classification
of surfaces (any surface is a spheres with handles), Euler characteristic.
If you have any preferences as to which topics out of the
last three on the list to consider in the course, please email me.
Student Learning Outcomes
This
is a list from the Digital Measures course profile.
-The students will refine their capacities of reading
abstract mathematical texts and develop facilities to write brief mathematical
proofs.
-The students will develop a broad view of basic
topology and of some applications.
-The students will develop understanding of basic
structure and properties of topological spaces.
-The students will learn some fundamental properties
of continuous mappings of topological spaces.
-The students will be exposed to some important
classes of spaces, such as compact and connected ones.
Statement of Academic
Integrity
The Rensselaer Handbook of Student Rights and
Responsibilities define various forms of Academic Dishonesty and you should
make yourself familiar with these. In this class, all assignments that are
turned in for a grade must represent the student's own work. In cases where
help was received, or teamwork was allowed, a notation on the assignment should
indicate your collaboration. Submission of any assignment that is in violation
of this policy may result in a penalty of a grade of F. If you have any
question concerning this policy before submitting an assignment, please ask for
clarification.
Homework Assignments
Assignment #1, due September 7 One of the problems in the first assignment (Problem
1.34) was incorrect in the first printing of the Textbook. I was not aware of
this because in the 2nd printing that I have the error was
corrected. My apologies
Topics for Presentations in
Class:
1.The Alexander Horned Sphere (pp.
339-340 of the textbook)
3.The Ham-Sandwich Theorem
4.Turning the sphere S2
inside-out
Please let me know if you are
interested in giving a presentation (probably about 20-30 minutes long) on any
of these topics or any other topological topic of your choice.
Tests
Test #1 will be given on Friday October 19 in class.
The test will include topics covered by the first five homework assignments.
Namely,
1.Topological
spaces, bases.
2.Interior,
closure, and boundary. Limit points.
3.Subspaces,
product spaces, quotient spaces.
4.Continuity
and homeomorphisms.
5.Metric
spaces.
6.Connected
spaces, not including path connectedness.
Test questions will be similar to the shorter homework
questions from the homework assignments 1-5. You will
be allowed the use of one sheet of hand-written notes.
The advanced grade is determined
by the performance on the homework assignments (65% of the grade) and the test
(35%). The final exam is optional; it will include the material covered by the homework
exercises. |
Algebra Buster is one of the best resources that can offer help to people like you. When I was a novice, I took support from Algebra Buster. Algebra Buster offers all the principles of Remedial Algebra. Rather than utilizing the Algebra Buster as a step-by-step guide to work out all your homework assignments, you can use it as a tutor that can offer the basics of 3x3 system of equations, difference of cubes and function domain. Once you assimilate the basics, you can go ahead and solve any tough assignments on Algebra 1 within minutes. |
Overview - MATH FOR THE WORLD OF WORK - STUDENT WORKBOOK
Teach students the math skills they need to enter the workforce.
Plan a business-oriented curriculum for your students with this full-color,
easy-to-read text that focuses on the skills students need on the job. Math
for the World of Work covers critical skills like whole numbers, fractions,
decimals, averages, estimating, measurements, and ratios. Each skill is introduced
in a cross-curricular context that helps students learn about the business world.
Lessons are reinforced with problem-solving activities, exercises, and review
questions to give students plenty of practice and solidify their understanding
of new skills. And features like Application Activities and Technology Connections
ensure that students understand how to apply the skills they acquire.
Teacher's Resource Library on CD-ROM contains the Student Workbook offering
dozens of reinforcement activities (also available in print), Self-Study Guide
for students who want to work at their own pace, two forms of chapter tests,
plus midterm and final tests. Just select and print out the materials as needed.
Everything is reproducible. For Windows and Macintosh.
Teaching Strategies in Math Transparencies stimulate learning and discussion
in the classroom. Graphic organizers present concepts in a meaningful, visual
way and help you teach students how to manage information. Comes with instruction
book and blackline masters.
Skill Track Software, a CD-ROM program, allows students to review each
lesson and/or chapter within the textbook at their own pace. Includes hundreds
of multiple-choice items that directly relate to the textbook's content. Built-in
teacher management software allows the instructor to track student progress
and print reports. For Windows and Macintosh. |
Final Review
Sample Topics and Questions
This is not an exclusive list. It is merely meant to highlight some
of the major topics covered since the second midterm. It also includes
topics that may be appropriately asked on the two midterms. Students are also
referred to the topics listed on the review pages for the first and
second midterms.
Avoid "Catastrophic cancellation" in certain expressions.
Find the next n intervals using the bisection method for
a function.
Given the time it takes to solve a certain sized system
via Gaussian elimination, how long does it take to solve a different
sized system.
Decompose a matrix into an LU-decomposition.
Find the normal equations for a linear system.
Use the Gauss-Seidel iteration method to find several
iterations for a linear system.
Use the trapezoidal rule to approximate the integral.
Use Richardson's extrapolation to get a better approximation.
How many panels are needed to get a certain degree of
accuracy via Simpson's rule?
Use Gaussian quadrature to evaluate an integral.
Create a new quadrature formula.
Change an n-th order ODE into a coupled system of first
order ODEs.
"Solve" an ODE-BVP by discretization techniques, i.e.,
set up the appropriate linear system in matrix form. |
Elementary Linear Algebra Applications Version
9780471669593
ISBN:
0471669598
Edition: 9 Pub Date: 2005 Publisher: John Wiley & Sons Inc
Summary: This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. The applications version features a wide ...variety of interesting, contemporary applications. Clear, accessible, step-by-step explanations make the material crystal clear. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues |
Strategic Math
Course Grade Level Description
Introduction to Strategic Math
This course is required for students whose mathematics proficiency is below grade level as indicated by eighth grade diagnostic assessments and teacher recommendation. This course meets daily for 90 minutes and is taken at the same time as their Integrated Algebra I class.
Strategic Math Goal Statement
This course is designed to help students improve the transition from arithmetic and pre-algebra understandings to algebraic understandings. This course is designed for students to increase the skills needed to be successful in Algebra. The balanced approach to mathematics in this course will provide diagnostic interventions based on individual student needs, and provide support for the Integrated Algebra I class.
Additional benefits of this course are:
targeted support to students so that they are successful in Algebra
boost self-confidence in mathematics
review/preview Algebra concepts
show students how effort is related to success in mathematics
strengthen vocabulary
Data from the Algebra course and collaboration amongst the Algebra/Strategic Mathematics teachers will be used to inform instruction. |
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This teacher guide illustrates how to sustain successful implementation of the CCSS for mathematics for grades 6–8. Discover what students should learn and how they should learn it at each grade level. Acquire strategies for meeting the rigor of the grades 6–8 standards, including the unique content around ratios, proportions, and relationships at grades 6 and 7. Get insight into the new expectations for grades 6–8 assessment as well as the readiness required for the high school standards.
More]]>14385Fri, 04 Jan 2013 00:00:00 GMTCommon Core Mathematics in a PLC at Work, High SchoolCopublished with Solution TreeMore]]>14386Thu, 21 Jun 2012 00:00:00 GMTDeveloping Essential Understanding of Geometry for Teaching Mathematics in Grades 6-8 (List Price $35.95 Member Price $28.76)More]]>14122Tue, 20 Mar 2012 00:00:00 GMTBeyond Good Teaching: Advancing Mathematics Education for ELLs (List Price $35.95 Member Price $28.76)
Many languages, many cultures, one goal—high-quality mathematics education…More]]>14118Thu, 19 Apr 2012 00:00:00 GMTDeveloping Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Grades Pre-K-8 (List Price $32.95 Member Price $26.36)794Tue, 25 Oct 2011 00:00:00 GMTCommon Core Mathematics in a PLC at Work, Grades 3-5 3–5. Discover what students should learn and how they should learn it at each grade level, including deep support for the unique work for Number & Operations—Fractions in grades 3–5 and learning progression models that capstone expectations for middle school mathematics readiness.
By connecting the CCSSM to previous standards and practices, the book serves as a valuable guide for teachers and administrators in implementing the CCSSM to make mathematics education the best and most effective for all students.
More]]>14327Wed, 30 Jan 2013 00:00:00 GMTEyes on Math: A Visual Approach to Teaching Math Concepts (List Price $29.95 Member Price $23.96)
A unique teaching resource that provides engaging, full-color graphics and pictures with text showing teachers how to use each image to stimulate mathematical teaching conversations around key K–8 concepts.
Copublished with Teachers College PressMore]]>14573Mon, 17 Dec 2012 00:00:00 GMTDeveloping Essential Understanding of Statistics for Teaching Mathematics in Grades 6-8 (List Price $36.95 Member Price $29.56)
This book focuses on the essential knowledge for mathematics teachers about statistics. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings.More]]>13800Mon, 25 Feb 2013 00:00:00 GMTAdministrator's Guide: Interpreting the Common Core State Standards to Improve Mathematics Education (List Price $23.95 Member Price $19.16)More]]>14288Wed, 12 Oct 2011 00:00:00 GMTDeveloping Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3-5 (List Price $32.95 Member Price $26.36)
Help your upper elementary school student develop a robust understanding of rational numbers. More]]>13493Tue, 12 Oct 2010 00:00:00 GMTDeveloping Essential Understanding of Algebraic Thinking for Teaching Mathematics in Grades 3-5 (List Price $32.95 Member Price $26.36) More]]>13796Tue, 19 Apr 2011 00:00:00 GMTDeveloping Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3-5 (List Price $32.95 Member Price $26.36)
Move beyond the mathematics you expect your students to learn More]]>13795Tue, 19 Apr 2011 00:00:00 GMTDeveloping Essential Understanding of Geometry for Teaching Mathematics in Grades 9-12 (List Price $35.95 Member Price $28.76)
This book focuses on essential knowledge for teachers about geometry. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings.
More]]>14123Thu, 19 Apr 2012 00:00:00 GMTDeveloping Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9-12 (List Price $35.95 Member Price $28.76)
This book focuses on essential knowledge for teachers about proof and the process of proving. It is organized around five big ideas, supported by multiple smaller, interconnected ideas—essential understandings. More]]>13803Wed, 17 Oct 2012 00:00:00 GMTDefining Mathematics Education – Presidential Yearbook Selections 1926-2012 (List Price $59.95 Member Price $47.96)
The 75th Anniversary Yearbook: Celebrating a Valued Tradition of Defining Mathematics Education
More]]>14551Mon, 08 Apr 2013 00:00:00 GMTDeveloping Essential Understanding of Statistics for Teaching Mathematics in Grades 9-12 (List Price $32.95 Member Price $26.36)
This book examines five big ideas and twenty-four related essential understandings for teaching statistics in grades 9–12. More]]>13804Thu, 14 Feb 2013 00:00:00 GMTRich and Engaging Mathematical Tasks: Grades 5-9 (List Price $36.95 Member Price $29.56)
A valuable resource to any mathematics teacher, this rich collection of mathematical tasks will enliven students' engagement in mathematical thinking and reasoning and help them succeed in the classroom. More]]>13516Wed, 07 Mar 2012 00:00:00 GMTFocus in Grade 2
More]]>13790Tue, 05 Apr 2011 00:00:00 GMTDeveloping Essential Understanding of Addition and Subtraction for Teaching Mathematics in Pre-K-Grade 2 (List Price $32.95 Member Price $26.36)
Move beyond the mathematics you expect your students to learn. More]]>13792Tue, 25 Jan 2011 00:00:00 GMTDeveloping Essential Understanding of Number and Numeration for Teaching Mathematics in Pre-K-2 (List Price $29.95 Member Price $23.96)
Move beyond the mathematics you expect your students to learn. More]]>13492Wed, 28 Apr 2010 00:00:00 GMTMore Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction (List Price $29.95 Member Price $23.96)
Differentiate math instruction with less difficulty and greater success! More]]>13782Thu, 15 Apr 2010 00:00:00 GMTFocus in High School Mathematics: Reasoning and Sense Making (List Price $36.95 Member Price $29.56)
A framework to guide the development of future 9–12 mathematics
curriculum and instruction. More]]>13494Tue, 06 Oct 2009 00:00:00 GMTMathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learning (List Price $38.95 Member Price $31.16)
Award-winning author Page Keeley and mathematics expert Cheryl Rose Tobey apply the successful format of Keeley's best-selling Science Formative Assessment to mathematics. They provide 75 formative assessment strategies and show teachers how to use them to inform instructional planning and better meet the needs of all students. Research shows that formative assessment has the power to significantly improve learning, and its many benefits include:
Copublished with Corwin
More]]>14303Wed, 12 Oct 2011 00:00:00 GMTPutting Essential Understanding of Fractions into Practice in Grades 3-5 (List Price $35.95 Member Price $28.76)
What tasks can you offer—what questions can you ask—to determine what your students know or don't know—and move them forward in their thinking?
This book focuses on the specialized pedagogical content knowledge that you need to teach fractions effectively in grades 3–5. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with fractions—not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts.
More]]>14542Fri, 12 Apr 2013 00:00:00 GMTTeaching Mathematics through Problem Solving: Prekindergarten–Grade 6 (List Price $8.76 Member Price $8.76)
This volume and its companion for grades 6–12 furnish the coherence and
direction that teachers need to use problem solving to teach
mathematics.
More]]>12576Tue, 04 Nov 2003 00:00:00 GMTMath Jokes 4 Mathy Folks (List Price $11.95 Member Price $9.56)
Intended for all math types. Provides a comprehensive collection of math humor, containing over 400 jokes. It's a book that all teachers from elementary school through college should have in their library. More]]>13837Tue, 27 Apr 2010 00:00:00 GMTNavigating through Number and Operations in Grades 3-5 (with CD-ROM) (List Price $46.95 Member Price $37.56)
Activities in this book invite students to use fraction circles to compare fractions and dot arrays to explore multiplication and the distributive property. The authors present many other hands-on approaches as well. More]]>12952Wed, 28 Mar 2007 00:00:00 GMTAdministrator's Guide: How to Support and Improve Mathematics Education in Your School (List Price $20.95 Member Price $16.76)
Describes what administrators need to know about mathematics education
and how to support and improve mathematics education in their
schools.
More]]>12706Wed, 30 Jul 2003 00:00:00 GMTCommon Core Mathematics in a PLC at Work, Grades K-2 K–2. Discover what students should learn and how they should learn it at each grade level, including insight into prekindergarten early childhood readiness expectations for the K–2 standards, as well as the unique Counting and Cardinality standards for kindergarten.
Copublished with Solution Tree PressMore]]>14383Wed, 09 May 2012 00:00:00 GMTNavigating through Geometry in Grades 3–5 (with CD-ROM) (List Price $37.95 Member Price $30.36)
The "big ideas" of geometry–shape, location, transformations, and spatial visualization–are the focus of this book. More]]>12173Sat, 01 Sep 2001 00:00:00 GMTNavigating through Measurement in Grades 3–5 (with CD-ROM) (List Price $41.95 Member Price $33.56)
This book follows students' natural progression from measuring with informal or nonstandard units to using standard units to measure such attributes as length, weight, angle, and temperature. More]]>12525Wed, 02 Feb 2005 00:00:00 GMTThe Impact of Identity in K-8 Mathematics: Rethinking Equity-Based Practices (List Price $36.95 Member Price $29.56)
Each teacher and student brings many identities to the classroom. What is their impact on the student's learning and the teacher's teaching of mathematics?
This book invites K–8 teachers to reflect on their own and their students' multiple identities. Rich possibilities for learning result when teachers draw on these identities to offer high-quality, equity-based teaching to all students. Reflecting on identity and re-envisioning learning and teaching through this lens especially benefits students who have been marginalized by race, class, ethnicity, or gender. More]]>14119Wed, 10 Apr 2013 00:00:00 GMTAchieving Fluency: Special Education and Mathematics (List Price $36.95 Member Price $29.56)
"Is it a learning disability or a teaching disability?"
Achieving Fluency presents the understandings that all teachers need to play a role in the education of students who struggle: those with disabilities and those who simply lack essential foundational knowledge. This book serves teachers and supervisors by sharing increasingly intensive instructional interventions for struggling students on essential topics aligned with NCTM's Curriculum Focal Points, the new Common Core State Standards for Mathematics, and the practices and processes that overlap the content. These approaches are useful for both overcoming ineffective approaches and implementing preventive approaches.
More]]>13783Tue, 15 Mar 2011 00:00:00 GMTFocus in High School Mathematics: Reasoning and Sense Making in Statistics and Probability (List Price $29.95 Member Price $23.96)
The development of statistical reasoning must be a high priority for school mathematics. This book offers a
blueprint for emphasizing statistical reasoning and sense making in the high
school curriculum. More]]>13526Thu, 15 Oct 2009 00:00:00 GMTStrength in Numbers: Collaborative Learning in Secondary Mathematics (List Price $29.95 Member Price $23.96)
This practical, useful book introduces tested tools and concepts for creating equitable collaborative learning environments that supports all students and develops confidence in their mathematical ability. More]]>13791Thu, 08 Mar 2012 00:00:00 GMTFocus in Pre-K26Tue, 23 Feb 2010 00:00:00 GMTFocus in High School Mathematics: Reasoning and Sense Making in Algebra (List Price $27.95 Member Price $22.36)
This volume is one of a series of books that support NCTM's Focus in High School Mathematics: Reasoning and Sense Making by providing additional guidance for making reasoning and sense making part of the mathematics experiences of all high school students every day.
More]]>13524Fri, 09 Apr 2010 00:00:00 GMTNavigating through Discrete Mathematics in Prekindergarten - Grade 5 (with CD-ROM) (List Price $50.95 Member Price $40.76)
More]]>13221Fri, 17 Apr 2009 00:00:00 GMTFocus in Grade 128Fri, 07 May 2010 00:00:00 GMTThe Common Core Mathematics Standards: Transforming Practice Through Team Leadership (List Price $31.95 Member Price $25.56)
Transform math instruction with effective CCSS leadershipThis professional development resource helps principals and math leaders grapple with the changes that must be addressed so that teachers can implement the practices required by the CCSS.
More]]>14404Wed, 16 May 2012 00:00:00 GMTNavigating through Geometry in Grades 6–8 (with CD-ROM) (List Price $37.95 Member Price $30.36)
This book examines the study of geometry in the middle grades as a pivotal point in the mathematical learning of students and emphasizes the geometric thinking that can develop in grades 6–8 as a result of hands-on exploration. More]]>12174Sat, 01 Sep 2001 00:00:00 GMTUsing the Common Core State Standards for Mathematics with Advanced and Gifted Learners (List Price $19.95 Member Price $15.96)
Using the Common Core State Standards for Mathematics With Gifted and Advanced Learners provides teachers and administrators examples and strategies to implement the new Common Core State Standards (CCSS) with advanced learners at all stages of development in K–12 schools. The book describes—and demonstrates with specific examples from the CCSS—what effective differentiated activities in mathematics look like for top learners. |
Connections in Mathematics
Course Description:
This course provides students with introductory experiences in symbolic logic, binary and other bases, probability, conditional probability, set theory, non-routine problem solving, topics of personal finance and investment, and the calculus necessary to participate in the Senior Science Scenario project during the final six weeks of the year. Both EXCEL and a variety of website-based applications will be used throughout the year. Emphasis is placed on conceptual understanding, solving real world applications, and fostering mathematical reasoning and communication.
Course Materials:
The text for this course will be "The Nature of Mathematics", 10th ed., by Smith (no relation). You will be responsible for the text while it is in your possession.
Methodology:
The beginning of most class periods will be used to answer questions on the material that is due for that day. The rest of the class period will consist of a variety of activities which will include lecture, individual and group problem solving, and exploration of questions and concepts. It is strongly advised that you prepare for each class meeting by working assigned homework problems and by reading and taking notes on the text to be covered in the next class meeting.
Study Aids:
There are many reference books and web sites widely available that can serve as study aids for this course. However, it is unlikely that any materials beyond those provided in class will be necessary. If you feel at any time that you require additional assistance, please discuss this with me at the beginning or end of the next class meeting.
Participation:
You should plan to be actively involved in class. This means being attentive and participating in class discussions and activities.
Absences (consult the Student Handbook for additional information):
When you miss any amount of class time, for any reason, it is your responsibility to contact a student colleague in the class to obtain the information you missed.
Foreseeable absences for any reason need to be discussed with the instructor in advance. Failure to do so will result in an unexcused absence.
If a student is absent (excused) for only one class meeting, upon return he/she is expected to have completed the work which was due on the day of absence. If a test was missed, the student is expected to take the test on the day of return. If a student misses two or more consecutive class meetings, he/she should talk to the instructor to devise a plan to catch up.
Work missed because of an unexcused absence cannot be made up. If a test is missed because of an unexcused absence, then that test grade will be lowered by 10 points for each day late.
Tardiness (consult the Student Handbook for additional information):
You are expected to be in our class, ready to learn, by our starting time. Given my responsibilities as the Director of the Governor's School, I might not be in the room; that does not relieve you of your responsibility to be in the class, ready to learn, by the beginning of class. I will permit one unexcused tardy without any grade penalty. After that, I will lower your semester grade by ½ a point for each unexcused tardy.
Honor Code:
Students are required to pledge all work that they turn in for a grade. Refer to CVGS Student Handbook for complete requirements.
Grading:
The grading scale is a standard 11/10/10/10 point scale.
Percentage and Grade Equivalent:
89.5-100
A
79.5-89.4
B
69.5-79.4
C
59.5-69.4
D
Earning less than 60 points will result in a failing grade for the course.
Course Description (First Semester):
During the first semester students will work with introductory experiences in symbolic logic, binary and other bases, voting methods, apportionment schemes and paradoxes, probability, conditional probability, set theory, and non-routine problem solving. Emphasis is placed on conceptual understanding, solving real world applications, and fostering mathematical reasoning and communication.
Specific Course Content and Objectives (First Semester):
the student will be able to:
translate sentences to symbolic form,
construct truth tables,
state the converse, inverse and contrapositive of statements,
determine the validity of an argument,
design a simple circuit (or a gate) as a logic application,
understand and use basic set theory concepts, including intersections, unions, complements, distributive and De Morgan's laws, and cardinality,
recall and be able to compare and contrast voting methods, voting dilemmas, apportionment methods and paradoxes
convert numbers in the decimal, binary, octal, and hexadecimal systems,
Class Participation (30 pts): Asking or answering questions well, putting problems on the board, and generally being attentive and engaged
It is your responsibility to keep track of the points you have earned and the assignments you have completed. Progress reports will report progress for the entire semester thus far. To reiterate, all grades will be cumulative from the beginning of the semester!
Tentative Course Schedule for First Semester:
We will follow the sequence of topics below, although adjustments will be made depending on how quickly we are able to move as a group.
2.1: Symbolic Logic
2.2: Truth Tables and Conditionals
2.3: Operators and Laws of Logic
2.4: Logical Proof
2.6: Logic Circuits
16.1: Voting Methods
16.2 Voting Dilemmas
16.3: Apportionment
16.4: Apportionment Paradox
Project #1
3.4: Binary + Octal + hexadecimal
10.1: Sets, subsets, Venn diagrams
10.2: Sets—combined operations, DeMorgan's Laws
10.3: Permutations
10.4: Combinations
10.5: Complex Counting
Project #2
11.1: Probability
11.2: Math Expectation
11.3 Probability Models
11.4: Calculated Probabilities
Project #3
15.1: Euler Circuits and Hamiltonian Cycles
15.2: Trees and Minimum Spanning Trees
Special Topics
REVIEW FOR EXAMEXAMS
Course Description (Second Semester)
This course provides students with experiences in topics of personal finance and investment and the use of EXCEL to facilitate calculations such as those used in an amortization schedule. Students will also learn the calculus basics necessary to participate in the Senior Science Scenario project during the sixth six weeks. The use of EXCEL and the free website will be explored.
Throughout the course emphasis is placed on conceptual understanding, solving real world applications, and fostering mathematical reasoning and communication.
Specific Course Content and Objectives (Second Semester): the student will be able to:
Class Participation: Asking or answering questions well, putting problems on the board, and generally being attentive and engaged is expected. Failing to do so can result in a deduction of points from the total points earned.
S-Cubed grade (1@150 pts) |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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FinalCS105Spring 2010May 7th, 2010DO NOT START UNTIL INSTRUCTED TO DO SO. YOU WILL LOSE POINTS IF YOU START WORKING ON THE TEST BEFORE WE TELL YOU. THIS IS A 150 MINUTE EXAM.Do not leave this blankfill it in now:Name: Discussion Section: TA:FORMA
Midterm 1CS105Fall 2010September 28
Midterm 2CS105Fall 2010November 2ndF
Midterm 1CS105Spring 2010February 23rd
Midterm 2CS105Spring 2010April 6FO
Math 241 Exam 1 2PM V1 September 25, 2008 2 2PM V1 October 16 2PM V1 November 13 4 2PM V1 December 7 9AM V1 November 16, 2008 55 points possible1. Let f : Rn R.Name: Section Registered In:(a) (3pts) State the formula for the second-order Taylor polynomial of f at the point a in Rn . (b) (2pts) In order for this expansion to be valid, w
Math 241 Exam 3 Version 1 1. (5pts) Determine if the following statement is true or false. You do not need to justify your answer. For each part, you will receive 1 point for a correct answer, 1 point for an incorrect answer, and 0 points for no answer. E
Name:Math 380 Exam 3 August 1, 2007 50 points possible 1. If the density of a wire that lies along the planar curve (t) = (3t, t4 ), 0 t 1, is given by the function f (x, y ) = xy , nd the total mass of the wire.2. Let D be a region appropriate for Gree |
Lesson Plans & Activities
TAKS 9th Grade Math Objective 1 -10
Objective 1: The student will describe functional relationships in a variety of ways.
Objective 2: The student will demonstrate an understanding of the properties and attributes of functions.
Objective 3: The student will demonstrate an understanding of linear functions.
Objective 4: The student will formulate and use linear equations and inequalities.
Objective 5: The student will demonstrate an understanding of quadratic and other nonlinear functions.
Objective 6: The student will demonstrate an understanding of geometric relationships and spatial reasoning.
Objective 7: The student will demonstrate an understanding of two- or three- dimensional representations of geometric relationships and shapes.
Objective 8: The student will demonstrate and understanding of the concepts and uses of measurement and similarity.
Objective 9: The student will demonstrate an understanding of percents, proportional relationships, probability, and statistics in application problems.
Objective 10: The student will demonstrate an understanding of the mathematical processes and tools used in problem solving. |
Kalkules Description:
Kalkules is an universal scientific freeware calculator with an amount of untraditional functions, which can be used particularly by high school or university students. It also offers a wide range of tools, which make your calculations easier and faster.
- Added new tools: unit converter and quadratic equation - New window with basic prefix values, which can be easily inserted into the expression - Program can remember the state it was in during the last execution(chosen number set, angle mode, precision, and so on) - New setting window with more available settings: - what to insert as new expression after evaluating the current expression and inserting an operator - what to use as a decimal separator (dot, coma, or the operating systems default separator) - choosing between mathematical and electrotechnical format of complex numbers (5-2i vs. 5-j2) - programs default state (the state right after start - chosen number set, angle mode, precision, and so on) - result notation: ordinary (0,02) or exponential (2E-2) - the evaluation result can ... |
A basic problem in computer vision is to understand the structure of a real world scene given several images of it. Techniques for solving this problem are taken from projective geometry and photogrammetry. Here, the authors cover the geometric principles and their algebraic representation in terms of camera projection matrices, the fundamental matrix and the trifocal tensor. The theory and methods of computation of these entities are discussed with real examples, as is their use in the reconstruction of scenes from multiple images. The new edition features an extended introduction...
The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational...
Digital geometry is about deriving geometric information from digital pictures. The field emerged from its mathematical roots some forty-years ago through work in computer-based imaging, and it is used today in many fields, such as digital image processing and analysis (with applications in medical imaging, pattern recognition, and robotics) and of course computer graphics. Digital Geometry is the first book to detail the concepts, algorithms, and practices of the discipline. This comphrehensive text and reference provides an introduction to the mathematical foundations of digital...
The methods used to digitize and reconstruct complex 3-D objects have evolved in recent years due to increasing attention from industry and research. 3-D models have applications in various domains, including reverse engineering, collaborative design, inspection, entertainment, virtual museums, medicine, geology and home shopping. <br><b>3-D Surface Geometry and Reconstruction: Developing Concepts and Applications</b> provides developers and scholars with an extensive collection of research articles in the expanding field of 3-D reconstruction. This reference book investigates the...
An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector fields with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail.
A useful tool for any scientist...
This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n + 2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n + 1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation...
This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. Its primary focus is the spectral rigidity problem: Can the metric of a given Riemannian symmetric space of compact type be characterized by means of the spectrum of its Laplacian? It also addresses a question rooted in the Blaschke problem: Is a Riemannian metric on a projective space whose geodesics are all closed and of the same length isometric to the canonical metric?...
Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the...
Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea. From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E...
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level...
The study of the mapping class group Mod( S ) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod( S ), from finite generation by Dehn twists and low-dimensional homology to the...
Get ready to master the concepts and principles of geometry! Master Math: Geometry is a comprehensive reference guide that explains and clarifies the principles of geometry in a simple, easy-to-follow style and format. You'll begin with the language of geometry, deductive reasoning and proofs, and key axioms and postulates. And as you understand the most basic fundamental topics you'll progress through to the more advanced topics, with step-by-step procedures and solutions, along with examples and applications, to help you as you go. A complete table of contents and a comprehensive index...
Having trouble with geometry? Do Pi, The Pythagorean Theorem, and
angle calculations just make your head spin? Relax. With Head First
2D Geometry, you'll master everything from triangles, quads and
polygons to the time-saving secrets of similar and congruent angles
-- and it'll be quick, painless, and fun.
Through entertaining stories and practical examples from the world
around you, this book takes you beyond boring problems. You'll
actually
use
what you learn to make real-life decisions,
like using angles and parallel lines to crack a mysterious CSI
case. Put geometry to work for you, and... |
Cheverly, MD Precalculus now, you mostly studied the basics of addition, subtraction, multiplication and division with various numbers of digits. With prealgebra, though, you start learn more complex types of numbers like decimals, fractions and variables. As a lover of puzzles, I like teaching this concept in that was as finding a missing piece in an equation.
...Algebra is the start of solving for the unknown. If at any point in time you have solved the mathematical problem, 2+2=, you have done algebra. If you look at it from this standpoint, you now have a foundation to build from |
View of /trunk/webwork2/courses.dist/modelCourse/templates/setDemo/screenHeaderFile1.pg
1 ##Screen set header for set 0, Fall 1998
2 3 &DOCUMENT;
4 5 loadMacros(
6 "PG.pl",
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11 12 13 14 BEGIN_TEXT
15 This is a demonstration set designed to illustrate the range of types of questions which can be asked using WeBWorK rather than to illustrate a typical calculus problem set.
16 17 $PAR
18 $BBOLD 1. Simple numerical problem. $EBOLD A simple problem requiring a numerical answer. It illustrates how one can allow WeBWorK to calculate answers from formulas (e.g. an answer such as sqrt(3^2 +4^2) can be entered instead of the answer 5.). It also shows
19 an example of feedback on the correctness of each answer, rather than grading the entire problem.
20 $PAR
21 $BBOLD 2. Graphs and limits. $EBOLD The graph in this example is constructed on the fly. From the graph a student is supposed to determine the values and limits of the function at various points. The immediate feedback on this problem is particularly useful, since students often make unconcious mistakes.
22 $PAR
23 $BBOLD 3. Derivatives. $EBOLD An example of checking answers which are formulas, rather than numbers.
24 $PAR
25 $BBOLD 4. Anti-derivatives. $EBOLD This example will accept any anti-derivative, adjusting for the fact that the answer is only defined up to a constant.
26 $PAR
27 $BBOLD 5. Answers with units. $EBOLD Try entering the answer to this question in meters (m) and also centimeters (cm).
28 $PAR
29 $BBOLD 6. A physics example. $EBOLD Includes a static picture.
30 $PAR
31 $BBOLD 7. More graphics. $EBOLD An example of on-the-fly graphics. Select the graph of f, it's derivative and it's second derivatives.
32 $PAR
33 $BBOLD 8. JavaScript example. $EBOLD I'm particularly fond of this example. The computer provides an "oracle" function: give it a number \(x\) and it will provide you with the value \(f(x)\) of the function at \(x\). Using this, calculate the value of the derivative of \(f\) at 2. (i.e. \(f'(2)\) ). Students are forced to use the Newton quotient, since there are no formulas to work with. I don't think this problem could be asked as written homework.
34 $PAR
35 $BBOLD 9. Java example. $EBOLD This gives an example of incorporating a java applet which can be used experimentally to determine answers for WeBWorK questions. This example is of historical interest since it comes from the first site after Rochester, Johns Hopkins University, to use WeBWorK. It currently gives an example of what happens when a WeBWorK problem called an applet residing on a server that no longer exists.
36 $PAR
37 $BBOLD 10. Palindrome. $EBOLD To answer this problem enter any palindrome. This problem illustrates the power of the "answer-evaluator" model. For each problem the problem designer writes a function which accepts a student's answer and produces a 0 or 1 (for incorrect or correct). Usually this is done by comparing with an answer given by the problem designer, but in this case the function checks if the answer is the same forward and backward.
38 $PAR
39 END_TEXT
40 41 42 43 BEGIN_TEXT
44 $HR
45 46 Use this box to give information about this problem
47 set. Typical information might include some of these facts:
48 $PAR
49 WeBWorK assignment number $setNumber is due on : $formatedDueDate.
50 51 52 $PAR
53 The primary purpose of WeBWorK is to let you know if you are getting the right answer or to alert
54 you if you get the wrong answer. Usually you can attempt a problem as many times as you want before
55 the due date. However, if you are having trouble figuring out your error, you should
56 consult the book, or ask a fellow student, one of the TA's or
57 your professor for help. Don't spend a lot of time guessing -- it's not very efficient or effective.
58 $PAR
59 60 You can use the Feedback button on each problem
61 page to send e-mail to the professors.
62 $PAR
63 Give 4 or 5 significant digits for (floating point) numerical answers.
64 For most problems when entering numerical answers, you can if you wish
65 enter elementary expressions such as 2^3 instead of 8, sin(3*pi/2) instead
66 of -1, e^(ln(2)) instead of 2,
67 (2+tan(3))*(4-sin(5))^6-7/8 instead of 27620.3413, etc.
68 $PAR
69 Here's the
70 \{ htmlLink(qq! of the functions") \}
71 which WeBWorK understands.
72 73 Along with the \{htmlLink(qq! "list of units")\} which WeBWorK understands. This can be useful in
74 physics problems.
75 END_TEXT
76 77 ENDDOCUMENT(); |
Description The first half of a modern high school algebra sequence with a focus in seven major topics: transition from arithmetic to algebra, solving equations & inequalities, probability and statistics, proportional reasoning, linear equations and functions, systems of linear equations and inequalities, and operations on polynomials. Students enrolled in this course must take the WA State High School End of Course Algebra Assessment if they have not attempted it once already. Prerequisite: Must be working toward a high school diploma. |
Mathematics Tools 2.6 Full Screenshot
Mathematics Tools 2.6 Keywords
Mathematics Tools 2.6 Description
Mathematics Tools is a tools that help people in solving Mathematical problems such as quadratic equation and cubic equation, System of equations. Calculate the Greatest Common Divisor or Least Common Multiple and lots of features will be update in the nextMathematics Tools |
Mathematics Theory Tests and Solutions for Grades 9-12- By Liliana Usvat
This book is designed primarily to assist students in acquiring knowledge and proficiency in the high school mathematics. It includes a thorough coverage of algebra, plane trigonometry, plane analytic geometry together with selected topics in solid analytic geometry and a brief introduction to the calculus.
Copy of the exercises and problems in this web site may be freely used or adapted for classes or math competitions. We ask only that you refere to this website: Promoting free public universities (government founded) in Canada and around the world.
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Developing a mathematical thinking is the first step in building the future generations of scientists and engineers that will solve the tomorrow's energy crisis or find new ways of solving the social problems without destroying the forest and preserving the environment for the future generations.
Email or mail us proposed problems with solution, open problems articles. We are pleased to publish them on line. |
In a departure from traditional teaching methods, this text focuses on theory more than computations, relying on independent study. Its material is geared toward aspects of high-school mathematics that promise to prove particularly useful
Covering all the Programs of Study and Attainment Targets of the British National Curriculum in mathematics for Key Stages One to Three, this text is intended as a comprehensive handbook for in-service education in mathematics intended fo
Right-Ordered Groups (Siberian School of Algebra and Logic)
Editorial review
s. Published simultaneously with a Russian edition by Scientific Books in Novosibirsk. Annotation c. by Book News, Inc., Portland, Or.
Reviewed by Osher Doctorow, Ph.D., (Culver City, CA)
The important applications of semigroups and Clifford algebras and quantum lattice field theory in the last 5 years are paralleled by this book from the Siberian School of Algebra and Logic. Semigroups are used to characterize right-order
The theory of Boolean algebras is concerned with algebras of subsets relating to the operations of union, intersection, and complement in various branches of mathematics. Goncharov (mathematics, Novosibirsk State U., Russia) presents the |
Tailored to both the specification and the tier, this Student Book delivers exactly what students and teachers need to cover the unit in exactly the right depth.
Synopsis:
* Supports teachers' understanding of AO2 and AO3 through clearly labelled AO2/3 questions in the exercises. * Packed with graded questions reflect the level of demand required, so students and teachers can see their progression. * Includes worked examples throughout the book break the maths down into easy chunks. * Uses feedback to highlight common errors . |
User ratings
Review: Euclid's Elements
This is going to be a long term project to get through this. We'll see if I come out on the other side.Read full review
Review: Euclid's Elements
User Review - Rlotz - Goodreads
Euclid's Elements is one of the oldest surviving works of mathematics, and the very oldest that uses axiomatic deductive treatment. As such, it is a landmark in the history of Western thought, and has ...Read full review |
So pretty much the calculus class my class offers goes beyond the scope of calculus AB which in itself goes beyond Calculus I. My math teacher told me I only need to look over 2 chapters to be ready for the BC test so I figured I might as well do it since I'm pretty good at math. The question would be what next? My counsler seems to not know what's next she mentioned I might take Calculus for Engineers 1 and 2 online but that seems really redundant to me. So what are my options?
I'd suggest a multi-variable calculus course at your local college. Stats is good, if you haven't already taken it, but math people will tell you stats isn't "real" math sometimes. (I've heard my own D say this).
Calculus BC is usually equivalent to a year of freshman calculus in college. The usual follow-on courses, which should be available in your local community college, are:
* multivariable calculus
* linear algebra
* differential equations
Note that linear algebra and differential equations are often combined into one course, so if they are offered separately at your local community college, take both if you decide to take either, so that you won't have to partially repeat it to get the rest of the course.
Other possibilities (these are all typically semester-long courses, except for AP statistics in high school):
* AP statistics in high school or non-calculus-based statistics at a community college (often not worth subject credit for majors that also require calculus)
* calculus-based statistics at a community college (more likely to be given subject credit, but rarely offered at community colleges)
* discrete math at a community college (often recommended or required for computer science majors) |
Algebra, says Devlin, is a language, a very precise language written in symbols, and it's everywhere: in nearly all electronic devices, every statistic and each Internet search engine - and, indeed, in every train leaving Boston.
"You can store information using it. You can communicate information using it," Devlin said. "Google has made billions capitalizing on algebra."
Yet our schools don't always do a very good job teaching it, Devlin said. Instead of showing students the possibilities and beauty algebra offers, they ultimately steer frustrated and bored students away from math and the 21st century careers that use it - the opposite of the intended result.
...
Algebra, by the dictionary's definition, is essentially abstract arithmetic, letters and symbols representing relationships between groups, sets, matrices or fields. It's a way to find a piece to a puzzle using the pieces you already have in place.
It comes in very handy for engineers, financial analysts and sociologists, not to mention World of Warcraft video game players, some of whom use algebraic formulas to decide which weapon is more effective under certain circumstances - perhaps another hook to lure unsuspecting teens into seeing the useful side of algebra.
...
Laptop computer. The computer is just an implementation in electrical circuits of a special form of algebra (called Boolean algebra) invented in the 19th century. Ordinary algebra is used to design and manufacture computers, and is at the heart of how to program them.
Cell phone. A cell phone is a particular kind of computer. An important feature of cell phones is that your phone receives all the signals sent to every cell phone in the region, but only responds to signals sent to your phone. This is achieved by using signal coding systems built on algebra.
Parking cop. Today's parking enforcement officers may carry equipment connecting them directly to a central vehicle database that registers your parking fine before you get back to the car and see the ticket on the windshield. Without algebra, such a system could not exist.
Hybrid car. Modern cars often come equipped with GPS, a highly sophisticated system that is designed using enormous amounts of mathematics that builds on algebra.
Delivery truck. Large retail chains use mathematical methods to determine the routing and scheduling of their delivery trucks; algebra is fundamental to those methods.
Stoplight. These days, stoplights are centrally controlled by computers, so there is even algebra involved in turning the light from red to green.
IPod. This is a math device in your hand. The iPod stores music using sophisticated mathematics built on algebra. And the iPod shuffle mechanism uses regular school algebra to order your songs randomly.
...
Even though it is a very pro-algebra article, my favorite quote was by an unknown source:
"Algebra ... the intensive study of the last three letters of the alphabet."
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I had to solve two problems for myself today. I am posting my solutions here, mainly for my own reference but maybe somebody out there might have the same issues to be solved.
The first problem I faced was installing a network printer so that it would be available to all users on that machine. This is probably a minor problem for seasoned IT pros, but since I am not one, it took some investigating. I learned that local printers are installed automatically for all users, while network printers are associated with user profiles. This means that when you install a network printer it is only available to the user profile that you used when installing.
The solution is to install the network printer as a local printer. In other words, go to Control Panel .. Printers. Click "Add a printer". Select that you want to install a local printer. At this point you will create a new port, using a Standard TCP/IP port. You'll need to have the IP address of the printer to do this and you'll also want to have the drivers handy.
Since it is installed as a local printer it will now be available to all users when they log in. The bug I still haven't worked out, though some of you may have an idea, is that even though I have selected it to be the default printer in my profile, it is not necessarily the default printer for other users. If is the first printer installed, no problem, but otherwise it is not the default for other users. |
Math Welcome 122 Survey of Calculus and its Applications I1
Instructor: Quanlei Fang
Dept. of Math, University at Buffalo, Spring 2009
Instructor contact Information Text Grading In-class work/ Hw / Tests Make-up policy Special needs
Come to lectures regularly Do homework regularly Go to recitations regularly Prepare for the quizzes / tests Mark the test dates Make friends and help each other
Calculus is the study of change. In particular, it looks at the rates in which quantities change (i.e., areas, volumes, distances, etc.). It was developed in the later part of the 17th century by Gottfried Leibnitz and Isaac Newton.
The two key areas of Calculus are Differential Calculus (having a quantity and finding the rate of change) and Integral Calculus. (knowing the rate of change and finding the quantity)
The big surprise is that these two seemingly unrelated areas are actually connected via the Fundamental Theorem of Calculus.
If you choose a career path that requires any level of mathematical sophistication, you will need Calculus.
To succeed in Calculus (and Mathematics in general) you must be able to: solve problems, reason logically and understand abstract concepts..
Function a set of ordered pairs (x, y) such that for each x-value there is one and only one y-value. y = f Domain (x) of a function the set of all xs that we can input into the function. Range of a function all images y of all of the xs. Vertical line test Is it a function a not? If any vertical line intersects the graph more than once, then the graph is not a function.
Polynomial
y = x 5 , y = ( x + 10) 4 x 7
Algebraic
y = x + 4,
y = x , y = (x + 1) e
2 5
Rational
y=
x+6 2 , y= x2 + 5 x+4
Exponential and Logarithmic
x x x +4 y = e , y = 2 , y = 2e
y = ln(4 x 2 + 5)
Piecewise y= x Trigonometric* Inverse Trigonometric*
Linear function Quadratic function Cubic Function Absolute Value Function
y= x
Rational
Exp & Log
Differential Calculus
15 y
10
5
x -6 -4 -2 2 4 6 8
-5
Based on the rate of change of one variable in comparison to another. For example if y=x3 , we talk about the rate of change of y in comparison to x. Another example: if t=time and s= the distance travelled and s and t are related by the equation s=2t2+5. We then talk about the rate of change of the distance with respect to time.
Derivative Limit
as slope formula
definition of derivative
f '( x) = lim
h 0
f (x + h) f ( x) h
How
to compute derivatives
Applications
About Office hrs: Please write down your preferred time spots. For example, one spot could be: Monday 11:00am-11:50Welcome toMath 122 Lecture 4 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Group workYou will have 4 problems based on MTH 121. Form a group (no more than 3 for each group) a
Welcome toMath 122 Lecture 5 Survey of Calculus and its Applications I1Instructor: Quanlei Fang Dept. of Math, University at Buffalo, Spring 2009Chapter 7 Functions of Several VariablesLast timeExamples of Functions of Several Variables 7.2
Welcome toMath 122 Lecture 10 Survey of Calculus and its Applications I1Instructor: Quanlei FangDept. of Math, University at Buffalo, Spring 2009!Integration by SubstitutionIf u = g(x), then 9.2Integration by Parts!Integration by Part
C-037_2006_IBC.titlepage.qxp12/12/200511:00 AMPage 1A Member of the International Code Family INTERNATIONAL BUILDING CODE2006Color profile: Generic CMYK printer profile Composite Default screen2006 International Building CodeFirst Printing: Janua
AD-AS analysis 10) Which kind of problem with the price system can lead to a break down in the coordination of economic activity? A) The price system works silently in the background. B) Prices can be slow to adjust. C) Prices may be flexible. D) all
Introduction to Economics 5) Because resources are limited: A) only the very wealthy can get everything they want. B) firms will be forced out of business. C) the availability of goods will be limited but the availability of services will not. D) peo
Ec 100FIRST MIDTERM SAMPLEName_ 1. Typical written questions are to discuss: A free market is great for society; what is it that free markets are bad at doing? Non-market systems of allocation; What makes a price elasticity high or low? Etc. (Not
Demand and Supply Most used concepts in economics Demand and supply are the forces that operate in the market to make it work. Microeconomics is about demand, supply, and market equilibrium.Copyright 2004 South-WesternMARKETS Where buyers an
Lecture 2Graphic Vocabulary Symbols Plan Views Elevations Sections and DetailsSymbolsIn construction drawings, standard symbols are used to show various construction materials and building elements such as plumbing fixtures & fittings, electr
Hong Kong International AirportGroup 6 Habacuc Flores, Mehrnaz Golzar, Kolotita FueIntroduction Why was it built? Who designed and constructed it? When was the airport started and completed? How much did it cost? The airport was constru
Civil Engineering ProgramCurriculumAccreditation ABET - Accreditation Board for Engineering and Technology Engineering programs must demonstrate that their students attain (Outcomes a through k): a) an ability to apply knowledge of mathematics |
Chapter 10 Factorisation Techniques
Knowledge of factorisation enables us to learn advanced
mathematics and solve problems which occur in science, business,
computer programming and
engineering. In this chapter, we will consider the highest common
factor, the difference of two squares, factors of quadratic trinomials
over Q, use of perfect squares, factorisation of four terms and
factors of quadratic trinomials over R. |
Use the multiplication property of probability for these problems. In Problem
48 also use the property of complements.
Problems 47-48
These are both lengthy, but important problems.
Take your time working through the various parts, as shown in Example 7.
Problems 49-50
Build a tree diagram as shown in Example 8.
Note: Homework Hints are given
only for the Level 1 and Level 2 problems.
However, as you go through the book be sure you look at
all the examples in the text. If you need hints for the
Level 3 problems, check some sources for help on the internet
(see the LINKS for that particular section. As a last resort,
you can call the author at (707) 829-0606.
On the other hand, the problems designated "Problem Solving"
generally require techniques that do not have textbook examples.
There are many sources for homework help on the internet.
Algebra.help
Here is a site where technology meets mathematics. You can
search a particular topic or choose lessons, calculators,
worksheets for extra practice or other resources.
Ask Dr. Math
Dr. Math is a registered trademark. This is an excellent site
at which you can search to see if your question has been previously
asked, or you can send your question directly to Dr. Math
to receive an answer.
Quick Math
This site provides online graphing calculators. This is especially
useful if you do not have your own calculator.
The Math Forum @ Drexel
This site provides an internet mathematics library that
can help if you need extra help. For additional homework
help at this site, click one of the links in the right-hand
column. |
Basic College Mathematics, CourseSmart eTextbook, 4th Edition
Description
Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Basic College Mathematics, Fourth Edition was written to help readers effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
1. The Whole Numbers
1.1 Tips for Success in Mathematics
1.2 Place Value, Names for Numbers, and Reading Tables
1.3 Adding Whole Numbers and Perimeter
1.4 Subtracting Whole Numbers
1.5 Rounding and Estimating
1.6 Multiplying Whole Numbers and Area
1.7 Dividing Whole Numbers
Integrated Review–Operations on Whole Numbers
1.8 An Introduction to Problem Solving
1.9 Exponents, Square Roots, and Order of operations
Group Activity
Vocab Check
Highlights
Review
Test
2. Multiplying and Dividing Fractions
2.1 Introduction to Fractions and Mixed Numbers
2.2 Factors and Prime Factorization
2.3 Simplest Form of a Fraction
Integrated Review–Summary on Fractions, Mixed Numbers, and Factors
2.4 Multiplying Fractions and Mixed Numbers
2.5 Dividing Fractions and Mixed Numbers
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
3. Adding and Subtracting Fractions
3.1 Adding and Subtracting Like Fractions
3.2 Least Common Multiple
3.3 Adding and Subtracting Unlike Fractions
Integrated Review–Operations on Fractions and Mixed Numbers
3.4 Adding and Subtracting Mixed Numbers
3.5 Order, Exponents, and the Order of Operations
3.6 Fractions and Problem Solving
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
4. Decimals
4.1 Introduction to Decimals
4.2 Order and Rounding
4.3 Adding and Subtracting Decimals
4.4 Multiplying Decimals and Circumference of a Circle
Integrated Review–Operations on Decimals
4.5 Dividing Decimals and Order of Operations
4.6 Fractions and Decimals
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
5. Ratio and Proportion
5.1 Ratios
5.2 Rates
Integrated Review–Ratio and Rate
5.3 Proportions
5.4 Proportions and Problem Solving
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
6. Percent
6.1 Introduction to Percent
6.2 Percents and Fractions
6.3 Solving Percent Problems Using Equations
6.4 Solving Percent Problems Using Proportions
Integrated Review–Percent and Percent Problems
6.5 Applications of Percent
6.6 Percent and Problem Solving: Sales Tax, Commission, and Discount
6.7 Percent and Problem Solving: Interest
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
7. Measurement
7.1 Length: U.S. and Metric Systems of Measurement
7.2 Weight and Mass: U.S. and Metric Systems of Measurement
7.3 Capacity: U.S. and Metric Systems of Measurement
Integrated Review–Length, Weight and Capacity
7.4 Conversions Between the U.S. and Metric Systems
7.5 Temperature: U.S. and Metric Systems of Measurement
7.6 Energy: U.S. and Metric Systems of Measurement
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
8. Geometry
8.1 Lines and Angles
8.2 Plane Figures and Solids
8.3 Perimeter
8.4 Area
8.5 Volume
Integrated Review–Geometry Concepts
8.6 Square Roots and the Pythagorean Theorem
8.7 Congruent and Similar Triangles
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
9. Statistics and Probability
9.1 Reading Pictographs, Bar Graphs, Histograms, and Line Graphs
9.2 Reading Circle Graphs
Integrated Review–Reading Graphs
9.3 Mean, Median and Mode
9.4 Counting and Introduction to Probability
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
10. Signed Numbers
10.1 Signed Numbers
10.2 Adding Signed Numbers
10.3 Subtracting Signed Numbers
Integrated Review–Signed Numbers
10.4 Multiplying and Dividing Signed Numbers
10.5 Order of Operations
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
11. Introduction to Algebra
11.1 Introduction to Variables
11.2 Solving Equations: The Addition Property
11.3 Solving Equations: The Multiplication Property
Integrated Review–Expressions and Equations
11.4 Solving Equations Using Addition and Multiplication Properties
11.5 Equations and Problem Solving
Group Activity
Vocab Check
Highlights
Review
Test
Cumulative Review
Appendices
Appendix A: Tables
Appendix B: Unit Analysis
Student Resources
Study Skills Builders
Bigger Picture–Study Guide Outline
Practice Final Exam
Answers to Selected Exercises
Solutions |
From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience.
Description
Australian Signpost Maths 3 has been updated and redesigned to reflect current best practice in the teaching and learning of maths concepts, activities and digital technology. Written by Alan McSeveny and his experienced author team, Australian Signpost Maths provides a complete year's work and addresses all aspects of the Australian Mathematics Curriculum, including content and proficiency strands.
All activities in this student book have been matched to the Australian Curriculum content strands and develop students' conceptual understanding, logical reasoning and problem solving. Worked examples and explanations are given throughout the student book where new ideas are introduced, and a maths pictorial dictionary is provided to help students' digest new vocabulary. Open-ended problem solving and inquiry-based investigations and activities are designed to meet differentiated needs and learning styles. Exercises are carefully graded and colour-coded by content strand.
The sequence of the units within this text are ordered in a suggested teaching sequence, however a flexible structure has been provided to suit you. Australian Curriculum references are on every lesson page to allow you to link your planning to curriculum descriptors and specific lesson plans.
Pages are clear and colourful throughout this book, and retain features from previous Signpost editions including quirky, engaging cartoons and illustrations which customers have come to know and appreciate.
Features & benefits
Provides a complete year's work with full coverage of the Australian Curriculum.
The Proficiency strands are explained in this Student Book.
All activities have been matched to the content strands of the Australian Curriculum: Mathematics, developing students' conceptual understanding, logical reasoning and problem solving.
Australian Curriculum references on every lesson page to allow you to link your planning to curriculum descriptors and specific lesson plans.
Clear, colourful pages throughout this student book, with quirky, engaging cartoons and illustrations.
Meaningful new icons identifying Concepts, Investigations, ICT use and other activities.
Open-ended problem solving and inquiry-based investigations and activities designed to meet differentiated needs and learning styles.
Provides a maths pictorial dictionary.
A LiveText version of this student book is available with interactive activities on the Interactive Whiteboard DVD.
Author biography
Australian Signpost Maths' author team is made up of Alan McSeveny and his experienced author team, including Rachel McSeveny, Diane McSeveny-Foster, Alan Parker and Erika Johnson, are specialists in Primary Mathematics. Alan McSeveny is one of Australia's leading authors for Maths textbooks. He taught Maths for 25 years, and has produced market leading Mathematics series both in print and online.
Target audience
Suitable for Year 3 students.
Series overview
The long-awaited national edition of this Australian favourite provides new content while retaining the flexible structure, engaging cartoons and closely-aligned curriculum links that Australian educators love. Teachers can rely on the proven track record of Signpost in the Australian Curriculum edition.
Providing a complete year's work with full coverage of the Australian Curriculum, Australian Signpost Maths develops students' conceptual understanding, logical reasoning and problem solving with open-ended problem solving, inquiry-based investigations and activities designed to meet differentiated needs and learning styles.
Australian Signpost Maths covers Foundation to Year 6, with a student book, teacher resource book and interactive whiteboard DVD for each year level. There is also a mentals book for Years 1 to 6.
Completely revised to align with the Australian Curriculum, Australian Signpost Maths offers a simple, clear system for linking the Australian Curriculum: Mathematics' content across all components. With references on every lesson page, Australian Signpost Maths allows you to link your planning to curriculum descriptors and specific lesson plans. |
Topology
9780072910063
ISBN:
0072910062
Edition: 1 Pub Date: 2004 Publisher: McGraw-Hill College
Summary: Sheldon Davis' text is written for introductory courses in topology taken by advanced undergraduate and beginning graduate students. Designed to be flexible, the text is divided into two parts to accomodate different courses, course configurations, and instructor preferences. Part I of the text covers the bare essentials every student should know about topology before continuing on to study point-set or set-theoretic... topology, algebraic topology, funcitonal analysis, continuum theory, or the many other important areas in mathematics that utilize topology fundamentals. To keep the text manageable for beginning students, use of set theory in Part I is kept to an intuitive level. Part II contains a complete beginning course in general topology, or set-theoretic topology. General topology courses that assume prior background in the fundamentals can start directly with Part II and use the material in Part I for conceptual review. This text is part of the Walter Rudin Student Series in Advanced Mathematics |
Here's a real-world lesson using a business simulation. Two business accounts are used to find slope and intercept functions. The class graphs and interprets the information to find a break even point. There are plenty of worksheets and assessments included in this lesson.
In this recognizing idioms worksheet, students match beginning and ending phrases and sentences by drawing lines to connect each word or words in the left column to words in the right columns. Students create twenty-two idioms. In addition, students may choose from three functional activity ideas.
Design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Middle schoolers graph and write an equation for a line of best fit. They use their derived equation to make predictions about the amount of water that whould be wasted from one leak over a long period of time or the amount wasted by serveral leaks during a specific time period.
In this math worksheet, students give examples of functions that will satisfy given conditions. Students tell the tabulations for a given function. Students use the definition of a derivative to compute the inverse of a function. they state the Fundamental Theorem of Calculus and describe its usefulness. Students give an example of a function that can not be integrable.
Investigate non-linear functions based upon the characteristics of the function or the representation of the function. The functions are displayed in multiple formats including as graphs, symbols, words, and tables. Learners use written reflection scored on a rubric to assess understanding.
This Mean Value Theorem and Rolle's Theorem worksheet is very thorough in explaining the two Theorums and showing the formulas. There are six prractice problems for classwork, and eight additional problems for homework.
In this continuity instructional activity, students solve 5 short answer problems about continuity. Students determine where functions are continuous and find the limits of functions at points of discontinuity.
Wow! Students examine a geometric sequence. In this geometry lesson, students measure the lengths of strings on a musical instrument and explore the geometric sequence the frets generate. Students compare and contrast geometric sequences and exponential functions. |
Our seminar series offers brief presentations by senior Wolfram Research
technical staff on topics of interest to Mathematica newcomers
as well as to experienced users. These seminars provide you with an
easy way to learn about what's new in Mathematica and find out
about emerging technologies. They give you a special opportunity to learn
from Mathematica experts, and best of all, they're free!
Online seminars run 30-60 minutes and include live Q&A with Wolfram
Research technical staff. Online seminar dates and times are listed on the Wolfram Education Group
seminar calendar. On Demand seminar recordings are now available, so you can watch anytime.
Using Mathematica in the classroom This seminar provides an overview of the Mathematica functionality that makes it easy for educators to integrate the software into precollege, community college, and higher education classrooms. Whether you have used Mathematica for years or have no technical computing experience, you'll see many examples of Mathematica's use for education that can be implemented immediately. Resources and presentation materials are made available to participants.
Insights and materials from a former high school and university calculus instructor This seminar discusses some limitations with traditional approaches to teaching calculus and shows how Mathematica can remove those limits for a more enriching learning experience for your students. We'll compare Mathematica versus traditional methods of instruction for teaching calculus topics such as squeeze theorem, derivatives, Newton's method, Riemann sums, and solids of revolution. Courseware, lab activities, and other resources for exploring these topics will be made available to attendees for immediate use within the calculus classroom.
Latest features demonstrated This seminar gives an overview of the new features in Mathematica 8. Topics range from free-form linguistic input and Wolfram|Alpha data integration all the way to C code generation and new functions in probability and statistics, finance, control systems, graphs and networks, image processing, wavelet analysis, and much more.
Use Mathematica to strengthen key concepts This seminar provides a look at topics found in introductory calculus courses and illustrates Mathematica's application to those concepts. In addition to demonstrating Mathematica's built-in calculus functions, this example-driven seminar provides a look at how to expand Mathematica's functionality by creating custom functions to further explore specific topics in the classroom such as computation of Riemann sums, optimizing area, and computing trajectories. Tools and resources for exploring these topics will be made available to attendees for immediate use within the calculus classroom.
Taught by a senior graphics developer This seminar provides a closer look at the visualization options in Mathematica. Attendees receive an introduction to MaxRecursion and PlotPoints, the basic concepts necessary to achieve high-quality plots. Several examples are presented.
Presented by a Demonstrations editor This seminar gives a brief introduction to the Wolfram Demonstrations Project, and shows how Mathematica users can write and publish their own Demonstrations and thereby join the growing community based around the project.
Discussions with senior Mathematica developers Participate in a Q&A session with a senior Mathematica developer. Developers (one per session; see schedule) share their expertise about the system's structure and design, and its broad application in a variety of professional and academic fields. Discuss exciting new innovations and technologies with the pros.
Insights from a Mathematica senior developer This seminar offers an overview of calculus in Mathematica along with applications such as solitary waves, minimal surfaces, and the Painlevé differential equations. Mathematica's internal problem-solving methods are also compared with conventional computation by hand. Significant historical and practical calculus examples are presented and solved, using the symbolic, graphical, and interactive features available in Mathematica.
Seamlessly import hundreds of formats This seminar presents an introduction to the Import and Export functions in Mathematica, including Mathematica formats for geospatial, graph, chemical, and biomolecular data. With the help of dozens of examples, it illustrates how to work with data formats from a variety of application areas, such as computational biology, chemistry, geospatial information systems, image processing, multimedia, audio, databases, medical imaging, chemical informatics, astronomy, 3D geometry, vector graphics, and scientific data.
First-ever comprehensive system for discrete symbolic calculus This seminar offers an overview of discrete calculus in Mathematica
along with applications such as random number generation, chaotic
dynamical systems, and the theory of algorithms. Examples illustrating
the capabilities for sequence analysis, symbolic summation, and
convergence testing of infinite series in Mathematica are given. Insight into the internal implementation and user-extensibility of these features is also provided.
Work with built-in computable data sources This seminar introduces computable data collections and shows how to work with them in Mathematica. Examples are drawn from mathematics, physics, chemistry, economics and finance, geopolitics, linguistics, and more.
Updated for webMathematica 3 This seminar provides an introduction to webMathematica. Topics covered include an overview of webMathematica technology, a tour of example sites highlighting key and new features, and webMathematica development tools. Presentation and example materials are made available to participants.
Tips for creating great presentations and technical documents This seminar provides useful tips and tools for creating and working with Mathematica notebooks that are designed for presenting to others. Examples show you how to incorporate traditional mathematical notation, auto-numbered objects, hyperlinks and buttons, slide shows, and more to create powerful presentations.
Tips for working with data more efficiently in Mathematica Mathematica provides a variety of tools for importing and manipulating data. This seminar walks through several concrete applied examples of working with imported data in some commonly used formats, such as XLS, HDF, text, DXF, and FASTA, as well as a time-series data example.
Introduction to basic image analysis features This seminar provides an overview of the fundamental integrated image processing features in Mathematica 8. A broad range of topics are covered, including image creation, manipulation, color conversions, arithmetic, linear/nonlinear operations, and morphology. All topics are accompanied by fun, task-oriented, interactive examples
Introduction to creating dynamic interfaces in Mathematica Want to create a dynamic interface, but aren't a C++, Java, or .NET/Link programmer? We've got you covered. In one line of code and faster than you can move a slider from left to right, you'll be creating and manipulating graphics, formulas, and even notebooks themselves.
Explore statistics charts and compare and visualize distributions and datasets This seminar provides an overview of the new statistical visualization functionality in Mathematica 8. Topics include visual inspection of
the shape of data and comparisons to distributions and datasets. Histograms, quantile plots, box-and-whisker plots, probability plots, distribution charts, and many more will be covered.
Analyze and design control systems, simulate models, and interactively evaluate controllers This seminar explores the new suite of control system tools in Mathematica 8, used to do analysis, design, and simulation of continuous and discrete-time systems. Topics include the construction and manipulation of state space and transfer function models, system interconnections, frequency response plots, and controller design.
In-depth examples demonstrating control system design and simulation This seminar gives a step-by-step approach to working with control systems in Mathematica. Each example begins with a problem definition and works toward a
solution and a simulation using several controller design methods, including pole placement, optimal control, and Bode plot manipulation.
Unlock the power of your graphics card with Mathematica This seminar provides an introduction to performing computation on the graphical processing unit (GPU) in Mathematica 8 using CUDA. With this new technology, users can accelerate their programs. The seminar topics include reasons for using the GPU, an overview of CUDA and OpenCL, some use cases for CUDA and OpenCL, how to use CUDA from within Mathematica, and the GPU programming workflow from within Mathematica. Upon completion of the seminar, attendees will understand the basics of how to speed up their Mathematica programs by using the GPU.
Advanced CUDA programming methods in Mathematica 8 This seminar provides an in-depth overview of the new GPU programming
functionality in Mathematica 8 through CUDA. Topics include how to
compile CUDA code into an executable, load user-defined CUDA functions
into Mathematica, use CUDA memory handles to increase memory
bandwidth, and use Mathematica parallel tools to compute
on multiple GPUs either on the same machine or across networks, as well
as a discussion about the general workflow of CUDA programming within
Mathematica.
Introduction to using OpenCL and Mathematica 8 for GPU programming This seminar provides an introductory overview of the new GPU
functionality in Mathematica 8 by using OpenCL. Topics include reasons
for using the GPU, overviews of OpenCL and CUDA, some use cases for
OpenCL, how to use OpenCL from within Mathematica, and the GPU
programming workflow within Mathematica. |
In districts nationwide, as many as 50% of students fail Algebra I the first time and must repeat it—some more than once. What happens to those who are one or more grade levels behind before they begin Algebra I? Intensified Algebra I is a comprehensive program for an extended-time Algebra class that helps students who are significantly behind become successful in algebra within one academic year. It transforms the teaching of algebra to students who struggle in mathematics.
This program is designed for lower level math students, which I am teaching in inner city Chicago. The curriculum is perfect for my students. The reading is manageable, and the focus is on getting students to really think through problems. |
The CCGPS Coordinate Algebra Program is a complete set of teacher and student materials developed around the Common Core Georgia Performance Standards (CCGPS) and the Coordinate Algebra Frameworks, Curriculum Map, and Teacher's Guide. The course design has benefited from direct input from Georgia teachers.
Topics are built around accessible core curricula, ensuring that Coordinate Algebra is useful for striving students and diverse classrooms. This program realizes the benefits of exploratory and investigative learning and employs a variety of instructional models to meet the learning needs of students with a range of abilities. Review and purchase
Coordinate Algebra Station Activities for CCGPS The Coordinate Algebra Station Activities for CCGPS is a collection of hands-on, problem-solving activities to provide students with opportunities to practice and apply the math skills and concepts they are learning in their Coordinate Algebra class.
You may use these activities to complement your regular lessons or in place of your regular lessons, if students have the basic concepts but need practice.
The CCGPS Analytic Geometry Program has been organized to coordinate with the CCGPS Analytic
Geometry Frameworks and Curriculum Map. Each lesson includes activities that offer opportunities for exploration and investigation. These activities incorporate concept and skill development and guided practice, then move on to the application of new skills and concepts in problem-solving situations. Throughout the lessons and activities, problems are contextualized to enhance rigor and relevance.
Download the Content Map for an overview of the course units, lessons, sub-lessons, and standards.
CCGPS Advanced Algebra
A complete CCGPS Advanced Algebra Program will be available for school year 2014-2015 and we're working to have Units 1-3 by the end of 2013 for those teaching Accelerated Analytic Geometry. In addition to complete course materials, Digital Enhancements and Online Assessments will also be available.
"I am truly enjoying teaching from the Walch Coordinate Algebra text. I have never found a textbook that matches the Georgia state standards so well. It seems to be tailored to fit our curriculum. The Walch materials are also easily differentiable. This book is usable from accelerated to support classrooms."
- Laura Blair, Math Teacher, Southeast Bulloch High School
"Walch has created the only textbook that truly follows the standards. I have looked at every book available to me and they all simply rearranged the old texts to match up, but did not add or remove anything to ensure that all standards are met. Using the Coordinate Algebra text has made my job so much easier! The chapters are organized in the same order as the CCGPS for Georgia. The Teacher's Edition even provides a timeline so that I know when it is appropriate to pull in the state's tasks. The electronic versions of the student edition and teacher's edition have been a huge help, as well!"
- Heather Lloyd, Math Teacher, Hart County
We are pleased to offer additional high school math resources to Georgia, listed below:
DeKalb County High utilizes Walch High School Science Programs for the GHSGT, covering the Characteristics of Science and the five content domains: Cells and Heredity; Ecology; Structure and Properties of Matter; Energy Transformations; and Forces, Waves, and Electricity.
Summer School and Intercessions
Fulton County uses summer-school support programs for mathematics in grades 6, 7, and 8.
In addition to our GPS-based materials for secondary classrooms, we have a wide variety of research-based materials aligned to national standards that can be readily incorporated into your educational programs. See the results: Clarke County Achieves 12.8% CRCT Gains in Five Weeks... |
Overview
Main description
All of the courses in the junior high, high school, and college mathematics curriculum require a thorough grounding in the fundamentals, principles, and techniques of basic math and pre-algebra, yet many students have difficulty grasping the necessary concepts. Utilizing the author's acclaimed and patented fail-safe methodology for making mathematics easy to understand, Bob Miller's Basic Math and Pre-Algebra for the Clueless enhances students' facility in these techniques and in understanding the basics.
This valuable new addition to Bob Miller's Clueless series provides students with the reassuring help they need to master these fundamental techniques, gives them a solid understanding of how basic mathematics works, and prepares them to perform well in any further mathematics courses they take.
Author comments
Bob Miller has been a mathematics lecturer at City College of New York for more than 28 years. |
This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics:The term used in the title of this volume--thinking practices--evokes questions that the authors of the chapters within it begin to answer: What are thinking practices? What would schools and other learning settings look like if they were organized for the learning of thinking practices? Are thinking practices general, or do they differ by disciplines?...How does the brain represent number and make mathematical calculations? What underlies the development of numerical and mathematical abilities? What factors affect the learning of numerical concepts and skills? What are the biological bases of number knowledge? Do humans and other animals share similar numerical representations and processes? WhatThe combined impact of linguistic, cultural, educational and cognitive factors on mathematics learning is considered in this unique book. By uniting the diverse research models and perspectives of these fields, the contributors describe how language and cognitive factors can influence mathematical learning, thinking and problem solving. The authors... more...
Total Domination in Graphs gives a clear understanding of this topic to any interested reader who has a modest background in graph theory. This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured include the interplay between total domination in graphs and transversals in hypergraphs, and the... more...
Solidly grounded in up-to-date research, theory and technology,? Teaching Secondary Mathematics ?is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers, and shows how concepts typically found in a secondary mathematics curriculum can be taught in... more... |
The José Valdés Math Institute is an organization whose mission is to provide a comprehensive math education to middle and high school students, particularly the underrepresented, to achieve academic success.
The original vision of Mr. José Valdés was to ensure that underrepresented children be given equal opportunities to succeed in mathematics. This ideal provides the foundation of our philosophy at Valdés.
Classes Offered by the Jose
Valdés
Summer Math Institute
Brief
descriptions of the classes offered by the Valdés
Math Institute are
below. For a greater description of subjects covered in each class,
please click on the class name.
The
standards for all classes were developed in the early days (1988-1993)
of the Institute by the teaching staff. When California adopted
standards in the mid to late 1990's, the staff carefully went over them
to see how they fit into the Institute classes.
It
was decided that the college prep courses (Algebra 1 and higher) were a
good match for what the Institute expected. The link for each class
will take you to the standards for that subject on the California Dept.
of Education site.
However,
our elementary classes (Math 1 through Intro to Algebra) had to combine
standards from grades 3 through 8 in the different classes. A committee
of teachers met to prepare a rough draft for each class, then the
entire staff reviewed and made changes to the draft. (It has been
reviewed twice since then). You will thus find standards from different
grades in these classes. We hope that these pages will give you a
better idea of what to expect in each class.
Emphasis
on whole number operations and introduction to fractions and decimals:
Student goal is to master addition, subtraction, multiplication, and
division of whole numbers. Additional topics include patterns,
measurement, money, word problems, and applications.
Emphasis
on fractions and decimals with a review of whole numbers: Student goal
is to master all four operations with both fractions and decimals.
Introduction to ratio, percentage, graphing, statistics, word problems,
and enrichment topics.
Math 3
MASTERY
of whole number operations, fractions, decimals, ratio and percentage
plus a significant introduction to integers and number theory,
relationships, reasoning, and problem solving. May be similar to
standard 7th grade math course.
INT-AL
Number
theory, integers, positive and negative exponents, radicals, problem
solving, geometry, graphing, solving basic equations and inequalities:
Students should have previously mastered topics covered in Math 1-2-3.
May be similar to 8th grade math which will prepare students to enter
high school in Algebra 1.
A
class designed for those students having difficulty with Algebra due to
the absence of some basic skills. Students in this class receive
elective high school credit but must still pass Algebra 1 and Geometry.
This
class is for students who have successfully passed the first semester
of Algebra 1. Students in this class will complete the Algebra 1
requirement and will also be given some coursework to prepare them for
Geometry.
ALGEBRA 1
First
year college prep course that serves as the foundation for all advanced
math classes. Basic arithmetic properties on subsets of numbers. Powers
and roots, functions, polynomials and graphing of simple equations.
Quadratic equations are introduced. Practical applications of algebra
(area, distance, mixture problems).
GEOMETRY
Use
of axioms, postulates, and theorems for geometric proofs. Study of
congruent and similar triangles, lines and their properties, polygons,
circles and their properties. Introduction to co-ordinate geometry.
Real world applications.
ALGEBRA 2
Continuation
of Algebra 1 topics including a more in-depth look at graphing,
polynomials, and rational expressions. Complex numbers, probability,
roots of equations, systems of equations, matrices, and conics are
explored. Use of computer and its usefulness in mathematics studied.
MATH ANALYSIS
Preparation
for Calculus. Study of trigonometric functions (circular and right
triangle). Study of linear, quadratic, and circular functions and
solving equations and inequalities. Graphing all of the above and an
introduction to series and limits. |
Peer Review
Ratings
Overall Rating:
This applet is part of a larger collection of lessons on graph theory. The focus of this particular applet is on Euler Circuits, Directed Graphs and Hamilton Circuits.
Learning Goals:
Investigate existence of Euler Circuits and Hamilton Circuits for a variety of graphs. The applet also defines directed graphs and n cubes.
Target Student Population:
Undergraduate graph theory and discrete mathematics courses.
Prerequisite Knowledge or Skills:
Basic terms and definitions in graph theory and the lessons 1-11 given on the parent site.
Type of Material:
Tutorial & simulation
Recommended Uses:
Classroom demo, student tutorials
Technical Requirements:
JAVA 2 enabled browser, Peterson software
Evaluation and Observation
Content Quality
Rating:
Strengths:
This lesson begins with brief definitions of an Euler circuit and Euler path. The student is then asked to explore Euler circuits on complete graphs using an applet. The applet efficiently demonstrates what an Euler circuit is. There are more questions about which other graphs contain Euler circuits, and the student is asked to use the Peterson software (see below) to make this investigation. The lesson is well laid out and the coordinated use of text, Java, and the Peterson software is handled well. The second part of the lesson, directed graphs, continues with the theme of text, Java, and the Peterson software. The third part of the lesson provides a definition of a Hamiltonian Circuit and explores their existence in the same manner as previously discussed for the Euler Circuit. Upon completion of the lesson, the user can easily compare the criteria required for existence of the Euler and Hamilton Circuits on the specified graphs.
When the author uses a term that was introduced in a previous lesson, he makes sure to provide a link to the page with its definition. At the bottom of the page there is a link to the answers for the lesson.
The lessons are well sequenced and include all of the expected topics in introductory graph theory. Instructions and definitions are clear and followed by examples for the user to follow, both in the applet and using the Peterson software. Lessons reinforce concepts defined in earlier lessons, increasing retention.
The author forwarded an exam copy of the Peterson software for completion of the review. It was excellent in its instruction, but limited to 16 vertices. Occasionally a lesson requested use of a larger number of vertices than the program could accommodate,
but using a smaller number was equally instructive. The complete version of Peterson software is available from the author for $15 and accommodates 64 vertices.
Concerns:
none
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This applet is part of a large series of lessons that comprehensively address elementary graph theory. Assuming that the student has worked through lessons 1-11, the student can work on lesson 12 without the aid of the instructor. It will serve as an excellent supplement to any discussion of Euler circuits, Hamilton Circuits and directed graphs. Both the applet and the Peterson software show the Euler circuits and Hamilton Circuits animated through its graph. The questions encourage exploration and the answers are provided via a link.
Concerns:
none
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Drawing the vertices and edges are easy and the user can easily modify a graph without starting over. The Peterson software has a menu interface and is also very easy to use. By starting with the simpler Java applet before working on the Peterson software, the student may create his/her graphs and experiment with them, gradually learning the concepts without becoming frustrated.
Concerns:
This lesson would be difficult to follow if the student didn't work through the prior lessons first. This is more of a caution than a concern. On some screens, the student will need to change the graph size to "smaller" in order to fit the whole graph on the screen. |
2 – Systems of Linear Equations: Equivalent systems. Matricial representation of a system of linear equations. Resolution and discution of systems.
3 – Determinants: Definition and properties. Determinant of the product.Classical adjoint (adjugate) of a matrix. Computation of the inverse from the adjugate.
4 – Vector Spaces: Definition and properties. Subspaces. Intersection and sum of subspaces and the relation of their dimensions. Linear combinations and subspace generated by a system of vectors. Principal results about linear dependence/independence of a system of vectors. Bases. Extension to a basis of a linearly independent system of vectors.
5 – Linear Transformations: Properties. Dimension theorem and other fundamental results. Matrix of a linear transformation and of composition of transformations. Matrices and changing of bases. |
As part of a nationwide movement, the Mathematics Department has changed its approach to teaching mathematics
to one which is "leaner, livelier, and more relevant to real-life problems."
The main purpose of this fresh approach is to help you learn to think about
mathematics.
The text, as you will see, emphasizes understanding concepts and de-emphasizes
rote memorization.
Since our goal is to prepare you for further study in all mathematical subjects,
there will be a strong emphasis on mathematics in everyday life and many of
the applications will come from the physical and social sciences.
In addition to the text, we will be using graphing calculators to help us
better visualize the fundamental ideas, to do routine computations,
and to make the course more interesting.
You will find the graphing calculator very easy to learn and to use.
Former students have consistently said that the use of calculators was a "big plus."
In all of our department's introductory courses there is an emphasis
on cooperative learning.
Your instructor will be facilitating group activities and discussion
rather than just repeating the content of the text to you at the
blackboard.
This means that we will be asking you to read the material and attempt
the homework before it is "covered" in class.
There will be times when you will have to learn topics which will not
be formally discussed in the classroom.
Along with your individual homework, another feature of the course
will be team homework assignments.
Each of the team problems will require considerable thought and a
complete, well-written solution.
You will often find that team homework problems are best solved
in a cooperative environment.
Your grade for each team homework assignment will be assigned to the
team as a whole, so everyone in your group will be responsible for
each other's learning of the material.
Most students using homework teams in previous terms have found them
helpful.
Typical student comments include:
"Discussing homework with other students makes the material easier and more understandable."
"The group work lets us learn from each other instead of always from the instructor."
"Doing homework in teams is effective - it provides a supportive environment."
You will be cooperating with other students; not competing.
Your course grade will depend on achievement and effort, and there is
no limit to the number of students who can receive good grades in this
course.
We are excited about this new approach to teaching and learning mathematics,
and we hope that you will join us in this excitement. Have a good semester!
Students often ask,
"Why do we have to do all this writing?
Writing has nothing to do with mathematics!"
The purpose of having you write explanations of your work is to
improve your understanding.
The more carefully and clearly you write your mathematics,
the more likely it is to be correct,
and the more likely you will be to remember it.
Writing is a crucial part of the thinking process itself.
As you are solving problems in this course, remember that getting
the "answer" is only one of the steps.
Don't think of what you write as just showing your instructor that
you have done the homework.
Think of writing as part of the process of learning.
During this course you will have to do a significant amount of group work.
It is a growing trend in professional schools and business to have teams
work on various projects.
For the team homework in this course,
each member of the team has an important role.
These roles are to be rotated each week so that everyone has the
opportunity to try each role.
The roles are the scribe, the clarifier, the reporter, and the manager.
Scribe:
The scribe is responsible for writing up the single final version of the
homework to be handed in.
This is the only set of solutions which will be accepted or graded.
Each member of the group will receive the same grade as long as they work with the team. Students who do NOT participate will receive a zero.
Whenever possible, your solutions should include
symbolic, graphical and verbal explanations or interpretations.
Diagrams and pictures should also be provided if possible.
Clarifier:
During the team meeting the clarifier assists the group by
paraphrasing the ideas presented by other group members,
e.g. "Let me make sure I understand, the graph goes up ...".
The clarifier is responsible for making sure that everyone in the
group understands the solutions to the problems and is prepared
to present the problems to the class if the team is called on.
Reporter:
The reporter writes a record of how the homework sessions went,
how long the team met, what difficulties or successes the team
may have had (with math or otherwise).
If there is disagreement about the solution of a problem,
the reporter should present sketches of alternate solutions
and explain the difference of opinion.
The report should list the members of the team
who attended the session and their roles.
The report should be on a separate sheet of paper and the first
page of the team's homework solutions. You may use a copy
of the sample cover sheet for this purpose., if you like.
Manager:
The manager is responsible for arranging and running the meetings.
If the team has only three members, or if one of the four members
cannot attend, the manager should also take one of the other roles.
When the homework is returned, the manager sees that it is photocopied
and distributed so that each team member's portfolio contains a copy
of the corrected problems.
The goal of team homework is to ensure that everyone learns with and from
the other members of the group.
This means that when the work is completed and submitted, every member
of the group should be able to explain how to solve all the problems.
Here are some ideas that past students have come up with to help your
group function at its full potential.
Schedule enough meetings, and don't schedule them at the last minute.
Go to every meeting and be on time. (Woody Allen says, 80% of life is just showing up.)
Do the reading and work on each of the problems before the group meets.
In this course, it is absolutely essential that you do the reading
assignments.
Your experience with previous math courses may make it seem unlikely,
since it may have been possible to avoid reading the text,
yet do adequately well by copying down examples the instructor did
in class and then doing the homework exercises by just changing
the numbers in those "pattern examples" and the pattern examples
given in the text.
Also, older-style texts subtly encouraged students to skip the
reading assignments by putting procedures
for doing exercises in boxes, thereby essentially telling the
students that "everything you really need to know to do
the exercises can be found inside the boxes; you might as well
skip reading everything else."
Unfortunately, this approach resulted in students being able to do
the mechanical computations quite well,
but having no real understanding of the material and no real
ability to apply it in situations that are even a little bit
different from that covered by the pattern examples.
In essence, students were only being programmed
like computers to do computations that computers can do faster
and more accurately anyway.
It is this deficiency in the old-style math courses that led
to the national movement toward reformed courses,
like this one, which stress understanding.
This modern approach to learning requires new methods in the
classroom emphasizing learning rather than lecturing,
as well as new texts such as the one for this course.
The difference between the text for this course and an old-style
math text is apparent from even a cursory scanning of the first
chapter.
If you open the text and just begin turning pages, you will
probably be struck by the following:
The amount of text to be read outside of examples is much greater
than in old-style books.
Older books would typically have brief explanations, sometimes
single paragraphs, followed by one or more pattern examples.
This book has longer explanations that attempt to convey
understanding of the concepts involved rather than just
the mechanics of how to do computations.
The examples tend to be much longer than those in an old-style text,
and they often arise from actual real-world problems.
The exercises,
which also tend to be much longer than those in an old-style text,
are often quite different from each other and from the examples
in the text, and use real-world numbers that are not as "nice"
as the made-up numbers in the shorter exercises typical of old-style texts.
Doing the exercises requires an understanding of the material in the text,
not just the ability to change numbers in pattern examples.
Also, your instructor will be counting on you to read the text, since
he or she will not be lecturing very much and will be relying on you
to have seen the material before you work with it in class.
Like other courses outside mathematics (but perhaps unlike other
mathematics you have taken), not every small point on which you will
be tested will be covered by in-class examples.
Since the reading is so very important, some hints on how to it
might be helpful.
You may find that slight variations on the following scheme will work
well for you.
Plan to do the reading more than once, and do not make it an essential
goal to understand everything in the reading the first time through it.
The first reading should be devoted only to getting a general
overview of the material in the section.
After the first reading, stop for a few minutes and attempt to summarize
to yourself, in your own words, what the section is all about.
Then immediately re-read the section.
During the second reading, make a serious effort to understand all
of the material in the section.
This does not mean to memorize it, but rather to understand
all of the points before going on.
If you do not understand something during the second reading, put
the book aside awhile and return to it later when your mind is fresher.
If you still do not understand it after returning to it,
ask your instructor or your homework group members about it.
Do make sure you eventually understand all of the material.
You will probably get tripped up in later reading, in doing
the homework, or on test if you treat material you don't quite
understand as "probably not all that important."
Do not get discouraged if some points require some time to understand.
It is not uncommon to have to think about a point in a math test
for a half hour (or more, for more complicated concepts)
before it becomes clear what is really going on.
Study Time.
This course requires a solid effort.
The faculty at the University of Michigan expects you to
study a minimum of two hours outside class for each credit hour,
which means that we expect you to spend at least eight hours
a week outside of class working on mathematics.
Math Lab.
The Mathematics Department runs a free tutoring center for all
introductory mathematics courses.
The Math Lab, as it is called, is located in B860 East Hall
and is staffed by course instructors and advanced undergraduate students.
This is an excellent place for your homework team to meet or you to go
when you need a little extra clarification.
Lab hours and additional information are available on the Math Lab website or by calling
(734) 936-0160.
Calculator.
You must have a high-end programmable graphing calculator;
this is not optional.
The TI-84 is strongly recommended.
You may use another equivalent calculator, but you will be
responsible for translating the supplied calculator programs into
programs for your own calculator.
Your instructor and the Math Lab will be most familiar with the
TI-83 and may not be able to offer you help with other calculators.
Attendance & Student Absences.
Since much of the learning in this course occurs interactively
during class time, attendance is essential.
For that reason, the instructor is allowed to reduce
the student's course grade if the absences become excessive;
that is, if the student misses more than two or three classes
during the course of the semester.
Absences will usually be excused if due to a serious emergency.
However, it is our policy that an emergency serious enough to
cause an absence from a class activity or a test is also
serious enough to require documentation.
Students anticipating more than one or two absences
due to athletic commitments (or any other type of predictable
commitment) really should rearrange their class schedules to
accommodate this, since frequent absences may not be excused.
Absences will be dealt with on a case-by-case basis, however,
two situations occur commonly enough to merit attention.
Travel plans are never sufficient cause for an excused absence.
In particular, the availability of cheap plane tickets for particular
days near final exam time is not enough reason to reschedule a
student's final exam.
Also, an activity related to the social functions of a student's
current of anticipated future residential organization,
whether a university residence hall, apartment complex, sorority,
or fraternity, is never sufficient excuse for an excused absence.
Conflicts With Uniform Exams.
The two uniform exams during the course of the semester are
scheduled for 6:00 - 7:30 p.m. to make it possible for all
students to attend, but we are aware that there can be conflicts
with other scheduled academic activities such as a class
or another evening test.
If this happens, notify your instructor well in advance
so that we can clear up the problem.
Due to the nature of the final exam schedule, there are seldom
conflicts between regularly scheduled final examinations.
If a problem does occur, notify your instructor as early in
the term as possible.
Grades in this math course.
All sections of this course use the same grading guidelines to ensure a fair, standardized
evaluation process. Your grade in this course will be determined
primarily by your work on the "uniform component," which is the same for all sections of the course. The majority of this component comes from your scores on the uniform exams. Your grade as determined by the uniform component may be influenced by the "section component" of the course, which includes your work in your class-section. In some cases, your section component may adjust your grade up or down (as explained below). In addition, there is a "gateway component" to your grade which may also adjust your grade downward. The details follow.
1. The uniform component.
This includes two uniform midterm exams, a uniform final exam, and your scores on web homework.
Each of the exams will be taken by all students
in all sections at the same time, and are graded by all the instructors
working together.
Your uniform component score will be determined from your scores on each exam as follows:
Midterm Exam 1
25% of uniform component score
Midterm Exam 2
30% of uniform component score
Final Exam
40% of uniform component score
Web HW
5% of uniform component score
After each exam, a letter grade will be assigned to your uniform component score using
a scale determined
by the course coordinator specifically for that exam.
We do not use the "10-point scale" often seen in high school
courses in which scores in the 90's get an A,
in the 80's get a B, and so forth;
the level of difficulty of the exams will be considered.
The scale for the uniform component score will apply to all students in all sections.
The scale for final course grades will be set by the coordinator based upon the above percents for each component. Most students will receive the course grade assigned by that scale.
2. The section component. To help you learn the material,
you will be given a variety of reading assignments, team homework,
quizzes and other in-class activities. Your instructor will decide how the section component is determined for your particular section and grade
the section work.
If, at the end of the term, your rankings on the section component and uniform component differ significantly from one another, your course grade will be examined to see if an adjustment should be made. If you have participated in section activities but your section component is significantly lower than your uniform grade, your course grade may be lowered by one third of a letter grade. Students who have not seriously attempted to contribute to the section component of the course (i.e., quizzes, team homework, etc.) may have their final course grade lowered by up to a full letter grade. If, on the other hand, you have struggled on an exam and your in-class performance is significantly higher than the uniform component grade, your instructor may in some cases adjust your grade upward by one-third of a letter grade. This raise is generally only given for students whose uniform component places them near the top (or at the "cusp") of a letter grade category. The majority of students will find that their in-class performance and their exam scores are quite reflective of one another. Thus, in the majority of cases, no adjustment is made to the uniform course grade.
The best way to gauge your in-class performance is to keep an eye on the median grade in your section for each assignment and quiz. It is not useful to compare quiz and homework grades with students from other sections, because instructors write their own quizzes and determine the grading rubric for homework in a section.
3. The gateway component. There will be one or two (depending
on the course you are taking)
online basic skills gateway test(s) which you need to pass by the
deadline announced in the course schedule. These tests may be taken multiple times, and cover skills that every student who passes the course should have. Therefore, students who are keeping up with the course work can and will pass the gateway---if they start taking it early enough! You may practice each test online as many times as you like, and you may take a test for a score as often as twice per day without penalty until the deadline. Because the gateway tests cover skills that every student must have, the gateway tests do not raise your baseline grade; instead, if they are not passed by the deadline, your final grade in the course will be automatically reduced. Opening dates, deadlines and grade penalties will be announced in your class. All sections of your course have the same open/closing dates and penalties assigned to the gateway component.
Section averages.
Course policy is that a section's average final letter grade cannot differ
too much from that section's average baseline letter grades.
This means that the better your entire section does on the uniform exams,
the higher average letter grade your instructor can assign in your section.
It is therefore in your best interest to help your fellow students in
your section do well in this course.
In other words, cooperation counts!
Grades at the university.
Many students who come to the University of Michigan have to adjust
themselves to college grading standards.
The mean high school grade point average
(recalculated using only strictly academic classes)
of our entering students is around 3.6,
so many of you were accustomed to getting "straight A's"
in high school.
Students' first reaction to college grades is often,
"I've never gotten grades like these."
However, a grade of 15/20 on a team homework assignment
(which you might previously have converted to 75% - a high school C)
may well be a good score in a college math course.
Your own instructor is your best source of information on
your progress in the class.
The classroom is place where all students need to be engaged in learning.
This means that it cannot be a place for casual conversations,
reading the newspaper, doing homework for other classes, etc.
Be ready to concentrate on math and discuss the day's material.
Be respectful and polite.
Listen to your instructor and your fellow students when they are talking.
In order to benefit from being in an interactive class,
each student must come to class prepared.
Come to class having done the assigned reading and attempted
the homework problems.
Contribute to your homework team.
Work on the problems ahead of time.
Go to every meeting promptly and do your
share to make sure that the meeting is valuable to everyone.
Be in your seat and ready to start when your class is scheduled
to begin and remain until the class is dismissed.
Students at the University of Michigan are expected to exhibit
academic integrity.
Each College has its own standards for treating cases
of academic misconduct,
but in all Colleges there can be serious consequences
for violating the Code of Academic Conduct.
Sanctions can include:
suspension, disciplinary probation,
and receiving a failing grade.
Some examples of cheating, as stated in the LS&A
Code of Academic Conduct, include:
submitting work which has been previously submitted in another
term or another section of the course.
using information from another student or another student's
paper or an examination which is supposed to be individual work.
altering a test after it has been returned, and then resubmitting
the work claiming that it was improperly graded. |
Introductory Algebra is typically a 1-semester course that provides a solid foundation in algebraic skills and reasoning for students who have little or no previous experience with the topic.& The goal is to effectively prepare students to transition into Intermediate Algebra.
Table of Contents
Preface
vii
Prealgebra Review
1
(1)
Factors and the Least Common Multiple
3
(6)
Fractions
9
(10)
Decimals and Percents
19
Activity: Interpreting Survey Results
29
(1)
Highlights
30
(3)
Review
33
(2)
Test
35
Real Numbers and Introduction to Algebra
1
(88)
Symbols and Sets of Numbers
3
(10)
Introduction to Variable Expressions and Equations
13
(10)
Adding Real Numbers
23
(8)
Subtracting Real Numbers
31
(10)
Multiplying Real Numbers
41
(6)
Dividing Real Numbers
47
(10)
Integrated Review---Operations on Real Numbers
55
(2)
Properties of Real Numbers
57
(8)
Reading Graphs
65
(24)
Activity: Analyzing Wealth
75
(1)
Highlights
76
(5)
Review
81
(4)
Test
85
(4)
Equations, Inequalities, and Problem Solving
89
(100)
Simplifying Expressions
91
(8)
The Addition Property of Equality
99
(10)
The Multiplication Property of Equality
109
(8)
Further Solving Linear Equations
117
(12)
Integrated Review---Solving Linear Equations
127
(2)
An Introduction to Problem Solving
129
(12)
Formulas and Problem Solving
141
(10)
Percent, Ratio, and Proportion
151
(12)
Solving Linear Inequalities
163
(26)
Activity: Investigating Averages
175
(1)
Highlights
176
(3)
Review
179
(6)
Test
185
(2)
Cumulative Review
187
(2)
Exponents and Polynomials
189
(80)
Exponents
191
(12)
Negative Exponents and Scientific Notation
203
(12)
Introduction to Polynomials
215
(10)
Adding and Subtracting Polynomials
225
(6)
Multiplying Polynomials
231
(6)
Special Products
237
(10)
Integrated Review---Operations on Polynomials
245
(2)
Dividing Polynomials
247
(22)
Activity: Modeling with Polynomials
255
(1)
Highlights
256
(3)
Review
259
(6)
Test
265
(2)
Cumulative Review
267
(2)
Factoring Polynomials
269
(78)
The Greatest Common Factor
271
(8)
Factoring Trinomials of the Form x2 + bx + c
279
(8)
Factoring Trinomials of the Form ax2 + bx + c
287
(8)
Factoring Trinomials of the Form ax2 + bx + c by Grouping
295
(6)
Factoring Perfect Square Trinomials and the Differences of Two Squares
301
(12)
Integrated Review---Choosing a Factoring Strategy
311
(2)
Solving Quadratic Equations by Factoring
313
(10)
Quadratic Equations and Problem Solving
323
(24)
Activity: Factoring
335
(1)
Highlights
336
(3)
Review
339
(4)
Test
343
(2)
Cumulative Review
345
(2)
Rational Expressions
347
(82)
Simplifying Rational Expressions
349
(8)
Multiplying and Dividing Rational Expressions
357
(10)
Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator
367
(8)
Adding and Subtracting Rational Expressions with Different Denominators |
Hours of operation
How JavALab Courses Work
These courses take advantage of an advanced technology adapted to learning mathematics: Assessment and LEarning in Knowledge Spaces, or ALEKS. Students take an initial assessment
the first day of class that determines the mathematical objectives they have already mastered,
and sets up the objectives they will master during the course to fill their learning "pie." Students
commit at least three hours each week in the Javelina Algebra Lab (JavALab) and additional
hours outside the lab practicing in the Learning Mode. This adds pieces to the learning "pie."
Students also meet as a class once a week for 50 minutes. During this time instructors review
as a class, or individually, those topics with which students need help or further understanding.
For every 20 objectives students complete, or after each ten hours of time in ALEKS, students
take an automatic ALEKS Assessment. Assessments ensure mastery of the objectives and must
be taken in the JavALab.
Grading In JavALab Courses
There are a total of 184 objectives which cover all three courses. Grading is based on completion
and mastery of the required number of objectives outlined below for each course. |
Curriculum
MS Mathematics
The primary goals of the Mathematics Department are to provide students with solid foundation in the basics of the various fields of mathematics (arithmetic, algebra, geometry, functions, as well as numerical, graphical and statistical analysis); and the ability to solve application problems in a variety of ways; and with an appreciation for the beauty and power of mathematics.
Calculator technology is emphasized and teachers make use of interactive whiteboards and various software packages to provide dynamic visualizations of the concepts being studied. Students are provided with opportunities to practice standardized testing skills and they can participate in local and national competitions through our Math Club program. We encourage our most advanced Upper School students to accelerate through our summer Honors offerings, thereby allowing them to complete AP Calculus AB, AP Calculus BC and Multi-Variable Calculus before graduating.
The Honors Sequence
Tailored to develop the depth of understanding, flexibility, creativity and critical thinking that will be required of a student in any university major that is intensively math-related.
The Advanced Sequence
Tailored for the majority of our students, this is the standard college preparatory sequence in mathematics.
The (Regular) Sequence
This is tailored for those students with career goals in fields which are not heavily dependent on mathematics. This sequence provides the fundamentals necessary for admission to a post-secondary institution.
The course progression for a Buckley student in the "Advanced" mathematics program consists of Math 6 Advanced in the sixth grade, Pre¬-Algebra Advanced in the seventh grade, Algebra I Advanced in the eighth grade, Geometry Advanced in the freshman year, Algebra II Advanced in the sophomore year, Pre-calculus Advanced in the junior year, and Calculus Advanced in the senior year.
The course progression for a regular-level student, after Algebra II, would be Pre-Calculus in grade eleven and Topics in Math in grade twelve.
Placement in mathematics classes is determined by the department in conjunction with the administration and is based on performance in the current and past mathematics classes, teacher recommendations, and performance on standardized tests. In addition, in order to remain in the "Honors" sequence, a student must maintain a B or better and in order to move from the "Advanced" to the "Honors" sequence, a student must maintain an A average.
Teaching Strategies
Manipulatives are used whenever possible in the Middle School and in the Geometry course where a hands-on approach is beneficial. Cooperative learning is employed in various ways throughout our program, thus encouraging cooperation and enhancing comprehension. Numerous aids are employed including interactive whiteboards, computer graphing software (to analyze functions in Algebra I and beyond), dynamic algebraic applications using Geometer's Sketchpad software. In addition, several math teachers offer on-line support and discussions to assist students.
Calculators
The use of calculators is incorporated throughout the Middle and Upper school programs. Students are formally instructed in the use of this technology, but only after they are able to do the computations, algebraic manipulations, and functional graphing exercises by hand. Students in Math 6 and Pre-Algebra must purchase the TI-34 (a Texas Instruments scientific calculator), those in Algebra I must purchase the TI-83, TI-83+, TI-84 or TI-84+ (a programmable graphing calculator),.
Math Lab
The Math Lab is a tutorial setting designed to help students with any problems they may be experiencing in mathematics. The Lab is staffed with a mathematics teacher and several volunteer students who excel in the subject. The Lab is open during "sunrise" period and during both the Middle and Upper school lunch periods.
Classes
Math 6
An in-depth review of the properties of whole numbers, decimals, and fractions precedes the development of equality, metric measurement, and the definition of basic geometric figures and geometric relationships. The concepts of ratio, proportion and percent are explored, and integers are introduced. Data organization and the creation and interpretation of graphs are studied. Problem-solving strategies are reinforced throughout the year. An introduction to algebraic expressions and equations, functions, patterns, graphing, and number theory is also provided.
Algebra I
This course presents the language of algebra and explores a variety of conceptual applications. The relationships among method, application, and theory are examined. Equations, polynomials, radicals, functions and graphing are studied. Developing critical thinking skills, and applying concepts are encouraged and enhanced through problem solving. Graphing calculators are introduced and incorporated throughout the curriculum.
Pre-Algebra 6 Honors
Pre-Algebra
Students study algebraic expressions, equations, inequalities, ratios, proportions, coordinate geometry and radicals. Additional topics may include polynomials, Euclidean geometry and elementary statistics and probability. Facility in computation with whole numbers, integers, decimals and fractions is reinforced throughout the year. Problem-solving techniques are emphasized. |
Algebra and Trigonometry
Chegg does not guarantee CDs, access codes, or lab manuals with this book.
HARDCOVER:
ISBN:
0878911774
|ISBN-13:
9780878911776
PUBLISHER:Research & Education Association algebraic laws and operations, exponents and radicals, polynomials and rational expressions, equations, linear equations and systems of linear equations, inequalities, relations and functions, quadratic equations, equations of higher order, ratios, proportions, and variations. Take the Super Review quizzes to see how much you've learned - and where you need more study. Makes an excellent study aid and textbook companion. Great for self-study!DETAILS- From cover to cover, each in-depth topic review is easy-to-follow and easy-to-grasp - Perfect when preparing for homework, quizzes, and exams!- Review questions after each topic that highlight and reinforce key areas and concepts- Student-friendly language for easy reading and comprehension- Includes quizzes that test your understanding of the subject. «Show less,... Show more»
Rent Algebra and Trigonometry today, or search our site for other |
This is a lecture course in elementary algebra with a review of Pre-Algebra that will meet for a total of six hours per week with a focus on student-centered learning techniques. Review topics include whole numbers, operations of whole numbers and order of operations, fractions and mixed numerals, decimals, and percent notation. Topics include the real number system, operations of real numbers, simplification of algebraic expressions, and solving equations and inequalities. Topics also include graphing of linear equations, slopes, equations of lines, and graphing inequalities in two variables, systems of linear equations, applications and problem solving. Additional topics are exponents, scientific notation, and operations with Polynomials. This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC. Students must achieve a C- or better to pass the course. This is a developmental course. Credit for this course will not be counted toward fulfilling graduation requirements at STCC. |
See-and-Calc is an on-screen calculator with big number display and keypad to improve visibility. It simulates a big and friendly desktop calculator with the following main features: 4 arithmetic functions; Optional sound on clicking the keys; Memory functions; Percentage and square root; Math sign inversion; 00 and 000 buttons; Choice of 2 basic color patterns |
Lulu Marketplace
Measure and Integration: First Steps
This book introduces a beginning graduate student in Mathematics to the essentials of measure theory. This theory extends the notion of the length of an interval to more general notions of the size of a set. These ideas are then used to build abstract versions of integration theory. We discuss how to build many such measures, Lebesgue and Lebesgue-Stieljes Integration and include a lengthy treatment of classical Riemann and Riemann-Stieljes integration tools
as these are covered very incompletely these days. |
Navigation Tree
Teaching Material
See also the page on
Learning GAP,
which refers to material that may help you if you want to learn
GAP on your own or to teach it.
GAP has been used in lecture courses of various levels,
both for providing examples and for creating teaching material, in
particular exercises. However, at present we know of rather few examples
of such teaching materiæl being made available to the public. We therefore
ask to inform us if you have such material and are willing to share it
with others. The person to contact is
Edmund Robertson at St Andrews who
has agreed to maintain and extend this page.
A lab manual
Abstract Algebra with GAP
by Julianne Rainbolt and
Joseph A. Gallian
containing a collection of exercises that use GAP
and are appropriate for a first course in abstract algebra.
This manual was originally developed to be used with Gallian's book
Contemporary Abstract Algebra).
Lectures and Workshops on Groups, Applications, and
GAP by
Alice Niemeyer,
held in September 2004 at the University of Malaya at Kuala Lumpur.
The course describes applications of GAP
to counting and randomised algorithms.
Graph Isomorphism Problem
by Vincent Remie, Eindhoven University of Technology.
This looks at ways to show that two graphs on n vertices
are not isomorphic. Code is given for a number of GAP
functions to examine graphs.
Information on usage of CommSemi and other semigroups functionality
in GAP can be found in "Tutorial - Computing with
semigroups in GAP" by
Isabel M. Araújo and
Andrew Solomon,
which is available
here.
Teaching material in Japanese:
The home page of
Toshiaki Shoji,
in its section 'Refresh Corner' provides links to PDF as well as
PostScript versions of two Japanese texts 'How to play GAP'
(dating from Oct. 2002 and Feb 2005, resp.) that contain parts
of the GAP tutorial with additional examples.
The package
ITC can be used to demonstrate the
working of some coset table methods. Examples are given in the
ITC manual. |
Many thanks to our online sponsors!
GED CONNECTION
Program Details
Air Time:
05/01/2013 - 6:00am - 6:29am
Program Title:
INTRODUCTION TO ALGEBRA
Program Service:
TV
Program URL:
Long Description:
This episode of GED Connection focuses on Algebra. Algebra is a symbol ic language used to describe relationships among numbers. On the GED t est you'll be expected to know how to use algebra to simplify equation s, and how to solve for variables. You'll also need to know how to wor k with signed (positive and negative) numbers. Some of the important t erms discussed in this program are: equation, balance, unknowns, varia bles, and inverse operations. Other important concepts such as isolati ng the variable, simplifying the equation, commutative properties, dis tributive properties, and positive and negative numbers are also discu ssed. |
Description: Algebra from the viewpoint of the elementary curriculum with emphasis on proportional and linear relationships. Also included: topic from probability and statistics with connections to other topics in the elementary curriculum. Problem solving is emphasized throughout. |
Mathematical Proofs A Transition to Advanced Mathematics
9780321390530
ISBN:
0321390539
Edition: 2 Pub Date: 2007 Publisher: Pearson Addison-Wesley
Summary: Mathematical Proofs: A Transition to Advanced Mathematics, 2/e,prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.KEY TOPICS: Communicating Mathematics, Sets, Logi...c, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory.MARKET: For all readers interested in advanced mathematics and logic |
Conclusion
In this article we have shown you how to create new and change existing mathlets very easily with GeoGebra. One important idea of open source tools (like GeoGebra) and collaborative software (like wikis and forums) is to share knowledge and ideas freely. Free software does not only take away the burdens of license fees and proprietary systems, above all it promotes cooperation.
"Free software" is a matter of liberty, not price. To understand the concept, you should think of "free" as in "free speech," not as in "free beer." (Free Software Foundation)
When authors of mathlets follow this idea and allow others to change their work (e.g. with a Creative Commons license), both quality and quantity of interactive materials on the Internet can increase. Our free environment - GeoGebra with the GeoGebraWiki and user forum - can be seen as an example for the change from static web pages and libraries with unchangeable content towards a collaborative Internet that is driven by its users - in our case by a community of creative mathematics educators. |
recommended textbook fo College Algebra
Written by Margaret L. Liala, John Hornsby, and David I. Schneider and available on Amazon. This book helps students develop both an understanding of matter and the skills to analyze and solve algebraic problems. The book covers a wide range of issues, in particular the participation of algebra: the algebra itself, trigonometry, arithmetic and statistics. The book adopts a student-centered, and it is therefore with great exercise, supplements and study aids. Recommended for students of all levels, even beginners can explore clean the next book.
Beginning Algebra
Written by Margaret L. Liala, John Hornsby, Terry McGinnis, and, once again available on Amazon. This book is for those who need to review your algebra or who need help to understand the fundamentals and basic concepts of algebra. The book begins with the basics of the most basic numbers with a discussion of linear equations, polynomials and quadratic equations. Seasoned students in mathematics, probably does not need this book.
College Algebra Demystified
Written by Rhonda Huettenmueller, this book has reached readers of respondents recommended the site stable and Noble, and has a rating of three and a half out of five. The book contains many exercises, test questions, reviews, and a grand finale. Topics include functions, graphs of logarithmic functions, and most if not all of the key issues and relevance to the algebra.
Algebra for college students
Written by Robert F. Blitzer is a profound book, looking for topics in algebra. Adopting a demand-driven approach to algebra for college students that theory around, then each chapter, the material in a problem solving real-life context, very unlike the books which are based on pure mathematics. The book is very interested in evaluation procedures and verify that the reader understand the topic. The book comes with a CD, which contains more video tutorials, quizzes and other activities that reinforce the concepts and ideas of the book.
Handbook of linear algebra
Written by Kenneth H. Rosen, this book is purely Basic Linear Algebra linear through linear algebra topics above, including matrices and graphs. The book also includes methods of numerical linear algebra, the calculation methods of linear algebra, linear algebra and application in various fields, including computer science, geometry, probability and statistics and analysis.
There are many books available on the market and in libraries. Its really worth reading through the books in the library to find ones that are closely related to what you need. Never put your eggs in one basket, explore, learn and have fun! |
TheGraphs and Modelsseries by Bittinger, Beecher, Ellenbogen, and Penna is known for helping students ''see the math'' through its focus on visualization and technology. These texts continue to maintain the features that have helped students succeed for years: focus on functions, visual emphasis, side-by-side algebraic and graphical solutions, and real-data applications.
With theFifth Edition, visualization is taken to...show more a new level with technology. The authors also integratesmartphone apps, encouraging readers to visualize the math. In addition, ongoing review has been added with newMid-Chapter Mixed Reviewexercise sets and newStudy Guide summariesto help students prepare for tests. ...show less
Brand New. Includes Graphics Calculator Manual. Dis-patched within one business day for delivery in 2-5 business days. Includes Free tracking #. Please order priority for faster shipping. . Delivery t...show moreo Canada takes approx 3-9 business days. Free Upgrade to Priority Shipping. Just order regular and you will automatically upgraded to Priority Shipping which is usually 1- 3 business days114.9810 +$3.99 s/h
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a Book company Lexington, KY
May contain some highlighting. Supplemental materials may not be included. We select best copy available. - 5th Edition - Package - ISBN 9780321824219 |
Algebra and Functions - Level 6
Topics
Type
6AF.1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results:
6AF.1.1 Write and solve one-step linear equations in one variable.
6AF.1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.
6AF.1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.
6AF.1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator.
6AF.2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:
6AF.2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).
6AF.2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.
6AF.2.3 Solve problems involving rates, average speed, distance, and time.
6AF.3.0 Students investigate geometric patterns and describe them algebraically:
6AF.3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = pd - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).
6AF.3.2 Express in symbolic form simple relationships arising from geometry. |
Curves and surfaces, along with their special features
and properties, are studied in math at all levels, from high school geometry
though the most advanced graduate courses. This digital library attempts
to collect together some mathematically interesting curves and surfaces,
along with formulas describing some of their properties, and text highlighting
special features. Each curve or surface also includes several plots of
the object; many also include a VRML (virtual reality) representation
that can be manipulated in real-time. All together, these tools allow
the user to visualize and understand a wide variety of curves and surfaces
that might otherwise be difficult to grasp. The library can be used by
anyone with even minimal mathematical background, but many of the more
complex properties will require some knowledge of vector calculus and
differential geometry to be understood fully. |
Chapter 5
Figure 5-1 displays the Algebra I Cognitive Tutor near the completion of a problem. The problem situation is presented in the scenario window in the upper left
corner of the screen:
Four questions are posed for the student to answer:
1) How long does the blimp take to descend to the height of one mile?
2) When will the balloon and the blimp be at the same height?
3) Assuming the balloon has been climbing steadily, when did it leave the groundPage 50
Chapter 5
Cognitive Tutor Algebra I: Adaptive Student Modeling in Widespread Classroom Use
Albert Corbett
Human-Computer Interaction Institute Carnegie Mellon UniversityFigure 5-1 displays the Algebra I Cognitive Tutor near the completion of a problem. The problem situation is presented in the scenario window in the upper left
corner of the screen:Four questions are posed for the student to answer:
1) How long does the blimp take to descend to the height of one mile?
2) When will the balloon and the blimp be at the same height?
3) Assuming the balloon has been climbing steadily, when did it leave the ground?
4) At this rate, when will the blimp land?
OCR for page 51
Page 51
The student answers the questions by filling in the worksheet immediately below the scenario window. The cells in the worksheet are blank initially. The student analyzes the problem
situation, identifies the relevant quantities that are varying (in this situation, time and height of the airships), and labels the worksheet columns accordingly ("TIME,"
"BALLOON," and "BLIMP"). The student enters the appropriate units for measuring these quantities in the second row of the table and enters a symbolic model relating
the three quantities in the third row. In the figure, the student has represented the quantity of time with the variable X, related the height of the balloon to time with the
algebraic expression 90X + 350, and similarly related the blimp's height to time with the expression 8500 - 250X. Early in the curriculum, the student enters algebraic
expressions near the end of the problem, and the individual questions are intended to help scaffold this algebraic modeling. By the time the student has reached the linear systems unit
represented by the current problem, he or she tends to enter the algebraic expressions early in the problem. The emphasis in these problems is on using the expressions as problem-solving
tools, both in symbol manipulation and to automatically generate values in the worksheet (as described below).
Figure 5-1 The Algebra I Cognitive Tutor.
~ enlarge ~
SOURCE: Carnegie Learning, Inc., 2000
The student answers the questions by filling in the corresponding rows in the worksheet. To answer the first question, "How long does the blimp take to descend to the height of one
mile?" the student needs to perform a unit conversion on the given value, "one mile," and enter 5280 in the question-1 cell of the BLIMP column, immediately below the
formula. To compute
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the solution, the student can set up the equation 5280 = 8500 - 250X in the solver window in the lower center of the screen, solve it in the window, and type the answer, 12.88, into
the question-1 cell of the TIME column. Or the student can type an arithmetic expression that unwinds the equation, (5280-8500)/ -250, directly into the question-1 cell of the TIME column,
where it will be converted to 12.88. Once the value of X has been typed in this cell, the worksheet automatically generates the corresponding height of the balloon, 1509.2 feet at 12.88
minutes, employing the algebraic expression for balloon height typed by the student.
In completing the problem, the student also graphs the two linear functions in the graph window in the upper right corner of Figure 5-1. The student labels the axes,
adjusts the upper and lower bounds on the axes, and sets the scales so that the data points in the table can be displayed. Note that in question 2, "When will the balloon and the blimp
be at the same height?" the student is asked to solve for the intersection of the two functions, and in questions 3 and 4, the student is asked to find the x-intercept of the two
functions. The student can answer these questions by finding the relevant points on the graph or by setting up and solving equations in the solver window. In Figure
5-1, the student has set up an equation to solve for the intersection of the two functions, 90X + 350 = 8500 – 250X, and proceeded to solve the equation by
isolating X.
ADAPTIVE STUDENT MODELING
A central claim of Knowing What Students Know, the recent National Research Council report on educational assessment (NRC, 2001), is that three essential pillars support
scientific assessment: a general model of student cognition, tasks in which to observe student behavior, and a method for drawing inferences about student knowledge from students'
behaviors. Cognitive tutors embody this framework. Each cognitive tutor is constructed around a cognitive model of the knowledge students are acquiring. As a student performs
problem-solving tasks such as that displayed in Figure 5-1, the cognitive model is employed to interpret the student's behavior, and simple learning and
performance assumptions are incorporated to draw inferences about the student's growing knowledge.
Model Tracing
In model tracing, the underlying cognitive model is employed to interpret each student action and follow the student's individual solution path through the problem space,
providing just the support necessary for the student to complete the problem successfully. The cognitive model is run forward step-by-step along with the student, and each student
action is matched to the actions that the model can generate in the same context. As with effective human tutors, the cognitive tutor's feedback is brief and focused on the
student's problem-solving context. If the student's action is correct, it is simply accepted. If the student makes a mistake, it is rejected and flagged (in red font). If the
student's mistake matches a common misconception, the tutor also displays a brief just-in-time error message (in the window in the lower left corner of Figure
5-1). The tutor does not provide detailed explanations of mistakes, but instead allows the student to reflect on mistakes. Finally, the student can ask for problem-solving
advice at any step. The tutor generally provides three levels of advice. The first level advises on a goal to be
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accomplished, the second level provides general advice on achieving the goal, and the third level provides concrete advice on how to solve the goal in the current context.
Knowledge Tracing
The cognitive model is also employed to monitor the student's growing knowledge in problem solving, in a process we call knowledge tracing. At each opportunity for the
student to employ a cognitive rule in problem solving, simple learning and performance assumptions are employed to calculate an updated estimate of the probability that the student has
learned the rule (Corbett & Anderson, 1995). These probability estimates are displayed in the skillmeter in the lower right corner of Figure 5-1. Each bar
represents a rule, and the shading reflects the probability that the student knows the rule. As advocated by NRC (2001), the goal of knowledge tracing is to improve learning outcomes. It
is employed to implement cognitive mastery. Within each curriculum section, successive problems are selected to provide the student the greatest opportunity to apply rules that
he or she has not yet mastered. The tutor continues presenting problems in a section until the student has "mastered" each of the applicable rules in the curriculum section.
(Mastery is indicated by a checkmark in the skill meter).
TRANSFORMING EDUCATIONAL PRACTICE
I believe that cognitive tutors for mathematics are the first intelligent tutoring systems that are beginning to have a widespread impact on educational practice. In the 2001-2002 school
year, Cognitive Tutor Algebra and Geometry courses are in use at about 700 sites and by more than 125,000 students in 38 states. This includes urban, suburban, and rural middle and high
schools, both public and private. This success in moving from the research lab into widespread classroom use depends on several factors, including project design, research-based
development, demonstrated impact, and classroom support.
Project Design
Several project design features were essential to the success of the dissemination project (Corbett, Koedinger, & Hadley, 2001).
Opportunity: Targeting a National Need
National assessments such as the NAEP and international assessments such as the TIMSS have raised awareness of the need to improve mathematics education. Cities and states have
increasingly mandated that all students need to master academic mathematics, and virtually every state has defined high-stakes academic mathematics assessments that are employed to
evaluate schools and/or govern student graduation. For more than a decade, the National Council of Teachers of Mathematics (NCTM, 1989) has been recommending that academic
mathematics for all students should place a greater emphasis on problem solving, reasoning among different mathematical representations, and communication of mathematical results.
As a result of these trends, school districts actively look for, and are open to trying, new solutions to mathematics education, and Cognitive Tutor Algebra I aligns well with the
NCTM-recommended objectives.
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Integrating Technology into a Comprehensive Solution
Teachers face a major "usability" challenge when they are trying to integrate educational technology into a course. It may be difficult to align course curriculum objectives
and technology curriculum objectives and to make time for the technology activities. In our cognitive tutor mathematics project, cognitive tutors are fully integrated into yearlong
courses. We develop both the paper text that is employed in 60 percent of class periods and the cognitive tutor that is employed in 40 percent of class periods. This coordinated
development helps ensure that the problem-solving activities presented two days a week by the cognitive tutors address and develop the same curriculum objectives that students explore in
small-group problem solving and whole-class instruction the other three days a week.
Interdisciplinary Research Team
The research team is a collaboration of cognitive psychologists, computer scientists, and practicing classroom teachers throughout the process of developing, piloting, evaluating, and
disseminating a cognitive tutor course.
Research-Based Development
Cognitive tutor design is guided by multiple research strands, including cognitive psychology of student thinking (Heffernan & Koedinger, 1997; 1998), research in student learning
(Koedinger & Anderson, 1998), and research in effective interactive learning support (Aleven, Koedinger, & Cross, 1999; Corbett & Trask, 2000; Corbett & Anderson, 2001).
Formative evaluations of tutor lessons are employed to guide iterative design improvements, including studies of learning rate, validity of the underlying student model, and pre-test to
post-test learning gains (Corbett, McLaughlin, & Scarpinatto, 2000).
Demonstrated Impact
Cognitive tutor courses have a demonstrable impact on the classroom, student motivation, and student achievement.
Substantial Achievement Gains
Beginning with our two earliest cognitive tutors, the ACT Programming Tutor (APT) and the Geometry Proof Tutor (GPT), cognitive tutor technology has an established history of yielding
substantial achievement gains compared to conventional learning environments (Anderson, Corbett, Koedinger & Pelletier, 1995). College students working with APT completed a problem
set three times faster and scored 25 percent higher on tests than students completing the same problems in a conventional programming environment. High school students in geometry
classes that employed GPT for in-class problem solving scored about a letter grade higher on a subsequent test than students in other geometry classes who engaged in conventional
classroom problem-solving activities. Koedinger, Anderson, Hadley, and Mark (1997) demonstrated that the Cognitive Tutor Algebra I course yields similar achievement gains.
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High school students in the Cognitive Tutor Algebra I course scored about 100 percent higher on tests of algebra problem solving and reasoning among multiple representations, and about 15
percent higher on standardized assessments than similar students in traditional Algebra I classes.
Student-Centered Learning-by-Doing
In cognitive tutor courses, students actively learn-by-doing, both in the cognitive tutor lab and in small-group problem solving in the classroom. Schofield (1995) formally documented the
impact of cognitive tutors on the student-teacher relationship in a field study of the Geometry Proof Tutor in the mid-1980s. This was the first cognitive tutor deployed in high school
classrooms. She found that teachers in the cognitive tutor lab serve as collaborators in learning. Teachers shift their attention to the students who need more help, and they can engage
in more extended interactions with an individual student while other students in the class make substantial progress as they work with the cognitive tutor.
Increased Student Motivation
In the same study, Schofield (1995) documented that students are highly motivated and highly engaged in mathematics in the cognitive tutor lab. Teachers are excited about student
attitudes and about engaging students in individualized discussions of mathematics. Letters from some of our Cognitive Tutor Algebra I teachers include such comments as "Gone are
the phrases 'this is too hard—I can't do this,' instead I hear 'how do you do this? why is this wrong?'" and "Students now love coming to class.
They also spend time during their study halls, lunch, before and after school working on the computers. Self-confidence in mathematics is at an all time high."
Classroom Support
When a school adopts a cognitive tutor mathematics course, we also provide comprehensive classroom support that includes pre-service and in-service professional development, both on the
cognitive tutor technology and on small-group problem solving in class. We also provide software installation, hotline support (both email and telephone) for pedagogical questions and
technical problems, and email user groups and teacher focus group meetings.
U.S. Department of Education Exemplary Curriculum
In 1999 Cognitive Tutor Algebra I was designated an "exemplary" curriculum by the U.S. Department of Education. Sixty-one K-12 mathematics curricula were reviewed on three
criteria: the program's quality, usefulness to others, and educational significance. Of these 61 curricula, five were awarded the highest, "exemplary," designation.
Comments on Continued Scaling Up
Perhaps two key issues arise in considering the future growth in impact of cognitive tutor courses: the cost of developing new cognitive tutor courses and the need to provide high-quality
site support.
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Cognitive Tutor Course Development
Our best current estimate of the development cost for a cognitive tutor course comes from our current Cognitive Tutor Middle School Mathematics Project in which we are developing three
full-year courses. In this project, just over 100 hours of effort yields one hour of classroom activity. It should be emphasized that this estimate includes all aspects of design,
development, piloting support, and evaluation including: developing the cognitive task analysis that underlies text and cognitive tutor design: writing the text: programming the cognitive
model; programming the tutor interface; writing and coding the tutor problems; installing and maintaining the tutor; conducting teacher training; and designing, conducting, and analyzing
formative and summative evaluations.
We believe that this cost level is already economically competitive, given the substantial impact of cognitive tutor courses on achievement outcomes and the demonstrable impact on student
motivation. Evaluations of the mathematics and programming cognitive tutors indicate that model tracing alone can yield a one-standard deviation effect size, which is about half the
benefit of the best human tutors (Anderson et al., 1995). Our estimations, based on evaluations of knowledge tracing and cognitive mastery in the programming tutor, suggest that this
method of dynamic assessment and curriculum individualization can add as much as another half-standard deviation effect size (Corbett, 2001). We believe that the cost/benefit ratio will
continue to improve as new research leads to improvements in tutor effectiveness. Perhaps the more important limiting factor in cognitive tutor course development is not the cost, but the
availability of trained professionals to conduct cognitive task analyses and develop cognitive models.
Site Support
The single greatest challenge in site support is teacher training. As the Algebra and Geometry Cognitive Tutors become more robust, technical support is not a problematic issue. Teachers
and students need little training in the use of the cognitive tutor software. Instead, the greatest need is to help students become not just "active problem solvers" but
"active learners," who view problem solving not as an end in itself, but as a vehicle for learning. Teachers need professional development to help students make use of the
learning opportunities that arise in problem solving, not just in the cognitive tutor lab but also in small-group problem-solving activities during other class periods. As the deployment
of cognitive tutor mathematics courses has grown, we have relied on a growing number of experienced cognitive tutor mathematics teachers to offer professional development. But this need
for effective teacher development is not limited to our project. Research is needed to define effective teaching methods that support active student learning, and this knowledge needs to
become integrated into pre-service teacher education.
COGNITIVE THEORY AND DYNAMIC ASSESSMENT
Cognitive tutors are grounded in cognitive psychology. The cognitive model underlying each tutor reflects the ACT-R theory of skill knowledge (Anderson, 1993). ACT-R assumes a fundamental
distinction between declarative knowledge and procedural knowledge. Declarative
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knowledge is factual or experiential and goal-independent, while procedural knowledge is goal-related. For example, the following sentence and example in an algebra text would be encoded
declaratively:
If the same amount is subtracted from the quantities on both sides of an equation, the resulting quantities are equal. For example, if we have the equation X + 4 = 20, then we can
subtract 4 from both sides of the equation and the two resulting expressions X and 16 are equal, X = 16.
ACT-R assumes that skill knowledge is initially encoded in declarative form when the student reads or listens to a lecture. Initially the student employs general problem-solving rules to
apply this declarative knowledge in problem solving, but with practice, domain-specific procedural knowledge is formed. ACT-R assumes that procedural knowledge can be represented as
production rules—if-then rules that associate problem-solving goals and problem states with actions and consequent state changes. The following production rule may emerge when the
student applies the declarative knowledge above to equation-solving problems:
If the goal is to solve an equation of the form X + a = b for the variable X, Then subtract a from both sides of the equation.
Substantial cognitive tutor research has validated production rules as the unit of procedural knowledge (Anderson, Conrad, & Corbett, 1989; Anderson, 1993).
Evaluating Knowledge Tracing and Cognitive Mastery
As the student works, the tutor estimates the probability that he or she has learned each of the rules in the cognitive model. The tutor makes some simple learning and performance
assumptions for this purpose (Corbett & Anderson, 1995). At each opportunity to apply a problem-solving rule, the tutor
uses a Bayesian computational procedure to update the probability that the student already knew the rule, given the evidence provided by the student's response
(whether the student's action is correct or incorrect), and
adds to this updated estimate the probability that the student learns the rule at this opportunity if it has not already been learned.
The goal of knowledge tracing is to promote efficient learning and enable cognitive mastery of the problem-solving knowledge introduced in the curriculum. Within each curriculum section,
the tutor presents an individualized set of problems to each student, until the student has "mastered" the rule (typically defined as a 0.95 probability of knowing the rule).
Validating Knowledge Tracing: Predicting Tutor Performance
The same learning and performance assumptions that allow us to infer the student's knowledge state from his or her performance also allow us to predict student performance from the
student's hypothesized knowledge state. A series of studies validated knowledge tracing in
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the ACT Programming Tutor by predicting student problem-solving performance, both in the tutor environment and in subsequent tests (Corbett & Anderson, 1995; Corbett, Anderson, &
O'Brien, 1995). Figure 5-2 displays the mean learning curve, both actual and predicted, for a set of problem-solving rules in an early section of the ACT
Programming Tutor. The first point in the empirical curve indicates that students had an average error rate of 42 percent in applying each of the rules in the set for the first time. Average
error rate declined to under 30 percent across the second application of all the rules, and it continued to decline monotonically over successive applications of the rules. As can be seen,
the knowledge-tracing model very accurately predicts students' mean production-application error rate in solving tutor problems.
~ enlarge ~
Figure 5-2 Actual error rate and predicted error rate for successive applications of problem-solving rules in the ACT Programming Tutor.
SOURCE: Corbett, Anderson, & O'Brien, 1995, p. 26.
Validating Knowledge Tracing: Individual Differences in Post-test Performance
The more important issue is whether knowledge tracing accurately predicts students' performance when they are working on their own. A sequence of studies (Corbett & Anderson,
1995) examined the accuracy of the knowledge-tracing model in predicting students' post-test performance after they had completed work in the ACT Programming Tutor. Figure 5-3 displays quiz results for 25 students in the final study of the series. The figure displays each student's actual post-test accuracy (proportion of
problems completed correctly), plotted as a function of the knowledge-tracing model's accuracy prediction for the student. As can be seen, the model predicted individual differences
in test performance quite accurately. The model predicted that this group of students would average 86 percent correct, and they actually averaged 81 percent. The correlation of actual
and expected performance across the 25 students is 0.66.
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~ enlarge ~
Figure 5-3 Student post-test accuracy plotted as a function of accuracy predicted by the ACT Programming Tutor knowledge-tracing model. SOURCE: Corbett & Anderson, 1995,
p. 274.
Cognitive Mastery Effectiveness
A recent study examined the efficiency of cognitive mastery learning (Corbett, 2001). In this study 10 students in a fixed-curriculum condition worked through a set of 30 ACT Programming
Tutor problems. Twelve students in a cognitive mastery condition completed the fixed set of 30 problems and an additional, individually tailored sequence of problems as needed to reach
mastery. On a subsequent test, students in the mastery condition averaged 85 percent correct on the test, while students in the fixed-curriculum condition averaged 68 percent correct.
This difference is reliable, t(20) = 2.31, p < .05. Of the cognitive mastery students, 67 percent reached a high mastery criterion on the test (90 percent correct), while only 10
percent of students in the fixed-curriculum condition reached this high level of performance. Students in the cognitive-mastery condition completed an average of 42 tutor
problems—40 percent more problems than students in the fixed-curriculum condition—and they only required 15 percent more time to do so. This investment of 15 percent more time
yielded a high payoff in achievement gains.
Future Research
Three lines of research can be identified to enhance the educational effectiveness and broaden the impact of cognitive tutors in classrooms around the country:
We need to develop cognitive tutor interventions that will help students become more active learners and develop a deeper, conceptual knowledge of the problem-solving
domain.
We also need to better understand how teacher interventions can help students become more active learners.
We need to develop authoring systems that can make cognitive tutor development faster.
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Students working with cognitive tutors are active problem solvers. The principal strength of cognitive tutors is that they expose learning opportunities in detail. They reveal students'
missing knowledge and misconceptions step-by-step and afford students the opportunity to construct knowledge. However, the tutors' feedback and advice capabilities are limited. Both take
the form of short written messages, with multiple levels of help available upon request at each problem-solving step. Studies show that students do not always make effective use of the
assistance available. Eye-tracking studies of students working with the Algebra I cognitive tutor show that they often do not read or even notice the error feedback message (Gluck, 1999).
Other studies with the Geometry Cognitive Tutor show that students often make poor use of the help that is available (Aleven & Koedinger, 2000). The knowledge-tracing validation research
in the ACT Programming Tutor reveals a related point. The knowledge-tracing model consistently overestimates students' test performance by a small amount, about 10 percent. Studies
suggest that this happens because some students are learning some shallow rules in the tutor that do not transfer to the test (Corbett & Knapp, 1996; Corbett & Bhatnagar, 1997).
Cognitive tutors are already at least half as effective as the best human tutors and two or three times as successful as conventional computer-based instruction (Corbett, 2001). They can
become far more effective if they provide scaffolding to help students become not just active problem solvers, but active learners when learning opportunities are exposed. We have already
had some success in engendering deeper learning with graphical feedback (Corbett & Trask, 2000) and student explanations of problem-solving steps (Aleven & Koedinger, in press), but
we need to develop a more general framework for understanding effective tutorial scaffolding for student knowledge. Recent research is continuing to develop our understanding of effective
human tutor tactics (e.g., Chi, Siler, Jeong, Yamauchi & Hausmann, 2001). We need to integrate these results into a general theory and to implement effective scaffolding in cognitive
tutors.
Similarly, we need to better understand how the teacher in a cognitive tutor class can effectively scaffold active student learning. In the cognitive tutor lab, the teacher has the
opportunity to interact with individual student tutors on an extended basis (Schofield, 1995), and there is preliminary evidence that the benefits of cognitive tutors can depend on the
teacher's activities in the lab (Koedinger & Anderson, 1993). Research on effective human tutor tactics is relevant, but the classroom teacher needs some additional skills:
recognizing when a "teachable moment" arises for one student in a classroom of 20-30 students and being able to jump into the student's problem-solving context to provide
effective scaffolding. We also need to understand how teachers can best support small-group problem solving in cognitive tutor courses and integrate these group-paced classroom activities
with the individually paced cognitive tutor activities. And we need to develop effective professional development based on this research in effective teacher strategies.
Finally, to broaden the impact of cognitive tutor technology, we need to develop authoring tools that can speed its design and implementation. These tools need to make cognitive tutor
development more accessible to domain experts who do not have computer science or cognitive science backgrounds. At minimum, these tools should facilitate curriculum (problem situation)
authoring. At best, these can be intelligent tools that make cognitive modeling more accessible to domain experts. In conjunction with this tool development, we need to begin designing
cognitive tutors for other domains to examine how well the lessons |
Background: Sophisticated mathematical methods are
becoming ever more important
in the financial industry. This trend started with the advent of
exchange traded options in the 1970's and the fundamental research
by Black, Merton and Scholes, later awarded the Nobel Prize. Today,
Financial Mathematics is used not only by investment banks
and hedge funds on Wall Street, but also by energy companies and
large corporations in need of managing financial risk.
Goals:
Using Financial Mathematics (like many branches of applied mathematics)
in practice involves two tasks.
First, one has to develop mathematical models that
accurately describe the ``real'' objects that one wishes to
study. In our case, this typically means finding models, based on
probability theory, for the evolution of stock prices, interest rates
and other underlying financial quantities. It also means to derive
theoretical equations or formulas for prices
of derivative securities (options, caps, etc).
The second task is to get actual numbers out of these equations.
Doing so involves both calibration, ie finding the parameters
in the models (eg the volatility of a stock) from financial data,
and numerically solving the equations that were obtained
theoretically.
While the two tasks cannot, in practice, be separated from each other,
we will in this course emphasize the second of them.
Namely, the students are assumed to be familiar with
the more theoretical parts of mathematical finance
(at the level of Math 542/IOE 552) and we will
focus on the numerical implementing and calibration of
financial models.
Contents: .
The course has four components. In the first part we study
finite difference methods. This is a technique for solving
partial differential equations (PDEs) numerically. We will apply
this to the Black-Scholes equation as well as PDEs appearing
in fixed income. Both explicit and implicit schemes will
be discussed, as will concepts such as stability and convergence.
After that we will turn to Monte Carlo simulations
a quite general method for computing expected values numerically.
The importance of this method stems from risk-neutral pricing,
an important principle saying that prices of derivative securities
can often be expressed as a the discounted expected payoff under
a risk-neutral measure. In addition to ``vanilla'' Monte Carlo,
which is normally quite easy to understand and implement,
we will study variance reduction techniques, which are often
necessary for obtaining accurate results.
The third part involves lattice and tree methods. The idea behind
this method is to approximate a continuous-time stochastic process
by discrete time process and then compute prices using this
approximate model. Alternatively, lattice models can be used
as financial models in their own right.
Finally, we shall discuss calibration, that is, finding
parameters in the models from available financial data.
As we shall see, calibration to stock prices or options
data is done quite differently.
In the homework, which forms an integral part of the class,
you will implement many of the models yourself in a
computer language of your choosing.
Grading: The grade for the course will be determined from
performances on 6 homeworks (45%) and a final exam (55%).
Fall 2012 final exam: Thursday December 13 from 1.30 pm until 3.30 pm in East Hall 1360.
The final is a closed book exam. You may bring up to ten one sided A4 pages of notes to the exam.
You may also use a calculator but not its memory function. |
Tools
"... Abstract ..."
Abstract Mathematics Subject Classi cation. 03B70, 03D65, 68Q55. 1. |
Perrine, FL Calculus notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations... |
Algebra Proficiency and Mathematics Placement
A general discussion of placement at the College can be found
at the placement page.
Algebra Proficiency
All students must establish algebra proficiency before enrolling
in any other mathematics course (and hence satisfying any mathematics
Foundations requirements). Algebra proficiency may be established
by: passing MA 115 Fundamentals of Algebra, presenting sufficient
ACT or SAT scores, or passing the algebra proficiency exam given
during orientation week. All new students should complete this
requirement during the first year at the College, and preferably
during the first term.
Course Placement
The mathematics faculty reviews each student's application
materials and determines the appropriate level of mathematics courses
for that student. This information is provided to the student's
advisor prior to orientation. While students may place out of certain
mathematics courses, credit for those courses can only be earned
through AP or IB credit.
As part of the Skills Foundations requirement, each student must
take one mathematics course in statistics, modeling, or calculus.
Students interested in mathematics or a mathematics-related field
should begin in calculus or statistics. Students not interested
in more advanced study in mathematics should enroll in statistics
or a modeling course.
Please note that MA 124 Precalculus Mathematics does not satisfy
the Skills Foundations mathematics requirement, but is a preparation
for calculus. Depending on their prior experience, students may
place out of MA 124. |
Bob the terrorist wrote:If you got a C in maths GCSE, I wouldn't do maths A levelHah. Nah, AS physics is just an easier version of maths with some added splainin to do★ Economic Left: 91.2% Social Libertarian: 90.3%
We are convinced that freedom without Socialism is privilege and injustice, and that Socialism without freedom is slavery and brutality.
Bob the terrorist wrote:Agreed. It's when you look back at a gcse paper lieing about and can do a whole page with about 10 marks on in less than 30 seconds (the page i looked at was surds and powers), but in Alevel you are expected to know that stuff inside out - if you're lucky you might get a 1 marker for them.
Chris Kettle wrote:I only got a C in my Maths GCSE. I am hoping to do maths A Levels next year but I need to brush up on it, I can barely remember pythagoras theorem and quadratic equations. :/
ghqwerty wrote:I agree that Chris may struggle with the A-level course, but IIRC, you get a quick refresher in some of the stuff covered in GCSE (surds, quadratics etc.) anyway. To be completely honest, Core 1 - the first paper I took as part of AS maths - is basically just an extension of the topics from GCSE (for example, solving polynomials would probably replace quadratics, but the process is not too dissimilar).
In terms of the grades at GCSE, the grade boundaries are completely off what you'd expect from other subjects (as far as I know). IIRC, an A* for GCSE maths is about 60-70%, so you only need to get just over half of each paper correct to get into the top tier. I guess this has something to do with sixth forms/colleges only accepting students wanting further education to A-Level having at least a 'C' in GCSE maths and English.
To put your mind at ease Chris, some of the people I did maths with were around the B/C boundary at GCSE, and they didn't find AS too much of a chore. After doing a few mocks, you realise quite a lot of it is just repetition; so if you struggle, it may be worth trying to get the processes nailed so you can apply it again and again for a similar question with different values.
jimbojoy wrote:Never got round to doing it, I'd assumed it was just formulas/graphs?
LOL no.
Actually I guess graphs yes, but not really mathematical graphs. Most of them won't even need values on the axes to answer any given question. There are also some "divide one number by another" formulas too. But it's mainly just reasoning and saying why things should happen, and the worst thing is that it's completely subjective and you can't really be wrong. |
Book Description: Students throughout the world fear and dread solving word problems. As students' reading skills have declined, so have their abilities to solve word problems. This book offers solutions to the most standard and non-standard word problems available. It follows the suggestions of the National Council of Teachers of Mathematics (NCTM) and incorporates the types of problems usually found on standardized math tests (PSAT, SAT, and others). |
Applied Mathematics
Summary:
Mathematics may be applied in a vast array of situations. The first step is usually to translate the problem into mathematical language (often having to make some assumptions concerning what is important, at least at the first try, and what is not). The second step will be to use appropriate mathematical techniques to solve the problem, and this often means determining the evolution of a system over time. |
Math Applets
- For middle school students, high school students, college
students, and all who are interested in mathematics.
You will find interactive programs that you can manipulate and a lot
of animation that will help you to grasp the meaning of mathematical
ideas.
NEWTON'S METHOD: Calculator
- Enter an equation in terms of the variable x. Then enter a
starting guess for x. For example, to find the square root
of 2 you might enter x^2-2 for the equation, and 1 as an initial
guess.
REAL ROOT FINDER
(Program) - JavaScript ROOT FINDER Learn to find the root of an
equation like F(z)=0 or z=F(z) by using any of the following
traditional methods: Bisection, Fixed Point, Newton-Rapson and
Secant.
Sine Law Calculator and Solver. Calculator that solves
triangle problems given 2 angles and one side (ASA and AAS cases) or
2 sides and one opposite angle (SSA case).
The SSA case inludes one, two or no solutions.
Tangent Function.
The tangent function f(x) = a*tan(bx+c)+d and its properties such as
graph, period, phase shift and asymptotes by changing the parameters
a, b, c and d are explored interactively using an applet.
Secant Function. The secant function f(x) = a*sec(bx+c)+d
and its properties such as period, phase shift, asymptotes domain
and range are explored using an interactive applet by changing the
parameters a, b, c and d.
Graphs of Basic Trigonometric Functions. The graphs and properties
such as domain, range, vertical asymptotes of the 6 basic trigonometric
functions: sin(x), cos(x), tan(x), cot(x), sec(x) and csc(x) are explored using
an applet. |
Lulu Marketplace
Introduction to Matrix Algebra
Between 2002-2007, the Introduction to Matrix Algebra book was downloaded free of charge by more than 30,000 users from 50 different countries. This book is an extended primer for undergraduate Matrix Algebra. The book is either to be used as a refresher material for students who have already taken a course in Matrix Algebra or used as a just-in-time tool if the burden of teaching Matrix Algebra has been placed on several courses. In my own department, the Linear Algebra course was taken out of the curriculum a decade ago. It is now taught just in time in courses like Statics, Programming Concepts, Vibrations, and Controls.
There are ten chapters in the book 1) INTRODUCTION, 2) VECTORS, 3) BINARY MATRIX OPERATIONS, 4) UNARY MATRIX OPERATIONS, 5) SYSTEM OF EQUATIONS, 6) GAUSSIAN ELIMINATION, 7) LU DECOMPOSITION, 8) GAUSS-SEIDAL METHOD, 9) ADEQUACY OF SOLUTIONS, 10) EIGENVALUES AND EIGENVECTORS.
Ratings & Reviews
"Matrix Algebra " I found this text on Matrix Algebra a good refresher on the subject. I took this course many years ago. I liked the format and examples provided. His explanation of the Gauss-Seideal Method was good. His method of not providing a complex math explanation was nice. The chapter on Eigenvalues and Eigenvectors was robust. |
Pre-Algebra This study guide is appropriate for students
who took one year or less of high school algebra or have not taken a math
course in several years. This should be used if you are trying to test
into Pre Algebra/EBM4401 or Elementary Algebra/EBM4405.
Algebra This study guide is appropriate
for students who have recently completed 2 years of high school algebra
and/or are an average to below average math student. This should be used
if you are trying to test into EBM4405 Elementary Algebra, MTH4410 Intermediate
Algebra and/or MTH4420 College Algebra.
College
Algebra This study guide is appropriate for students
who have recently completed 2 or more years of high school algebra and/or
are an average to above average math student. This should be used if you
are trying to test into MTH4420 College Algebra, MTH4425 Trigonometry and/or
MTH4435 Calculus. |
Reshaping School Mathematics
Perhaps most obvious is the change needed for everyday
life. Whereas daily activities once required a considerable
amount of paper-and-pencil calculation, virtually all routine
household arithmetic is now done either mentally or with an
inexpensive hancl-held calculator, It is not just that the kinds of
solutions we have at our disposal have changed, but so too
have the problems. Today to be mathematically literate one
must be able to interpret both quantitative and spatial infor-
mation in a variety of numerical, symbolic, and graphical con-
texts. These changes provide an unprecedented opportunity
to redirect much of current elementary school mathematics to
more fruitful and important areas especially to the new world
of sophisticated electronic computation, As calculators and
computers diminish the role of routine computation, school
mathematics can focus instead on the conceptual insights
and analytic skills that have always been at the heart of math-
ematics.
The changes in mathematics needed for intelligent citizen-
ship have been no less significant. Most obvious, perhaps, is
the need to understand data presented in a variety of differ-
ent formats: percentages, graphs, charts, tables, and statisti-
cal analyses are commonly used to influence societal deci-
sions. Largely because data are now so widely available, daily
newspapers employ a considerable variety of quantitative
images in ordinary reporting of news events. Citizens who cans
not properly interpret quantitative data are, in this day and
age, functionally illiterate.
It is, however, the professional and vocational needs for
mathematics that have changed most rapidly. Mathematics is
essential to more disciplines than ever before. The explosive
growth of technology in the twentieth century has amplified
the role of mathematics. By increasing the number and variety
of problems that can be solved, calculators and computers
have significantly increased the need for mathematical knowl-
edge and changed the kind of knowledge that is needed.
Computers have moved many vocations (e.g., farming) to
become more quantitative and thus more productive. The
result is that people in an expanding number of vocations and
professions need to know enough mathematics to be able to
recognize when mathematics may be helpful to them.
Because of society's preoccupation with the practical and
professional roles of mathematics, schools rarely emphasize
cultural or historical aspects of mathematics. Like all subjects,
mathematics is dehumanized when divorced from its cultural
contributions and its history. To the extent that these subjects
are discussed at all, students are likely to get the impression
that mathematics is static and old-fashioned. While it is com-
monplace for school children to become familiar with modern
concepts in the sciences such as DNA and atomic energy,
OCR for page 9
9
A Philosophy and Framework
rarely are children introduced to any mathematics (such as
statistics or topology) discovered less than a century ago. Chil-
dren never learn that mathematics is a dynamic, growing dis-
cipline, and only rarely do they see the beauty and fascina-
tion of mathematics. The mathematics curriculum can no
longer ignore the twentieth century.
Fundamental Questions
To realize a new vision of school mathematics will require
public acceptance of a realistic philosophy of mathematics
that reflects both mathematical practice and pedagogical
experience. One cannot properly constitute a framework for a
mathematics curriculum unless one first adciresses two funda-
mental questions:
· What is mathematics?
· What does it mean to know mathematics?
OCR for page 10
10
Reshaping School Mathematics
Although few mathematicians or teachers spend much
time thinking about these philosophical questions, the unstat-
ed answers that are embecided in public ancl professional
opinion are the invisible hancis that control mathematics edu-
cafion. No change in education can be effective until the hicl-
den influences of these creep issues are redirected toward
objectives more in tune with today's woricl.
Yet even as forces for change are providing new directions
for mathematics eclucation, the public instinct for restoring tra-
clitional stability remains strong. Unless the 3uiclance system for
mathematics education is permanently reset to new and
more appropriate gocis, it will surely steer the curriculum back
to its Al path once present pressure for change abates.
Answers to these fundamental questions would help clarify
for both eclucators and the pubic what mathematics is really
about-what it stuclies, how it operates, what it is good for
(Romberg, 1988~. Appropriate answers would provide a con-
vincing platform on which to erect a new mofhe-matics cur-
riculum of the twenty-first century in which children would be
introcluŁecJ not only to the traditional themes of number and
space, but also to many newer themes such as logic, chance,
computation, and statistics. From these answers would flow a
pragmatic philosophy of mathematics that could help explain
the creative tension that bincis the two funclamenfal poles of
mathemofical reality:
· Theory: That in mathematics, reasoning is the test of truth.
· Applications: That mathematical models are both apt
and useful.
One might think that the many definitions of mathematics
provided by scholars in centuries past would suffice for this
task. But in the past few years, as computers have begun to
unfold new potentials of mathematical systems, we have
been able to see mathematics in a significantly broadened
context. As the Apollo missions for the. first time enabled peo-
ple to see and describe the back side of the moon, so com-
puters have now enabled us to grasp a much richer land-
scape of the mathematical sciences. It is now time to reshape
mathematics education to reflect both the significant role of
computers in the practice of mathematics ant] the frans-
formed role played by mathematics in modern society.
Describing Mathematics
We begin with a simple approximation: mathematics is a
science. Observations, experiment, discovery, and conjecture
OCR for page 11
11
A Philosophy and Framework
are as much part of the practice of mathematics as of any
natural science. Trial ancl error, hypothesis and investigation,
and measurement and classification are part of the mathe-
matician's craft and should be taught in school. Laboratory
work and fieldwork are not only appropriate but necessary to
a full understanding of what mathemofics is ancl how it is used.
Calculators ancl computers are necessary tools in this mathe-
matics lab, but so too are sources of real data (scientific
experiments, demographic clata, opinion polls), objects to
observe ancl measure (clice, blocks, balls), ancl tools for con-
struction (rulers, string, protractors, clay, graph paper).
As biology is a science of living organisms ancl physics is a
science of matter ancl energy, so mathematics is a science of
patterns. This description goes back at least to Descartes in a
slightly different form (he called mathematics the "science of
order"), and has been refined by physicist Steven Weinberg
who used it to explain the uncanny ability of mathematics to
anticipate nature (Steen, 1988~. A sirni~ar view of mathematics
as the science of "patterns and relationships" forms the basis
for the expression of mathematics in Science for All Americans
(American Association for the Acivancement of Science
(AAAS), 19891. By classifying, explaining, ancl describing pat-
terns in all their manifestations-number, data, shape, arrange-
ments, even patterns themselves mathematics ensures that
any pattern encountered by scientists will be explained some-
where as part of the practice of mathematics.
Patterns are evident in every aspect of mathematics. Young
children learn how arithmetic clepencis on the regularity of
numbers; they can see order in the multiplication table and
wonder about clisorder in the pattern of primes. The geometry
of polyhedra exhibits a regularity that recurs throughout nature
and in architecture. Even statistics, a subject which studies dis-
order, depencis on exhibited patterns as a yardstick for assess-
ing uncertainty.
As a science of patterns, mathematics is a mode of inquiry
that reveals fundamental truth about the order of our world.
But mathematics is also a form of communication that com-
plements natural language as a tool for describing the world
in which we live. So mathematics is not only a science, but
also mathematics is a language. It is, as science has revealed,
the language in which nature speaks. But it is also an apt lan-
guage for business ancl commerce.
From its beginnings in ancient cultures, the language of
mathematics has been widely used in commerce: measure-
ment ancl counting-geometry ancl arithmetic-enabled
trade and regularized financial transactions. In recent cen-
turies, mathematics (first calculus, then statistics) provided the
intellectual end inferential framework for the growth of sci-
ence. The mathematical sciences (inclucling statistics) are now
the founclation disciplines of natural, social, ancl behavioral
sciences, Moreover, with the support of computers ancl woricl
OCR for page 12
12
Reshaping School Mathematics
wide digital communication, business and industry depend
increasingly not only on traditional but also on modern mathe-
matical methods of analysis.
Mathematics can serve as the language of business and
science precisely because mathematics is a language that
describes patterns. In its symbols and syntax, its vocabulary
and idioms, the language of mathematics is a universal means
of communication about relationships and patterns, It is a lan-
guage everybody must learn to use,
Knowing Mathematics
If mathematics is a science and language of patterns, then
to know mathematics is to investigate and express relation-
ships among patterns: to be able to discern patterns in com-
plex and obscure contexts; to understand and transform rela-
tions among patterns; to classify, encode, and describe
patterns; to read and write in the language of patterns; and to
employ knowledge of patterns for various practical purposes.
To grasp The diversity of patterns-indeed, to begin to see pat-
terns among patterns -it is necessary that the mathematics
curriculum introduce and develop mathematical patterns of
many different types. As the patterns studied by mathematics
are not limited to the rules of arithmetic, so the patterns stucl-
ied in school mathematics must break the bonds of this artifi-
cial constraint.
A person engaged in mathematics gathers, discovers, cre-
ates, or expresses facts and ideas about patterns. Mathemat-
ics is a creative, active process very different from passive
mastery of concepts and procedures. Facts, formulas, and
information have value only to the extent to which they sup-
port effective mathematical activity. Although some funda-
mental concepts and procedures must be known by all stu-
dents, instruction should persistently emphasize that to know
mathematics is to engage in a quest to understand and com-
municate, not merely to calculate, By unfolding the funda-
mental principles of pattern, mathematics makes the mind an
effective tool for dealing with the world. From these views can
flow an effective and dynamic school curriculum for the next
century.
Practical Effects
The practical test of a philosophy is the effect it should have
on practice-in this case, on the teaching of mathematics.
OCR for page 13
13
A Philosophy and Framework
~ ABCD -EF`H=2
AIR ~ :( ~
ABED ' FHJK= ~ En.
ICKY
D Draw
Label
E Erase
M Measure ~ Repeat
S $~e change N New shape
Q Quit I;
~ Education Dsvelopm~l Cenlor. 1989
The Geometric Supposer is a set of software learning environments
deliberately designed to change school plane geometry from a
closely guided museum tour (where the guide points out certain arti-
facts to be "proven") to an active process of building and exploring
conjectures. For example, a student who constructs the three medi-
ans of a triangle and notices that they all intersect in a point might
wonder if this is a fluke, or whether it might hold for other triangles. By
using a repeat feature, the student can quickly execute the same
construction on a series of triangles, either generated at random by
the computer or produced by the student in a way designed to stress
the conjecture in some particular way (e.g., on a long, thin obtuse tri-
angle).
In the six figures above, a student uses the Supposer to generalize
a basic construction where corresponding points of adjacent sides of
a square are joined and the ratio of the area of the square and the
interior figure are calculated. From left to right, the construction and
calculation are repeated on different quadrilaterals. In the top row,
the sides of each figure are divided into two equal parts; in the bot-
tom row, the sides of each figure are divided into three equal parts.
What conjectures emerge? How can these conjectures be justi-
fied?
The
Geometric
Supposer
OCR for page 14
14
Reshaping School Mathematics
Many important ideas follow from the view of mathematics as
a science and language of patterns.
· By expressing a broad view of the mathematical sci-
ences, this proposed philosophy encompasses all tracli-
tional topics covered by school mathematics. Arithmetic
ancl geometry, algebra and calculus are richly endowed
with patterns of number, shape, and measure-patterns
that will supporl much of the traclitiona~ curriculum.
· By suggesting that mathematics encompasses all kincis of
patterns wherever they arise, this perspective compels a
broader vision of school mathematics that inclucles, for
example, mathematical structures in probability ancl
statistics, in discrete mathematics ancl optimization.
· By stressing that mathematics is a science, this philosophy
supports a style of instruction that rewarcis exploration,
encourages experiments, ancl respects conjectural
approaches to solving problems.
· By recognizing that mathematics is an apt language of
business ancl science, this view underscores the universal
importance of mathematics as a subject that all students
must learn to use.
· By invoking the metaphor of science in which experiment
complements theory, the perspective of mathematics as
a science of patterns helps bridge the gap between
"pure" and "appliecl" mathematics. The patterns studied
by mathematicians are, for all practical purposes, as real
as the atomic particles studied by physicists.
By emphasizing that mathematics is a process rather
than a set of facts, this perspective makes clear that stu-
dents need to experience genuine problems-those
whose solutions have yet to be developed by the stu-
dents (or even perhaps by their teachers). Problem situa-
tions should be complex enough to offer challenge, but
not so complex as to be insoluble, Learning should be
guided by the search to answer questions-first at an intu-
itive, empirical level; then by generalizing; ancl later by
justifying (proving).
By making clear that mathematics is the study of patterns
rather than merely a craft for calculation (or an art with
no evident purpose), this pragmatic view highlights the
philosophical basis for using calculators in school
mathematics: as microscopes are to biology ancl tele-
scopes to astronomy, calculators ancl computers have
become essential tools for the study of patterns.
· By recognizing that practical knowledge emerges from
experience with problems, this view helps explain how
OCR for page 15
15
A Philosophy and Framework
experience with problems can
help develop students' ability
to compute. This recognition
contrasts sharply with the pre-
vailing expectation in schools
that skill in computation should
precede encounter with word
problems. Present strategies
for teaching need to be
reversecl: students who recog-
nize the need to apply partic-
ular concepts have a stronger
conceptual basis for recon-
structing their knowledge at a
later time.
By stressing mathematics as a
language in which students express
ideas, we enable students to devel-
op a framework that can be cirawn
upon in the future, when rules may
have been forgotten but the struc-
ture of mathematical language
remains embecicled in memory as
a foundation for reconstruction.
Learning the language of mathe-
matics requires immersion in situa-
tions that are sufficiently simple to
be manageable, but sufficiently
complex to offer diversity: incliviclu-
a~, small-group, or large-group instruction; a variety of mathe-
matical domains; and open and flexible methods.
By affirming the importance of mathematics as a language
and science of patterns we reset the gyroscopes that guide
school mathematics. instead of being viewed as an
immutable collection of absolute truths, mathematics will be
seen as it is-as an evolving, pragmatic discipline that seeks to
understand the behavior of patterns in science, in society, and
in everyday life.
Philosophical Perspectives
Changing the public philosophy of school mathematics is
an essential step in effecting reform of mathematics educa-
tion. An effective practical philosophy of mathematics can be
based on two considerations:
OCR for page 16
16
Reshaping School Mathematics
· That mathematics is a science and language of patterns;
· That to know mathematics is to investigate and express
relationships among patterns.
Nothing in this approach implies that these are unique or
necessary considerations. They are, however, sufficient to
meet certain important criteria that any effective philosophy
of mathematics education must satisfy:
· They encompass new as well as traditional topics;
· They provide a substantive rationale for using calculators
and computers in school mathematics;
· They encourage experience with genuine problems;
· They stimulate exploration, use of real data, and appren-
ticeship learning;
· They help bricige the gap between pure and applied
mathematics;
· They emphasize active modes of learning;
· They are understandable to a broad segment of the public.
The framework for mathematics education that follows from
this practical philosophy provides an environment to support
present efforts at curricular reform. Other philosophies can also
provide similar support, and surely many others will emerge in
the process of national curricular change. The counterpoint
between a philosophy and a framework of mathematics edu-
cation will continue as long as the process of change remains
vigorous. |
Every aspect of Math 121 is highly interactive: Students spend most of classtime working in groups on problems and they then present their work and discuss as a class. Each student is responsible for some part of the in-class problems.
This debate about whether judicial review is compatible with democracy is meant to get students thinking about what sort of ideal democracy is, and to see both its procedural and substantive components. |
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Project Exchange
California State Content Standards
Math AII.2.0: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.
Math LA.2.0: Students interpret linear systems as coefficient matrices and the Gauss-Jordan method as row operations on the coefficient matrix.
Math LA.5.0: Students perform matrix multiplication and multiply vectors by matrices and by scalars.
Math LA.6.0: Students demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly one solution, or have infinitely many solutions.
Math LA.9.0: Students demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to solve systems of linear equations.
Math LA.11.0: Students know that a square matrix is invertible if, and only if, its determinant is nonzero. They can compute the inverse to 2 x 2 and 3 x 3 matrices using row reduction methods or Cramer's rule. |
A Basic Course in Statistics 5e
This new edition includes computing exercises at the end of each chapter to reflect the growing use of computers in teaching statistics. It is designed for students taking introductory courses in statistics in school, technical colleges and universities.
For courses in First-year Russian - Introductory Russian. Golosa is a two-volume, introductory Russian-language program that strikes a balance between communication and structure. It is designed to ... |
Course Aims: This course introduces fundamental mathematical methods and analysis in ordinary differential equations and basic knowledge of partial differential equations. It will help students develop skills in solving ordinary differential equations by analytical methods and solving simple partial differential equations by the method of separation of variables. It trains students in the ability to think quantitatively and analyze problems criticallysolve several classes of first order ordinary differential equations, higher order equations with constant coefficients, and systems of linear differential equations.
4
2.
develop skills in making mathematical development for objects which cannot be solved analytically, through the study of solutions of second order ordinary differential equations with varying coefficients.
3
3.
evaluate series solutions of ordinary differential equations.
3
4.
solve simple partial differential equations by the method of separation of variables.
2
5.
explain at high levels concepts and ideas from differential equations, and develop advanced mathematical models to a range of problems in science and engineering involving differential equations.
1
Teaching and learning Activities (TLAs): (Indicative of likely activities and tasks students will undertake to learn in this course take-home assignments helps students understand fundamental mathematical methods and analysis in ordinary differential equations and solve simple partial differential equations by the method of separation of variables.
1--5
after-class
Learning through online examples for applications helps students set up mathematical models by means of differential equations and apply to some problems in science and engineering.
5
after-class
Learning activities in Math Help Centre provides students extra help.
1--4
after-class
Assessment Tasks/Activities: (Indicative of likely activities and tasks students will undertake to learn in this course—2
15--30%
Questions are designed for the first part of ordinary differential equations to see how well the students have learned the basic concepts, fundamental theory, analytical methods and some applications.
Hand-in assignments
1—5
0--15%
These are skills based assessment to enable students to demonstrate the basic concepts, techniques and fundamental theory of differential equations and related applications.
Examination
1—5
70%
Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student's versatility in ordinary differential equations and elementary partial differential equations.
Formative take-home assignments
1—4
0%
The assignments provide students chances to demonstrate their achievements on differential equations learned in this course. |
Students are encouraged to seek my help or get help from one another. There are also tutors in the MS building (the Math Foundations Tutoring Center) and the library, along with computer-assisted instruction available and videos within My Math Lab (Course Compass).
Class participation and active learning:
Often, you will find that your classmates have different perspectives than you and can offer tips or techniques that can enhance your learning and understanding. You have a lot to learn from the instructor, but you also have a lot to learn from each other! You can expect to work in groups with your peers quite often in this course, and you are expected to be a contributing member to your group. You should come to class prepared to participate. Remember, none of us is as smart as all of us! Everyone has something to offer. If you keep an open mind and willingness to participate, you will be pleasantly surprised at how your mathematical abilities improve.
Mesa Community College is committed to the success of all our students. Numerous campus support services are available throughout your academic journey to assist you in achieving your educational goals. MCC has adopted an Early Alert Referral System (EARS) as part of a student success initiative to aid students in their educational pursuits. Faculty and Staff participate by alerting and referring students to campus services for added support. Students may receive a follow up call from various campus services as a result of being referred to EARS. Students are encouraged to participate, but these services are optional.
Early Alert Web Page with Campus Resource Information can be located at: or at the "Early Alert" selection at the mymcc link from MCC's home page.
If you have any disabilities which may hinder your learning the material presented in this class, please contact Disability and Resources Services (DRS) and complete the appropriate forms as soon as possible, along with letting the instructor know immediately after class. Everything reasonably possible will be done to help you be successful in this class. |
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The books gdunne have linked to are really great, i also self-studied math using those books. |
Schaum's Easy Outlines : Trigonometry - 02 edition
Summary: Boiled-down essentials of the top-selling Schaum's Outline series and ...show moreupdated format and the absolute essence of the subject, presented in a concise and readily understandable form.
Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials.
Designed to appeal to underprepared students and readers turned off by dense text
Cartoons, sidebars, icons, and other graphic pointers get the material across fast
Concise text focuses on the essence of the subject
Delivers expert help from teachers who are authorities in their fields |
To call Linear Algebra easy is like calling basic algebra easy. Sure, it kind of is. But anybody who's ever taken a look at the USAMO or other olympiad questions can tell you that problems requiring nothing more than basic algebra and logic can be EXTREMELY hard.
Your experience with linear algebra depends on what class you're in and/or what book you use. It can be either very easy or one of the hardest math classes you'll ever take.
---> the most useful math course you can take is statistics. you analyze a lot of data and draw conclusions from every day situations. i absolutely love it. calc etc are for those in "engineering, electricity" etc, but can be for business majors as well.
statistics is the most fun math too. god, every time i was looking at sins/cosins and graphs, and matricies, i thought 'when on god's green earth am i going to use this gibberish language'.
i HATED that cosine graph with a PASSION. so TEDIOUS and so BORING.
stats is from everything in every day life, finding the probablity of copius events in copious situations, it can just go on. a lot of reading though, and it is more conceptual math whereas every other one is mechanical.
I thought stats was so contrived. All we did was cookbook math with made-up recipes. Even the book said the procedures were prescribed recipes. It was so boring. I wish we touched more upon theory in stats instead of simply using recipes to find p or whatever.
Like why can you only use sampling distribution for an SRS? Or why the equation for the normal distribution is the way it is? And how the hell do you derive all those recipes to find p? How the hell can you prove the Students T distribution? It was like they give you a recipe and you are supposed to follow it blindly without any sense of the mechanics you are working with. I felt like a robot in that class.
I agree with Cherrybarry-- the handfed formulas were basic and led to little learning. However, I will say that in college-level Statistics you can/will prove/derive those formulas so that's kind of interesting I guess. Also, Calculus is just as applied to the real world as Statistics. Engineers use it in all the world they do, NASA scientists use it non-stop, it has it's application in the corporate world (including Economic analysis). Just because there are x's, y's, and z's instead of N's, p's, and t's doesn't make Calculus any less applicable to the real world.
Yeah. One of the things that frustrates me the most is when some kids in math or science class question the usefulness of the things we are studying. They ask....when are we ever going to use this?
It's so ignorant. I mean, the whole reason the world runs the way it does it because of science and math. Without it, there would be no airplanes, cars, electricity, chemicals, computers, houses, streets, buildings, civilization.
You don't hear any math geeks complaining about the usefulness of writing Petrarchan sonnets, so what right do English freaks have to question the useful of math and science?
In fact, calculus has more practical applications than Petrarchan sonnets.
Eww statistics? I am in stats right now and find it soo boring. Perhaps because I am the number crunching type of person who finds Calculus, Differential Equations, Number Theory beautiful. Wait until you need to do stats with continuous variables in college..yup calc will be there.
Calculus is extremely applicable to everyday situations, but only with respect to theory. The problem is that in the US we don't teach theory and understanding, we teach formulas and other garbage which help you pass the AP test, but that's about IT.
However, that is not to say taking Calculus is not worthwhile. To my experience, the people that complain about advanced math/sci not being necessary for daily life are the people who are not doing very well in the class, and don't put forth the effort to actually understand stuff.
So the problem is two-fold: schools are too concerned with test scores to show kids the meaning behind subjects, and kids are too damn lazy to find it for themselves, preferring to just whine incessantly about the system.
ANY subject, whether Calculus, Statistics, or Literature, can be meaningful if you make the effort to look deeper and figure out the reasoning behind it. If you don't make this effort, and only try to ace the tests, of course it will be meaningless, and a waste of your youth.
lol how is it hard...it's just really intuitive proofs and a few key concepts, like row echelon form and reduced echelon form. i'm not saying it's super primitive/easy, but compared to calc or even stats, there's just not as much breadth and depth in linear algebra.
mathematics in school should teach understanding rather than just memorizing the formulas, does it?, not really. Well, im doing it on my own then. that's the whole beauty of mathematics.
I remember one experience of mine, when i was first acquinted with calculus back when i was fifteen or so. And i remember looking at this rate question while flipping through the book, and that's when i saw the difference between higher math and lower math. Because i saw that the rate was changing, and then i became very interested in the subject.
Irock, 54M isn't the super-hardcore one at Berkeley. H54 is the one that's scary.
My sister was a math major at Berkeley. H54 was the class that single-handedly convinced her to change to business :D. She realized there was very little chance that she would get even a B in H54 even with hours of work every day, so she dropped it for regular 54 (maybe 54M...I think they're similar in difficulty) and easily got an A. |
1. Perform common, trinomial and perfectsquare factoring .
2. Perform fundamental operations with algebraic fractions, simplify complex fractions and solve rational equations.
3. Sketch and inter pret the graphs of linear equations .
4. Determine the equation of a line using slope-intercept and
point-slope forms of a line.
5. Solve systems of linear equations by graphing, addition
and substitution methods.
6. Perform fundamental operations with square roots and
solve radical equations .
7. Solve quadratic equations by factoring and by quadratic
formula.
8. Demonstrate a "sense of numbers" by determining if a
mathematical solution is "reasonable."
9. Present organized written work and show a check to avoid
careless mistakes.
10. Perform mental arithmetic, use a calculator effectively to
solve and check mathematical calculations and determine
when each is appropriate.
11. Read critically and think logically when solving application
problems.
12. TECHNOLOGY OBJECTIVES:
i. Use the arithmetic operations on the scientific
calculator to solve algebraic and real world algebraic problems.
ii. Demonstrate an understanding of the keys: key/inv key
iii. Demonstrate an understanding of order of operations on the
scientific calculator.
It is recommended that at least 3 hourly exams be given
during
the semester. Instructors are encouraged to use additional methods of evaluation to include: weekly quizzes, graded
assignments, and take-home tests. It is helpful to include review
questions in exams throughout the course. |
The vision of the mathematics standards is focused on achieving one central goal: to enable ALL of New Jersey's children to acquire the mathematical skills, understandings and attitudes that they need to be successful in their careers and daily lives.
Students at JohnP.StevensHigh School are required to successfully complete a mathematics course in grades 9, 10, 11 and 12.Student placement is based upon aptitude, district criteria and classroom performance.
Department offerings are available in the district's program of studies.All courses are aligned with the New Jersey Core Curriculum Standards for Mathematics.
Mathematics teachers at John P. Stevens are the department's greatest resource.Besides an excellent and thorough knowledge of the subject, each teacher utilizes differentiated instructional strategies that enhance student success.In-service programs and workshops are conducted throughout the year to assure professional growth for all of our teachers.
The John P. Stevens Mathematics Department focuses not only on the content of the curriculum but it's application to real-life situations.Our students will always be prepared for the challenges they will face during their college experience.Calculators, computers, manipulatives, technology and the Internet are used as tools to enhance learning and assist in problem solving.
In this changing world students who have a good understanding of mathematics will have many opportunities throughout their lives.The John P. Stevens Mathematics Department is committed to providing all students with the opportunity and support necessary to learn and understand significant mathematics. |
This webinar offers a quick and easy way to learn some of the fundamental concepts for using Maple. Learn the basic steps on how to compose, plot and solve various types of mathematical problems. This webinar will also demonstrate how to create professional looking documents using Maple, as well as the basic steps for using Maple packages.
The typical multivariate calculus course begins with a unit on vectors, lines and planes, material that serves as an introduction to the linear geometry of R³. This webinar will provide solutions for a number of typical, and not-so-typical problems in the "lines-and-planes" section of the calculus course. The problems will be solved with a suite of commands in the Student MultivariateCalculus package, commands specifically designed to handle manipulations of lines and planes in R³. In addition, these problems will also be solved in a syntax-free way via the Context Menu system because the relevant commands have been completely incorporated into that environment.
In this webinar, an introduction is made to modeling, simulation, and analysis with MapleSim by studying a full vehicle model equipped with electric power steering. The webinar will cover modeling and simulation aspects such as a 3D multibody steering mechanism, and multi-domain modeling by inclusion of electrical and 1D translational components.
This webinar, presented by Dr. Robert Lopez, Maple Fellow and Emeritus Professor from the Rose-Hulman Institute of Technology, will provide you with tips and techniques that will help you get started with Maple 17.
The Möbius Project is a revolutionary initiative that brings the power of Maple to even more people, in even more ways. This webinar will demonstrate: how to create Möbius Apps in Maple, how to share Möbius Apps with your colleagues and students using the MapleCloud, and how to grade Möbius Apps in Maple T.A. |
Kimberton Algebra comes putting intervals together to build chords, how major, minor, augmented, and diminished chords are formed. And there are also inversions and 7th chords. Finally comes which chords appear in the different keys, which chords in a key will be major or minor or diminished or augmented and why, and how it changes depending on whether it's in major or minor key
...I aim to help the student understand what the theorems and axioms mean physically, so the student will better understand the concept theoretically and ultimately feel comfortable solving a geometric proof. The first pre-algebra topic to focus on is knowing and understanding types of numbers, suc...
...I feel that I could be of assistance to anyone who seeks assistance with the complicated college application or financial aid process, is trying to select the school that is right for them and/or is otherwise thinking about whether and/or how to enter a college program. Publisher is a very easy ... |
I have this math assignment due and I would really be glad if anyone can assist pre-algebra skills practice workbook on which I'm stuck and don't know how to start from. Can you give me a helping hand with multiplying matrices, equivalent fractions and multiplying matrices. I would rather get help from you than hire a algebra tutor who are very pricey. Any pointer will be highly treasured very much.
The attitude you've adopted towards the pre-algebra skills practice workbook is not the a good one. I do understand that one can't really think of something else in such a scenario . Its nice that you still want to try. My key to easy equation solving is Algebrator I would advise you to give it a try at least once.
Hi there. Algebrator is really amazing ! It's been months since I tried this software and it worked like magic! Math problems that I used to spend answering for hours just take me 4-5 minutes to answer now. Just enter the problem in the software and it will take care of the solving and the best part is that it displays the whole solution so you don't have to figure out how did the software come to that answer.
I remember having difficulties with triangle similarity, perfect square trinomial and algebra formulas. Algebrator is a really great piece of math software. I have used it through several math classes - Basic Math, Intermediate algebra and College Algebra. I would simply type in the problem from a workbook and by clicking on Solve, step by step solution would appear. The program is highly recommended. |
Scotch College
MATHEMATICS
Year 9 — 2012
Mathematics touches on many and various aspects of our lives. It has applications in many activities and
provides a universal way of solving problems in areas such as science and engineering, business and finance,
technology, arts and crafts and many everyday activities. Competence in Mathematics may enhance both our understanding of the world and the quality of our participation in society. Regular Problem Solving Assignments will be an integral part of the course.
At Year 9 there are three levels of study in Mathematics:
- Core classes that provide an opportunity for reinforcement of core concepts of the Year 9 course.
- Analysis classes that provide a standard course
- Advanced analysis classes, for the more able students, that provide additional course content and enrichment material.
Student Outcomes
acquire mathematical skills and knowledge in order to cope confidently and competently with daily life
develop knowledge and skills in using mathematics for employment, further study and interest
become able to interpret and communicate quantitative and logical ideas accurately
use technology to support the learning of mathematics, and in carrying out mathematical activities in context
build knowledge, facts and technical skills
develop depth of conceptual understanding
develop the ability to communicate using clear and precise mathematical language |
Mathematical modelling is an essential tool for science. Our researchers collaborate with partners from academia and industry to help tackle real-life problems.
Dr Robert Whittaker, Lecturer
Mathematics is critical to almost every field of human endeavour. Mathematics students at UEA are highly adaptable and high-achieving problem solvers.
Dr Paul Hammerton, Senior Lecturer
The mathematics department is incredibly supportive, offering assistance through problem classes and seminars that really help with coursework.
Kathryn O'Reilly, BSc Mathematics Student
The School of Mathematics at UEA is a flourishing department committed to excellence in teaching and research.
Since the National Student Survey started in 2005, we have consistently featured in the top six mathematics departments in the country. In the most recent National Student Survey, the School achieved an overall student satisfaction of 100% for BSc Mathematics. The School has a strong international reputation for its research and students are taught by leading experts in a broad range of topics in Mathematics. The 2008 Research Assessment Exercise (RAE) judged over half of the research activity in the School to be world-leading or internationally excellent. |
College Algebra
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Document Description
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Topics Covered in Algebra Given below are some of the main topics covered in our Algebra Tutorial: * Algebraic equations * Linear equations * Radicals * Factoring polynomials * Inequalities Besides these main topics, there are other topics that are covered in the tutorial. Gain Knowledge of al these topics with an expert tutor now! Read More on algebraic expressions |
Apple MacSingle Single User for Apple Mac. Software is supplied by download link.
Autograph Activities: Teacher Demonstrations for 16-19
The fifteen teacher demonstrations will allow you dynamically to introduce, review, extend or illustrate important topics or concepts in ways not previously possible. They are intended for use on an interactive whiteboard or by means of a digital projector.
The demonstrations are presented in an easy to follow, step-by-step manner, complete with full colour screenshots, suggested questions and prompts, thus allowing even a first time user to feel confident enough to deliver them.
Topics covered include: Introducing Volumes of Revolution; Discovering the Chain Rule; and Things to Watch Out For when Integrating.
This book will unlock the wonders of Autograph, and one thing is for sure: you will never teach these topics in the same way again.
£25, by C N Barton
Autograph Activities: Students Investigations for 16-19
Autograph is an excellent tool for investigation, and mathematics is at its strongest and most appealing when students can embark upon such journeys of self-discovery.
The ten activities are designed to allow students to fully utilise Autograph's power to explore, investigate and ultimately understand concepts at a depth which the normal classroom setting would not allow.
Areas covered include vectors, differentiation, integration and trigonometry.
Students are equipped with the tools to learn and then encouraged to set off alone on their epic quest for answers.
Both books come with a CD with support material for each chapter and a 30-day trial of Autograph.
£25, by C N Barton, 2009
There's also a discount bundle of 5 of each book for £160.15.00 excl Vat
Price:
£18.00 inc Vat
A total of 108 items are available. You are currently viewing page 1 of 11. |
It covers all core subjects, including American, English and World Literature, U.S. History, Art, Science, and Math, including Pre-Algebra, Algebra I and II, Geometry, Calculus, and Trigonometry. It also includes valuable extras, such as the Rapid Calculation Method that teaches how to solve math problems without pencil and paper. |
This is a free, online textbook. According to the author, "This text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text."
Primary Audience:
College Lower Division,
College Upper Division
Mobile Compatibility:
Not specified at this time
Technical Requirements: According to the site, As part of these terms, we offer this text free of charge to students using it for self-study, and to lecturers evaluating it as a required or recommended text for a course. All other uses of this text are subject to a charge of $10US for individual use and $300US for use by all individuals at a single site of a college or university." |
Mathematics can be viewed as a language for describing the world around us. Indeed, this is largely how mathematics developed. For instance, Calculus was invented by Newton in order to describe how a cannon ball falls to the ground or to describe how the moon orbits the Earth.
This course will be very much in this tradition. We will consider problems or objects that we might observe or encounter every day, for instance: "Why (in terms of the reproductive function of a pine cone) is a pine cone shaped as it is?" Or "Can California water shortages be alleviated by towing icebergs from Antarctica?" Such systems as the human body, the stock market, and sports games are amenable to description, called models, via the mathematics that we encounter early in our college years (and of course, more advanced mathematics can provide more detailed models!).
The goal of this course will be to increase the mathematical literacy of the students taking it. We will provide a set of tools and frameworks with which students can use familiar mathematics to predict and analyze real world problems. The mathematics required will be a "just in time production:" that is, it will be taught when it is needed.
The principal text for this course is Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics by R.B. Banks. On occasion we will use Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics also by R.B. Banks, as well as Topics in Mathematical Modeling by K.K. Tung.
Each class will feature a focus problem or focus problems for which we will develop a mathematical model that attempts to describe and predict the system in question. These in-class projects will typically be tackled in teams, and thus attendance for each class is required. In addition to these in-class projects, there will be at least two large modeling problems given to teams for which 5 to 6 page research reports will be required. Some homework- as preparation for the coming discussion- will be required weekly. |
Math 4xx/6xx
Math 410/610 Complex Analysis (Johnson or Kumjian)
Complex analysis is the study of calculus on the complex numbers. While the theory superficially resembles ordinary calculus of functions on the real numbers, the details and applications are very different. The theory is much richer and more elegant than ordinary calculus, and there is some beautiful geometry involved which has unexpected applications to problems in physics and engineering. Ideas and techniques from complex analysis are used throughout pure and applied mathematics, and in many scientific fields. The familiar pictures from fractal geometry are made using complex analysis. Prerequisites: MATH 283 required; MATH 310 recommended.
Math 430/630 Linear Algebra II (Jabuka or Olson)
The linear algebra behind the following applications will be developed:
1. Network design.
2. Least squares approximations for statistical analysis.
3. The Fast Fourier Transform.
4. Eigenvalues, Eigenvectors, Diagonalization and Jordan Cannonical Forms for matrix exponentiation (differential equations) and powers of matrices (for finite difference
equations).
5. Finite Element Methods.
6. Minimization/Maximization problems.
7. Machine efficient methods for finding eigenvectors and solving the matrix equation Ax = b. [This includes knowing when the coefficient matrix is ill conditioned so that numerical results are likely to be of questionable accuracy, as well as being able to take advantage of certain features of A that occur in various applied problems to improve accuracy and efficiency].
This course will be highly motivated by applications and examples. Prerequisite: MATH 330.
Math 440/640 Topology (Deaconu, Jabuka, Naik)
A topological space is a collection of points and a structure that endows them with some coherence, in the sense that we may speak of nearby points or points that in some sense are close together. We will start by recalling some general notions about sets and functions. Then we will discuss metric spaces, which are natural generalizations of the real line with the usual distance between two points. Finally, we will introduce the general concept of a topological space, studying the notions of continuity, connectedness and compactness. We will have plenty of examples, including familiar curves and surfaces. Prerequisite: MATH 310.
Math 441/641 Algebraic Topology (Jabuka or Keppelmann)
Topology is popularly known as "the rubber sheet geometry". Topologists are jokingly referred to as mathematicians who can't distinguish between a coffee cup and a doughnut, since the surface of one can be continuously stretched ijnto the surface of the other. A doughnut and a two-holed doughnut cannot be stretched into one another; the same goes for a once-punctured disc and a twice-punctured disc. Perhaps surprisingly, group theory (see MATH 331) proves to be a useful tool in the study of questions like this. In this course we will learn two ways of associating algebraic objects to a topological space, namely homology and homotopy. We will study fundamental groups, covering spaces, and homology theory. [SN 2003] Prerequisite: MATH 440/640. Co-requisite: MATH 331.
Math 442/642 Differential Geometry (Herald or Jabuka)
The course will be of interest to: MATH students who want to use their calculus and linear algebra skills to study fascinating geometric problems; COMPUTER SCIENCE students who are into computer graphics and want to come to a deeper understanding of the shapes of curves and surfaces in space; for PHYSICS students who want an introduction to the math behind much of modern theoretical physics. Differential Geometry is used in such diverse fields as Relativity Theory, Mechanics, Control Theory, Computer Graphics, much of Theoretical Physics, as well as in other branches of Mathematics. Prerequisites: MATH 311 or the consent of the instructor. [CH 2001]
Math 449/649 Geometry and Topology -- Knot Theory (Herald, Jabuka or Naik)
We will study the mathematical theory of knots and links and discuss the applications to biology, chemistry and physics. This course will not have any prerequisites, however some background in 300 level math courses (eg. MATH 310, MATH 330) will be necessary. Prerequisites: Consent of the instructor. A corequisite of MATH 311 or 441/641 is strongly recommended. Familiarity with elementary group theory will be useful, but not required. [SN 2001]
Math 461/661 Probability Theory (Formerly Math 451/651) (Kozubowski)
Probability models are used to represent river flows, customer arrivals, atoms, chemical reactions, epidemics, election results, and stock markets. Probability theory is the basis for all of these mathematical models. An infinite series represents the average number of customers arriving this month. An integral gives the average jump in daily stock market prices. A double integral gives the probability that the river will rise higher this year than last year. In this course you will learn to apply the tools of calculus and analysis to problems in probability. Topics to be discussed should include: probability space axioms; random variables; expectation; univariate and multivariate distribution theory; sequences of random variables; Tchebychev inequality; the law of large numbers and the central limit theorem. MATH 461/661 is a beautiful chapter of pure mathematics, as well as the foundation for stochastic processes, statistics, econometrics, and quantum mechanics. Take this course and prepare for a brilliant future in an uncertain world. [TK 2005] Prerequisite: MATH 283. Note: MATH 461 is required for BA and BS in Mathematics (all options) while MATH 661 is required for MS in Mathematics, Statistics option.
Math 466/666 Numerical Methods I (Formerly Math 483/683) (Mortensen, Olson, Telyakovskiy)
This course is a one semester introduction to the subject of Numerical Analysis. Numerical analysis concerns algorithms and methods for obtaining solutions to mathematical problems. We will survey many of the tools and techniques of the field. Some of the topics include interpolation, integration, linear systems, differences, differential equations, nonlinear equations and optimization. This course will be a "hands-on" course focusing on use of the computer, with much less emphasis on theory (an introduction to FORTRAN will be provided). The student will be able to leave this course able to obtain solutions to seemingly intractable problems and understand the basis of many large software packages now available. Prerequisite: MATH 330.
Math 467/ 667 Numerical Methods II (Formerly Math 484/684) (Mortensen, Olson, Telyakovskiy)
Numerical solution of ordinary differential equations; boundary value problems; finite difference methods for partial differential equations; finite element method. Since MATH 466/666 is NOT a prerequisite for this course, there will be a brief review of relevant topics from MATH 466/666, including numerical differentiation and integration. Prerequisite: MATH 285 or equivalent, and a knowledge of computer programming. Note: An introduction to Maple and Matlab will be provided. [JM 2003]
Math 474/674 Sets and Numbers (Deaconu, Pfaff)
After a brief review of logic, we present two axioms for set theory, the Axiom of equality and the Axiom of set formation. Algebra of sets, relations, functions, equivalence relations, partitions, and arbitrary unions and intersections are studied with emphasis on proving the appropriate theorems about them. With set theory established on a more or less secure foundation, we proceed through a series of constructions. In succession, we build set theoretical models for the Natural Numbers, Integers, Rational Numbers (Here the students do all the work since the process is similar to what we went through for the Integers), Reals, and Complex Numbers (again, it is up to the students to prove the theorems here). The Reals are constructed using Dedekind cuts, which forces them to come to grips with reasoning with inequalities and mixed quantifiers. The Completeness Property of the Reals is proved, using sups and infs. Prerequisite: MATH 373 [DP 2001]
Math 475/675 Euclidean and non-Euclidean Geometry (Herald, Jabuka, Pfaff)
After showing dramatically how dangerous it is to reason from a picture, we introduce axioms gradually and examine their consequences. Emphasis is placed not only on the theorems of geometry, but also on metatheorems about independence. Elementary Absolute Geometry is studied rigorously, including the concepts of betweenness, coordinate systems, separation, SAS, and the Exterior Angle Theorem. After a discussion of the history of Euclid's Fifth Postulate, we introduce the Klein and Poincare models to motivate the study of Hyperbolic Geometry. After a brief digression on the completeness of the Reals and the Archimedean Property, we introduce the Hyperbolic Parallel Postulate and spend the rest of the semester coming to grips with the properties of this new world. As always, throughout, the emphasis is on proofs, how to find them and how to write them. Prerequisite: MATH 373 [DP 2001]
Math 485/685 Combinatorics and Graph Theory (Quint)
Combinatorics is the study of arrangements, patterns, designs, assignments, schedules, connections, and configurations. Graph theory is the study of networks. Together these areas constitute one of the fastest growing fields of modern mathematics. We present the basic mathematical theory of these areas, together with many applications. Topics Covered: Counting rules; generating functions; recurrence relations; inclusion-exclusion; pigeonhole principle; Ramsay theory; fundamental graph theory concepts (connectedness, coloring, planarity); Eulerian and Hamiltonian chains and circuits. Prerequisites: MATH 330 or consent of the instructor. MATH 285 is recommended. No previous background in combinatorics or graph theory assumed. [TQ 2001]
Math 486/686 Game Theory (Quint)
Game theory is the mathematical modeling and analysis of conflict situations involving more than one player. In particular, we study issues such as the existence of equilibria and the formation of coalitions in such situations. Applications will be given in economics and political science. Topics Covered: Extensive and strategic form games; Nash equilibrium; repeated games; matrix/bimatrix games; minimax theorem; TU/NTU solution; marriage, college admis-sions, and houseswapping games; core and Shapley value; power indices; NTU games.
Prerequisites: MATH 330 or consent of the instructor. Background in linear programming (MATH 487/687 or 751) would be helpful but is not required. No previous background in game theory assumed. [TQ 2001]
Math 487/687 Deterministic Operations Research (Quint)
In MATH 487/687 we cover the techniques of deterministic operations research. Topics include linear and integer programming, shortest paths in a network, project scheduling, dynamic programming, deterministic inventory theory, and nonlinear programming. Although we will study the theory of linear programming (in particular the simplex method) and also that of nonlinear programming, much of the focus of the course will be on model formulation of applied problems. Students will go "on line", using LINDO and GINO to solve business-school style "cases".
Prerequisites: MATH 330 or permission of the instructor. [TQ 2003]
Math 488/688 Differential and Difference Equations II (Formerly Math 423/623) (Pinsky) Partial differential equations are often used in various disciplines to model complicated problems. The goal of this course is two-fold: to study how to interpret a partial differential equation, and to investigate various methods one can use to solve different types of partial differential equations (analytical methods for exact solutions and approximate methods for numerical solutions).
Topics include classification of partial differential equations, interpretations of the heat equation, the wave equation and Laplace's equation, solutions by various analytical methods (separation of variables, eigenfunction expansion, the sine and cosine transforms, the Fourier transform, the Laplace transform, method of characteristics, change of coordinates) and approximate methods (explicit and implicit finite difference methods).
Prerequisite: MATH 285.
Stat 4xx/6xx
Stat 452/652 Statistics: Continuous Methods (Kozubowski, Panorska, Zaliapin)
"Statistics is the art of making numerical conjectures about puzzling questions." Is the medicine effective? What is the association between the Sierra snow pack and the clarity of Lake Tahoe? Is there a trend in inflation rate? What drives development around Reno? Why does a casino make a profit on the roulette?
In this course you will learn to choose appropriate models for real world situations, exercise these models using appropriate mathematical and computer techniques, and interpret the results in plain language. The topics covered in this course include: goodness of fit testing, methods of estimation, parametric and nonparametric approaches to correlation and multivariate regression, trend analysis, analysis of variance, analysis of categorical data. There will be a significant emphasis on hands-on statistical computations and data analysis and modeling methods using a statistical package (MINITAB). No prior programming experience is required.
Text: Devore, Jay, L. Probability and Statistics for Engineering and the Sciences, 5th Ed., Duxbury. The book will be supplemented with information available on the web.
Prerequisites: MATH/STAT 352 or STAT 467/667 or permission of instructor.
Note: STAT 452 is required for BA and BS in Mathematics, statistics option, while STAT 652 is required for MS in Mathematics, Statistics option. [TK 2005]
Stat 467/667 Statistical Theory (Kozubowski or Panorska)
Deepen your understanding of statistics. Discover the interesting mathematics behind the common statistical procedures used in practice such as estimation, testing hypotheses, and linear regression. Topics to be discussed should include multivariate probability distributions; details of point and interval estimation, including the methods of moments and maximum likelihood; derivations of common statistical tests and the corresponding power calculations; mathematical details of the method of least squares and the corresponding linear regression problems. Prerequisites: MATH 283, 330, and either MATH/STAT 352 or MATH 461/661.
Note: STAT 467 is required for BA and BS in Mathematics, Statistics option.
Math 7xx
Math 713 Abstract and Real Analysis I (Blackadar, Kumjian, Naik, Olson)
The focus of this course will be to develop the modern theory of integration of real- valued functions based on Lebesgue measure. The Riemann integral, familiar from Calculus, does not behave well with respect to limits. The Lebesgue integral does, and this makes it well-suited as a tool in Modern Analysis and Probability theory. The syllabus follows:
1. Set Theory
2. The Real Number System
3. Lebesgue Measure
4. The Lebesgue Integral
5. Differentiation
6. The Classical Banach Spaces
Text: H. L. Royden, Real Analysis, 3rd Edition. Prerequisites: Consent of the instructor. MATH 311 and 440/640 are recommended.
Math 721 Nonlinear Dynamics and Chaos I (Pinsky)
Dynamical systems theory explores modern ideas, techniques, and computer algorithms developed for modeling, analyzing and controlling the time-evolution of natural and man- made systems.
Pretend, for example, that you observe the initial state of a system modeling dynamics of connected elastic bodies or atoms in molecules, evolution of chemical reactions or competition in biology, ecology or economics, as well as problems in meteorology, hydrology or, say, laser physics. How do you predict the evolution of these kinds of
dynamical systems? Although questions of this nature have guided progress in science for hundreds of years, emergence of chaos theory was a turning point in these studies resulting in the development of new thinking across science and engineering.
In this course, we will study how to describe and analyze some of complex phenomena arising in nonlinear systems using relatively simple analytical and numerical techniques. We attempt to make a sound connection of mathematical derivations and physical intuition and comprehend the behavior of various dynamic models arising in engineering and physical sciences.
First part of this course two-semester course starts with analysis of relatively simple nonlinear systems described by second order differential equations. We show that despite their relative simplicity, these models describe complex phenomena that have no analog in linear dynamics. Next we study the synchronization and competition of nonlinear modes, nonlinear resonances, local bifurcations undergoing in continuous and discrete models of natural and engineering systems and enter the area of nonlinear wave. Prerequisite: MATH 330. MATH 285 is recommended. [MP 2003]
Math 722 Nonlinear Dynamics and Chaos II(Pinsky)
The second part of this two-semester course centered on deeper study of bifurcation phenomena leading to development of chaotic behavior. In this connection, we study bifurcation and chaos in continuous Lorenz equations and discrete dynamical systems as well as introduce fractals and Mandelbrot and Julia sets. Essential time is dedicated to analysis of bifurcation and chaotic behavior in various applied systems such as optical resonators, chemical reaction, and communication models, as well as to control of chaotic systems. Prerequisites: MATH 721. [MP 2003]
Math 731 Modern Algebra I (Blackadar, Jabuka, Naik, Kumjian)
The Essence of Pure Mathematics. Some of the deepest (as well as most useful) theorems in Analysis, Topology and Applied Mathematics rely on algebraic concepts. The fundamental concept of symmetry in Physics and the other Sciences depends in an essential way on the mathematical notion of group. We will revisit the material of abstract algebra with the hope that it will provide a higher understanding of its concepts. We hope reach the cyclic decomposition theorem by the end of the semester, which has the Jordan decomposition theorem as one of its most important consequences. Thereafter we investigate the role of groups in field extensions (i.e. Galois Theory). If there is time we will explore category theory and its foundational role in mathematics. Prerequisites: Consent of the instructor. We recommend MATH 330 and 331.
Math 751 Operations Research I - Linear Programming and Extensions (Quint)
A linear programming problem is a problem in which one is to optimize a linear function (of n variables) subject to linear constraints. We define an algorithm for such problems, called the simplex algorithm, and prove that it converges. We investigate the theory of
duality and that of sensitivity analysis. We extend the simplex algorithm so as to be able to solve integer programming problems and fractional programming problems. Finally we cover topics in nonlinear programming, such as the linear complementarity problem and Kuhn-Tucker theory. Note: The focus of this course is on theory, not applications. For the "applications" side of things, enroll in Math 487/687. Prerequisite: MATH 310, 330. [TQ 2003]
Math 752 Operations Research II – Stochastic Models (Quint)
In Math 752 we consider operations research models with a probabilistic component. In particular, we cover decision analysis, reliability theory, Markov Chains, queueing theory, and probabilistic inventory theory. We will also study some applications of these models. Prerequisites: MATH 330 and MATH 461/661, or consent of the instructor.
IMPORTANT NOTE: Math 751 is NOT a prerequisite for this course. [TQ 2001]
Math 753 Stochastic Models and Simulation (Kozubowski)
Stochastic models are used to represent random processes which evolve over time. Inventory levels are modeled by a Markov chain. Decay times for radioactive particles are modeled by a Poisson process. The number of customers waiting in line is modeled by a Markov process. The diffusion of a chemical through the water table is modeled by a Brownian motion. The flood stage of the Truckee River is modeled by a time series. In this course you will learn to choose appropriate models for real world situations, exercise these models using appropriate mathematical and computer techniques, and interpret the results in plain language. Topics to be discussed include stochastic process models with applications; analytic and computer modeling techniques for Markov chains; Poisson and Markov processes; Brownian motion and special topics. Prerequisites: MATH 330, MATH 461. [TK 2005]
Math 761 Techniques in Applied Mathematics (Olson or Telyakovskiy)
This course will serve as an introduction to mathematical techniques found in various fields of engineering and natural sciences. We will try to strike a balance between studying the mathematical aspects of the subject and dedicating an appropriate attention to empiric origins of our methods that should stimulate intuitive thinking and embrace multiple connections with important physically motivated problems.
We begin with Dimensional Analysis and Scaling and show its applications to problems from such diverse disciplines as chemical reactions, hydrodynamics, wave propagation and population dynamics, and also to mathematical modeling in certain softer fields where the explicit models are still unknown. We will follow with the perturbation techniques and consider their application to some of the problems already considered in this course. After that, we turn our attention to Calculus of Variations and subsequently to Integral Equations, Integral Transforms, and Green's function method. Prerequisites: MATH 283, 285, and 330. MATH 488/688 is desirable. [MP 2003]
Math 762 Techniques in Applied Mathematics (Olson or Telyakovskiy)
The second part of this two-semester sequence is centered on deeper study of various phenomena described by partial differential equations. In this broad area, we focus on analysis of dynamic behavior described by linear and nonlinear parabolic and hyperbolic PDEs as well as on analysis of more general wave phenomena occurred in continuous systems.
In this connection, we emphasize various perturbation and calculus of variation techniques that help reduce the complexity and furnish the mathematical analysis in a way consistent with physical intuition. We also explore connection between analytical and numerical techniques that leads to their fruitful cross-fertilizing. Prerequisites: MATH 283, 285, and 330. MATH 488/688 and 761 are desirable but not mandatory. [MP 2003]
Math 767 Advanced Mathematics for Earth Sciences
Applications of advanced mathematics for earth scientists and engineers. Includes elements of vector calculus, linear algebra, differential equations, probability, and statistics. These useful mathematical methods will be presented and applied in the context of real world problems. Co-requisite: MATH 283 or equivalent [MM 2003]
Stat 7xx
Stat 754 Mathematical Statistics (Kozubowski or Panorska)
This introduction to classical mathematical statistics is intended to cover mathematical details of the basic problems of parameter estimation and testing hypotheses. Topics to be discussed include statistical models and applications; modes of convergence used in statistics; methods of point and interval estimation, including Bayesian inference; elements of large sample theory; unbiasedness, sufficiency, and completeness; hypothesis testing, including likelihood ratio tests, Neyman-Pearson lemma, and most powerful tests; introduction to linear models and special topics. Prerequisite: MATH 311, 330, 461/661. Note: This course is required for MS in Mathematics, Statistics option. [TK 2005]
Stat 755 Multivariate Data Analysis (Kozubowski or Panorska)
In various areas of science, researchers frequently collect measurements on several variables. In this course we shall discuss basic statistical techniques for analyzing such multivariate data. Our focus will be both understanding theoretical concepts and practical implementation of the methods on real data sets. Topics to be discussed should include sample geometry and random sampling, the multivariate normal and related distributions,
estimation of the mean vector and the covariance matrix, multivariate linear regression models, principal components, factor analysis, canonical correlation analysis, discrimination and classification, and cluster analysis. Basic knowledge of multivariate calculus, linear algebra, and probability/statistics are assumed. Prerequisites: MATH 330, MATH 461/661. Co-requisite: STAT 452/652.
Note: This course is required for MS in Mathematics, Statistics option.
Stat 756 Survival Analysis
Researchers in the engineering, actuarial, and biomedical sciences are often faced with the problem of analyzing failure time data which represent times to occurrence of point events such as failure of an electronic component in an engineering study, filing of a claim of an insured unit in an actuarial setting, or recovery of a patient in a clinical trial. In most of these cases, one will not be able to observe the exact failure times of all observations due to monetary or time constraints, but will only be able to observe censored data. In this course, statistical methods that will handle these censored data will be discussed. Methods will vary from tools used to analyze data from a single population to regression tools. There will be a balance of theory and applications for a better understanding and appreciation of the concepts of survival analysis. Prerequisite: MATH 283 and MATH/STAT 352, or permission of instructor. Corequisite: STAT 452/652. [IA 2001]
Stat 757 Applied Regression Analysis
Learn the basic concepts of linear regression analysis such as least-squares estimation and statistical inferential procedures for model parameters. Methods for checking the adequacy of the model (residual analysis) as well as choosing the best model in light of the data gathered will also be discussed. [TK 2005]
Stat 758 Time Series Analysis (Zaliapin)
Time series analysis concerns random quantities that evolve over time. Practical examples include temperature, rainfall, river flows, stock market prices, interest rates, unemployment levels, electrical signals, customer demand, and population. In this course we will survey analytic and computer methods for time series analysis. We will explore both the time domain (autocorrelation) and frequency domain (spectral) approach. Prerequisite: MATH 311, MATH 330, and MATH/STAT 352, or permission of instructor. [TK 2005] |
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