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Employing a practical and empathetic approach, this mathematics resource advocates for a new teaching methodology that removes any anxiety associated with math. Covering topics such as addition, multiplication tables, fractions, probabilities, algebra, and ratios, this book enables readers to feel in control and to understand, for the first time, how math can be used in one's daily life. With techniques that link facts, procedures, and ideas, both teachers and students will find this easily accessible work provides a stable foundation upon which an advanced understanding of mathematics can be built. |
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This is the first part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. The book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The book's approach begins with the question "what are the most important applications" and proceeds to try to answer this question. The applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. The presentation is self-contained. As for prerequisites, the reader should be familiar with some basic facts of calculus. The second part of this textbook has been published under the title, Applied Functional Analysis: Main Principles and Their Applications.
The first part of a self-contained, elementary textbook, combining linear functional analysis, nonlinear functional analysis, numerical functional analysis, and their substantial applications with each other. As such, the book addresses undergraduate students and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world. Applications concern ordinary and partial differential equations, the method of finite elements, integral equations, special functions, both the Schroedinger approach and the Feynman approach to quantum physics, and quantum statistics. As a prerequisite, readers should be familiar with some basic facts of calculus. The second part has been published under the title, Applied Functional Analysis: Main Principles and Their Applications. |
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Show More approach increases student interest, motivation, and the likelihood for success. Many students think in visual, concrete terms and not abstractly. This text helps students learn mathematics better by moving from the concrete to the abstract. It makes use of multiple representations (verbal, graphical, numerical, and symbolic), applications, visualization, and technology |
Applied mathematics, which investigates theoretical models of real world systems, expressed in the language of differential equations. Such equations are used to model, for example, fluid flow (eg the flow of air over an aircraft wing) and dynamical systems and chaos theory (used to model global and local atmospheric conditions)
Statistics, which involves finding order where there is, at first sight, only randomness. Statistical techniques are constantly finding new uses, such as in the detection of long-term changes in the environment, the analysis of DNA structure, or in quality assurance
You have the flexibility to tailor the combination of pure mathematics, applied mathematics and statistics content to suit your interests.
There is also some flexibility at each Stage to choose topics from other areas of the University, for example, accounting, music, a foreign language or another science.
Quality and ranking
The quality of the mathematics and statistics study experience at Newcastle is recognised with an overall student satisfaction score of 91% in the 2012 National Student Survey.
We assess your performance in each module through a combination of assignments (many of which take place online) and examinations. Teaching and assessment methods may vary from module to module; more information can be found in our individual module listings.
Visit our Teaching and Learning pages to read about the outstanding learning experience available to you at Newcastle University.
Flexible degree structure
Studying mathematics and statistics builds on the knowledge you have gained at school/college. Some topics will be familiar and others will be completely new.
All of our mathematics and statistics degrees follow a common core of modules at Stages 1 and 2. These common modules are designed to equip you with the key skills and knowledge that all mathematicians and statisticians need.
They include topics such as:
analytical geometry
modelling with differential equations
foundations of analysis
vector calculus
probability
linear algebra
They constitute a significant proportion of your time in the early Stages of your programme. This provides you with a solid foundation on which to build more specialist knowledge later in your degree, as well as making it relatively easy to transfer between degrees within the School.
Learning technologies
We have excellent computing facilities and make extensive use of IT to support teaching, preparation and revision, including:
computer-based exercises with instant review of model solutions
problem-solving video tutorials
recording system for video capture of lectures, which you can download and watch again to help with your revision
The School also has a dedicated mathematics and statistics library and reading room that complements the wealth of resources available through the main University Library Service.
School of Mathematics and Statistics
We run an induction programme for first-year students including social events to help you to get to know your fellow students and the members of staff who will be teaching you. We also have a 'buddy scheme', which begins before you even arrive at the University.
As well as the support of a personal tutor, you will be encouraged to join our extremely active student society, MathSoc. MathSoc organises a range of social events throughout the year to help you get to know people on your course and beyond.
Visit the School's website to take a virtual tour of the Herschel Building, which is on the central campus and a two-minute walk from the city centre.
At Newcastle, we offer mathematics and statistics degrees at two levels:
Bachelor of Science (BSc) – three years
Master of Mathematics (MMath)/Master of Mathematics and Statistics (MMathStat) – four years
Whilst broadly similar, our four-year degrees (also known as Integrated Masters' degrees) cover more advanced topics, a wider choice of modules and a specialist study, tailored to your own interests, that develops your skills in research and communication.
They also cover more technical skills for those who wish to enhance their employability or proceed to postgraduate study.
Transfer between the MMath/MMathStat and BSc degree programmes is possible up until the middle of Stage 3.
We recommend registering for the MMath/MMathStat degree initially if it is at all likely that you will want to take one of these degrees.
To qualify for Stages 3 and 4 of the MMath/MMathStat degree, you must normally have obtained at least an upper-second-class average mark in Stages 2 and 3. |
PREREQUISITE:
Placement, Grade of C or better in AMTH 108, or consent of the Department
TEXT: Precalculus:
Functions and Graphs (4th edition), Demana, Waits,
Foley, and
Kennedy, and Graphing Calculator Resource Manual
SUPPLIES:Texas Instruments TI-83 Graphing
Calculator (note: If you are purchasing a calculator for this class, you are
required to purchase the TI-83. If you already have a graphing calculator,
consult your instructor about its acceptability)
TOPICS TO BE
COVERED:
Prerequisite
Chapter – Graphing, lines, equations and inequalities
Chapter 1 – Functions and Graphs
Chapter 2 – Quadratic, Power, Polynomial, and Rational
Functions
Chapter 3 – Exponential, Logistic, and Logarithmic Functions
Chapter 6 – Parametric Equations (If time permits).
EXPECTED
STUDENT COMPETENCIES TO BE ACQUIRED: The successful student, at the end
of the course, will be able to produce well-written correct solutions for
problems similar to those assigned for homework in this course.
COURSE OBJECTIVE:
To solve, both graphically and by calculation, mathematical problems that
involve:equations and inequalities
graphs, functions, and inverse functions polynomial, logarithmic, and
exponential expressions.
ASSIGNMENTS:
Homework will be assigned daily and will occasionally be collected as a check on
how you are keeping up. Although most of the homework assignments will not be
collected, that doesn't mean you don't have to do it! A major part of learning
mathematics involves DOING
mathematics! Also, homework is useful in preparing for the type of questions,
which may appear on quizzes or exams.Many
homework problems will be given on quizzes and some on tests.
Evaluations:There will be given two tests and one final
exam during this short summer term.There will also be given quizzes once or twice a week depending on
whether a test is given that week or not.
GRADING: Your success in meeting the course objectives
will be measured by your scores on homework, quizzes, lab activities, two exams
(June 10 and June 24), and a cumulative final exam (last day of class or on
July 3, 11:00AM: to be discussed in class).
The weights of the various components of your grade in
determining your final course gradeare shown below, along with the grade
scale for the course.
WEIGHTS:
GRADE SCALE
1. Two exams (50%)
90-100
A
70-74
C
2. Quizzes, homework (20%)
85-89
B+
65-69
D+
3. Cumulative Final Exam (30%)
80-84
B
60-64
D
75-79
C+
0-59
F
NOTES:
One quiz/homework
grade will be dropped to determine your final quiz/homework average.They will be no makeup quizzes.There will be no makeup tests, except under
special (documented) circumstances.In
the case you cannot take an exam at the scheduled time, contact the instructor
as soon as possible after (or before) the test, to arrange a make up.Exams not made up within 2 days of the
scheduled date will be recorded 0.
SPECIAL NOTES:
If you have a physical, psychological, and/or learning disability which might affect
your performance in this class, please contact the Office of Disability
Services, 126A B&E, (803) 641-3609, and/or see me, as soon as possible. The
Disability Services Office will determine appropriate accommodations based on
medical documentation.
ATTENDANCE
POLICY: I may occasionally take attendance. It is highly recommended
that the student not miss any class, especially for the very fast pace of the
summer sessions. However, the Attendance Policy established by the Department
of Mathematical Sciences states
that the maximum number of unexcused absences allowed in this class before a
penalty is imposed is four for a regular semester. So you understand that
missing two class meetings for a summer session is already too many.
ACADEMIC CODE OF
HONESTY: Please read and review the Academic Code of Conduct relating to Academic
Honesty located in the Student Handbook. If you are found to be in violation of
this Code of Honesty, a grade of F(0) will be given
for the work. Additionally, a grade of F may be assigned for the course and/or
further sanctions may be pursued. |
e-books in this category
The Algebraic Theory of Modular Systems
by Francis Sowerby Macaulay - Cambridge University Press , 1916 Many of the ideas introduced by F.S. Macaulay in this classic book have developed into central concepts in what has become the branch of mathematics known as Commutative Algebra. Today his name is remembered through the term 'Cohen-Macaulay ring'. (1311 views)
Determinantal Rings
by Winfried Bruns, Udo Vetter - Springer , 1988 Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. The book gives a coherent treatment of the structure of determinantal rings. The approach is via the theory of algebras with straightening law. (2138 views)
The CRing Project: a collaborative open source textbook on commutative algebra
by Shishir Agrawal, et al. - CRing Project , 2011 The CRing project is an open source textbook on commutative algebra, aiming to comprehensively cover the foundations needed for algebraic geometry at the EGA or SGA level. Suitable for a beginning undergraduate with a background in abstract algebra. (1498 views)
A Primer of Commutative Algebra
by J.S. Milne , 2011 These notes prove the basic theorems in commutative algebra required for algebraic geometry and algebraic groups. They assume only a knowledge of the algebra usually taught in advanced undergraduate or first-year graduate courses. (1596 views)
Introduction to Commutative Algebra
by Thomas J. Haines - University of Maryland , 2005 Notes for an introductory course on commutative algebra. Algebraic geometry uses commutative algebraic as its 'local machinery'. The goal of these lectures is to study commutative algebra and some topics in algebraic geometry in a parallel manner. (1777 views)
Trends in Commutative Algebra
by Luchezar L. Avramov, at al. - Cambridge University Press , 2005 This book focuses on the interaction of commutative algebra with other areas of mathematics, including algebraic geometry, group cohomology and representation theory, and combinatorics, with all necessary background provided. (3638 views)
A Course In Commutative Algebra
by Robert B. Ash - University of Illinois , 2006 This is a text for a basic course in commutative algebra, it should be accessible to those who have studied algebra at the beginning graduate level. The book should help the student reach an advanced level as quickly and efficiently as possible. (8465 views) |
This presentation will demonstrate voicing math using any version of Dragon NaturallySpeaking 6.0 or 7.0 - MathTalk/Scientific Notebook 5.0 and MathPad by Voice. Includes voicing math into Braille, as well as voicing the graphs and the Windows calculator! A discussion of assessing the user and system requirements will also be included in this presentation.
Assessment of Speech Recognition User:
Assessing needs of user.
Evaluate environment.
Meeting system requirements.
Which version of Dragon NaturallySpeaking to use.
Creating interest for certain students.
Use of Training Modules for learning different levels of math.
Extra amenities of using speech recognition.
Providing access to math for certain students.
Building confidence.
Speak math language.
Helps user focus when voicing math.
Formulate thoughts before speaking.
Clearer, more distinct speech.
Legible work.
Task accomplished faster.
MathTalk/ScientificNotebook for Dragon Naturally Speaking- MT/SN
MathTalk/Scientific Notebook 5.0 combined with any version of Dragon NaturallySpeaking 6.0 or 7.0 (Professional, Preferred, Standard, Essentials) - the perfect combination for voicing mathematics and text dictation. Our new MathTalk has an Enhanced List of "sentence commands" which allows the user to speak more variables within a single command.
This demonstration of MT/NS will show:
Beginning with "train initial commands".
Use of Training Modules for learning/training different levels of math--pre-algebra, algebra, trig, calculus, stat. For example, to train algebra, say "train algebra".
Using voice commands to search MathTalk for help.
Using the Enhanced List to speak variables-with-variables in a single command to accomplish math FASTER!
Use of voice commands to translate the math into Braille in the Duxbury Braille Translator 10.3/10.4 .
Text addition to MathTalk with Dragon NaturallySpeaking (DNS) 7.0 by saying "show dictation box", dictate text, then say "OK". If using DNS 6.0, also add text easily to MathTalk by saying "go to dragon", dictate the text, and then say "go to MathTalk".
Videos accessible by voice commands which show the use of special features of the product!
MathTalk/ScientificNotebook for Naturally Speaking- MT/SWP
This demonstration of MT/SWP will show:
LaTex which is the industry standard for mathematics typesetting.
Formatting and typesetting.
These features make this product different than MT/SN.
MathTalk For Visually Impaired & Learning Disabilities - MT VI/LD
This product is designed for persons who are Visually Impaired or have Learning Disabilities.
This program is our MathTalk/Scientific Notebook 5.0 with "echo" and "highlight" features, as well as a brief highlight of the math that is created by the voice command. For use with Dragon NaturallySpeaking 6.0 or 7.0. For purposes of the readback, it is necessary to use the Professional or Preferred version.
Using MathPad By Voice is the easiest entree into speech recognition! The vocabulary is restricted -- number(s) 1-9, borrow from ..., carry the..., etc. are some examples of the voice commands. This program has an optional toggle readback of entries, rows, problem. The user may use also utilize a combination of the keyboard and voice to input entries. |
Precalculus Functions and Graphs A Graphing Approach
9780618394760
ISBN:
0618394761
Edition: 4 Pub Date: 2004 Publisher: Houghton Mifflin College Div
Summary: As part of the market-leadingGraphing ApproachSeries by Larson, Hostetler, and Edwards,Precalculus Functions and Graphs: A Graphing Approach,4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality and quantity of the exercises, combined with interesting applications, cutting-edge design, and innovative resources, make teaching easier and help ...students succeed in mathematics. This edition, intended for precalculus courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills. Enhanced accessibility to students is achieved through careful writing and design, including same-page examples and solutions, which maximize the readability of the text. Similarly, side-by-side solutions show algebraic, visual, and numeric representations of the mathematics to support students' various learning styles. TheLibrary of Functionsthread throughout the text provides a definition and list of characteristics for each elementary function and compares newly introduced functions to those already presented to increase students' understanding of these important concepts. ALibrary of Functions Summaryalso appears inside the front cover for quick reference. Technology Supportnotes provided at point-of-use throughout the text guide students to theTechnology Support Appendix,where they can learn how to use specific graphing calculator features to enhance their understanding of the concepts presented. These notes also direct students to theGraphing Technology Guideon the textbook web site for keystroke support. Houghton Mifflin'sEduspaceonline classroom management tool offers instructors the option to assign homework and tests online, provides tutorial support for students needing additional help, and includes the ability to grade any of these assignments automatically |
Mathematics for Eighth Edition of Mathematics for Business continues to provide solid, practical, and current coverage of the mathematical topics students must master to succeed in business today. The text begins with a review of basic mathematics and goes on to introduce key business topics in an algebra-based context. Chapter 1, Problem Solving and Operations with Fractions, starts off with a section devoted to helping students become better problem solvers and critical thinker while reviewing basic math skills. Optional scientific calculator boxes are i... MOREntegrated throughout and financial calculator boxes are presented in later chapters to help students become more comfortable with technology as they enter the business world. The text incorporates applications pertaining to a wide variety of careers so students from all disciplines can relate to the material. Each chapter opener features a real-world application. |
To train the mind to be analytical and provide
a foundation for intelligent and precise thinking.
The goal is to: - become problem solvers who can recognize and
solve
routine problems readily and can find ways to reach a
solution when no routine path is apparent. - communicate precisely about quantities,
logical
relationships, and unknown values with through the use
of signs, symbols, models, graphs and mathematical
terms. - reason mathematically by gathering data,
analyzing
evidence, and build arguments to support or refute
hypotheses. - make connection among mathematical ideas
and
between mathematics and other disciplines.
Math 120 Student Learning Outcomes
·A student will be able to employ both inductive and
deductive reasoning appropriately.
·A student will be able to construct visual representations
of certain problems and then analyze those constructs to attain a
solution.
·A student will be able to identify patterns in
observations presented in a problem and then predict other outcomes
using the patterns they identified.
·A student will be able to employ logic in solving a
problem to arrive at a conclusion.
·A student will be able to categorize given problems and
then employ the correct procedures to solve the problems.
Grade: The possible
grades in this course are A, B,
C, D, or F. The cutoffs are as follow,
Grades are assigned on an absolute scale, and your work will
not be graded on a curve. You get what
you earn,
and other people's performances have no effect on your grade.
California Education Code
Section 76224(a) states:
"When grades are given for any course of instruction taught in a community
college district, the grade given to each student shall be the grade
determined by the instructor of the course and the determination of the
student's grade by the instructor, in the absence of mistake, fraud, bad
faith, or incompetence, shall be final" (2004)
Homework will be assigned everyday but will be collected only
after a quiz. It must be written on the original
packet provided by
the instructor. Late homework will be penalized (4 points per
lecture day)
and quizzes cannot be made up unless arrangement is made with
the instructor prior to the quiz.
In case of an emergence, you have to
(1) inform the instructor within 24 hours counting from the
beginning of the exam and
(2) provide proof of valid reason(s), otherwise heavy penalty
will apply
Each student can have at most 2 make-ups in each semester.
Partial credit is at the discretion of the instructor.
No extra credit.
Attendance: Attendance is mandatory and is vital to
the success in this course.
You are an important person to your group and hence you may be
dropped from the class if you miss more than 3
meetings. Tardiness
and early departure
will be penalized according to the following pattern.
Bring a notebook, pen or pencil, calculator and textbook to
each class.
Come to class with a positive attitude and be ready to
learn.
Take notes in each
lecture.
Actively participate in
class but do not
disrupt lectures with private conversation.
Respect
other students' opinion and be open to accept different ideas as well as
perspectives.
Spend about 2 hours
after each lecture to read textbook, organize lecture notes,
and do homework.
Write your answers neatly
in the provided homework packet. It is the student's
responsibility to keep all graded
assignments. Contact the instructor immediately if you
notice any assignment missing.
Turn off your cellphone and pager (or change it to the
flashing or vibrating mode) during lectures.
If you decide to drop the class, it is your responsibility
to complete the paper work otherwise
you may receive an F even if you do not attend
classes anymore.
If you expect a reply to your phone message, please say
your phone number clearly and slowly.
Special accommodations:
Students with disabilities who may need accommodations in
this class are encouraged to notify the instructor and contact Disabled Student Programs & Services (DSPS)
early in the semester so that reasonable accommodations may be implemented as soon as possible. Students may contact DSPS in person in Room 110 or by telephone at
(619) 644-7112 or (619)644-7119 (TTY for deaf).
Supervised Tutoring Referral
Students requiring additional help or
resources to achieve the stated learning objectives of the courses
taken in a Mathematics course are referred to enroll in Math 198,
Supervised Tutoring. The department will provide Add Codes.
Students are referred to enroll in the
following supervised tutoring courses if the service indicated will
assist them in achieving or reinforcing the learning objectives of
this course:
·IDS 198,
Supervised Tutoring to receive tutoring in general computer applications
in the Tech Mall;
·English 198W,
Supervised Tutoring for assistance in the English Writing Center
(70-119); and/or
To add any of these
courses, students may obtain Add Codes at the Information/Registration
Desk in the Tech Mall.
All Supervised Tutoring courses are
non-credit/non-fee. However, when a student registers for a
supervised tutoring course, and has no other classes, the student
will be charged the usual health fee.
Academic
Integrity Cheating and plagiarism (using
as one's own ideas, writings or materials of someone else without
acknowledgement or permission) can result in any one of a variety of
sanctions. Such penalties may range from an adjusted grade on the particular
exam, paper, project, or assignment to a failing grade in the course. The
instructor may also summarily suspend the student for the class meeting when
the infraction occurs, as well as the following class meeting. For further
clarification and information on these issues, please consult with your
instructor or contact the office of the Assistant Dean of Student Affairs.
Daily Schedule: Click on the appropriate section number on the top of this page to view the
schedule. |
This book is the result of the experience acquired by the authors while lecturing Projective Geometry to students from a three year course leading to a degree in Mathematics in the University of Pisa (Italy). The authors recognize the existence of modern textbooks on this subject published in Italian but felt the need of a different type of book. In fact this book is mainly designed to accompany the student in the learning process. It is not to be read as a treaty on the subject. It is divided into two parts. The first part (pages 1-60) deals with the notation and recalls the main theorems and concepts of projective geometry. It contains nine chapters dealing with: Projective spaces and subspaces and projective transformations (1.2); projective frames and homogeneous coordinates (1.3); dual projective space and duality (1.4); projective spaces of dimension 1 (1.5); conjugation and complexification (1.6); affine and projective hypersurfaces (1.7); quadrics (1.8); and plane algebraic curves (1.9). I.e. the first part of the book contains some fundamental results of projective geometry without proofs. According to the authors this part of the book aims to give the reader a more global idea of the subject and to introduce the notation and concepts used afterwards. The second part of the book (the next 200 pages) include three different chapters and present the solutions for different types of exercises. Exercises on projective spaces, exercises on curves and hypersurfaces and exercises on conics and quadrics. The authors do not prefer the analytic or the synthetic method. The solution given here is the one the authors consider the most interesting, the most elegant or the fastest regardless of the method. In many exercises there is more than one solution. In some exercises as many as three different solutions are given. The authors use an interesting notation to call the reader's attention to some of the problems given in the book. More difficult exercises are marked with a cup which means according to the authors "mettiti comodo, prenditi un caffé o un té, armati di pazienza e determinazione, e vedrai che ne verrai a capo" (sit comfortably, have a cup of coffee or tea, arm yourself with patience and determination and you will see it through). In some exercises the authors show an alternative solution that is more elaborated but leads to a deeper understanding of the subject. This type of solutions is also signaled. This is an impressive collection of very interesting exercises: 52 for projective spaces, 67 for curves and hypersurfaces and 87 for conics and quadrics.
Reviewer:
Ana Pereira do Vale (Braga) |
Synopses & Reviews
Publisher Comments:
As in previous editions, the focus in ESSENTIAL MATHEMATICS with APPLICATIONS remains on the Aufmann Interactive Method (AIM). Students To this point, simplicity plays a key factor in the organization of this edition, as in all other editions. All lessons, exercise sets, tests, and supplements are organized around a carefully-constructed hierarchy of objectives. This "objective-based" approach not only serves the needs of students, in terms of helping them to clearly organize their thoughts around the content, but instructors as well, as they work to design syllabi, lesson plans, and other administrative documents. The Eighth Edition features a new design, enhancing the Aufmann Interactive Method and the organization of the text around objectives, making the pages easier for both students and instructors to follow.
Synopsis:
Synopsis:
About the AuthorTable of Contents
Note: Each chapter begins with a Prep Test and concludes with a Chapter Summary, a Chapter Review, and a Chapter Test. Chapters 2-12 include Cumulative Review Exercises. AIM for Success. 1. WHOLE NUMBERS. Introduction to Whole Numbers. Addition of Whole Numbers. Subtraction of Whole Numbers. Multiplication of Whole Numbers. Division of Whole Numbers. Exponential Notation and the Order of Operations Agreement. Prime Numbers and Factoring. Focus on Problem Solving: Questions to Ask. Projects and Group Activities: Order of Operations; Patterns in Mathematics; Search the World Wide Web. 2. FRACTIONS. The Least Common Multiple and Greatest Common Factor. Introduction to Fractions. Writing Equivalent Fractions. Addition of Fractions and Mixed Numbers. Subtraction of Fractions and Mixed Numbers. Multiplication of Fractions and Mixed Numbers. Division of Fractions and Mixed Numbers. Order, Exponents, and the Order of Operations Agreement. Focus on Problem Solving: Common Knowledge. Projects and Group Activities: Music; Construction; Fractions of Diagrams. 3. DECIMALS. Introduction to Decimals. Addition of Decimals. Subtraction of Decimals. Multiplication of Decimals. Division of Decimals. Comparing and Converting Fractions and Decimals. Focus on Problem Solving: Relevant Information. Projects and Group Activities: Fractions as Terminating or Repeating Decimals. 4. RATIO AND PROPORTION. Ratio. Rates. Proportions. Focus on Problem Solving: Looking for a Pattern. Projects and Group Activities: The Golden Ratio; Drawing the Floor Plans for a Building; The U.S. House of Representatives. 5. PERCENTS. Introduction to Percents. Percent Equations: Part I. Percent Equations: Part II. Percent Equations: Part III. Percent Problems: Proportion Method. Focus on Problem Solving: Using a Calculator as a Problem-Solving Tool; Using Estimation as a Problem-Solving Tool. Projects and Group Activities: Health; Consumer Price Index. 6. APPLICATIONS FOR BUSINESS AND CONSUMERS. Applications to Purchasing. Percent Increase and Percent Decrease. Interest. Real Estate Expenses. Car Expenses. Wages. Bank Statements. Focus on Problem Solving: Counterexamples Projects and Group Activities: Buying a Car. Final Exam. Appendix. Solutions to You-Try-Its. Answers to Selected Exercises. Glossary. Index.
"Synopsis"
by Netread,"Synopsis"
by Netread, |
Is your student's Intermediate Algebra fast approaching? Are you like many homeschool parents feeling just a bit overwhelmed! At Alpha Omega Publications, we've got the help you need! During the high school years, it is vitally important that math instruction provide adequate preparation for college entrance exams. Now that your child has completed Algebra I and Geometry, it's time for the LIFEPAC Algebra II Set. In this homeschool program, students focus on mastery of a single skill, and then move on to learn new concepts, laying a foundation for ever-increasing levels of proficiency. In LIFEPAC Algebra II, students will study concepts such as axioms, relations and functions, absolute value, graphs, linear equations, operations with polynomials, radical expressions, laws of radicals, quadratic equations and formulas, quadratic relations and systems, exponential functions, matrices, progressions, permutations, and probability.
But we've added even more features to help make homeschooling parents' lives easier! In LIFEPAC Algebra II, student worktexts include detailed math instruction and review, as well as plenty of opportunity for assessment of student progress. In order to encourage individualized instruction, we have included a teacher's guide designed to help you guide your student's learning according to his specific interests and needs. The Alpha Omega curriculum teacher's guide includes detailed teaching notes and a complete answer key which includes solutions for algebra-challenged parents! Are you ready to give it a try? Order the LIFEPAC Algebra II Set for your high school student |
Buying options
Elementary Number Theory:
Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research.
Written in David Burton's engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.
show more show less
List price:
$172.20
Edition:
7th 2010
Publisher:
McGraw-Hill College
Binding:
Cloth Text
Pages:
528 Elementary Number Theory: - 9780077349905 at TextbooksRus.com. |
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10 Units 2000 Level Course
Available in 2013
Provides the essential mathematical techniques of Physical Science and Engineering. These are the methods of Multivariable Calculus and Differential Equations. Multivariable Calculus involves a study of the differential and integral calculus of functions of two or more variables. In particular it covers introductory material on the differential calculus of scalar and vector fields, and the integral calculus of scalar and vector functions. Differential Equations arise from mathematical models of physical processes. Also includes the study of the main analytical and numerical methods for obtaining solutions to first and second order differential equations. The course also introduces students to the use of mathematical software in the investigation of problems in multivariable calculus and differential equations.
Objectives
At the successful completion of this course students will have: 1. a sound grounding in the differentiation and integration of functions of several variables and in the methods of solution of ordinary differential equations.
2. skills in solving a range of mathematical problems involving functions of many variables.
3. basic skills in modelling real world problems involving multivariable calculus and ordinary differential equations, and in interpreting their solutions as they relate to the original problem.
4. skills in the application of computer software in the exploration of mathematical systems and in the solution of real-world problems relevant to the content of the course. |
Comment
I only had a chance to look through it briefly, going through the main menu (the links), probably for about 10 minutes or so, and so far it looks pretty useful for a student taking an Algebra course. I looked at the links provided, and it's pretty useful for both student and teachers who want to review the algebraic concepts.
The content is pretty simple to use. Under the main menu, there are links that takes you to the different concepts, which provides an brief explanation about what it is, and then continues on to show examples of how it is used in the math. It takes you from angles and circles all the way to vectors, and although it is not as thorough and detailed like it would be in a textbook, it does provide to be a good reference. They even have math games and riddles for the student to ponder and try out as well.
It's effective as a reference, and maybe a brief study on the concepts before taking it head on in a math course or text. A student can prepare him/herself using this site.
The layout of the site isn't as intuitive as other sights, so it might be a little harder on the eyes to navigate around. But once you've learn to navigate around, it makes it a lot easier for you to bookmark and figure out where to go. |
This is an instruction
system designed for students who have successfully completed a first year of Algebra.
The instruction extends all topics of Algebra while emphasizing the function concept.
Topics include: graphing on the xy-plane, the use of rational number exponents,
absolute values, exponential functions, and logarithm functions.
Every objective
is thoroughly explained and developed. Numerous examples illustrate concepts and
procedures. Students are encouraged to work through partial examples. Each unit
ends with an exercise specifically designed to evaluate the extent to which the
objectives have been learned. The student is always informed of any skills that
were not mastered.
The instruction
depends only upon reasonable reading skills and conscientious study habits. With
those skills and attitudes, the student is assured a successful math learning
experience. |
College Algebra An Early Functions Approach
Bob Blitzer has inspired thousands of studentswith his engaging approach to mathematics, making this beloved series the #1 in the market. Blitzer draws on his unique background in mathematics and behavioral science to present the full scope of mathematics with vivid applications in real-life situations.
Students stay engaged because Blitzer often uses pop-culture and up-to-date references to connect math to students' lives, showing that their world is profoundly mathematical.
show more show less
List price:
$188.67
Edition:
3rd 2014
Publisher:
Prentice Hall PTR
Binding:
Trade Cloth
Pages:
912
Size:
8.60" wide x 10.90" long x 1.40" tall
Weight:
4 An Early Functions Approach - 9780321729644 at TextbooksRus.com. |
Math, Tenth Edition unlocks the world of math by showing how it is used in the business world. Written in a conversational style, the book covers essential topics such as banking, interest, insurance, taxes, depreciation, inventory, and financial statements. It carefully explains common business practices such as markup, markdown, and cash discounts—showing students how these tools work in small business or personal finance. Authors encourage self-starters from the beginning, with the review of basic math... MORE, annotated examples, stop and check exercises, skill builders and application exercises. This edition includes updated problem sets, new trends and laws, a revised financial statements chapter and the one-of-a-kindMyMathLab website. |
Elementary Algebra, 5th Edition
ISBN10: 0-547-10227-5
ISBN13: 978-0-547-10227-6
AUTHORS: Larson
Larson IS success! ELEMENTARY ALGEBRA owes its success to the hallmark features for which its authors are known: learning by example, a straightforward and accessible writing style, emphasis on visualization through the use of graphs, and comprehensive exercise sets to help you practice and hone your skills. These pedagogical features are carefully coordinated to ensure that you are able to make connections between mathematical concepts and understand the content. With a bright, appealing design, the Fifth Edition builds on the book's tradition of guided learning by incorporating new features to better help you develop proficiency, understand concepts, and succeed in the algebra course |
Book DescriptionBook Description
SMP Interact at Key Stage 3 has been written to support the new Framework for teaching mathematics: Years 7, 8 and 9. Teacher's Guide to Book C2 accompanies the second book of the C (Circle) series, which provides a route to the Key Stage 3 SATs at levels 5-7.
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more |
2. Abacus Math Writer MathWriter is a java stand-alone program that allows for the production of, Mathematical, Scientific and Engineering equations and formulae.Schoolteachers and Lecturers will find MathWriter useful for producing notes, reports and test papers.
4. Animated Arithmetic Teaches addition, subtraction, multiplication and division for children from 1st through 4th grades. It provides exercises in addition and subtraction with and without regrouping. Problems can involve up to 9 digits. Puzzle and maze game rewards.
6. BibTexMng BibTexMng is a program for manipulating BibTeX database files. It combines searching, reference management, bibliography making, and information sharing into a single user-friendly environment. It was written to be used with Latex, using Bibtex
7. BiScope BiScope is free educational software that allows you to visually explore the relationship between binary, hexadecimal, octal and decimal numbers. BiScope also serves as a base conversion calculator.
8. CurvFit a curve fitting program: Lorentzian, Sine, Exponential and Power series are available models to match your data. A
Lorentzian series is recommended for real data especially for multiple peaked data.This is a Fortran Calculus demo application.
9. DeadLine DeadLine solves algebraic equations. It displays the graph of the function and a list of the real roots of the equation. It also includes the option to evaluate the function and its derivative. |
Discrete Mathematics will be of use to any undergraduate as well as post graduate courses in Computer Science and Mathematics. The syllabi of all these courses have been studied in depth and utmost care has been taken to ensure that all the essential topics in discrete structures are adequately emphasized. The book will enable the students to develop the requisite computational skills needed in software engineering.
...
Mathematics lays the basic foundation for engineering students to pursue their core subjects. In Engineering Mathematics-III, the topics have been dealt with in a style that is lucid and easy to understand, supported by illustrations that enable the student to assimilate the concepts effortlessly. Each chapter is replete with exercises to help the student gain a deep insight into the subject. The nuances of the subject have been brought out through more than 300 well-chosen, worked-out examples interspersed across the book.
...
A First Course in Computational Algebraic Geometry is designed for young students with some background in algebra who wish to perform their first experiments in computational geometry. Originating from a course taught at the African Institute for Mathematical Sciences, the book gives a compact presentation of the basic theory, with particular emphasis on explicit computational examples using the freely available computer algebra system, Singular. Readers will quickly gain the confidence to begin performing their own experiments.
...
Applied Mathematical Methods covers the material vital for research in today's world and can be covered in a regular semester course. It is the consolidation of the efforts of teaching the compulsory first semester post-graduate applied mathematics course at the Department of Mechanical Engineering at IIT Kanpur for two successive years.
...
Praise for the Third Edition
"This book provides in-depth coverage of modelling techniques used throughout many branches of actuarial science. . . . The exceptional high standard of this book has made it a pleasure to read." —Annals of Actuarial Science...
Practical Approaches to Reliability Theory in Cutting-Edge Applications
Probabilistic Reliability Models helps readers understand and properly use statistical methods and optimal resource allocation to solve engineering problems.
The author supplies engineers with a deeper understanding of mathematical models while also equipping mathematically oriented readers with a fundamental knowledge of the engineeringrelated applications at the center of model building. The book showcases the use of probability theory and mathematical statistics to solve common, real-world reliability problems....
A reference guide for applications of SEM using Mplus
Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers...
A practical approach to estimating and tracking dynamic systems in real-worl applications
Much of the literature on performing estimation for non-Gaussian systems is short on practical methodology, while Gaussian methods often lack a cohesive derivation. Bayesian Estimation and Tracking addresses the gap in the field on both accounts, providing readers with a comprehensive overview of methods for estimating both linear and nonlinear dynamic systems driven by Gaussian and non-Gaussian noices.
Featuring a unified approach to Bayesian estimation and tracking, the book emphasizes the...
Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to combinatorics, algorithms, and data structures. They
emphasize theFor the maths-phobic, this 2nd edition of the best-selling How to Master Nursing Calculations, is ideal practice for learning key numeracy skills. The perfect companion for your training and in the first few crucial years of your career, it builds your competency through practice, revision and every day examples. Contents includes a review of the basics, clear illustrations of instrument scales, medical administration records and pharmaceutical labels as well as a detailed guide to reading drug dosage charts.
Including a brand new list of important abbreviations and a section on how to make...
New Bayesian approach helps you solve tough problems in signal processing with ease
Signal processing is based on this fundamental concept—the extraction of critical information from noisy, uncertain data. Most techniques rely on underlying Gaussian assumptions for a solution, but what happens when these assumptions are erroneous? Bayesian techniques circumvent this limitation by offering a completely different approach that can easily incorporate non-Gaussian and nonlinear processes along with all of the usual methods currently available.
This text enables readers to fully exploit the...
An interdisciplinary approach to understanding queueing and graphical networks
In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the...
While typically many approaches have been mainly mathematics focused, graph theory has become a tool used by scientists, researchers, and engineers in using modeling techniques to solve real-world problems.
Graph Theory for Operations Research and Management: Applications in Industrial Engineering presents traditional and contemporary applications of graph theory in the areas of industrial engineering, management science, and applied operations research. This comprehensive collection of research introduces the useful basic concepts of graph theory in real world applications.
...
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy,... |
More from this developer
Description
Application made to make mathematical calculus, that are considered laborious and exhaustive when made by hand, and make easier the life of engineers and mathematicians. Solve 2nd grade equations, equations linear systems, make conversions between rectangular and polar formats... You can also work with matrices. Calculate determinant, make multiplications between matrices, calculate the inverse and adjoint.
Test review and rating
What's New
New features: - History salved of each calculation made, and you can rescue the typed values to redo the calculation; It's possible to setup how many lasts histories to save: 10, 20 or 30, of each operation. - The number of decimal places rounded on the calculations are settable, from 1 up to 15. - New visual on the operations list. - Change on the visual of the operation: Quadratic Equation. - New operation: Cartesian and Spherical coordinates |
Math-software syntax
It can be useful to add new boxes into math-related topics on wiki - boxes with examples and explaining how to solve this problem using popular software like wolframalpha, Matlab etc. For example, you can solve integral in wolframalpha with this syntax: integrate x**2 for x from 2 to 3. Many users dont know how to solve math problems with math software. |
In the last 200 years, harmonic analysis has been one of the most influential bodies of mathematical ideas, having been exceptionally significant both in its theoretical implications and in its enormous range of applicability throughout mathematics, science, and engineering.
In this book, the authors convey the remarkable beauty and applicability of the ideas that have grown from Fourier theory. They present for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization). While concentrating on the Fourier and Haar cases, the book touches on aspects of the world that lies between these two different ways of decomposing functions: time-frequency analysis (wavelets). Both finite and continuous perspectives are presented, allowing for the introduction of discrete Fourier and Haar transforms and fast algorithms, such as the Fast Fourier Transform (FFT) and its wavelet analogues.
The approach combines rigorous proof, inviting motivation, and numerous applications. Over 250 exercises are included in the text. Each chapter ends with ideas for projects in harmonic analysis that students can work on independently.
This book is published in cooperation with IAS/Park City Mathematics Institute.
Readership
Undergraduate students interested in harmonic analysis.
Reviews
"[T]he panorama of harmonic analysis presented in the book includes very recent achievements like the connection of the dyadic shift operator with the Hilbert transform. This gives to an interested reader a good chance to see concrete examples of contemporary research problems in harmonic analysis. I highly recommend this book as a good source for undergraduate and graduate courses as well as for individual studies." |
The program performs visualization of 4 most popular graph algorithms: Dijkstra, Floyd, Prim and Kruskel algorithms. It supports definition of color and width of edges, color and size of vertices, step delay time. It also has a convenient function of upload of the graphs to a remote server for futher storage and download on user's computer. Some graphs are already included into the installation, others can be created by user.
A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra.
Is 200 seconds.
gcd and lcm for any type and amount of numbers. Two are the aspects that distinguish this small software from others of its genre: the amount of numbers to be analyzed and the type of numbers to analyze. There are no limits on the amount of numbers on which to calculate lcm and gcd. A walkthrough will guide you through data entry, following four well-defined phasesThis is an interactive times table practice program that any student use get a good understanding of the times table. The student can work on just the numbers that he needs work on. If it becomes too difficult, the student should go back to a lower level that he fully understood and go over that again. Once that is mastered then the student can move forward from there. The objective is to make math fun and interesting. |
Chapter 10
Money and Inflation
What Is Money?
Money: that part of a person's wealth that can be readily used for transactions, serves as a store of value, and serves as a unit of account.
Copyright Houghton Mifflin Company. All rights reserved.
1
Section P.2
Graphs of Equations
5 Course Number
Section P.2 Graphs of Equations
Instructor Objective: In this lesson you learned how to sketch graphs of equations by point plotting or using a graphing utility. Date
Important Vocabulary
Define ea
History of Calculus
Development First steps were taken by Greek mathematicians, when Archimedes (around 225BC) constructed an infinite sequence of triangles starting with one of area A and continually adding further triangles between those already t
The Rules for Boiling Points The boiling points of compounds depend on how strongly they stick together: The more strongly they stick together, the higher the boiling point (the more heat it takes to rip them apart). There are two main forces that
How often do you eat a bowl of Cereal?
A) B) C) D) Hardly Ever 1 to 2 times a week 3 or 4 times a week More than 3 or 4 times a week
Copyright Houghton Mifflin Company. All rights reserved.
2|2
How often do you eat cereal other than for breakfast
Part Five Product Decisions
11
Product Concepts
Objectives
1. To understand the concept of a product 2. To explain how to classify products 3. To examine the concepts of product item product line, and product mix and understand how they are connect
Chapter 1
Functions and Their Graphs
Course Number Instructor Date
Section 1.1 Functions
Objective: In this lesson you learned how to evaluate functions and find their domains.
Important Vocabulary
Define each term or concept.
Function A functi
04 524984 Ch01.qxd
8/6/03
9:34 AM
Page 9
Chapter 1
What Is Calculus?
In This Chapter
You're only on page 1 and you've got a calc test already Calculus - it's just souped-up regular math Zooming in is the key The world before and after calculus |
Welcome to Santa Ana College Math Center!
The Math Center is a resource center that provides individual and group assistance in mathematics. The Math Center also facilitates Directed Learning Activities. Faculty instructors, instructional assistants, and Student tutors are available to assist students with challenging topics, answer questions, encourage understanding, and provide support for all math students. Students also have access to textbooks, graphing calculators, instructional videos, and computer programs.
Math Center's Goals
To help some students further develop basic skills in mathematics and keep them coming to school.
To assist other students to further sharpen their pre-existing math skills and advance through math courses.
To guide all students toward success in math and encourage them to excel through their scholastic endeavors and beyond.
What is SAC Math Jam?
Math Jam is a free 2 week intensive math review session designed to improve a student's preparation for up coming math classes. It is usually held 2 weeks prior to the start of each semester. The session consists of: interactive learning, group learning, tutoring, individual instruction.
How can students benefit from it?
•Build stronger mathematics knowledge and study skills
•Boost your math confidence.
•Have fun with math and make friends who share the same goals.
•Enhance your chances for success in college
Who can sign up?
All Santa Ana College students who are going into Math 160-Trigonometry, Math 170-PreCalculus, or Math 180 Calculus 1. |
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 |
Your password is the last four digits of your ISU ID number. Please change this as soon as you can.
To access the homework you will have to use the access code that came
with your book. There is a temporary access code available if you
don't have one yet, but it only lasts a short time (two weeks I think).
Quizzes: We will have quizzes approximately every Wednesday.
Exams:
Midterm
Wednesday, October 10th
In-Class
Final
TBA
Note that it will be at a common time with the other sections of Math 140, not at the time based on first meeting
Think
about trying the Problem of the
Week Solving one of these will count instead of the extra credit assignment above if you would like.
140 in the subject line. |
Algebra
I 1998-2025
Students are often confused to how important homework actually
is for math class. Let me explain in a clear manner.
HOMEWORK IS THE MOST IMPORTANT WORKyou can do in a math
class!Please complete it daily!
Make sure you do your homework before doing anything else in your busy
day. If you complete & learn how to do your homework problems, you
will do well on test and quizzes. If you do not complete homework, I
guarantee that your test grade, as well as your overall class grade will
suffer greatly.
Homework is assigned everyday for each of my math classes, including
Fridays and even for holidays. Homework is worth 2 points for each
assignment. It adds up quick. By the end of quarter, your homework is worth an
approximate 60 points, the same as two quiz scores.
Would you ever decide to throw away 60 points on a test? By the end
of a semester, your homework is worth approximately 120 points of your total
grade. This is more than a test grade! GET INTO A GOOD HABIT, DO
YOUR HOMEWORK.
Homework is due at the start of each class period. I will either collect
homework at the start of class, or check to see that you have done it.
I DO NOT accept late homework. Do not ask me if I do.
Some minor changes always occur throughout the semester. Some
extra assignments will be added, and some may be retracted. Please pay
attention in class for any changes that may occur.
If you have missed class or have forgotten your assignment, please use the
Assignment link found on the left hand side of this page to find your current
assignment. Make sure to check with one of your "buddies" from
your buddy list to confirm your daily assignmentand to help if
needed.
Some changes will be made during class time on certain assignments. I may
allow for half credit for an assignment turned in one day late in the future
so it is always best to attempt homework and have it ready on time.
If you have any questions about homework, please feel free to ask me in
class or use the email link below. I hope for you to be successful and
have a wonderful time in my math class. |
Costs
Course Cost:
$300.00
Materials Cost:
None
Total Cost:
$300
Special Notes
State Course Code
02061Integrated Math I provides a first-year integrated math curriculum that combines material traditionally covered in high school algebra, geometry, and statistics courses. Integrated Math I is uniquely organized around thematic learning tasks that integrate concepts from the various strands of math. Within the course, a balance is struck between task-based discovery and focused development of skills and conceptual understanding.
Carefully paced, guided instruction is accompanied by interactive practice that is engaging and accessible. Interactive tasks allow students to approach and explore topics through real-world situations, helping them to gain an intuitive understanding while learning at the appropriate depth and rigor of a standards-based curriculum. Formative assessments help students to understand areas of weakness and improve performance, while summative assessments chart progress and skill development. Throughout the course, students develop general strategies to hone their problem-solving skills.
The content is based on the National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics, as well as the Georgia Performance Standards and Instructional Frameworks in Mathematics. Detailed correlations to state-specific standards are available on request. |
Speedstudy Algebra 1
Speedstudy Algebra 1 provides a solid educational foundation that will raise grades and test scores and improve math skills in the classroom and beyond. Using step-by-step animations, real-time quizzes and a fun 3-D interface, Quickstudy Algebra 1
* Improve grades and test scores
* Multimedia learning system makes even the toughest math concepts come alive
* Great for new learners or students studying for college entrance exams |
Lulu Marketplace
Boolean Algebra at School, Vol 1
The main focus of this book is on actively engaging students in the mathematical processes of modeling and axiomatization. The book starts off with some challenging problems involving switching circuits. Students are then engaged in gradually developing a mathematical model in order to solve these problems. Suitable notation is firstly introduced for series and parallel switches, and then followed by truth tables, and the discovery of several interesting mathematical properties related to switching circuits.
After development of the model and solution of the original problems, a section on systematization follows where students are led through some proof activities to identify a suitable set of axioms. The book concludes with a short historical overview of the development and application of Boolean Algebra. |
Math
Mathematics Department
Mathematics is one of the cornerstones of human knowledge and has been recognized as such since earliest times. It is the foundation of science and technology, and increasingly, it plays a major role in determining the strength of the nation's work force.
Today, many more students can and must attain a level of mathematics understanding traditionally reserved for only a few. In order to succeed in our information-based society, students must have a solid understanding of the basics -- reading, science, history, the arts -- and at the center of this base of essential knowledge must be mathematics. It is important that all students learn how to problem solve and to apply concepts in real-world settings.
Workers can no longer get by with a single, well-practiced assembly-line skill, and a few reading and computation skills. Businesses want capable people with broad, transferable knowledge who can learn quickly on the job, master new technologies, and adapt to career changes. They are demanding higher order, problem-solving skills that cut across disciplines.
The mathematics curriculum provides a concrete and sequential study of mathematics while providing rigor and challenge for all students. Students are given the opportunity to master challenging mathematics, which includes algebra, geometry, trigonometry, statistics, and calculus. |
Pre-Calculus Homework Help
Pre-calculus is an interesting area of math for students because of its multi-purpose nature. It reviews previously learned topics like trigonometry, introduces new topics like matrices and determinants, and prepares students for a formal course in calculus for the following year.
Typical content for a regular pre-calculus course includes:
functions and their graphs
polynomial and rational functions
exponential and logarithmic functions
trigonometry
systems of equations and inequalities
matrices and determinants
sequences, series, and probablility
While all these topics are important, it is fair to say that the topic of exponential and logarithmic functions is the most widespread in various fields of study, from business math to theoretical physics. As an interesting example, consider the following equation where we would like to solve for x:
ex + 2e-x = 3
A quick review of three basic logarithm rules:
product rule: ln (ab) = ln a + ln b
quotient rule: ln (a/b) = ln a - ln b
power rule: ln an = n ln a
shows that none will be helpful here. One technique for solving this equation is to multiply both sides by ex. The result is:
e2x + 2 = 3ex
After subtracting 3ex from both sides, we have:
e2x - 3ex + 2 = 0
After careful consideration of this equation, you may recognize it as a quadratic, with ex taking the place of x. We can therefore factor this just as we would any quadratic equation:
(ex-2)(ex-1) = 0
Setting each factor equal to zero, we have:
ex-2 = 0 and ex-1 = 0
Adding 2 and adding 1 to the left and right equations, respectively gives:
ex = 2 and ex = 1
Now, finally, in each case we can take the natural log of both sides:
ln ex = ln 2 and ln ex = ln 1
Remembering that ln ex = x, we have our two solutions:
x = ln 2 and x = 0
This example has served to review some of the basic properties of logarithms and to illustrate an early creative twist that was necessary for solving the given equation.
To fulfill our mission of educating students, our online tutoring centers are standing by 24/7, ready to assist students who need extra practice in pre-calculus. |
A Catalog of Mathematics Resources on the WWW and the Internet (M. Maheswaran, University of Wisconsin, Marathon County). Comprehensive links to mathematics sites, organized into categories including pure and applied mathematics. Over 100 links under Activities for College and Pre-college Mathematics, although many are K-12. Other categories offer useful information and materials for college mathematics teachers.
Teaching Tips (Thomas Garrity and Frank Morgan, American Mathematical Society). Tips for becoming a more successful teacher of mathematics, with an example from a lecture in calculus.
Ted Panitz's Teaching/Learning Website. Scroll down the page for links to several articles by Panitz and others on using cooperative learning and writing to reduce math anxiety, increase learning, and create a student-centered learning environment in college math courses.
MERLOT Mathematics Portal (Multimedia Educational Resource for Learning and Online Teaching). The portal for online teaching and learning materials from faculty and educators in higher education around the world.
World Lecture Hall: Mathematics. Syllabi and course materials for a wide range of mathematics courses in higher education. Type mathematics or specific areas or courses into the search engine for these links.
What Is QL/QR? (Bill Briggs, University of Colorado at Denver). This page offers definitions of quantitative literacy/reasoning set forth in various publications and describes its importance in contemporary life.
Quantitative Reasoning for College Graduates: A Complement to the Standards, 1998. (Mathematical Association of America). An online handbook for implementing a QL program on college and university campuses. Includes goals and expectations (with thorough discussions of rationales); moves from "why" to "actions and strategies" to "assessment."
Center for Mathematics and Quantitative Education at Dartmouth College. Offers links to resources for college and university QL education in a wide variety of disciplines including art, literature, the sciences, and mathematics. Most are downloadable at no cost.
Colleges with QL/QR Programs: QuIRK, Carleton College's Quantitative Inquiry, Reasoning, and Knowledge Initiative. The material on this site, designed with grants from FIPSE, NSF, and the Keck Foundation, is intended to help institutions "better prepare students to evaluate and use quantitative evidence in their future roles." The site provides curricular materials for infusing quantitative reasoning throughout the curriculum, assessment, program design, and more. See also the QuIRK page of links to other quantitative reasoning programs and additional QR teaching resources.
Quantitative Reasoning Across the Curriculum at Hollins University. Describes their QR Program instituted in 2001 with Basic and Applied requirements. Lists courses that fulfill these requirements. Links to brief descriptions of QL courses in a variety of disciplines.
Mathematics Across the Curriculum at Dartmouth College. The MATC Project ended in 2000, but this site has their goals, principals, links to MATC courses, and the Evaluation Summary for this five-year project. The resources they compiled are described above with a link to those in higher education.
Professor Freedman's Math Help (Camden County College, Blackwood New Jersey). This site addresses the learning needs in mathematics of the community college adult learner. Useful for both students and teachers, the site offers math tutorials, homework assignments, video snippets on math topics, information about learning styles, and much more. |
Powderly, TX Algebra am knowledgeable at the TI-83 and TI-84 calculators since I coached UIL calculator applications. Algebra 2 revisits Algebra 1 and some Geometry. However, Algebra 2 goes into more depth and adding more concepts. |
History of Mathematics
9780130190741
ISBN:
0130190748
Pub Date: 2001 Publisher: Prentice Hall
Summary: For junior and senior level undergraduate courses, this text attempts to blend relevant mathematics and relevant history of mathematics, giving not only a description of the mathematics, but also explaining how it has been practiced through time. |
Courses
Mathematics
MA 100. TOPICS IN CONTEMPORARY MATHEMATICS (3) (GEN. ED. #5) Selected topics to illustrate the nature of mathematics, its role in society, and its practical and abstract aspects. Applications of mathematics to business and social sciences are explored. Three hours lecture. Prerequisite: placement exam. Fall semester, repeated spring semester.
MA 110. PROBLEM SOLVING AND MATHEMATICS: NUMBER SYSTEMS (4) (GEN. ED. #5) For students majoring in elementary education. Explores various approaches to problem solving by examining topics such as estimating numerical quantities, probability and statistics, the nature of numeric patterns, functions, and relations. The course focuses on the use of various tools, such as calculators and physical models, as aids in problem solving. Four hours lecture. Prerequisite: placement exam. Fall semester. Department.
MA 113. PROBLEM SOLVING AND MATHEMATICS: GEOMETRY (4) (GEN. ED. #5) For students majoring in elementary education. Explores various approaches to problem solving by examining topics such as spatial sense and measurement with respect to various geometries, properties of curves and surfaces, coordinate geometry, and transformations. The course focuses on the use of various tools, such as calculators and physical models, as aids in problem solving. Four hours lecture. Prerequisite: placement exam. MA 110 is recommended but not required. Spring semester. Department.
MA 140. INTRODUCTION TO STATISTICS (FORMERLY MA 105) (4) (GEN. ED. #5) Basic concepts of descriptive statistics, simple probability distributions, prediction of population parameters from samples. Problems chosen from the natural and social sciences. Use of the computer in the analysis and interpretation of statistical data. Four hours lecture. Prerequisite: placement exam. Credit will not be given for those who have received credit for MA 141. Fall semester, repeated spring semester. McKibben,Webster.
MA 141. STATISTICAL DATA ANALYSIS WITH ENVIRONMENTAL ISSUES IN VIEW (4) (GEN. ED. #5 AND #11) Basic concepts of descriptive statistics, simple probability distributions, and prediction of population parameters from samples are developed as a means to analyze environmental issues and the debates centered on them. Use of computer in analysis and interpretation of statistical data. Four hours lecture. Prerequisite: placement exam. Credit will not be given for those who have received credit for MA 140. Fall semester, repeated spring semester. McKibben,Webster.
MA 160. PRECALCULUS (FORMERLY MA 114) (4) (GEN. ED. #5) An applications-oriented, investigative approach to the study of the mathematical topics needed for further coursework in mathematics. The unifying theme is the study of functions, including polynomials; rational functions; and exponential, logarithmic, and trigonometric functions. Graphing calculators and/or the computer will be used as an integral part of the course. Four hours lecture. Prerequisite: placement exam. Fall semester, repeated spring semester.
MA 170. CALCULUS I (FORMERLY MA 117) (4) (GEN. ED. #5) The concepts of limit and derivative are developed, along with their applications to the natural and social sciences 171. Fall semester, repeated spring semester. Department.
MA 171. CALCULUS I-ENVIRONMENTAL (4) (GEN. ED. #5 AND #11) The concepts of limit and derivative are developed, along with their applications to planet and environmental sustainability issues 170. Fall semester.Webster.
MA 180. CALCULUS II (FORMERLY MA 118) (4) (GEN. ED. #5) The concepts of Riemann sums and definite and indefinite integrals are developed, along with their applications to the natural and social sciences. A symbolic algebra system is used as both an investigative and computational tool. Three hours lecture, two hours laboratory. Prerequisite: placement exam or MA 170 or 171 with a minimum grade of C-. Prerequisite to MA 222. Fall semester, repeated spring semester. Department.
MA 260. HISTORY OF MATHEMATICS (3) (GEN. ED. #4 AND #7) Selected topics in the history of mathematics chosen to show how mathematical concepts evolve. Topics include number, function, geometry, and calculus. Consideration of the cultural, social, and economic forces that have influenced the development of mathematics. Three hours lecture. Prerequisites: MA 221 and 222. Spring semester. Offered 2010-11 and alternate years. Lewand.
MA 290. INTERNSHIP IN MATHEMATICS (3-4) Students interested in the application of mathematics to government, business, and industry are placed in various companies and agencies to work full time under the guidance of a supervisor. The director confers with individual students as needed. Students are selected for internships appropriate to their training and interest in mathematics and related fields. Prerequisites: junior standing and a major in mathematics. This course is graded pass/no pass only. Fall semester, repeated spring semester. Department.
MA 299. INDEPENDENT WORK IN MATHEMATICS (1-4) Department.
MA 311. INTRODUCTION TO HIGHER MATHEMATICS (3) An introduction to proof techniques within the context of the following topics: elementary set theory, functions and relations, and algebraic structures. Three hours lecture. Prerequisites: MA 221 and 222. Fall semester. Lewand, McKibben, Webster.
MA 313. FUNDAMENTALS OF REAL ANALYSIS (3) A rigorous development of differential and integral calculus, beginning with the completeness of the real number system. The topological structure of the real number system is developed, followed by a rigorous notion of convergence of sequences. Limit, continuity, derivative, and integral are formally defined, culminating in the Fundamental Theorem of Calculus. Three hours lecture. Prerequisites: MA 311. Spring semester. Offered 2010-11 and alternate years. McKibben, Webster.
Computer Science
CS 105. EXPLORATIONS OF COMPUTER PROGRAMMING (3) (GEN. ED. #5) Introduction to the concepts of computer programming using 3-D virtual worlds. Programming constructs such as looping, selection, and data structures, along with the control of objects will be explored. No prior programming experience is required. Spring semester. Zimmerman.
CS 116. INTRODUCTION TO COMPUTER SCIENCE (4) (GEN. ED. #5) Introduction to the discipline of computer science and its unifying concepts through a study of the principles of program specification and design, algorithm development, object-oriented program coding and testing, and visual interface development. Prerequisite: placement exam or CS 105 with a minimum grade of C-. Fall semester. Zimmerman.
CS 220. COMPUTER ARCHITECTURE (3) Organization of contemporary computing systems: instruction set design, arithmetic circuits, control and pipelining, the memory hierarchy, and I/O. Includes topics from the ever-changing state of the art. Prerequisite: CS 119. Fall semester. Offered 2011-12 and alternate years. Kelliher.
CS 230. ANALYSIS OF COMPUTER ALGORITHMS (3) The design of computer algorithms and techniques for analyzing the efficiency and complexity of algorithms. Emphasis on sorting, searching, and graph algorithms. Several general methods of constructing algorithms, such as backtracking and dynamic programming, will be discussed and applications given. Prerequisites: CS 119. Fall semester. Offered 2010-11 and alternate years. Zimmerman.
CS 245. SOFTWARE ENGINEERING (3) This course emphasizes the application of tools of software engineering to programming. The focal point of the course is the design, implementation, and testing of a large programming project. Students gain familiarity with the standard programmer's tools, such as debugger, make facility, and revision control. Prerequisite: CS 119. Fall semester. Offered 2010-11 and alternate years. Kelliher.
CS 290. INTERNSHIP IN COMPUTER SCIENCE (3-4) Students interested in the application of computer science to government, business, and industry are placed in various companies and agencies to work full time under the guidance of a supervisor. The director confers with individual students as needed. Students are selected for internships appropriate to their training and interest in computer science and related fields. Prerequisites: junior standing and a major in computer science. This course is graded pass/no pass only. Fall semester, repeated spring semester. Department. |
Summary: Provides completely worked-out solutions to all odd-numbered exercises within the text, giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer.
2007 |
The Saxon Difference
Saxon is an integrated curriculum. Concepts in each math strand are broken into small increments that are interwoven together to create rich mathematical connections. Once taught, the increments are systematically distributed and practiced throughout a full year of instruction. No skills are ever dropped. It is this consistent review and practice that makes the difference in helping all students achieve long-term success
Stephen Hake, Author of Saxon Math Intermediate 3-5 and Courses 1-3
When I read the published field-test results of John Saxon's Algebra 1 manuscript and learned that John Saxon taught students with the same methods I did, I placed an order and began using John's book with my eighth grade students with great success. Recognizing the country's need for an effective math program from grade school through high school, we joined our efforts and soon Saxon Math was helping millions of students across America succeed in math. Students can learn math and are advanced through the subject matter in a way that gently guides them step by step and provides the time and practice necessary to learn and remember the foundational concepts of mathematics.
Saxon Math is written the way I taught–one bit of instruction each day with plenty of practice on previous instruction. The excellent performance of my students on problem-solving contests and on standardized tests convinced me that this method of instruction works. It produces excellent problem-solving skills and long-term learning of key math concepts.
Pat Wrigley, Author of Adaptations for Saxon Math
I began to adapt Saxon's intermediate grades series in 1991 for use with my own Special Ed students. When other resource specialists began to request copies of my work, I realized it might be of value to Saxon users. The Saxon approach is reliable. I've seen repeated proof that this program works for all students. Even as I reach my 40th year as a full-time resource specialist, seeing the happiness of my students' faces as they achieve beyond their dreams is still the greatest joy of my life.
Dr. Frank Wang, Author of Saxon Calculus
"My passion is for teaching and for helping students learn more mathematics than they ever thought possible. I am a fervent advocate for the Saxon pedagogy and highly recommend its mathematics textbooks as the best textbooks for providing students with a solid and firm foundation for further study in mathematics."
Dr. Wang holds an undergraduate degree from Princeton University and a Ph. D. in pure mathematics from MIT. He began working for Saxon Publishers at age 16 as a high school student. He was president of the company from 1994 to 2001. Frank has taught at the University of Oklahoma and currently teaches at the Oklahoma School of Science and Mathematics. |
Authors
Document Type
Contribution to Book
Publication Date
2011
Source Publication
Early Algebraization, Volume 2
Abstract
This chapter highlights findings from the LieCal Project, a longitudinal project in which we investigated the effects of a Standards-based middle school mathematics curriculum (CMP) on students' algebraic development and compared them to the effects of other middle school mathematics curricula (non-CMP). We found that the CMP curriculum takes a functional approach to the teaching of algebra while non-CMP curricula take a structural approach. The teachers who used the CMP curriculum emphasized conceptual understanding more than did those who used the non-CMP curricula. On the other hand, the teachers who used non-CMP curricula emphasized procedural knowledge more than did those who used the CMP curriculum. When we examined the development of students' algebraic thinking related to representing situations, equation solving, and making generalizations, we found that CMP students had a significantly higher growth rate on representing-situations tasks than did non-CMP students, but both CMP and non-CMP students had an almost identical growth in their ability to solve equations. We also found that CMP students demonstrated greater generalization abilities than did non-CMP students over the three middle school years. |
Calculated Formula
A Calculated Formula question contains a formula, the variables of which can be set to change for each user. The variable range is created by specifying a minimum value and a maximum value for each variable. Answer sets are randomly generated. The correct answer can be a specific value or a range of values. Partial credit may be granted for answers falling in a range.
Since this question allows the Instructor to randomize the value of variables in an equation it may be useful when creating math drills to when giving a test when Students are seated close together.
The question is the information presented to students. The formula is the mathematical expression used to find the answer. Be sure to enclose variables in square brackets.
1. Open the Test Canvas for a test.
2. Select Calculated Formula from the Create Question drop-menu.
3. Enter the information that will display to students in the question text box. Surround any variables with square brackets, for example, [x]. The value for this variable will be populated based on the formula. In the Example [x] + [y] = z, [x] and [y] will be replaced by values when shown to students. Students would be asked to define z. Variables should be composed of alphabets, digits (0-9), periods, underscores, or hypens. All other occurrences of the opening rectangular brace ("[") character should be preceded by the back-slash ("\") character. Variable names must be unique and cannot be reused.
4. Define the formula used to answer the question in the Formula box. For example, x+y=z. Operations are chosen from the buttons across the top of the formula box.
5. Assign a point value for the question.
6. Define the correct answer range, plus or minus a numeric or a percentage
variation from the exact answer. If the correct answer must be exact,
the range should be 0. If partial credit is allowed, define the broader
range for partial credit and the percentage of the total points that
will be given if the answer is within the partial credit range. Units
can be required as part of the answer, and optionally a percentage of
the total points can be deducted from the points given if the units are
incorrect.
The checkboxes for Partial Credit and Units Required must be selected for options to fully expand.
7. Click Continue to define the variables to be used in the formula.
For each variable included in the question text set a minimum and maximum value.
In the Decimal Places column, use the drop-menu to define the decimal place for variables.
Under Answer Set Options, select the decimal places for the answer from the drop-menu. Users must provide the correct answer to the decimal place specified.
Next enter the number of Answer sets you wish to include. The answer sets will be randomized so that each student will be presented with a different set of variables.
Click Calculate to review the answer sets. Click the Remove button to remove unwanted number sets.
8. Click Submit to add the question to the test or pool.
Calculated Numeric
This question resembles a fill-in-the-blank question. The user enters a number to complete a statement. The correct answer can be a specific number or within a range of numbers. Please note that the answer must be numeric, not alphanumeric. For example, in a Geography class the Instructor may ask for the estimated population of a specific city.
1. Open the Test Canvas for a test.
2. Select Calculated Numeric from the Create Question drop-menu.
3. Enter the Question Text.
4. Enter a Correct Answer. This value must be a number.
5. Enter the Answer Range. If the answer must be exact, leave the default of zero. Any value that is less than or more than the correct answer by less than the answer range will be marked as correct. This question type does not allow for partial credit.
6. Specify feedback, categories, or keywords, as needed.
7. Click Submit to add the question to the test canvas.
Either/Or
Either/Or questions show two answer options, such as True/False or Yes/No. There is no partial credit option for Either/Or questions. For clarity, make sure the question is phrased to match the selected answer labels.
1. Select Either/Or from the question type drop-menu.
2. Enter the Question Text and Point Value.
3. Determine whether answer options are listed side-by-side (horizontal) or one on top of the other (vertical).
4. Using the Answer Choices drop-menu, select the pre-defined choice set you wish to use as answers.
5. Select the correct answer.
6. Add feedback, categories, or keywords, as needed.
7. Click the Submit button to add the question to the test canvas.
File Response
Users upload a file from the local drive or from the Content Collection as the answer to the question. This type of question is graded manually. This question type is a good option if the Instructor would like Students to work on something before a test and submit it with a test, or if the response to the questions is expected to take a long time to read.
1. Select File Response from the question type drop-menu.
2. Enter the question text and assign a point value.
3. Assign category and keyword options, as needed.
4. Click the Submit button to add the question to the test canvas.
Fill in Multiple Blanks
This question type builds on fill-in-the-blank questions with multiple fill in the blank responses that can be inserted into a sentence or paragraph. Separate sets of answers are defined for each blank. This question type may be used if there are multiple variables, such as "What color is the Italian flag?" This question type is also useful in foreign language classes. In this case the identifier and adjective may be left blank in a sentence, so as not to give away the gender of an object.
1. Select Fill in Multiple Blanks from the question type drop-menu.
2. Enter the question text. Include up to 10 variables in square brackets, corresponding to locations in the text where the fill in the blank fields should appear. Variables must be unique and cannot be reused. For example, "William [a] wrote Romeo and [b]."
3. Assign a point value and partial credit options, as needed.
3. Click Next to assign answer choices.
4. Assign the number of possible choices and answer choices for each variable. Students must type in one of the given answer choices exactly to receive credit.
5. Click Next to provide correct and incorrect response feedback. Once all options are set, click Submit to add the question to the test canvas.
Hot Spot
Users indicate the answer by marking a specific point on an image. A range of pixel coordinates is used to define the correct answer. Hot Spot refers to the area of an image that, when selected, yields a correct answer. The following are some examples of uses for this type of question:
Anatomy - to locate different parts of the body
Geography - to locate areas on a map
1. Select Hot Spot on the question type drop-menu.
2. Enter the question text.
3. Click Browse for Local File to attach an image file.
4. Select the coordinates of the "hot spot" on the question image. To set the hot spot, click and drag the mouse over an area of the image. Release the mouse button when the hot spot is in the correct location. The white border will not be visible to students. Any clicks within this area will result in a correct response.
5. Enter feedback and assign categories and keywords, as needed. Click submit to add the question to the test canvas.
Jumbled Sentence
Users are shown a sentence with a few parts of the sentence as variables. The user selects the proper answer for each variable from the drop-menus to assemble the sentence. Only one set of answers is used for all of the drop-menu lists included in the question. This type of question may be useful when teaching about proper grammatical order in a sentence, such as the location of a noun, verb, or adjective.
1. Assign the question text, including variables in square brackets corresponding to the locations in the text where the drop-menu lists of answers should appear. Variable names must be unique and cannot be reused. For example, [a], [b], [c], etc.
2. Assign a point value and partial credit options.
3. Choose the number of answers to be included in the drop-menu answer lists, and enter answer choices as needed.
4. Click Next to designate the correct answer choices.
5. Set feedback and category options, as needed.
6. Click Submit to add the question to the test canvas.
Opinion Scale/Likert Question
Most often used in Surveys, Opinion Scale or Likert Scale questions are designed to measure attitudes or reactions using a comparable scale. Users select a multiple choice answer that represents their attitude or reaction.
1. Select Opinion Scale/Likert on the question type list.
2. Enter the question text and point value.
3. Assign the number of answers, as well as answer choices. By default, answer choices are Strongly Agree, Agree, Neither Agree nor Disagree, Disagree, Strongly Disagree, and Not Applicable.
4. Set answer feedback and category options, as needed.
5. Click Submit to add the question to the test canvas.
Quiz Bowl
Quiz Bowl questions are phrased as statements that require the answer to be in the form of a question. For example, the statement, "It is the only country that is a continent," requires the answer, "What is Australia?"
1. Select Quiz Bowl on the question type list.
2. Enter the question text in the form of a statement.
3. If desired, click the Allow Partial Credit box and enter a percentage of credit allowed for answers that include the correct phrase but do not include the correct interrogative word.
4. Select the Number of Interrogative Words. Enter each acceptable interrogative word in the fields below. One of these words must appear in the response for the student to receive full credit.
5. Select the Number of Answer Phrases. Enter each acceptable phrase into the fields below. One of these phrases must appear exactly in the response for the student to receive any credit. |
Book Description: The first book to discuss fractals solely from the point of view of computer graphics, this work includes an introduction to the basic axioms of fractals and their applications in the natural sciences, a survey of random fractals together with many pseudocodes for selected algorithms, an introduction into fantastic fractals such as the Mandelbrot set and the Julia sets, together with a detailed discussion of algorithms and fractal modeling of real world objects. 142 illustrations in 277 parts. 39 color plates. |
While taking this unit you must take MA20216 and take MA20218 and before taking this unit you must take MA10207 and take MA10208 and take MA10209 and take MA10210 and take XX10190
Description:
Aims: To teach those aspects of Numerical Analysis which are most relevant to a general mathematical training, and to lay the foundations for the more advanced courses in later years.
Learning Outcomes: After taking this unit, students should be able to:
* Demonstrate knowledge of simple methods for the approximation of functions and integrals, solution of initial value problems for ordinary differential equations and the solution of linear systems
* Use basic methods for the analysis of the errors made in these methods.
* Show awareness of some of the relevant practical issues involved in their implementation, including coding of algorithms using MATLAB.
* Write the relevant mathematical arguments in a precise and lucid fashion.
USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2 |
ED Math Workbook
This self-teaching workbook offers extensive preparation and brush-up in math for all who plan to take the GED High School Equivalency Test. A ...Show synopsisThis math review that follows is supplemented with hundreds of exercises. All GED math topics are covered, including measurement, geometry, algebra, number relations, and data analysis. Four practice tests with answers reflect questions and question types found on the actual GED.Hide synopsis
Description:New. This self-teaching workbook offers extensive preparation...New. This ma |
This is probably not what you're looking for, but if I were teaching such a course I'd focus on the interplay between algorithms for various graph problems and the more traditional mathematical approach of proving theorems in graph theory.
For example, you can prove the "max flow-min cut" theorem by developing an algorithm that simultaneously finds a maximum flow and a corresponding min-cut. |
Search Journal of Online Mathematics and its Applications:
Journal of Online Mathematics and its Applications
Tool Building: Web-based Linear Algebra Modules
by David E. Meel and Thomas A. Hern
Student Responses
Tools such as Eigenizer are only as good as their ability to help students interact with and form their own conjectures concerning linear algebra content. After students interacted with Eigenizer, we asked them in the cognitively-guided activity to put their observations about eigenvalues and eigenvectors into their own words. The responses included reflections such as these:
"An eigenvalue when multiplied by an eigenvector yields the same result as when matrix A is multipled [sic] by the eigenvector. Thus matrix A acts like the scalar eigenvalue".
"An eigenvalue is a value that lets the matrix act like a scalar. An eigenvector is a nonzero vector that corresponds to the eigenvalue, if Ax = the eigenvalue * x".
"The eigenvector is multiplied by A to make A act like a scalar. The eigenvalue of the vector is the lambda that A acts as when the vector is multiplied by it".
"An eigenvalue of a matrix A is a scalar that when multiplied with a vector x yields the same resultant vector as A*x. An eigenvector of a matrix A is a vector that when multiplied with a scalar lambda yields the same resultant vector as when multiplied with the matrix A".
"In our words, an eigenvalue is a way of representing a matrix as a scalar. This will allow the investigation of a matrix of transformation (T) on a vector (T(x)) without complicated calculations. The eigenvector provides a relationship between the values of x for which the lines are co-linear [sic]".
"An eigenvalue, with it's eigenvector, 'mimic' A when multiplied together. Meaning, A acts like a scalar when multiplied with the eigenvector. Since lambda is derived by solving det(A - lambda In)x = 0, it 'unravels' to Ax = lambda x, which is what I described above".
"The eigenvalues are related to A in that when multiplied by the In matrix and subtracted from A, you can row reduce to find a basis to the corresponding R space. The corresponding eigenvectors form the basis that spans the R space".
Clearly, some of the students were able to make observations that were generally consistent with mathematical definitions of eigenvalue and eigenvector and others made remarks that were slightly askew from such definitions.
However, being able to explore the geometry associated with eigenvectors and eigenvalues allowed some students to identify that MATLAB provided anomalous results when they encountered the following problem (2c in the accompanying activity):
A =
Using Eigenizer, determine how many times the vectors x and Ax are collinear? When the vectors x and Ax are collinear, what is the significance of the value of the eigenvalue in relation to the direction of an eigenvector of A, x, and its image T(x)?
How many eigenvalues does A have? Are they real or nonexistent? Are they distinct or multiple? How many are positive? negative? zero? Is A invertible? Explain.
Obtain a rough estimate of an eigenvector for each eigenvalue and then reveal the rest of the eigenvalue equation by pressing one of the "Show lambda # equation" buttons. Is the eigenvalue equation a truth within reasonable error? Move the vector x so it is no longer an eigenvector. Is the new equation true? Is the set of eigenvectors linearly independent? Explain.
Compute by hand or by using Matlab the characteristic polynomial, the exact eigenvalues, and exact eigenvectors. Compare your results to your estimates in part 3. If you use Matlab,
v = poly(A) gives the coefficients of the characteristic polynomial of matrix A, starting with the highest-degree term.
k = roots(v) gives the roots of the characteristic polynomial of A, or use eig(A) to accomplish the same thing.
nulbasis(A-k(1)*eye(2)) and nulbasis(A-k(2)*eye(2)) will give the eigenvectors, where each k(i) is a particular eigenvalue of A.
If a matrix produced non-existent eigenvalues, what did you determine about the eigenvalues from part 4 when you computed them by hand or via Matlab?
Here are some sample solutions provided by students for the 2c matrix:
Better understanding of both the computational and geometric roles of eigenvalues and eigenvectors, when combined with enhanced understandings of change of bases and linear transformations, sets the stage for investigations into diagonalization and potentially Singular Value Decompositions. One of our goals in having students explore the geometric perspective associated with eigenvalues and eigenvectors is to get students to begin to recognize that computations cannot be taken at face value but need to be examined within context for validity. |
0387946144
9780387946146
Mathematical Analysis: Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level. «Show less
Mathematical Analysis: Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical... Show more»
Rent Mathematical Analysis today, or search our site for other Axler |
GeoGebra is a dynamic mathematics software for education in secondary schools that joins geometry, algebra and calculus.
On the one hand, GeoGebra is a dynamic geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards.
On the other hand, equations and coordinates can be entered directly. Thus, GeoGebra has the ability to deal with variables for numbers, vectors and points, finds derivatives and integrals of functions and offers commands like Root or Extremum.
The GeoGebraWiki is a free pool of educational materials for GeoGebra. Everyone can contribute and upload materials there:
International GeoGebraWiki - pool of educational materials for GeoGebra and the German GeoGebraWiki
The Dynamic Worksheets
GeoGebra can also be used to create dynamic worksheets:
Pythagoras
visualisation of Pythagoras' theorem
Ladder against the Wall
application of Pythagoras' theorem
Circle and its Equation
connection between a circle's center, radius and equation
Slope and Derivative of a Function (3 sheets)
relation between slope, derivative and local extrema of a function
Derivative of a Polynomial
interactive exercise to practice finding the derivative of a cubic polynomial
Upper- and Lower Sums of a Function
visualisation of the backgrounds of Riemann's Integral |
Comprehensive Instruction
To prepare students for algebra, the mathematics curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills. The development of these concepts and skills is intertwined, each supporting the other and reinforcing learning.
Teachers can help by providing students with sufficient practice distributed over time and including a conceptually rich and varied mix of problems to support their learning. In addition, teachers should encourage and support students in their efforts to master difficult mathematics content. Students who believe that effort, not just inherent talent, counts in learning mathematics can improve their performance.
Multimedia Overview
Developing Conceptual Understanding, Fluency, and Problem Solving
Use this multimedia overview to learn about the value of simultaneously teaching concepts, procedures, and problem solving; the importance of practice distributed over time in developing automaticity and improving fluency, including the use of technology-based tools; and the relationship between student beliefs about learning and mathematics performance.
(8:37 min) |
Math 7
The regular sequence course for Grade 7 students, this course focuses on mastery of math skills needed to apply concepts encountered in higher-level courses. Students review basic arithmetic skills, then apply these skills to operations with whole numbers, integers, decimals, fractions, and percents. Further topics include ratio, proportion and geometry. Students experience more abstract thinking through the introduction of variables and learn to solve simple equations. Additional math time is allotted for a math lab, which provides opportunities for students to reinforce math concepts through a hands-on approach. Students who successfully complete this course move on to Pre-Algebra in Grade 8. |
is the 6th edtion of barron's math2c good enough for math level 2? Everyone seems to say that barron's is the best for math 2 but do they mean the new versions or is the 6th edition(old version) good enough? Is it hard like the other ones? |
Buy now
Detailed description Math Essentials, Middle School Level gives middle school math teachers the tools they need to help prepare all types of students (including gifted and learning disabled) for mathematics testing and the National Council of Teachers of Mathematics (NCTM) standards. Math Essentials highlights Dr. Thompson's proven approach by incorporating manipulatives, diagrams, and independent practice. This dynamic book covers thirty key objectives arranged in four sections. Each objective includes three activities (two developmental lessons and one independent practice) and a list of commonly made errors related to the objective. The book's activities are designed to be flexible and can be used as a connected set or taught separately, depending on the learning needs of your students. Most activities and problems also include a worksheet and an answer key and each of the four sections contains a practice test with an answer key.
From the contents The Author.
Notes to the Teacher.
Section 1: Number, Operation, and Quantitative Reasoning.
Objectives.
1. Compare and order fractions, decimals (including tenths and hundredths), and percents, and find their approximate locations on a number line.
5. Generate the formulas for the circumference and the area of a circle; apply the formulas to solve word problems.
6. Generate and apply the area formula for a parallelogram (including rectangles); extend to the area of a triangle.
7. Generate and apply the area formula for a trapezoid.
8. Apply nets and concrete models to find total or partial surface areas of prisms and cylinders.
9. Find the volume of a right rectangular prism, or find a missing dimension of the prism; find the new volume when the dimensions of a prism are changed proportionally.
Practice Test.
Section 4: Graphing, Statistics, and Probability.
Objectives.
1. Locate and name points using ordered pairs of rational numbers or integers on a Cartesian coordinate plane.
2. Construct and interpret circle graphs.
3. Compare different numerical or graphical models for the same data, including histograms, circle graphs, stem-and-leaf plots, box plots, and scatter plots; compare two sets of data by comparing their graphs of similar type.
4. Find the mean of a given set of data, using different representations such as tables or bar graphs.
5. Find the probability of a simple event and its complement.
6. Find the probability of a compound event (dependent or independent). |
... Author(s): Shalayna Lair
Statistics Online Compute Resources This site offers software tools, instructional materials and online tutorials about college-level probability and statistics. The SOCR tool has interactive graphs and information about dozens of distribution models, as well as a large collection of statistical techniques for online data analysis, visualization, ... Author(s): Ivo Dinov
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angles standard position intro to positive West Virginia Math and Science Initiative - Trigonometry - angles standard position intro to positive - American Military University > ACADEMICS AND TRAINING > West Virginia Math and Science Initiative > Trigonometry > angles standard position intro to positive Author(s): No creator set
Introduction to Coordinate Geometry A web page that introduces the concepts behind coordinate geometry. Can be used as a reference for students to learn about the topic when away from class. Has links to other related pages that contain animated demonstrations. This resource is a component of the Math Open Reference Interactive Geometry textbook project at Author(s): John Page
Introduction to Storyboarding This lecture takes you through the steps to create a storyboard for film and animation projects. It is given by Illustration and Animation Lecturer Francis Lowe. Author(s): No creator set
Introduction to Ethical Studies These readings provide convenient sources for almost anyone seeking to learn about ethics and ethical theory. Our present collection is composed almost entirely of public domain sources, edited and emended, and subject to the legal notice following the title page which references Appendix A. Author(s): No creator set
Introduction to OpenOffice.org Impress An introduction to using OpenOffice.org Impress for presentations - aimed at getting learners comfortable with OOo Impress basics and giving them the confidence to go further on their own. Author(s): No creator set
Faith Complex: An Introduction Faith Complex is a show about the collision of religion, politics and art. Faith Complex is a joint production of Georgetown University's Program for Jewish Civilization and the Berkley Center for Religion, Peace and World Affairs, and it airs weekly at WashingtonPost.com Author(s): No creator set |
Ummer2013-05-19T07:29:04Z Mathematics with Mathematica for Economics, Business and Finance Ummer book can help overcome the widely observed math-phobia and math-aversion among undergraduate students in these subjects. The book can also help them understand why they have to learn different mathematical techniques, how they can be app...496 pages13.6 MB69.29 |
Specification
Aims
To show how the tools of Mathematical analysis can be used to prove results about prime numbers and functions defined on the integers.
Brief Course Description
We start by giving two proofs of the infinitude of primes. The methods are elementary but poor in that they do not tell us the truth of how many primes there are. Stronger tools are introduced, improving the results until we can give a proof of the Prime Number Theorem.
Learning Outcomes
On completion of this unit students
will be able to utilise the correspondence between the product of Dirichlet series and composition of arithmetic functions,
will be able to use the methods of Partial Summation and replacing sums by integrals,
be able to prove elementary results on sums over primes,
be able to prove some analytic properties of the Riemann zeta function,
appreciate a proof of the Prime Number Theorem,
will be able to use the Composition Method to estimate sums of arithemtic functions. |
Historical Modules for the Teaching and Learning of Mathematics
Victor Katz and Karen Dee Michalowicz, Editors
The beauty of this resource is that teachers only need to review the material in order to be able to use it. The topics need to be read in preparation for the lessons, although it is conceivable that most of the material can be used without prior knowledge of the historical background - and therefore this would be a chance for teachers to learn more about the history of mathematics, while making meaningful connections between different mathematical concepts. ...
If this was given in book format, the amount of material would be both admirable and useful, but as a CD-Rom it offers even greater convenience for the practicing teacher. The index, for example, is interactive, enabling easy subject and resource searching. For both teachers and students who want to explore more, an extensive bibliography is given at the end of each module, together with web links fore easy references to relevant topics and mathematicians.... I strongly recommend this publication to anyone who is any way involved in teaching and learning of mathematics. — Bulletin of the British Society for the History of Mathematics
These eleven eleven. |
This text for undergraduate students provides a foundation for resolving proofs dependent on n-dimensional systems. The author takes a concise approach, setting out that part of the subject with statistical applications and briefly sketching them. The two-part treatment begins with simple figuThis text for undergraduate students provides a foundation for resolving proofs dependent on n-dimensional systems. The author takes a concise approach, setting out that part of the subject with statistical applications and briefly sketching them. The two-part treatment begins with simple figures in n dimensions and advances to examinations of the contents of hyperspheres, hyperellipsoids, hyperprisms, parallelotopes, hyperpyramids, and simplexes. The second part explores the mean in rectangular variation, the correlation coefficient in bivariate normal variation, Wishart's distribution, correlations as angles, regression and multiple correlation, canonical correlations, and component analysis. 1961 edition.
Unabridged republication of the edition published by Hafner, New York, 1961 |
Revised edition of algebra II links all the activities to the NCTM standards
Activities provide students with practice in the skill areas necessary to master the concepts introduced in a course of second-level algebraReviewing concepts presented in beginning algebra plus exercises involving slope, intercepts, graphing linear inequalities, domain and range, graphing exponential functions, matrix operations, quadratic equations and much moreExamples of solution methods are presented at the top of each pageNew puzzles and riddles have been added to gauge the success of skills learned Contains complete answer key
Product Information
Subject :
Algebra
Grade Level(s) :
5-8
Usage Ideas :
Activities were designed to provide students with practice in the skill areas necessary to master the concepts presented in a second-level course in algebra |
Solvers
Information about the solvers in AIMMS such as the default solvers and extensions, the available math program types, a comparison between the Linear Programming and Mixed Integer Programming solvers and an explanation of the mathematical program abbreviations. |
Applied Calculus (looseleaf) - 4th edition
Summary: APPLIED CALCULUS, 4/E exhibits the same strengths from earlier editions including the "Rule of Four", an emphasis on concepts and modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.
The fourth edition gives readers the skills to apply calculus on the job. It highlights the appl...show moreications' connection with real-world concerns. The problems take advantage of computers and graphing calculators to help them think mathematically. The applied exercises challenge them to apply the math they have learned in new ways. This develops their capacity for modeling in a way that the usual exercises patterned after similar solved examples cannot do. The material is also presented in a way to help business professionals decide when to use technology, which empowers them to learn what calculators/computers can and cannot do |
I believe having a good foundation in pure math is very, very helpful for approaching applied math (in my experience, and as my teachers have also taught me). I believe the more math you know, the better off you will be.
To address your question on how much pure math to learn, I suggest at the very minimum the following: Real Analysis , Basic Functional Analysis, Graduate Real Analysis (Lebesgue Integration, Measure Theory, Lp Spaces), some familiarity with point set topology, and some familiarity with basic algebra.
To reiterate, learn your real analysis first. If you have absolutely zero background in proving things, start with a nice introductory book such as Elementary Analysis by Ross, which is an excellent introduction to analysis. Then, work your way up to a typical undergraduate course in real analysis (especially focus on the concepts of pointwise and uniform convergence of functions), which I personally strongly recommend N. L. Carothers extremely affordable and phenomenal textbook titled Real Analysis. Others will recommend Walter Rudin's Principles of Mathematical Analysis, and it is also quite good, but I prefer Carothers. These subjects will show you how calculus really works, and how the concept of convergence of functions works, which is very important for approximation theory, PDEs, etc. The reason these concepts are important is because in applied math (at least for me), we typically want to guess a function by using functions from some finite dimensional subspace (as in finite elements or other forms of approximation theory), so we want to have a solid, rigorous and meaningful way of saying "This approximate guess we constructed from our numerical algorithm will be very close to the true function we want to approximate".
Once you know these subjects, try out Kreyszig's Functional Analysis book, so you learn about the appropriate spaces to do analysis. All three fields you highlighted (Inverse problems, PDEs, Approximation Theory) rely on real and functional analysis, so learn it! If you're feeling up to it, approach graduate real analysis to learn measure theory and the Lebesgue integral (which will give you a solid footing in the concept of Lp spaces, which are spaces of functions often used in PDEs and numerical analysis). I recommend Folland's analysis book.
I personally really enjoy topology, so I'd say give Munkres Topology book a whirl and see if you enjoy it. I recommend this because its a wonderful subject and because it is important if you want to pursue any differential geometry (which has many, many applications! Physics uses this constantly).
You should be at least familiar with some basic algebra (groups, rings, fields), but I personally don't use too much algebra (at least, not explicitly). However, I would never say "don't learn it", because you'd be shocked at where these things pop up. Also, if you happen to take an interest in cryptography or computational algebraic geometry, this will be fundamental. I'll let someone else recommend a good introductory algebra textbook.
Elsewhere in this post, myFriendsCallmeRaz recommended going to the library and checking out Keener's book Principles of Applied Mathematics. I used this book for two semesters, and personally detest the writing, and yet I still completely agree with his suggestion. I don't like how its written, but it contains an incredible amount of information. It will teach you basic functional analysis and operator theory, calculus of variations, and more importantly, why we care about these fields. These are all pure topics, but you can use them to understand how to solve PDEs, how to construct a numerical algorithm to solve PDEs( the Galerkin method follows from results in functional analysis), learn how to mathematically derive the way a wire sags between two poles (calculus of variations, catenary), and other things.
Once you feel comfortable with all of this (this will take a long time!), you will have your basics down, and you will understand the fundamental language used in subjects like approximation theory and PDEs. I'm not saying you'll be able to pick up a paper in approximation theory and say "Ah, how clear", but you will have the basic tools down. Knowing your basics is crucial!
In that, do you not think that going into Applied Math to begin with is good enough?
I'm not exactly sure how to interpret this. I enrolled in a Ph.D. program and my program is just "Mathematics".I know some schools have separate "applied math" programs, and I honestly can't comment on them because I'm not familiar with them. When considering applying for a Ph.D. program, you should be very careful and study the school and how their program works. I can't comment on them, because there are so many and I really only know how my school works. At my school, however, I took the same breadth courses as any typical pure math student and was in no way separated as an "applied" student until I chose an adviser in an applied field (approximation theory, which the more I learn about, feels more and more pure to me). In my experience, my pure math classes have been helpful to me, not a hindrance. The only downside to the way I approached things is that I did not take many computational sort of classes which emphasize programming and scientific computation, so I have had to pick that up on my own. Hopefully other students in an Applied Math Ph.D. program can discuss how their programs work.
Feel free to ask any more questions (especially if you want some clarification on analysis, approx theory, etc.). Good luck! |
Analytic Trigonometry Lesson 1: Fundamental Identities begin the journey into Analytic Trigonometry through exploring basic identities. This lesson contains an eight-page "bound book" style Foldable (C) with an accompanied SmartBoard lesson. There is also a *.pdf file of the completed Foldable and Smart Notes. This teaching method minimizes wasted class time since the "skeleton" of the lesson is pre-printed. Students stay engage and focused.
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing.
2156.5 |
Be aware of the need for mathematical theory to support numerical problem solving techniques.
Understand the relationship between the theoretical solution of a problem and a computational solution.
Extend his/her mathematical abilities in linear algebra and analysis.
Construct programs and use current mathematical programming tools such as LINPACK and the International Mathematical and Statistical Library (IMSL) to solve problems involving systems of equations, interpolation and least squares approximation of functions.
COURSE OUTLINE:
Floating Point Arithmetic and Rounding Errors
Taylor's Theorem
Non-linear Equations
Solution of Systems of Linear Equations Using Direct and Iterative Methods, Error Analysis and Norms |
Weatherly StatisticsThe understanding of the importance of the applications of linear algebra to many different fields has grown significantly in recent years. As a result, students in many different majors are now required to complete linear algebra courses. I completed the basic undergraduate linear algebra course (for math majors) while obtaining my Bachelor's degree in math |
TI-34 MultiView scientific calculator was designed with educator input in mind for use in these middle grades math and science classes: Middle School Math, Pre-Algebra, Algebra I & II, Trigonometry, General Science, Geometry and Biology.
In Classic mode, the TI-34 MultiView can be used in the same classrooms as the TI-34 II Explorer Plus as the screen appears identical to the TI-34 II Explorer Plus in this mode.
MultiView Display View multiple calculations on a 4-line display and scroll through entries with ease. See math expressions and symbols, including stacked fractions, exactly as they appear in textbooks
Fraction Exploration The TI-34 MultiView scientific calculator comes with the same features that made the TI-34 II Explorer Plus so helpful at exploring fraction simplification, integer division and constant operators.
Data List Editor Enter statistical data for 1- and 2-var analysis as well as for exploring patterns via list conversions to see different number formats like decimal, fraction and percent side-by-side.
Scrolling & Editing Scroll through entries with ease. Students can investigate patterns similar to using a graphing calculator.
Learn more about the Texas Instruments TI-34 MultiView (34MV/TKT/1L1/A)
General
Brand
Texas Instruments
Model
TI-34 MultiView (34MV/TKT/1L1/A)
SellingUnit
Pack
Package Includes
10-unit EZ Spot yellow calculators
Storage caddy
Teacher's Guide in English and Spanish
Calculator poster and transparency
Feature
Features
The TI-34 MultiView scientific calculator was designed with educator input in mind for use in these middle grades math and science classes: - Middle School Math - Pre-Algebra - Algebra I & II - Trigonometry - General Science - Geometry - Biology
In Classic mode, the TI-34 MultiView can be used in the same classrooms as the TI-34 II Explorer PlusTM as the screen appears identical to the TI-34 II Explorer Plus in this mode.
Data List Editor: Enter statistical data for 1- and 2-var analysis as well as for exploring patterns via list conversions to see different number formats like decimal, fraction and percent side-by-side.
Scrolling & Editing: Scroll through entries with ease. Students can investigate patterns similar to using a graphing calculator.
Previous Entry
User-Friendly Menus
Power, Roots, and Reciprocals
Exact Radicals
One and Two Variable Statistics
7 Memories
Spec
Display Characters x Display Lines
16 x 4
Display Notation
Algebraic
Global Product Type
Calculators-Scientific
Number of Display Digits [Nom]
16
Power Source(s)
Battery, Solar |
College Algebra and Trigonometry, CourseSmart eTextbook, 5th Edition
Description
College Algebra and Trigonometry, Fifth Edition, by Lial, Hornsby, Schneider, and Daniels, engages and supports students in the learning process by developing both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Fifth Edition, the authors recognize that students are learning in new ways, and that the classroom is evolving. The Lial team is now offering a new suite of resources to support today's instructors and students.
New co-author Callie Daniels has experience in all classroom types including traditional, hybrid and online courses, which has driven the new MyMathLab features. For example, MyNotes provide structure for student note-taking, and Interactive Chapter Summaries allow students to quiz themselves in interactive examples on key vocabulary, symbols and concepts. Daniels' experience, coupled with the long-time successful approach of the Lial series, has helped to more tightly integrate the text with online learning than ever before.
Table of Contents
R. Review of Basic Concepts
R.1 Sets
R.2 Real Numbers and Their Properties
R.3 Polynomials
R.4 Factoring Polynomials
R.5 Rational Expressions
R.6 Rational Exponents
R.7 Radical Expressions
1. Equations and Inequalities
1.1 Linear Equations
1.2 Applications and Modeling with Linear Equations
1.3 Complex Numbers
1.4 Quadratic Equations
1.5 Applications and Modeling with Quadratic Equations
1.6 Other Types of Equations and Applications
1.7 Inequalities
1.8 Absolute Value Equations and Inequalities
2. Graphs and Functions
2.1 Rectangular Coordinates and Graphs
2.2 Circles
2.3 Functions
2.4 Linear Functions
2.5 Equations of Lines and Linear Models
2.6 Graphs of Basic Functions
2.7 Graphing Techniques
2.8 Function Operations and Composition
3. Polynomial and Rational Functions
3.1 Quadratic Functions and Models
3.2 Synthetic Division
3.3 Zeros of Polynomial Functions
3.4 Polynomial Functions: Graphs, Applications, and Models
3.5 Rational Functions: Graphs, Applications, and Models
3.6 Variation
4. Inverse, Exponential, and Logarithmic Functions
4.1 Inverse Functions
4.2 Exponential Functions
4.3 Logarithmic Functions
4.4 Evaluating Logarithms and the Change-of-Base Theorem
4.5 Exponential and Logarithmic Equations
4.6 Applications and Models of Exponential Growth and Decay
5. Trigonometric Functions
5.1 Angles
5.2 Trigonometric Functions
5.3 Evaluating Trigonometric Functions
5.4 Solving Right Triangles
6. The Circular Functions and Their Graphs
6.1 Radian Measure
6.2 The Unit Circle and Circular Functions
6.3 Graphs of the Sine and Cosine Functions
6.4 Translations of the Graphs of the Sine and Cosine Functions
6.5 Graphs of the Tangent, Cotangent, Secant, and Cosecant
6.6 Harmonic Motion
7. Trigonometric Identities and Equations
7.1 Fundamental Identities
7.2 Verifying Trigonometric Identities
7.3 Sum and Difference Identities
7.4 Double-Angle and Half-Angle Identities
7.5 Inverse Circular Functions
7.6 Trigonometric Equations
7.7 Equations Involving Inverse Trigonometric Functions
8. Applications of Trigonometry
8.1 The Law of Sines
8.2 The Law of Cosines
8.3 Vectors, Operation, and the Dot Product
8.4 Applications of Vectors
8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
8.6 De Moivre's Theorem; Powers and Roots of Complex Numbers
8.7 Polar Equations and Graphs
8.8 Parametic Equations, Graphs, and Applications
9. Systems and Matrices
9.1 Systems of Linear Equations
9.2 Matrix Solution of Linear Systems
9.3 Determinant Solution of Linear Systems
9.4 Partial Fractions
9.5 Nonlinear Systems of Equations
9.6 Systems of Inequalities and Linear Programming
9.7 Properties of Matrices
9.8 Matrix Inverses
10. Analytic Geometry
10.1 Parabolas
10.2 Ellipses
10.3 Hyperbolas
10.4 Summary of the Conic Sections
11. Further Topics in Algebra
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
11.4 The Binomial Theorem
11.5 Mathematical Induction
11.6 Counting Theory
11.7 Basics of Probability
Appendices
Appendix A. Polar Form of Conic Sections
Appendix B. Rotation of Axes
Appendix C. Geometry Formulas
Glossary
Solutions to Selected Exercises
Answers to Selected Exercises
Index of Applications
Index
Photo Credits |
The first analysis course I ever took used the book "Elementary Analysis" by Ross. It's basically baby-baby-Rudin. Ross's book (if you include the exercises and the optional sections) covers more or less the same material as the first 8 chapters of baby-Rudin, but the exposition is much friendlier and it's more easy-going for a beginner. When I say "beginner" here I really mean beginner -- someone who has never even written a rigorous mathematical proof. The book would probably be very boring and tedious for someone above this level. |
Recommendations...
Elementary Number Theory: Second Edition by Underwood Dudley Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 editionProducts in Number Theory
Advanced Number Theory by Harvey Cohn Eminent mathematician/teacher approaches algebraic number theory from historical standpoint. Demonstrates how concepts, definitions, and theories have evolved during last two centuries. Features over 200 problems and specific theorems. Includes numerous graphs and tables.
Our Price:$12.95Our Price:$10.95Our Price:$8.95
A Course in Algebraic Number Theory by Robert B. Ash Graduate-level course covers the general theory of factorization of ideals in Dedekind domains, the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.Our Price:$14.95
Elementary Number Theory: Second Edition by Underwood Dudley Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition.
Essays on the Theory of Numbers by Richard Dedekind Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.
Our Price:$8.95Our Price:$9.95The Number System by H. A. Thurston This book explores arithmetic's underlying concepts and their logical development, in addition to a detailed, systematic construction of the number systems of rational, real, and complex numbers. 1956 editionOur Price:$12.95 |
Success in these topics that comprise 5thgrade math is important if students are to be successful at higher levels.It is designed tointegrated and distributed strands of mathematical learning in order to achieve maximum long-term retention of mathematical skills and concepts.
Course Description:6thGrade Mathematics is an integration of problem solving, notetaking and assessment strategies that will help the students succeed in reasoning and proof, communication, connections and representation. 6thGrade Mathematics will mainly deal with Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability. The students will be able to further develop their skills in number sense, estimation, number operations, ratios and proportional reasoning, and properties of number and operations covered by 'Number and Operations.' On the other hand, 'Algebra' will specifically deal with patterns, relations and functions, algebraic representations, variables, expressions, and operations, and equations and inequalities. Under 'Geometry,' the lessons on dimension and shape, transformation of shapes and preservation of properties, relationships between geometric figures, position and direction, and mathematical reasoning will be discussed. 'Measurement' will enable students to measure physical attributes and know the systems of measurement. Finally, 'Data Analysis and Probability' will help students understand data representation, characteristics of data sets, experiments and samples and probability. |
Course Outline
This course is an exploration of great ideas in mathematics. The course will feature a variety of interesting mathematical topics accessible to the intelligent layperson. Topics will include infinity, paradox, dimension, Möbius strips, fractals, recursion, trees, space, and other topics. Students will write a non-technical paper, make a presentation on a mathematical topic, and keep a journal which summarizes their progress as well as their difficulties in understanding the topics of the course.
Textbook
Assignments
The homework problems do not require mathematical training, but they are challenging and require deep thought and independent thinking. They emphasize reasoning rather than technique. Late assignments are not accepted. It is better to hand in something incomplete than nothing at all. Do not, under any circumstances, make it seem complete (by writing nonsense) if you know it is not.
Click on the assignments below, login to google docs, and make your own copy of the assignment and then share your assignment with me (allowing me to comment) on google docs. I don't want a printout.
Question site
The question site for this course is located here. Please participate in the discussion by asking and answering questions on here.
Join the site, and enter your full name where it asks you to. I will be there regularly to answer questions, and your classmates will hopefully do the same.
Evaluation
Class participation: 10%
Assignments: 30%
Final project: 60%
Final project
The final project is an opportunity to explore independently a topic of your choosing in mathematics. You should aim for the style to be that of a popular science writer, such as these feature columns of the AMS, the columns of S. Strogatz in the NY Times, or the science writing of J. Bohannon. You would also benefit from the very interesting videos by Vi Hart. There are many fascinating topics in the textbook which we will not have time to cover, and you may use the book as a starting point for finding more resources.
The format is a 4000-5000 words document shared with me by google docs. The document will be developed in three stages:
(20%) Feb 16: Decide on a topic and submit a single page containing:
a (grammatically correct!) single paragraph topic description
a diagram of the possible structure of the paper including sections, subsections, and the purpose of each subsection (they could be examples, arguments, evidence, etc.)
a list of at least two references which will be used, besdies the textbook.
(40%) Mar 15: Submit a complete first draft on google docs. I will be marking with the following three criteria in mind:
Clarity of overall document structure: each part must have a clear purpose and must contribute to the whole paper.
Quality of the mathematical explanations: would this make sense to the average non-math student? Is the reasoning correct?
Quality of the language: Are the sentences carefully constructed? Are there spelling/grammar errors? Is it written in an engaging style?
(40%) March 29: Submit the final draft. I will comment on your first draft, and so will another student in the class. These issues must be addressed, and you must make your own improvements as well. The overall quality of the paper will be assessed using the same criteria as above.
Some ideas for final project topics: Projective geometry and the Renaissance, Special relativity and Minkowski space, Polytopes and the work of H. S. M. Coxeter, Sorting algorithms, Colour space, Voronoi diagrams and clustering, the Quaternions, Tessellations of the plane, The projective plane, the Dirac belt trick, the complex numbers and the Riemann sphere, combing the hair on a sphere... |
This is a mathematics course typically taken after Algebra 1. In this course, students will learn about geometrical shapes. They will apply geometrical mathematical concepts to hands on real life activities. |
quiz4
Course: MATH 1132, Fall 2009 School: UConn Rating:
Document Preview 7 Solutions s
Name: Math 1132 Section 4 Spring 2009 Quiz 5: Series Directions: There are two sides to this quiz. Clearly show your work and indicate your answers. 1. (4 pts) Circle T if the following statement is true and F if the statement is false. No justifica
Math 1132 Spring 2009 11.7 Homework Solutions1. Test the series for convergence or divergence.(1)nn=19n n+9Solution: The series is alternating, so lets try using the alternating series test. Condition (ii) is usually easier to verify:nli
Quiz 7 seriesn=1
Study Guide for the Final Exam The nal exam is comprehensive. It covers all the sections that we covered in class. This is: The review of Chapter 5. All of Chapter 6. Sections 7.1, 7.2, 7.3 (I guarantee at least one problem about work), and 7.4.
Josephson Effects and a -State in Superfluid HeliumPaul B. Welander May 6, 2002Abstract In this paper, I shall discuss the recent discovery of a metastable -state in a 3 He Josephson junction. This state is characterized by low frequency current os
CATALOG DESCRIPTION Graduate Certificate Program Graduate Certificate in NeuroscienceGeneral Information Neuroscience constitutes a truly interdisciplinary area of scientific study and research that incorporates physiology, molecular and cellular bi
CS 598CSC: Approximation Algorithms Instructor: Chandra ChekuriLecture date: April 15, 2009 Scribe: Qiang MaIn computer science, when dealing with dicult problems involving graphs and their associated metrics, one technique we usually resort to i
Exam 2 1.Math 115Fall 2007(15 pts) For each part, if the statement is always true, circle the printed capital T. If the statement is sometimes false, circle the printed capital F. For each T/F question, write a careful and clear justication or
Name Math 227 Exam 3: 1 May 2006Directions. Read each question on this exam before you start working so you can get the avor of the questions. If you arent sure what the question is asking for, its possible I can clarify for you. Please show all |
algebra
Tag details
Algebra is one of the basic building blocks to learning mathematics at a higher level.
According to Answers.com, the primary definition of algebra is "A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set." Within algebra, there are several categories within the discipline, including elementary algebra, abstract algebra, linear algebra, universal algebra, algebraic number theory, algebraic geometry, and algebraic combinatorics.
Latest blogosphere posts tagged "algebra"
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by edshelf: Reviews & recommendations of tools for education Trapper Hallam is a math teacher at Eisenhower High School that integrates technology seamlessly into his classroom. Among the websites and mobile apps that he recommends for Algebra... The post The Latest Math Apps: 15 Algebra 1 Tools From edshelf ...
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Öffnet 16. Mai in Berlin in der FSK-Kino unter dem poetischen Titel "Algebra in Love." Whit Stillman's Damsels in Distress (known as Algebra in Love in Germany), is opening in Berlin on May 16th at the FSK-KinoAlgebra 2 may be falling out of political favor in another state, this time Michigan. A Michigan House committee this month approved changes to state graduation requirements, including allowing students to skip Algebra 2 if they instead take a career and technical education course, the Associated Press reports . ...
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Motivation is important when you want to Improve your math skills You don't have to be born with math skills; solving problems is a matter of studying and motivation.That may not seem like such a surprise, but it's become easy to say 'I just can't do math.' While some element of math achievement may be [...]
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Dave brings Elihu Feustel on the show today to dig into the numbers behind his mathematical approach to sports betting. Elihu is a professional sports gambler, lecturer and author of the book Conquering Risk: Attacking Vegas and Wall Street.Elihu has a vast background in statistical analysis and specialises inOnly 5 percent of students will use calculus in college or the workplace, concludes a new report on college and career readiness by the National Center on Education and the Economy . Most community college students could succeed in college courses if they've mastered "middle school mathematics, especially ...
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Overview: Solving Linear Systems In order to solve systems of two sentences, the solution has to be true for both sentences. For example, the solution of a problem such as 2x-3y=13 and 3x +y = 3 has to work fox x and y all throughout the problem. Linear systems can be solved by graphing, by substitution, and byOverview: What Are Relations and Functions? A relation in algebra is a set of ordered pairs. The first element of the ordered pair is the domain, and the second element in the ordered pair is the range. If every first element is paired with only one second element, or every domain has a range, it is a function. ...
Combinatorics and more
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Margulis' paper Ramanujan graphs were constructed independently by Margulis and by Lubotzky, Philips and Sarnak (who also coined the name). The picture above shows Margulis' paper where the graphs are defined and their girth is studied. (I will come back to the question about girth at the end of the post.) ...
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Out in Left Field proudly presents the twelth in a series of letters by an aspiring math teacher formerly known as "John Dewey." All personal and place names have been changed to protect privacy. Dedicated readers of my letters may recall my reaction to the Common Core's "Standards for—
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Logical connectives (Photo credit: Cuito Cuanavale) In their infinity of appearance, numbers can be clothed in the generality and variability of letters. Then their difference in value is hushed over, covered up. Except in those languages where letters and numerals do have the same value – as it was in Ancient ...
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When you go to college, math becomes more complicated that you will find a hard time to understand it. If you search for help with solving college algebra problems, you can choose online tutoring as the most flexible option. Not only you can get the online tutoring anywhere you are, but also you can get [...]
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Overview: What Is a Conic Section? Conic sections are the curves formed when a right circular cone intersects with a plane. The angle that the plane makes when it "cuts through" the cone determines the shape of the section. The four main types of conic sections are the circle, the parabola, the ...
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Algebra Printable Book (9-12)
Page Description:
Make sure your high-school students have mastered the basics of algebra with this printable book. Students will practice problem solving, quadratic equations, polynomials, statistics and more.
Grade Levels: 9 |
Welcome to the Mathematics Research Guide!
WELCOME to the Mathematics Research Guide! This guide is designed to help students of Mathematics and Education students who are learning to teach students about math. Through this guide, you will learn to locate books and reference materials in mathematics, curriculum materials on math, and databases for articles about math topics. |
Flovilla CalculusAs a college student I am very adept with Microsoft PowerPoint. I have even made one to go to a college level honors society convention. I use it regularly and try to keep myself as up to date as possible on it...I am a talented, energetic, fun, demanding teacher. Students respond well to my teaching and sense of humor. I somehow make math and physics and engineering "cool."
In fact, on the website "ratemyteacher? I have the highest rating at my school where former students state "Rit is the best teac...
...Complex Numbers Here is a very quick primer on complex numbers and how to manipulate them. Solving Equations and Inequalities
Solutions and Solution Sets We introduce some of the basic notation and ideas involved in solving in this section. Linear Equations In this section we will solve linear equations, including equations with rational expressions. |
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Newsflash
Trion City Schools expands their educational technology integration through the use of mobile computing devices such as laptop computers, netbooks, and iPod Touches.
Math Program at THS
Lunes 09 de Febrero de 2009 14:57
Mathematics is the academic discipline that involves the study of such concepts as quantity, structure, space and change. Mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Knowledge and use of basic mathematics have always been a part of individual and group life.
For classes slated to graduate in 2009, 2010, or 2011, the math courses taken by a student will depend on whether the student is pursuing a college prep or tech prep diploma. These courses are based on Georgia's Quality Core Curriculum objectives. They include:
Pre-Algebra (Tech & Career)
Algebra I (College Prep)
Algebra I (Tech & Career)
Euclidean Geometry (Either level)
Algebra II (College Prep)
Algebra III (College Prep)
Trigonometry (College Prep)
Math Money Management (Either level)
Pre-Calculus (College Prep)
AP Calculus (College Prep)
For classes scheduled to graduate in 2012 and after, students will be taking courses aligned with Georgia's Performance Standards. Those courses include: |
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Algebra Readiness Course
Algebra Readiness Curriculum Overview
The Pitsco Education Algebra Readiness curriculum is specifically designed to provide students with a deeper and more refined understanding of fundamental mathematics in preparation for achieving success when they encounter the more abstract algebraic concepts in Algebra I. Its design and delivery methodology successfully provide students with a coherent focus on core mathematical concepts while providing relevant connections and hands-on opportunities to apply what they learn and successfully develop skill proficiency. |
Policies
Fred's Home Companion: Beginning Algebra
$14.00
Lesson plans for those studying Life of Fred: Beginning Algebra on their own. Each lesson offers you a "daily helping" of Fred.
Multiple Uses!
Lecture notes for those teaching Life of Fred: Beginning Algebra. Outlines for each lecture. Problems to present at the blackboard that are not in the textbook. Additional insights to present in class. Quiz and test material.
Answer key for Life of Fred: Beginning Algebra.
Additional exercises for those who want more drill. All answers are included. |
'ÄĒ Stewarts other calculus texts, and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the books website, Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewarts other books. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewarts textbooks the best-selling calculus texts in the world |
Use of Variables
Using segments and web interactives from Get the Math, this lesson helps students see how Algebra I can be applied to the world of fashion, challenging them to use algebraic concepts and reasoning to modify garments and meet target price points.
Using segments and web interactives from Get the Math, this lesson helps students see how Algebra I can be applied in the music world, challenging them to use algebraic concepts and reasoning to calculate the tempos of different music samples.
7-10
Self-paced Lesson
RESULTS 1-2 OF 2
Major funding for Teachers' Domain was provided by the National Science Foundation. |
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JOde: A Java Applet for Studying Ordinary Differential Equations
Course Topic(s):
Ordinary Differential Equations | Graphic Methods
A Java applet that allows one to interactively analyze systems of differential equations. It was designed to be a convenient aid in teaching differential equations, but is also useful for students. The webpage contains both a tutorial and complete instructions, and links to several different configurations of JOde for both 2D and 3D systems as well as several specific examples for population dynamics, circuits, tsunamis,two-body problem, and Van der Pol equation. |
Algebra 1 Resources Subscription is a creative
collection of over 370 (and growing) printable and multi-media materials to be used with students
studying a first year of high school level algebra. These resources are designed to be used by
teachers and parents to energize students'
mathematical experiences with algebra.
With over 60 years of combined teaching
experience (to date), we offer to you all of our creative,
engaging, and exciting materials which have
been, and continue to be, successful in the
mathematics classroom. We have also
included materials we have shared with other
educators at teacher conferences and workshops
along with some of our personal teaching
strategies and suggestions.
We chose this subscription format because it allows us to continually add and update materials. In addition, the subscription format brings you the largest number of materials in the most cost effective way.
Additions relating to the Common Core State Standards for Mathematics have begun. This site will be changed to full CCSS compatibility in the summer of 2013.
Click to see larger view
of our ad page.
The Algebra 1 ResourcesSubscription includes:
- creative, content specific worksheets,
activities, puzzles.
- a range of
materials appropriate for all levels of
learners.
- the "Ah-Bach" Series content-related worksheet
puzzles.
- the "Let Go of the Eggo" Series content-related worksheets.
- materials for best utilizing the TI-83/84+/Nspire calculator.
- directions and activities for using calculator
peripherals.
- directions for making inexpensive classroom manipulatives.
- on-line interactive games/activities for classroom use.
As an Algebra 1 Resources subscriber, you may request that
certain materials be personalized to meet your needs.
While we cannot guarantee that we will be able to grant all of
your requests, we will do our best to address reasonable
changes.
The Algebra 1 Subscription materials are compatible
with all Algebra 1 curricula,
including the new NYS Integrated Algebra curriculum.
The "Warm-up" level materials (as well as other
activities) are also appropriate for Intermediate level (Middle School) students.
The following samples will give you a flavor of the over
370 (and growing) worksheets, activities and
interactive materials
in the subscription area.
All sample materialsbelow are
to be used only byindividual teachers in their face-to-face classrooms.
These materials are not public domain and are
not to be re-posted to
the internet, distributed at conferences or
workshops, or sold in any form. Such
use is a violation of copyright law and is not considered "fair use".
Please refer to
the complete Terms of Use.
Worksheet (2 pages) for graphing
inequalities in a humorous setting of water splashing over surfers. To be done with,
or without,
a graphing
calculator. When done with the calculator, students practice
transferring results accurately to a labeled set of axes.
Worksheet for using the graphing calculator to
investigate the concept of slope. Students must accurately transfer from calculator to
labeled axes. Available for both TI-83+/84+ and TI-Nspire in
the subscription area. Accompanying note sheet on slope is included. (A .gsp file for Geometer's
Sketchpad is also available for"Hitting the Slopes with Ski Bird".) |
This activity would be done at the end of the school year in a pre-algebra class. It is a way to introduce algebra and its history, putting some personality into the abstractness of the subject by researching the individuals behind algebraic concepts. It was initially found on the following site five years ago when I first did it with my classes: It has since disappeared, however, so the specific modifications I made at the time are fuzzy at best, but I have made recent adjustments to every portion.
Introduction:
Algebra, what does it mean? Where did it come from? Who thought up this stuff? Have you ever wondered what the word algebra means or when and where algebra was developed or who developed algebraic concepts? In this project your group will go on a journey through time and the history of mathematics to discover the answers to these questions.
Task:
Each group will go on a quest to find the mathematicians' histories that have named as being the fathers or founders of algebra. On this journey your group will collect information about the mathematician responsible for developing the algebraic concept assigned to your group, create a timeline to show when the concept was developed in relation to other significant events in history, and find examples of the algebraic concept. Each group will prepare a Powerpoint to present the information to the class.
Group I The Father of Algebra (Algebraic thought and equations)
Group II Founder of Cartesian Plane and Graphing Equations
Group III Developer of Polynomials
Group IV Set Notation and Venn Diagrams Designer
Each group will need a Researcher, Recorder, Mathematician, and a Reporter.
Researcher - Using the resources below, work with the Recorder to find and record needed information for your topic.
Recorder - Record information on your topic and citation for where the information was found. Work with the Researcher and the Reporter to prepare a report of the findings of your group.
Mathematician - Work with the Researcher and the Recorder to find examples of mathematical problems from your assigned topic. Choose two examples that you can share, with which you can demonstrate the topic for the class.
Reporter - Work with the other members of your group to create a presentation, using PowerPoint, which you will present to the class. |
Mathematics Courses
MATH 020 1-5
credits
Mathematics Center 1
This course covers basic fundamentals of arithmetic including whole numbers, fractions, decimals, ratios, proportions and percentages. It is offered as a variable credit individualized program and designed for students who have a limited background in math.
Math Prep for the Sciences
This course provides a mathematical foundation for students who will be taking introductory science courses. Subjects covered include the metric system, dimensional analysis, scientific notation, significant figures using a scientific calculator, and translating word problems from all areas of science.
MATH 090 5
credits
Pre-Algebra
A course intended for students who have studied arithmetic but who are not ready for elementary algebra. Numerous introductory topics from grades 9 through 12 are covered which may include operations with signed numbers and rational numbers, simple algebraic equations, properties of real numbers, prime numbers and factoring, exponents and roots, geometric concepts, basic graphs, metrics, basic inequalities, or absolute value. Prerequisite: MATH 021 with 2.0 or better or appropriate placement score.
MATH 091 5
credits
Elementary Algebra I
This course covers beginning algebra concepts for students without high school algebra or those who need a review. Topics will include real numbers, algebraic expressions, equations and inequalities, polynomials and graphing. Other topics may include factoring. Prerequisite: MATH 021 or 090 with a 2.0 or better within the last three years; or appropriate placement score.
MATH 092 5
credits
Elementary Algebra II
This course is a continuation of MATH 091. Topics include factoring, rational expressions, linear equations in two variables and systems of equations. Other topics may include radicals and quadratic equations. Prerequisite: MATH 091 with a 2.0 or better within the last three years; or appropriate placement score.
MATH 095 1-5
credits
Mathematics Center 2
This course reviews arithmetic and pre-algebra and is offered as a variable credit individualized program in the Math Center for students preparing to take algebra. Prerequisite: Counselor or instructor referral.
MATH 096 5
credits
Introductory Algebra
This course covers introductory algebra skills. Topics include signed numbers, linear equations, graphing linear equations, linear systems of equations, polynomials and rational expressions. This course is designed for students who need a review of high school algebra. Prerequisite: MATH 021 or 090 with a 3.0 or better within the last three years; or appropriate placement score.
MATH 097 5
credits
Intermediate Algebra: A Modeling Approach
This course covers intermediate algebra skills through a modeling approach. Topics include linear, quadratic and exponential functions, and introductions to geometry, probability, sequences and statistics. Prerequisite: MATH 091 and 092 or MATH 096 with a 2.0 or better within the last three years; or appropriate placement score.
MATH 099 5
credits
Intermediate Algebra
This course covers intermediate algebra skills. Topics include a review of beginning algebra concepts, radicals, inequalities, functions and quadratic functions. Other topics may include exponential and logarithmic functions. Prerequisite: MATH 091 and 092 or 096 with a 2.0 or better within the last three years; or appropriate placement score.
MATH 100 1-6
credits
Vocational Technical Mathematics
Basic mathematics from whole numbers through elementary algebra and triangle trigonometry to fulfill the needs of professional/technical students at their current mathematical level. Courses are offered and objectives and credits determined by contract between math department and the requesting professional/technical program. Prerequisite: Registration in the requesting vocational area or permission of instructor.
MATH& 107 5
credits
Math in Society
This course is an option for students needing to satisfy a post-intermediate algebra requirement in which the field of study does not necessitate a specific course. Traditional coursework is combined with a discussion of what mathematics is and does, in addition to an examination of problem-solving techniques. Specific topics may vary at the discretion of the instructor. Prerequisite: MATH 097, 098 or 099 with a 2.0 or better within the last three years or appropriate placement score.
MATH 108 3
credits
College Algebra
This course bridges the gap between Intermediate Algebra and the next higher level math classes, specifically Pre-calculus. Topics in this course include, but are not limited to, functions, graphing, exponents, radicals, algebraic fractions, equations, inequalities, and various applications including the use of the graphing calculator. Course is not intended for students who have earned at least a 3.0 in MATH 099 or a 3.0 in MATH 098. Prerequisite: MATH 097, 098 or 099 with a 2.0 or better within the last three years or appropriate placement score.
MATH& 141 5
credits
Precalculus I
This course covers college algebra skills, which include polynomial, rational, exponential and logarithmic functions, systems of equations and matrix solutions, and graphs of polynomial functions. Other topics may include sequences, series and summations. Prerequisite: MATH 098 or MATH 099 with a 3.0 or better within the last three years or MATH 108 with a 2.0 or better within the last three years or appropriate placement score. College level reading scores recommended at SFCC.
MATH& 142 5
credits
Precalculus II
This course introduces circular functions and analytic trigonometry needed for further study in mathematics. Other topics include sequences and series, mathematical induction, conic sections, rotation and translation of axes, DeMoivre's theorem and nth roots of complex numbers, or vectors in the plane. Prerequisite: MATH& 141 with a 2.0 or better within the last three years; or appropriate placement score.
MATH& 148 5
credits
Business Calculus
A one-quarter introduction to differential and integral calculus. Specifically oriented for students in management, life sciences and social sciences. Prerequisite: MATH& 141 or MATH 201 with a 2.0 or better within the last three years; or appropriate placement score.
MATH& 151 5
credits
Calculus I
This is the first quarter of a three-quarter course in calculus and analytic geometry. This course includes an introduction to limits, rates of change and continuity. The course also deals with the definition of derivative of a function and rules of differentiation, curve sketching and other application of differentiation, introduction to integrals and the Fundamental Theorem of Calculus. Prerequisite: MATH& 141 and MATH& 142 with a 2.0 or better within the last three years; or appropriate placement score.
MATH& 152 5
credits
Calculus II
This is the second quarter of a three-quarter course in calculus and analytic geometry. This course also includes applications of integration, derivatives and integrals of exponential, logarithmic and the trigonometric functions, derivatives and integrals of hyperbolic functions and their inverses, indeterminate forms and L'Hopital's Rule, and techniques of integration. Other topics may include vectors and the geometry of space. Prerequisite: MATH& 151 with a 2.0 or better.
MATH& 153 5
credits
Calculus III
This is the third quarter of a three-quarter course in calculus and analytic geometry. This course includes an introduction to differential equations; parametric equations; polar, cylindrical and spherical coordinates; infinite sequences and series. Cylindrical and quadric surfaces, vector valued functions and their space curves, and derivatives and integrals of vector functions also are discussed. Prerequisite: MATH& 152 with a 2.0 or better.
MATH 201 5
credits
Introduction to Finite Mathematics
This course covers basics of mathematical models, including linear, quadratic and polynomial functions, systems of linear equations and inequalities, linear programming and matrices. Elementary concepts of probability and simulation are introduced. Particular emphasis is placed on business and social applications. Prerequisite: MATH 097, 098 or 099 with a 2.0 or better within the last three years; or appropriate placement score. College level reading scores recommended.
MATH 208 5
credits
Mathematics for Elementary Education - A
This is the first course in a three course sequence designed for prospective teachers at the elementary school level, focusing on the following topics: Problem solving, set theory, elementary logic, numeration systems, number theory, and the structure of the system of real numbers. Prerequisite: MATH 097, 098 or 099 with a 2.0 or better; or appropriate placement score. College level reading score recommended.
MATH 209 5
credits
Mathematics for Elementary Education - B
This is the second course in a three course sequence designed for prospective teachers at the elementary school level, focusing on the following topics: Statistics, probability, and the structure of the system of real numbers including integers, rational and irrational numbers. Prerequisite: MATH 208 with a 2.0 or better.
MATH 210 5
credits
Mathematics for Elementary Education - C
This is the last course in a three course sequence designed for prospective teachers at the elementary school level, focusing on the following topics: Problem solving, structures of geometry, to include shapes, measurements, triangle congruencies, and the coordinate system. Prerequisite: MATH 208 with a 2.0 or better.
MATH 211 5
credits
Mathematics for Elementary Education I
This is the first course in a sequence designed for prospective teachers at the elementary school level, focusing on the following topics: Set theory, numeration systems, number theory, the structure of the system of real numbers and problem solving. Prerequisite: Math 097, 098, or 099 with a 2.0 or better; or appropriate placement score. College level reading score recommended.
MATH 212 5
credits
Mathematics for Elementary Education II
This is the second course in a sequence designed for prospective teachers at the elementary school level, focusing on the following topics: Statistics, geometry and measurement. Prerequisite: MATH 211 with a 2.0 or better within the last three years; or appropriate placement score.
MATH 221 5
credits
Introduction to Probability and Statistics
Descriptive statistics, probability, probability distributions, sampling methods, hypothesis testing, statistical inference, correlations, regression and analysis of variance are covered in this course. Prerequisite: MATH 097, 098 or 099 with a 2.0 or better within the last three years; or appropriate placement score. College level reading scores recommended.
MATH 245 5
credits
Discrete Mathematics
An introduction to the theory of the mathematics found in computer science. Topics include logic, proofs, sets, counting, probability, matrices, functions and relations, graphs, and trees. Prerequisite: MATH& 151.
MATH& 254 5
credits
Calculus IV
A course designed to give students an introduction to the basic concepts of multivariable calculus using the tools of linear algebra as applicable; vector functions, real valued functions, differentiation of scalar functions, multiple integration, vector differentiation and integration, transformation of coordinates, Green's Theorem, Stoke's Theorem, Gauss' Theorem and Lagrange Multipliers. Prerequisite: SFCC: MATH& 153, MATH 220 with a 2.0 or better. SCC: MATH& 153 with a 2.0 or better. |
A Computational Introduction to Number Theory and Algebra
This book can serve several purposes. It can be used as a reference and for self-study by readers who want to learn the mathematical foundations of modern cryptography. It is also ideal as a textbook for introductory courses in number theory and algebra, especially those geared towards computer science students.
Appropriate for both math and computer engineering students, this text is a blend of carefully explained theory and practical applications, imparting the fundamentals of both information theory and ...
Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, ...
This monograph only requires of the reader a basic knowledge of classical analysis: measure theory, analytic functions, Hilbert spaces, functional analysis. The book is self-contained, except for a ... |
will never deduce a formula for your GCSE Mathematics courseworks, still, there is something you should know about in order to write a good GCSE Mathematics coursework, and we will present this "something" to you.
GCSE Mathematics coursework is a part of your GCSE Maths. It consists of 2 tasks that are worth 20 % of your final grade for the GCSE Maths. One part of the GCSE Mathematics coursework is your Algebraic Investigation, the other one is your Statistical Data Handling Project.
Now, let us consider the most common problems you may face while writing your GCSE coursework.
Unlikely the Maths lessons, when the materials are divided into small parts, GCSE Mathematics coursework writing requires self-study. It means that students have to break the area of investigation into the smallest parts by themselves, and it is sometimes very difficult to do.
Still, they are not left alone without any help. GCSE Mathematics coursework supervisors usually help students, direct them throughout the process of GCSE Mathematics coursework writing, and answer all the questions students have.
It is also rather a complicated task for the majority of students to state all their thoughts on a paper. That is why they keep putting the task off, although they should not.
There is one more thing you should know about your GCSE Mathematics courseworks: Plagiarism. Plagiarism is a very serious thing that can put you into big troubles. Plagiarism in your GCSE Mathematics coursework can be easily noted by your supervisor: such factors as your writing style or more mature use of language can play here an important role. That is why you should be extremely careful with plagiarism. It is better not to plagiarize your GCSE Mathematics coursework at all if you want to pass your GCSE exams.
So, try not to cheat on your GCSE Mathematics coursework, especially if you are not sure it will work. And good luck! |
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. |
More About
This Textbook
Overview
This is a masterly introduction to the modern and rigorous theory of probability. The author adopts the martingale theory as his main theme and moves at a lively pace through the subject's rigorous foundations. Measure theory is introduced and then immediately exploited by being applied to real probability theory. Classical results, such as Kolmogorov's Strong Law of Large Numbers and Three-Series Theorem are proved by martingale techniques. A proof of the Central Limit Theorem is also given. The author's style is entertaining and inimitable with pedagogy to the fore. Exercises play a vital role; there is a full quota of interesting and challenging problems, some with hints.
Editorial Reviews
From the Publisher
"Williams, who writes as though he were reading the reader's mind, does a brilliant job of leaving it all in. And well that he does, since the bridge from basic probability theory to measure theoretic probability can be difficult crossing. Indeed, so lively is the development from scratch of the needed measure theory, that students of real analysis, even those with no special interest in probability, should take note." D.V. Feldman, |
COMAP, the Consortium for Mathematics and Its Applications,Featured Products
Mathematical Modeling Handbook
The Mathematical Modeling Handbook is intended to support the implementation
of the Common Core State Standards high school Mathematics Modeling
conceptual category. The CCSS document provides a brief description of mathematical
modeling accompanied by 22 star symbols (*) designating modeling
standards and standard clusters. The CCSS approach is to interpret modeling
"not as a collection of isolated topics but in relation to other standards."
The goal of this Handbook is to aid teachers in implementing the CCSS approach
by helping students to develop a modeling disposition, that is, to encourage
recognition of mathematical opportunities in everyday events. The Handbook
provides lessons and teachers' notes for thirty modeling topics together with
reference to specific CCSS starred standards for which the topics may be appropriate. Learn More
Mathematics as a Second Language Glossary
The Mathematics as a Second Language Glossary features mathematical terms defined in both English and Spanish
with accompanying examples and/or drawings and is now available in epub format for the Amazon Kindle and Apple EReaders.
Algebra: Language for a Changing World (DVD)
What algebra is used by police to calculate speeding fines? Can algebra provide a useful tool in helping our environment? Algebra: Language for a Changing World is an overview of the most essential early concepts in Algebra. Interesting real world contexts and worked problems using real data introduce input and output variables, symbolic and graphical representation, order of operations, and linear relationships. This half-hour program includes a user's guide with reproducible student exercises and quizzes. Learn More
Based on feedback from users of the first edition, COMAP has completed a major revision of Courses 1-3, now available in both print and CD-ROM.
• Some chapters are completely rewritten (i.e., Pick a Winner and Landsat, which is now titled Scene from Above). Other chapters are streamlined while retaining the thematic, modeling approach. • Most chapters are shorter. The revised Course 1 has a total of 57 Activities— a 39% reduction from first edition's 93.
Learn More
NEW FREE course material A Course in Financial Mathematics
This is a free course in financial mathematics for upper high school and undergraduate students, with emphasis on personal finance. Teachers can make their own selections. Some of the lessons are articles published in various journals. Some are unpublished. This collection contains over forty lessons. A teacher can simply download and print a PDF, make copies, distribute them to students, and teach the lesson. Learn More |
Suitable for the GCSE Modular Mathematics, this book covers different concepts through artwork and diagrams.
Synopsis:
This book is revised in-line with the 2007 GCSE Modular Mathematics specification. This Student Book is delivered in colour giving clarity to different concepts through artwork and diagrams. Worked examples, practice exercises and examiners tips ensure students are fully prepared for their exams. It is written by an experienced author team, including Senior Examiners, which means you can trust that the 2007 specification is covered to ensure exam success |
MAA Review
[Reviewed by Allen Stenger, on 11/25/2012]
This is a very carefully written introduction to real analysis. When Apostol published the first edition in 1957, he intended it to be intermediate between calculus and real variables theory, and it still has a strong feeling of being a transitional course. It starts out with several chapters on the number line and point set topology, then proves all the basic facts that are taken for granted in differential calculus courses. It then proceeds into what is new material for most students, with two new theories of integration (Riemann-Stieltjes and Lebesgue), multivariable and vector calculus (focusing on existence theorems such as the Implicit Function Theorem rather than physical applications), some advanced theorems in sequences and series, approximation by sequences of functions and orthonormal bases, and a brief introduction to complex variables.
The book crams a lot of material into a modest number of pages, but without feeling rushed. This is done primarily by sticking to the main threads of the subject in the exposition, while moving a lot of related and more specialized results to the exercises. The proofs themselves are not overly brief, although there's not much handholding and only a few examples are given, so (a) you have to pay attention, and (b) it's very helpful to have already taken advanced calculus so that you can orient yourself. In many ways this book resembles the British analysis books of the early twentieth century, such as Hardy's A Course of Pure Mathematics and Titchmarsh's Theory of Functions. The approach is generally more modern, and there are many more exercises, but it has the same kind of concision.
The book makes a good balance between simplicity and generality. For example, the Riemann-Stieltjes integral rather than the plain Riemann integral is used for the elementary integration (before Lebesgue). It's not any harder, introduces some other valuable concepts such as functions of bounded variation, and gives us a tool which is often useful in discrete and discontinuous problems. For another example, Fourier series are developed first for orthogonal systems and then specialized for trigonometric series. Again, this is not any harder and gives us a better insight into why Fourier series work.
Rudin's Principles of Mathematical Analysis is the one to beat in this field. Apostol's treatment is not that different from Rudin's. The books were written about the same time, with Rudin having editions in 1953, 1964, and 1976, and Apostol in 1957 and 1974. The coverage of the two books is roughly similar. Rudin is slightly more abstract and slanted more toward multivariable analysis. Both have concise proofs, a shortage of examples, and numerous challenging exercises. Both cover the Riemann-Stieltjes integral rather than the plain Riemann integral. Both cover the Lebesgue integral, although Rudin is more skimpy and uses the conventional measure theory approach, while Apostol follows Riesz & Sz.-Nagy et al., using a functional-analysis approach through step functions.
Apostol has taken care to modularize his book, so that it can be used for several different courses and the material studied in different orders. Rudin's treatment is more tightly integrated. This often makes Apostol easier to use as a reference, because everything you need to understand a theorem will be close by. |
Math-for-all-grades.com is a math website aimed at math students of school and college. Even vocational math learners can find good use from this math website. All math subjects and lessons are explained in detail with the student in mind. Numerous examples are solved to help students thoroughly grasp all the concepts, formulas and relevant theory. At the beginning of every math lesson, the salient formulas, concepts and topics are listed in terse overview as links. Students can go through these links to capture a brief overview of the lessons or they also have a choice to directly start off with their math lesson.
Math for all grades covers in depth all math subjects :algebra, arithmetic, calculus with essential concepts and unlimited solved problems. Math formulas and Math glossary in the navigation bar is very useful for students to grasp all the essential formulas in a particular math lesson.
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Linear Algebra II
Linear algebra is the study of vector spaces and linear mappings between them. In this course, we will begin by reviewing topics you learned in Linear Algebra I, starting with linear equations, followed by a review of vectors and matrices in the context of linear equations. The review will refresh your knowledge of the fundamentals of vectors and of matrix theory, how to perform operations on matrices, and how to solve systems of equations. After the review, you should be able to understand complex numbers from algebraic and geometric viewpoints to the fundamental theorem of algebra. Next, we will focus on eigenvalues and eigenvectors. Today, these have applications in such diverse fields as computer science (Google's PageRank algorithm), physics (quantum mechanics, vibration analysis, etc.), economics (equilibrium states of Markov models), and more. We will end with the spectral theorem, which provides a decomposition of the vector space on which operators act, and singular-value decomposition, which is a generalization of the spectral theorem to arbitrary matrices. Then, we will study vector spaces: real, complex, and abstract (i.e., vector space of dimension N over an arbitrary field K) linear transformations. Vector spaces are structures formed by a collection of vectors and are characterized by their dimensions. We will then introduce a new structure on vector spaces: an inner product. Inner products allow us to introduce geometric aspects, such as length of a vector, and to define the notion of orthogonality between vectors. In this context, we will study the geometric aspects of linear algebra by using Euclidean spaces as a guide. If you encounter a theorem that seems difficult or does not seem intuitive, try to study that theorem in the simplest case possible and then move on to more abstract cases. For example, if you are uncomfortable with abstract vector spaces (V) over an arbitrary field (K), then you can fall back on intuition from such spaces as R and C (real and complex). Alternatively, you can reduce the dimension of the vector spaces involved as many notions can be understood in the two-dimensional case.
Note that you will only receive an official grade on your Final Exam. However, in order to adequately prepare for this exam, you will need to work through the resources in each unit and the activities listed above 117.5 hours to complete. This is only an approximation, and the course may take longer 32.5 hours to complete. Perhaps you can sit down with your calendar and decide to complete subunit 1.1 (a total of 11.5 hours) over three days, for example by completing sub-subunits 1.1.1, 1.1.2, and half of 1.1.3 (a total of 4.5 hours) on Monday; the second half of sub-subunit 1.1.3 and sub-subunit 1.1.4 (a total of 5 hours) on Tuesday; and sub-subunit 1.1.5 and 1.1.6 (about 2 hours) on Wednesday; etc.
Tips/Suggestions: As noted in the "Course Requirements," Linear Algebra I is a pre-requisite for this course. If you are struggling with the material as you progress through this course, consider taking a break to revisit MA211 Linear Algebra. It will likely be helpful to have a graphing calculator on hand for this course. If you do not own or have access to one, consider using this free graphing calculator. As you read, take careful notes on a separate sheet of paper. Mark down any important equations, formulas, and definitions that stand out to you. These notes will serve as a useful review as you study for the Final Exam.
Preliminary Information
Linear Algebra, Theory and Applications was written and submitted by Dr. Kenneth Kuttler of Brigham Young University. Dr. Kuttler wrote this textbook for use by his students at BYU. According to the preface of the text, "This is a book on linear algebra and matrix theory. While it is self-contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however." A solutions manual to the textbook is included.
This unit serves as a review of some of the material covered in Linear Algebra I, including linear equations, matrices, and determinants. Specifically, you will review properties of the real numbers and complex numbers. You will then learn the Fundamental Theorem of Algebra, which states that every polynomial equation in one variable with complex coefficients has at least one complex solution. You will also review how to solve linear systems of equations and perform operations on matrices. The key is to read through all the material below and complete all the exercises in this unit. The goal of this unit is to ensure that you are comfortable with the key matrix algebra concepts related to Euclidean spaces as these concepts will be referred to throughout this course. The skills and techniques you learn working with matrix theory will be generalized later in the course when you work in a more abstract linear algebra setting.
Instructions: Please click on the link above, select the "PDF version of book" link, and read Appendix A for a definition of sets and functions as well as to learn about associated vocabulary for these concepts. You will be using this text throughout the course, so it may help to save the PDF to your desktop for easy reference.
Studying this reading should take approximately 1 hour to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
Instructions: If you have not already downloaded the text, please click on the link above. Read Chapter 2. Pay particular attention to the polar decomposition of complex numbers and the associated geometric interpretationCompleting this activity should take approximately 3.5 hours text, please click on the link above. Read Chapter 3. Here, you will read about the important Fundamental Theorem of Algebra. In particular, note how the theorem is false when considering polynomials in the real number system document, please click on the link above. Complete calculational exercise 2 and the proof-writing exercise 3 (pages 34 and 35).
Completing this activity should take approximately 1.5 hours to complete.
Terms of Use: These materials have been reproduced for educational and non-commercial purposes, and can be viewed in their original format here. Any reproduction or redistribution for commercial use is strictly prohibited.
Studying this reading should take approximately 30 minutes to complete.
Terms of Use: These materials have been and select the "PDF version of book" link. Complete exercises 1b and 2 on page 9 and proof-writing exercise 1 on page 10. Read Sections 12.1–12.3 in their entirety. Most of this material should be a review PDF document, click on the link above and select the "PDF version of book" link. Read Sections 12.4 and 12.5 in their entirety. Note the relationship between matrices and linear transformations.
Studying this reading should take approximately 45 minutes Chapter 3 (pages 77–104) in its entirety. The determinant of a matrix is an extremely important number associated to the matrix as it provides us with a lot of information about the associated linear transformation.
Studying this reading should take approximately 1 click on the link above, and work through problems 2, 3, 6, 9, 11, 13, and 15 in Section 3.2 (pages 82 and 83) and problems 5, 6, 8, 9, and 11 in Section 3.6 (pages 102 and 103). When you are done, check your solutions with the answers on page 489.
Completing this activity should take approximately 5 hours.
Terms of Use: An Introduction to Linear Algebra was written by Kenneth Kuttler and was relicensed as CC-BY 3.0 as part of the Saylor Foundation's Open Textbook Challenge.
In this unit, you will study Spectral Theory, which refers to the study of eigenvalues and eigenvectors of a matrix. The name Spectral Theory is due to David Hilbert, who coined the phrase in his study of Hilbert space theory. Hilbert's original work was in the setting of quadratic forms, and only later was it discovered that Spectral Theory had applications to quantum mechanics, where it could be used to describe the behavior of atomic spectra. Eigenvalues and eigenvectors of a linear operator are two of the most important concepts in Linear Algebra with applications to many fields, such as computer science (Google's PageRank algorithm), physics (quantum mechanics, vibration analysis), and economics (equilibrium states of Markov models). You will then learn about trace and determinants, two important numbers associated to a matrix. There are several operations that can be applied to a square matrix, and the determinant is a very important operation of this type. The determinant is a number that is calculated from a square matrix and is used to check for many different properties of that matrix, including invertibility. We will learn to compute the determinant and study properties of determinants and the effects of row operations on them. The trace of a matrix is related to the characteristic polynomial of the matrix and can be used to detect nilpotency. You will then learn about Schur's Theorem, which describes how every matrix is related to an upper triangular matrix. Finally, you will learn about quadratic forms, the second derivative test, and some advanced theorems.
Instructions: Please read Sections 7.1–7.5. The eigenvectors and eigenvalues of a matrix help to describe the behavior of the associated linear transformation1 (pages 157–164) in its entirety. Work through the eigenvalue/eigenvector examples on your own and check your work with that in the text. Being able to accurately and efficiently perform these computations is essential Section 7.6. Note the relationship between the eigenvectors for a rotation matrix and the angle of rotation4 (pages 173–180) in its entirety. Schur's Theorem relates any matrix to an associated upper triangular matrix in which the eigenvalues for the original matrix appear on the diagonal. Read through the proof of this theorem and the accompanying lemmas and corollaries.
Studying this reading should take approximately 2 Chapter 8 in its entirety. Pay particular attention to the algebraic properties of the determinantIn this unit, we will begin by defining fields and discussing some important examples. Complex numbers (C) will give us insight into some of the key mathematical concepts of linear algebra. We will define vector spaces and study their basic properties before studying finite dimensional vectors spaces. Then, concepts of linear independence, span, bases, subspaces, and dimension are examined in the context of vector spaces. A strong understanding of vector spaces is necessary, because linear algebra is the study of linear maps on vectors spaces. Without a good grasp of vector spaces, understanding linear algebra becomes difficult. After studying vectors spaces, we will begin to study a special kind of function known as a linear map. These functions arise naturally in linear algebra. We will study linear maps from one vector space to another, as well as linear maps from a vector space to itself (these maps are known as operators and are extremely important in linear algebra). Keep in mind that most of the results in this unit are for finite-dimensional vector spaces only. We will then learn how some matrices can be transformed into Jordan canonical form, an upper triangular form for the matrix in which the eigenvalues appear on the diagonal. Note that linear maps have many applications in fields outside of mathematics, such as physics (quantum mechanics, etc.) and engineering (traffic flow, difference equations, etc.). You will finally learn about a certain kind of matrices, called Markov matrices, and see that the existence of the Jordan form is the basis for the proof of limit theorems for Markov matrices.
Instructions: Please read Section 8.1 (pages 199 and 200) in its entirety. The definition of a vector space is an important one, and you should compare the axioms with their more familiar analogs from algebra Pleaseread Sections 4.1 and 4.2. Here the notion of a vector is abstracted. Pay particular attention to the example of polynomial functions, which is the first example of a vector space which is not simply an ordered n-tuple of numbersInstructions: Please read Sections 8.2.1 and 8.2.2 (pages 200–205) in their entirety. The notions of basis and subspace are extremely important ones to master. Read through the examples and proofs on your own. If the proofs are confusing, try working them out in a low dimensional case first 4.3 and 4.4 Sections 5.1 and 5.2. The notions of span, basis, independence, and dimension are crucial to understanding linear algebra and its applications.
Studying this reading should take approximately 1.5 hour 5.3 and 5.4. Work through the examples on your own, and compare your work with that in the text 8.3 (pages 205–219) in its entirety. Note how the existence of roots of a particular polynomial depends heavily on the field being considered. You should also compare this to the situation regarding the Fundamental Theorem of Algebra 6.1–6.5 in their entirety. Linear maps are those which preserve the structure of a vector space and are a rich source of additional vector spaces. Work through the examples on your own, and compare your work with that in the text.
Studying this reading 6.6 and 6.7 in their entirety. A linear map between two vector spaces can be represented by a matrix, once a basis is chosen for each vector space click on the link above, and work through problems 1, 7, 11, 13, 15, and 19 in Section 9.5 on pages 242 through 244. When you are done, check your solutions with the answers on page 494.
Completing this activity should take approximately 2 2, 8, 10, 11, and 16 in Section 10.6 (pages 262 and 264) and problems 4–8 in Section 10.9 (pages 273 and 274). When you are done, check your solutions with the answers on pages 494 and 495.
Completing this activity should take approximately 4Linear algebra deals with not only Euclidean spaces but also abstract vector spaces. This unit will discuss lengths and angles in an abstract vector space. Inner products allow us to generalize notions such as length, because an inner product is a generalization of a dot product for Euclidean n-space. Having notions of length, angles, and distances in an abstract vector space allow us to apply more tools and methods which help us to better understand the structure of the space.
In this unit, we will discuss inner product spaces, which are vector spaces with an additional structure known as an inner product. Much of the motivation for the subject grew from the need to generalize some geometric properties of two-dimensional and three-dimensional Euclidean spaces to higher dimensional spaces. In this unit, we will finally begin to understand the geometric aspects of linear algebra, such as representing rotations in the three-dimensional Euclidean space as matrices. From this we will understand how to generalize and represent rotations in higher dimensional Euclidean spaces as matrices. The concepts in this unit, such as norm and inner product, provide structure on spaces. We will finally study the basic properties of inner product spaces, orthonormal bases, and the Gram-Schmidt orthogonalization procedure. We will further study range-nullspace decomposition, orthogonal decomposition, and singular-value decomposition of spaces.
Next, we will try to understand and answer the question of when a linear operator on an inner product space is diagonalizable. We will study the notion of an adjoint of an operator as well as normal operators and then discuss the spectral theorem, which characterizes the linear operators for which an orthonormal basis consisting of eigenvectors exists. The spectral theory studied here is closely related to that studied in Unit 2. In fact, the eigenvalues and eigenvectors for a matrix are the same as those for the linear transformation determined by the matrix. We will then learn about finding the singular-value decomposition of an operator. We will conclude by exploring some advanced topics.
Studying this reading should take approximately 1.5 hours to complete.
Terms of Use: . These materials have been reproduced for educational and non-commercial purposes and can be viewed in their original format here. Any reproduction or redistribution for commercial use is strictly prohibited.
Instructions: Please read Section 9.5. The Gram-Schmidt process can be used to turn any basis for an inner product space into an orthogonal basis 9.6 on pages 128–132 1–3, 9, 11, 14, 16, 21, and 22 in Section 12.7 (pages 299–302) and problems 1 and 3 in Section 12.9 (page 306). When you are done, check your solutions with the answers on pages 495 and 496.
This activity should take approximately 4.5 hours to complete.
Terms of UseAn Introduction to Linear Algebra was written by Kenneth Kuttler and was relicensed as CC-BY 3.0 as part of the Saylor Foundation's Open Textbook Challenge.
Instructions: Please read Sections 11.1 and 11.2 11.3 and 11.4. The Spectral Theorem describes the relationship between normal operators and eigenvectors 11.5 13.6–13.11 (pages 322–334) in their entirety. Here, you will learn about the singular-value decomposition of a matrix, which has applications in statistics and image analysis |
APPENDIX B
A Topical Listing
The list below of mathematics topics, IF LACED WITH GOOD
APPLICATIONS, addresses all of the issues raised in Part II at
least minimally. Although the topics are displayed here according
to subject matter components of traditional mathematics curricula,
one should NOT infer that this is the best organization with
which to address quantitative literacy . In fact, this kind of layer-cake organization
may inhibit the very essence of quantitative literacy : encouraging multiple
perspectives; informally developing intuition; and searching for
connections. It may actually deepen the pitfall of just preparing for
the next course. Nevertheless, the list suggests a common ground
from which to begin. How much time will need to be spent on topics
that the students have studied before will depend on circumstances,
but deadly reviews of more or less familiar material should be
avoided. (* means "less essential")
ARITHMETIC
estimation
percentage change
use of calculator:
rounding and truncation errors; order of operations.
OTHER
optimization: the notions of maxima and minima of functions with
or without constraints; graphical and computational methods for
finding them; simple analytic methods, such as completing the
square for quadratic polynomials.
linear programming*:
systems of equations in two variables with a linear objective
function. |
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