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This course develops students' ability to recognize, represent, and solve problems involving relations among quantitative variables. Key functions studied are linear, exponential, power and periodic functions using graphic, numeric and symbolic representations. Students will also develop the ability to analyze data, to recognize and measure variation and to understand the patterns that underlie probabilistic situations
This course prepares students to take the Advanced Placement Calculus Exam. It covers limits, differential calculus, and integral calculus. Terminology, theory, notation, and in-depth problems guide students through a rigorous study of calculus. Extensive use of the graphing calculator will be involved throughout the year.
Students will review and extend their knowledge of linear, quadratic, exponenetial, logarithmic, polynomial, trigonometric, step, and absolute value functions. Students will apply elements of probability, theory, and concepts of statistical design to interpret statistical findings. Other skills emphasized include imporving arithmetic skills, algebraic maniputlation, solving equations without calculators, and solving systems of equations.
This course is designed to prepare students with tools necessary to be successful when taking the MCA II. Students will learn test-taking skills and be exposed to the MCA II testing format in addition to learning how to use the TI-83 graphing calculator. Students will work on practice tests and study key components of the MCA II exam. | 677.169 | 1 |
Calculus Essentials For Dummies (For Dummies (Math & Science)) sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high schoolIn an artful interweaving of mathematics and literature, this series of lively mathematics activities jumps off from one of the well-known "Frog and Toad" stories, "The Lost Button." The story leads ...
For students competing for the decreasing pool of college scholarships, writing a stellar entrance essay can make all the difference. With discrete explanations of vital grammar rules, common usage ...
Learning a new language is a fun and challenging feat for students at every level. Perfect for those just starting out or returning to Spanish after time away, Spanish Essentials For Dummies focuses ... | 677.169 | 1 |
Overview
Main description
Written by Jack Mogab of Texas State University-San Marcos and Louis Johnson at College of St. Benedict/St. Johns University, this book, provides the following elements for each chapter: a Pretest; a Learning Objective Grid; a Key Point Review with Learning Tips; some Self-Tests (Key Term Matching, Multiple Choice, Problems) with answers; and an extension of the guide to the Web Site, where students may practice with graphing. | 677.169 | 1 |
Description: This book is a collection of thought-provoking essays that frame basic issues, provide background, and suggest ways to strengthen the mathematical education of all students. The essays present ideas for making mathematical education meaningful for all students--how to meet the ... Read More
Reviews:
"This book presents current issues in applied mathematics, standards and assessment, and curriculum in a way that is informative, interesting, and relevant to high school mathematics students. Where other resources may have described classroom techniques in general, this exemplary resource ...
Read More
Description
This book is a collection of thought-provoking essays that frame basic issues, provide background, and suggest ways to strengthen the mathematical education of all students. The essays present ideas for making mathematical education meaningful for all students--how to meet the practical needs of students entering the work force after high school as well as the needs of those going on to postsecondary education. The essays take up issues such as: finding common ground between science and mathematics education standards and improving the articulation from school to work. High School Mathematics at Work provides thoughtful views from mathematicians, educators, and other experts, and identifies rich possibilities for teaching mathematics and preparing students for the technological challenges of the future.
Reviews
"This book presents current issues in applied mathematics, standards and assessment, and curriculum in a way that is informative, interesting, and relevant to high school mathematics students. Where other resources may have described classroom techniques in general, this exemplary resource is specific." -- Regina Mistretta, The Mathematics Teacher | 677.169 | 1 |
Covers topics commonly taught in 8th grade math and some pre-algebra concepts. It is also suitable for high school students and adult learners who need to brush up on their basic math skills. Features include 25 standards-based lessons, over 300 interactive quiz questions, 25 skill-building animations, and a searchable database of over 500 key basic math terms. Featured Lessons includes Sequence and Series, Polynomials, Square Roots, Introduction to Geometry, Triangles and other Polygons, Pythagorean Theorem and Trigonometry. | 677.169 | 1 |
This well-written introduction to differential calculus features a refresher of prerequisite material, applications of derivatives, and concepts of limits and is designed to be particularly accessible and clear, while maintaining high standards of rigor. | 677.169 | 1 |
National HE STEM maths strand
The National HE STEM Programme is a 3-year, £21million, initiative funded by the Higher Education Funding Councils for England and Wales (HEFCE and HEFCW) that commenced on the 1 August 2009.
Building on the experience of the More Maths Grads project (MMG) a group of societies and others in the mathematical sciences have collaborated to oversee and direct the mathematical sciences input to the National HE STEM Programme. The bodies comprise: the Institute of Mathematics and its Applications (IMA), the London Mathematical Society (LMS), the Royal Statistical Society (RSS), the Heads of Departments of Mathematical Sciences (HoDoMS), sigma and the HEA MSOR Network.
The mathematical sciences programme will address the following main themes:
(a) Integration and diversity - drawing on and extending the work of MMG and others to widen and enlarge entry to mathematical sciences undergraduate courses, and embed approaches into universities.
(b) Employer engagement - looking at employer needs in basic and high-level mathematics and statistics and in the application of scientific and mathematical knowledge in order to meet the Government's wish to improve work-force skills, and exploring implications for the HE curriculum.
(c) HE curriculum innovation - exploring current learning, teaching and assessment practices within mathematical sciences departments, and disseminating good practice.
(d) Mathematical sciences support - establishing and extending a network for mathematical sciences support in universities, building on sigma's regional hub model, working together to share resources and experience.
This brochure has been created to give a broad overview of the work of the mathematics strand in the National HE STEM Programme. You can download a copy of the brochure below.
A more indepth and detailed report and brochure showcasing the work of the six Spoke Universities and four professional bodies working with the National HE STEM Programme will be made available on the HE STEM website in January 2013. | 677.169 | 1 |
Book description
Published in partnership with SEDL, The Problem with Math Is
English illustrates how students often understand fundamental
mathematical concepts at a superficial level. Written to inspire ?aha?
moments, this book enables teachers to help students identify and
comprehend the nuances and true meaning of math concepts by exploring
them through the lenses of language and symbolism, delving into such
essential topics as multiplication, division, fractions, place value,
proportional reasoning, graphs, slope, order of operations, and the
distributive property.
Offers a new way to approach teaching math content in a way that
will improve how all students, and especially English language
learners, understand math
Emphasizes major attributes of conceptual understanding in
mathematics, including simple yet deep definitions of key terms,
connections among key topics, and insightful interpretation
This important new book fills a gap in math education by illustrating
how a deeper knowledge of math concepts can be developed in all
students through a focus on language and symbolism.
Concepcion Molina, Ed. D., is a program associate with SEDL, a
private, nonprofit education research, development, and dissemination
corporation based in Austin, Texas. Dr. Molina supports systemic
reform efforts in mathematics and works to assist state and
intermediate education agencies in their efforts to improve
instruction and student achievement. | 677.169 | 1 |
Courses
Course Details
MATH 096 Intermediate Algebra and Geometry
5
hours lecture,
5
units
Letter Grade or Pass/No Pass Option
Description: Intermediate algebra and geometry is the second of a two-course integrated sequence in algebra and geometry. This course covers systems of equations and inequalities, radical and quadratic equations, quadratic functions and their graphs, complex numbers, nonlinear inequalities, exponential and logarithmic functions, conic sections, sequences and series, and solid geometry. The course also includes application problems involving these topics. This course is intended for students preparing for transfer-level mathematics courses. | 677.169 | 1 |
The arithmetic theory of quadratic forms is a rich branch of number theory that has had important applications to several areas of pure mathematics--particularly group theory and topology--as well as to cryptography and coding theory. This book is a self-contained introduction to quadratic forms that is based on graduate courses the author has taught many times. It leads the reader from foundation material up to topics of current research interest--with special attention to the theory over the integers and over polynomial rings in one variable over a field--and requires only a basic background in linear and abstract algebra as a prerequisite. Whenever possible, concrete constructions are chosen over more abstract arguments. The book includes many exercises and explicit examples, and it is appropriate as a textbook for graduate courses or for independent study. To facilitate further study, a guide to the extensive literature on quadratic forms is provided.
Readership
Graduate students interested in number theory and algebra. Mathematicians seeking an introduction to the study of quadratic forms on lattices over the integers and related rings.
Reviews
"Basic Quadratic Forms is a great introduction to the theory of quadratic forms. The author is clearly an expert on the area as well as a masterful teacher. ... It should be included in the collection of any quadratic forms enthusiast."
-- MAA Reviews
"Gerstein's book contains a significant amount of material that has not appeared anywhere else in book form. ... It is written in an engaging style, and the author has struck a good balance, presenting enough proofs and arguments to give the flavor of the subject without getting bogged down in too many technical details. It can be expected to whet the appetites of many readers to delve more deeply into this beautiful classical subject and its contemporary applications." | 677.169 | 1 |
Reviews the
fundamental
ideas of algebra including the real number system, polynomials,
rational
expressions, graphing, equations and inequalities, relations and
functions,
and systems of first degree equations and inequalities. Lecture 3 hours
per week.
GENERAL COURSE
PURPOSE
This course is
designed
to provide a bridge for students who have completed the prerequisite
courses
for either MTH 163 - "Precalculus I" or MTH 166 - "Precalculus with
Trigonometry"
but have not been able to obtain a satisfactory score of the
proficiency
examination for either of those courses. Grades given will be S, R, or
U. Successful completion of this course will provide the student with
the
skills necessary for MTH 163 or MTH 166.
ENTRY LEVEL
COMPETENCIES
Prerequisites are
a
satisfactory score on an appropriate proficiency examination and MTH 3
- "Algebra I" and MTH 4 - "Algebra II" or equivalent. The
student must also obtain a score in a designated range on the
proficiency
examination that tests for competency.
COURSE
OBJECTIVES
As a result of
the
learning experiences provided in this course, the student should be
able
to:
A. perform
operations on polynomials and rational expressions B. solve linear
and
quadratic equations C. graph lines and
parabolas on the Cartesian plane D. solve linear
inequalities
algebraically and graphically E. solve systems
of
linear equations and inequalities F. state the
definition
of a function and give examples of functions G. evaluate
logarithmic
and exponential expressionsMAJOR TOPICS TO
BE
INCLUDED
When possible,
include
problems that will help students to remember basic geometric facts like
perimeter, area, and volume formulas, angle relationships in triangles,
angles formed with intersecting lines, angles formed with parallel
lines
cut by a transversal, similar and congruent triangles, Pythagorean
theorem. | 677.169 | 1 |
Alexander Kheyfits
Alexander Kheyfits
A Primer in Combinatorics
(De Gruyter, 2010)
This textbook on combinatorics and graph theory, cornerstones of discrete mathematics, systematically employs the basic language of set theory. This approach is often useful for solving combinatorial problems, especially problems where one has to identify some objects, and significantly reduces the number of students' errors. The book uses simple model problems to begin every section. Following their detailed analysis, the reader is led through the derivation of definitions, concepts, and methods for solving typical problems. Theorems are then formulated, proved, and illustrated by more problems of increasing difficulty. Topics covered include elementary combinatorial constructions, graphs and trees, hierarchical clustering algorithms, more advanced counting techniques, and existence theorems in combinatorial analysis. The textbook is suitable for undergraduate and entry-level graduate students as well as for self-education. Alexander Kheyfits (Assoc. Prof., Bronx Community) is on the doctoral faculty in physics. | 677.169 | 1 |
Students build geometric models of polynomials exploring firsthand the concepts related to them. This is a great way to introduce hands-on algebra concepts using the Student Tiles Set. This 48-page activity book provides methods for modeling Algebraic themes for grades 6+. The pages are to be used with the Algebra Tiles Student Set and include | 677.169 | 1 |
Trade paperback (US). Glued binding. 512 pages. contains index, pages 509-512. Audience: General/trade. a work book that takes an adult through all the basic arithmetic: whole numbers, fractions, decimals, percents; then goes into consumer math, and how to read and handle paychecks, bank accounts, interest, buying a house; and then into geometry. sample tests and answers of course.[less] | 677.169 | 1 |
Nine PlanetsA Multimedia Tour of the Solar System: one star, eight planets, and more
Search for Lilburn ChemistryAlgebra is a key basic component of math that once understood is the building block of success in math. If the foundations are not solid, then whatever the building that is being built will not be strong and sturdy. Anyone can learn Algebra, all you have to know is multiplication and everything else builds on top of that | 677.169 | 1 |
Intermediate algebra
Book Description: Pat McKeague's passion and dedication to teaching mathematics and his ongoing participation in mathematical organizations provides the most current and reliable textbook series for both instructors and students. When writing a textbook, Pat McKeague's main goal is to write a textbook that is user-friendly. Students develop a thorough understanding of the concepts essential to their success in mathematics with his attention to detail, exceptional writing style, and organization of mathematical concepts. Intermediate Algebra: A Text/Workbook, Seventh Edition offers a unique and effortless way to teach your course, whether it is a traditional lecture course or a self-paced course. In a lecture-course format, each section can be taught in 45- to 50-minute class sessions, affording instructors a straightforward way to prepare and teach their course. In a self-paced format, Pat's proven EPAS approach (Example, Practice Problem, Answer and Solution) moves students through each new concept with ease and assists students in breaking up their problem-solving into manageable steps. The Seventh Edition of INTERMEDIATE ALGEBRA: A TEXT/WORKBOOK has new features that will further enhance your students' learning, including boxed features entitled Improving Your Quantitative Literacy, Getting Ready for Chapter Problems, Section Objectives and Enhanced and Expanded Review Problems. These features are designed so your students can practice and reinforce conceptual learning. Furthermore, iLrn/MathematicsNow™, a new Brooks/Cole technology product, is an assignable assessment and homework system that consists of pre-tests, Personalized Learning Plans, and post-tests to gauge concept mastery. | 677.169 | 1 |
MERA search of MERLOT learning exercisesCopyright 1997-2013 MERLOT. All rights reserved.Sat, 18 May 2013 21:08:42 PDTSat, 18 May 2013 21:08:42 PDTMER4434Finding the Domain of a Function Online Lesson
This lesson was created by Jennifer Anders and Nicole McGlashan of Huron High School, Huron, South Dakota. It is designed to help a student use the associated applet, and then extend the ideas it develops. | 677.169 | 1 |
Math Modeling
Math is definitely my favorite class even though my skills are somewhat lacking. Taught by Mr. Barys we learn math with a pretty interesting approach. If you're here to get a head start then it'll be a good idea to learn a programming language (we use a program called Mathematica ), but you'll get through it even if you don't know any programming. Mathematica is probably going to give you the biggest grief in the beginning of the year and if you can master this easily you're labs and POWs will become a lot easier.
What I like about math the most is how we take math that's actually challenging and we don't follow the "text book" approach. You do problems that make you think of math in different ways and it alters your perspective of math and how you view the world.
If you've never dealt with tetrahedrons start reading up. They're going to be with you for a while...
If you would like to see the kind of work we do, here are some of the very first labs done. All three utilized Mathematica:
GasWriteUp.pdf This was a small group porject that we worked on trying to model with trying to find how far should you go to find the best price. It was one of our first modeling things we've done so there are many things that we still have to learn, but hopefully it gives a taste on the kind of things we are trying to do.
Hanford,Oregon.pdf This lab was to learn how to use Mathematica to create linear models. Its basicly to get a handle and to become proficient in using the software.
TakeHome1.pdf This was the assesment that we had to do which sums up all our practices about linear models. The inclass part was a killer since you had no reference to other works (at least for me it was) but this one was a bit eaiser and I tried not to use my sources.
Composition Functions.pdf This assignment was to find out what happens to functions when certain functions are composed with each other. We were learning about the composition of functions which means using the output of one function as the input of another function: e.g f[x] and g[x] -> f[g[x]]. What we did before this lesson was discuss what the Tool box functions were (they're just the basic functions) and this lesson taught us how composing these functions together can make any function we wanted. | 677.169 | 1 |
Past Course Descriptions
Course Listings — Fall 2004
This is an introduction to mathematics at the beginning college level. MATH 112 will explore topics in contemporary mathematics with a problem-solving approach.
The class meetings will include lectures, problem-solving sessions, and group work. The final grade will be based on quizzes, exams, a project, and/or a comprehensive final. The prerequisite for this course is Math Placement Level 22 or higher. This course is not intended to prepare students for further courses in mathematics. Mathematical-reasoning intensive.
Study of number systems, number theory, patterns, functions, measurement, algebra, logic, probability, and statistics with a special emphasis on the processes of mathematics: problem solving, reasoning, communicating mathematically, and making connections within mathematics and between mathematics and other areas. Open only to students intending to major in education. Prerequisite: Math Placement Level 22 or higher. Every year. Mathematical-reasoning intensive.
Study of basic concepts of plane and solid geometry, including topics from Euclidean, transformational, and projective geometry. Includes computer programming experiences using Logo with a special emphasis on geometry and problem solving. Prerequisites: MATH 118. Every year. Mathematical-reasoning intensive.
MATH 120 ELEMENTARY FUNCTIONS
4 SEM HRS
HODEL
This is a standard pre-calculus mathematics course that explores the functions common to the study of calculus. Examination of polynomial, rational, exponential, logarithmic, and trigonometric functions will be done using algebraic, numeric, and graphical techniques. Applications of these functions in formulating and solving real-world problems will also be discussed.
The final grade in the course is based on quizzes, tests, and a comprehensive final exam. Students are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class and for homework assignments.
The prerequisite for this course is Math Placement Level 24 or higher. Mathematical-reasoning intensive.
MATH 127 INTRODUCTORY STATISTICS
4 SEM HRS
ANDREWS
A study of statistics as the science of using data to glean insight into real-world problems. Includes graphical and numerical methods for describing and summarizing data, sampling procedures and experimental design, inferences about the real-world processes that underlie the data, and student projects for collecting and analyzing data. Open to non-majors only.
Prerequisites: Math Placement Level 23 or higher (Note: A student may receive credit for only one of the following statistics courses: MATH 127, MATH 227, PSYC 107, or MGT 210). Mathematical-reasoning intensive.
MATH 131 ESSENTIALS OF CALCULUS
4 SEM HRS
TIFFANY
This one semester calculus course is an introduction to the techniques and applications of differential and integral calculus. The applications come primarily from the bio-sciences and do not involve any trigonometric models. The final grade in the course will be based on quizzes, tests, and a comprehensive final exam.
The prerequisite is MATH 120 or Math Placement Level 25. Students are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class and for homework assignments. Mathematical-reasoning intensive 201 CALCULUS I
4 SEM HRS
DAVENPORT/STICKNEY
Calculus is the mathematical tool used to analyze changes in physical quantities. This is the first course in the standard calculus sequence. It develops the notion of "derivative", which is used for studying rates of change, and then introduces the concept of "definite integral", which is related to area problems. The overall approach will emphasize the concepts of calculus using graphical, numerical, and symbolic methods.
The two-semester calculus sequence, MATH 201/202, is required for all students majoring or minoring in mathematics, computer science, physics, or chemistry. MATH 201 and MATH 202 can also count as "supporting science" courses for the BA and BS programs in Biology, Geology, and Biochemistry/Molecular Biology. Students who are sure they will take only one semester of calculus may be better served in the single-semester introduction to calculus, MATH 131: "Essentials of Calculus". Talk with your advisor or with any math professor for advice on which calculus course is most appropriate for you.
Students are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class, for homework assignments, and for tests. If you have a different calculator that you'd like to use for the class, contact the instructor to find out whether your calculator is appropriate.
Depending on the instructor, the final grade in the course could be based on homework, quizzes, tests, and a comprehensive final exam. The prerequisite for the course is MATH 120 or Math Placement Level 25. Mathematical-reasoning intensive.
NOTE: Students may not receive credit for both MATH 131 and MATH 201.
MATH 202 CALCULUS II
4 SEM HRS
HIGGINS
This is the second course in Wittenberg's three semester calculus sequence. MATH 202 is primarily concerned with integration and power series representations of functions. Topics covered include indefinite and definite integrals, the Fundamental Theorem of Calculus, integration techniques, elementary differential equations, approximations of definite integrals, improper integrals, applications of integrals, power series, Taylor's Series, geometric series, and convergence tests for series.
Students will be required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class, for homework assignments, and for tests.
The final grade in the course is based on quizzes, tests, and a comprehensive final exam. MATH 201 is a prerequisite. Mathematical-reasoning intensive.
MATH 205 APPLIED MATRIX ALGEBRA
4 SEM HRS
STICKNEY
A course in matrix algebra and discrete mathematical modeling which considers the formulation of mathematical models, together with analysis of the models and interpretation of the results. Primary emphasis is on those modeling techniques which utilize matrix methods. Such methods are now in wide use in areas such as economic input-output models, population growth models, Markov chains, linear programming, computer graphics, regression, numerical approximation, and linear codes.
Students in this course are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class, for homework, and for tests. A TI-89, TI-92, or TI-92 Plus is also acceptable.
This course is a prerequisite for MATH 360 (Linear Algebra), and should be taken by all sophomore mathematics majors. Prerequisites: MATH 201. Mathematical-reasoning intensive.
The final grade in this course is based on quizzes, tests, a computer project, and a comprehensive final exam. Prerequisite: MATH 202. Mathematical-reasoning intensive.
MATH 227 DATA ANALYSIS
4 SEM HRS
ANDREWS
This introductory statistics course is designed not just for students majoring or minoring in math, but for any student who would benefit from a more substantial introduction to the field. In fact, about half of the students who have taken this class are not math majors. Students must learn general principles and techniques for summarizing and organizing data effectively, for designing observational studies and experiments, and for drawing specific inferences from such studies. Data analysis software is used daily. In addition to regular homework and periodic tests and quizzes, students are expected to collaborate on data analysis projects.
Prerequisite: Math Placement Level 25 (Note: A student may not receive credit for more than one of the following: MATH 127, MATH 227, PSYC 107, or MGT 210). Mathematical-reasoning intensive.
MATH 320 NUMERICAL ANALYSIS
4 SEM HRS
DAVENPORT
An introduction to the numerical solution of mathematical problems. Primary emphasis is upon the development of use of computational algorithms to obtain an accurate numerical solution as well as methods for establishing error estimates and bounds for this solution. These algorithms will primarily be implemented on the computer using the Mathematica® system. Some algorithms may also be implemented in C/C++ or FORTRAN. Some work will also be done by using a scientific graphing calculator such as the TI-83 or TI-86. This course should also be of special interest to students in the physical sciences.
Grades will be based on assignments and exams. Prerequisites: MATH 202, MATH 205, COMP 150, and familiarity with the scientific graphing calculator. This course is cross-listed as MATH 320. Students may enroll in either COMP 320 or MATH 320, but not both. Mathematical-reasoning intensive.
MATH 327 STATISTICAL MODELING
4 SEM HRS
ANDREWS
In this second course in statistics, regression analysis is the main vehicle for illustrating the principles of statistical modeling in real-world contexts. After a brief review of techniques and principles of Exploratory Data Analysis, students learn strategies for selecting and constructing models, criteria for assessing and comparing models, and tools for making formal inferences using these models. Class sessions include discussion of conceptual issues with practice in data analysis, and they put strong emphasis on interpreting and communicating the results of analyses. Students are required to collaborate on projects in which they design studies, collect and analyze data, and present their findings orally and in writing. Prerequisite: MATH 227 (or permission of instructor). Mathematical-reasoning intensive.
MATH 360 LINEAR ALGEBRA
4 SEM HRS
HIGGINS
Introduction to abstract vector spaces. Topics include Euclidean spaces, function spaces, linear systems, linear independence and basis, linear transformations and their matrices. Students are required to have a TI-83, TI-83 Plus, or TI-86 graphing calculator for use in class, for homework, and on tests. A TI-89 or TI-92 is also acceptable.
The final grade in the course is based on written assignments, quizzes, tests, and a comprehensive final exam. Prerequisites: MATH 205 and MATH 210. WRITING INTENSIVE. Mathematical-reasoning intensive.
MATH 370 REAL ANALYSIS
4 SEM HRS
HIGGINS
Through a rigorous approach to the usual topics of one-dimensional calculus - limits, continuity, differentiation, integration, and infinite series - this course offers a deeper understanding of the ideas encountered in calculus. The course has two important goals for its students: the development of an accurate intuitive feeling for analysis and of skill at proving theorems in this area.
The final grade in this course is based upon written assignments, tests, and a comprehensive final exam.
This course is intended only for junior and senior mathematics majors or minors. Others will be enrolled only with the permission of the instructor. WRITING INTENSIVE. Prerequisite: MATH 210. Mathematical-reasoning intensive.
MATH 460 SENIOR SEMINAR
2 SEM HRS
SHELBURNE
This is a capstone course for mathematics majors. Its purpose is to let participants think about and reflect on what mathematics is and to tie together their years of studying mathematics at Wittenberg. The structure of the course will be taken from the book Journey Through Genius by W. Dunham which covers the story of mathematics from the 5th century B.C.E. up to the 20th century C.E. by looking at some of the famous problems, theorems, and "colorful" mathematical characters who worked on them. The course is a seminar where participants are expected to research areas of interest in mathematics and present their findings to the rest of the seminar. The grade will be based on class discussions and presentations. Mathematical-reasoning intensive. | 677.169 | 1 |
Linear Algebra Decoded Desciption:
Solve, step-by-step, 60 different problems from linear algebra. It provides to teachers the possibility to generate and print exams. Problem data can be entered indistinctly using any of the two modes: Tabular or Text. It is a multilingual software.
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Linear Algebra Decoded is a program designed to assist students in the subject of Linear Algebra, although it has features for professors, including the ability to generate tests where problems are customized and solutions are in the field of integers. It provides step-by-step solutions with detailed explanations, of 60 different problems concerning matrices, determinants, linear equations, vector spaces and linear transformations. It works with five different data types: matrices, systems of linear equations, vector subspaces, sets of vectors and linear transformations.
With Linear Algebra Decoded, you will be able to set a list of math problems for an exam. It has an exam generator tool where problems are generated using complex algorithms to ensure that the solutions to each problem satisfy the conditions imposed on its configuration, and whose numerical values are suitable for use in tests, providing to teachers the ability to generate and print exams, from the detailed specification of the questions it will contain.
It has a convenient interface that provides assistance at all times, with two different modes for entering the problem data to solve: Tabular or text, which can be used indistinctly. It keeps the latest data associated with each problem and the settings used for each problem. In Text mode the program uses a parser that translates the written text into a data structure that represents the correspondent data type. This parser makes automatic corrections in order to adapt the text to the data type and it size. It has a smart tool for pasting data from clipboard that automatically determining the data type of the source and converts it to the data type to be introduced in the control, where the source can be from any text or input control.
It is a multilingual software, which distribution contains the English as default language, and the Spanish as alternate language, with the possible inclusion of new languages.
This script defines the Matrix class, an implementation of a linear algebra matrix. Arithmetic operations, trace, determinant, and minors are defined for it. This is a lightweight alternative to a numerical Python package for people who need to do...
Universal Math Solver is a software package which, until now, students could only dream of. Universal Math Solver is a mathematical software which was designed to help you solve all the math problems. Universal Math Solver solves any math given......
This library is intended to be a set of HEP-specific foundation and utility classes such as random generators, physics vectors, geometry and linear algebra. CLHEP is structured in a set of packages independent of any external package... | 677.169 | 1 |
Find a Tolleson Calculus TutorLinear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many ... | 677.169 | 1 |
DYNAMIC CONTENT Some demonstrations contain
dynamic content. The user may receive an alert
concerning a potential security issue. However,
all of the demonstrations on this webpage
are completely safe. To proceed, click ENABLE
DYNAMICS.
Simulated Epidemics BY PHILLIP BONACICH CDF: SimulatedEpidemics.cdf
Explore how the density and size of a network
affects the simulated growth of an infectious disease.
CHAPTER 2 SETS
Boolean Algebra BY PHILLIP BONACICH CDF: BooleanAlgebra.cdf
Use homomorphisms to analyze social group
memberships
Set Intersection and Union BY PHILLIP BONACICH CDF:
SetIntersectionandUnion.cdf
This demonstration selects two randomly selected subsets of the alphabet
and shows their intersection, union, and set differences.
Venn Diagrams BY GEORGE BECK AND LIZ KENT Wolfram:
Link
Visualize the complete 127 nonempty unions
and intersections of three sets, A, B, and C through Venn Diagrams
CHAPTER 3 PROBABILITY
The Binomial Fit BY PHILIP S LU CDF: BinomialFit.cdf
Explore the binomial distribution by fitting a
curve to a randomly generated distribution. Adjust the n and
p values and see how close you can come!
Convergence of Proportions BY PHILLIP BONACICH CDF: Convergence.nbp
This demonstration shows that while the
proportion of coin flips approaches the
probability in the long run, the difference
between the number of heads and expected number
increases in the long run.
Finding Bridges BY PHILLIP BONACICH Wolfram:
Link
This demonstration will help you discern bridges
from local bridges. Generate random networks of different sizes and
density and challenge yourself to correctly categorizing each edge.
Random Graphs BY STEPHEN WOLFRAM Wolfram:
Link
Generate an array of random graphs and familiarize yourself with the
qualitative and quantitative similarities.
CHAPTER 7 MATRICES
Graphs from Matrices BY GEORGE BECK Wolfram:
Link
Each square matrix can correspond to a graph.
Design a zero-one matrix and see the resulting network structure based
on your matrix.
CHAPTER 8 ADDING AND MULTIPLYING MATRICES
Matrix Multiplication BY ABBY BROWN Wolfram:
Link
Learning to multiply matrices? This demonstration
helps you visualize the row and column operations that result in a
matrix product.
Finding Cliques BY PHILLIP BONACICH Wolfram:
Link
This demonstration will locate n-cliques and
k-plexes in randomly generated networks. Vary n and k
and observe how strict or lenient each group definition is.
Community Structure BY PHILLIP BONACICH CDF:
CommunityStructure.cdf
Explore how the community structure algorithm assigns group membership
in a network. Unlike other group definitions, community structure
partitions the networks, so each vertex belongs to one and only one
group.
CHAPTER 10 CENTRALITY
Network Centrality BY PHILLIP BONACICH CDF: MeasureCentrality.cdf
Generate random networks of different sizes and densities and explore
the various aspects of centrality, represented by node size.
Centrality Game BY PHILIP S LU CDF: CentralityGame.cdf
Centrality measures can be independent. Challenge yourself by designing
a network where the top vertex is the most central under one measure,
but near the bottom under another.
CHAPTER 11 SMALL WORLD NETWORKS
Small World Networks: Lattice Model BY FELIPE DIMER DE OLIVEIRA Wolfram:
Link
Generate small-world networks based on random rewirings of a circular
lattice.
CHAPTER 12 SCALE-FREE NETWORKS
Contagion in Random and Scale-Free Networks BY PHILLIP BONACICH Wolfram:
Link
This demonstration compares the spread of an epidemic in random and
scale-free networks of identical densities with and without inoculation
of the most central 10% of the nodes.
Attack in Random and Scale-Free Networks BY PHILIP S LU CDF: Attack.cdf
Explore how random and scale-free networks with the same density hold up
against random failure and calculated attack. Multiple methods are
offered to measure damage.
Zipf's Law BY GIOVANNA RODA Wolfram:
Link
Power-laws are everywhere. This demonstration highlights the prevalence
of the distribution in important political documents.
CHAPTER 13 BALANCE THEORY
Triad Census on Random Graphs BY PHILIP S LU Wolfram:
Link
This Demonstration illustrates the expected frequencies in which these
triads occur in random graphs of varying density.
CHAPTER 14 MARKOV CHAINS
Transition Matrices for Markov Chains BY PHILLIP BONACICH Wolfram:
Link
Create your own Markov matrix and explore the equilibria in the matrix
after a set number of transitions.
CHAPTER 15 DEMOGRAPHY
Population Projection Using Leslie Matrices BY PHILIP S LU CDF: PopProjection.cdf
Expose an initial population to death and birth
rates and observe how the population changes over time, eventually
approaching equilibrium. View the population as both a graph and a
Leslie Matrix.
CHAPTER 16 EVOLUTIONARY GAME THEORY
Evolutionary Prisoner's Dilemma Tournament BY PHILLIP BONACICH CDF: PDTournament.cdf
Vary an initial population of strategies and let them compete in a
100-round PD tournament. Strategies reproduce themselves based on their
payoff in the previous set of rounds. Learn how the effectiveness of a
strategy is dependent on the composition of other strategies.
Nash Equilibrium in 2x2 Mixed Extended Games BY VALERIU UNGUREANU Wolfram:
Link
Adjust payoffs in a 2x2 matrix, and observe how it affects the set of
Nash Equilibria.
CHAPTER 17 POWER AND COOPERATIVE GAMES
Exchange Networks BY PHILLIP BONACICH Wolfram:
Link
Explore a simulation of behavior and development of power differences in
negatively connected exchange networks. Observe how network position
affects payoffs in repeated rounds of bargaining over 24 points.
CHAPTER 18 COMPLEXITY AND CHAOS
Classic Logistic Map BY ROBERT M LURIE Wolfram:
Link Use the classic logistic map to explore the
properties of chaos dynamics. | 677.169 | 1 |
Beginning Algebra
9780495118077
ISBN:
0495118079
Edition: 8 Pub Date: 2007 Publisher: Thomson Learning
Summary: Easy to understand, filled with relevant applications, and focused on helping students develop problem-solving skills, BEGINNING ALGEBRA is unparalleled in its ability to engage students in mathematics and prepare them for higher-level courses. Gustafson and Frisk's accessible style combines with drill problems, detailed examples, and careful explanations to help students overcome any mathematics anxiety. Their prove...n five-step problem-solving strategy helps break each problem down into manageable segments: analyze the problem, form an equation, solve the equation, state the conclusion, and check the result. Examples and problems use real-life data to make the text more relevant to students and to show how mathematics is used in a wide variety of vocations. Plus, the text features plentiful real-world application problems that help build the strong mathematical foundation necessary for students to feel confident in applying their newly acquired skills in further mathematics courses, at home or on the job | 677.169 | 1 |
Course Description
(P)
This course covers basic arithmetic, introductory concepts in algebra,
and problem solving techniques. Specific topics include addition,
subtraction, multiplication and division of signed numbers, percentage, and
applications of these skills. The course introduces algebraic concepts,
including algebraic operations of polynomials, solving equations, formulas,
and an introduction to solving word problems. (Prerequisite: MATH C020 | 677.169 | 1 |
Thinking and Quantitative Reasoning
Designed for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need ...Show synopsisDesigned for the non-traditional Liberal Arts course, Mathematical Thinking and Quantitative Reasoning focuses on practical topics that students need to learn in order to be better quantitative thinkers and decision-makers. The author team's approach emphasizes collaborative learning and critical thinking while presenting problem solving in purposeful and meaningful contexts. While this text is more concise than the author team's Mathematical Excursions ((c) 2007), it contains many of the same features and learning techniques, such as the proven Aufmann Interactive Method. An extensive technology package provides instructors and students with a comprehensive set of support toolHide synopsis80618777389-5777372Good. Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780618777372Fine. Hardcover. Instructor Edition: Same as student edition...Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780618777389-2 | 677.169 | 1 |
Algebraic conventions
You can use these techniques and examples when planning lesson sequences on
algebraic conventions.
Pupils need to be as familiar with the conventions of algebra as they are with those
of arithmetic. Algebraic conventions should become a routine part of algebraic
thinking, allowing greater access to more challenging problems.
It is a common error to deal with these conventions rather too quickly.
How pupils understand and manipulate algebraic forms is determined by their
mental processing of the meaning of the symbols and the extent to which they can
distinguish one algebraic form from another.
A goal is to develop pupils' mental facility to recognise which type of algebraic form
is presented or needs to be constructed as part of a problem. Some time spent on
this stage of the process can reduce misconceptions when later problems become
quite complex.
For example, in the equation p+7=20 the letter p represents a
particular unknown number, whereas in p+q=20, p and q can each
take on any one of a set of different values and can therefore be called variables.
Equations, formulae and functions can describe relationships between variables. In
a function such as q=3p+5 we would say that 3p was a variable term,
whereas 5 is a constant term.
Be precise and explicit in using this vocabulary and expect similar usage by pupils.
Progression
Representing an unknown value in equations with a unique solution:
3x+5=11
Representing unknown values in equations with a set of solutions:
p+q=20
Representing variables in formulae:
2l+2b=p
Representing variables in functions:
y=x2-7
Identifying equivalent terms and expressions
It is often the case that pupils do not realise when an equation or expression has
been changed, or when it looks different but is in fact still the same. The ability
to recognise and preserve equivalent forms is a very important skill in algebraic
manipulation and one in which pupils need practice.
One way of approaching this is to start with simple cases and generate more
complex, but equivalent, forms. This can then be supported by tasks involving
matching and classifying.
Progression
Simple chains of operations, for example 2x+x+5
Some with unknown coefficients, for example ax+5
Linear brackets, for example 7(x+2)
Quadratic brackets, for example (x+2)(x+5)
Positive indices, for example x3×x.
Identifying types and forms of formulae
This will build on the understanding of equivalence and will rely on knowledge of
commutativity and inverse.
Encourage pupils to see general structure in formulae by identifying small collections
of terms as 'objects'.
These objects can then be considered as replacing the numbers in 'families of facts',
such as 3 + 5 = 8, 5 + 3 = 8, 3 = 8 – 5, 5 = 8 – 3. The equations are then more easily
manipulated mentally.
For example, consider these equivalent formulae:
ab=l
a=l×b
To develop pupils' understanding of the dimensions of a formula, make explicit
connections between the structure of the formula and its meaning. Consider the
units associated with each variable and how these build up, term by term.
For example, consider the dimensions of these formulae:
a=l×b
2l+2b=p
Involve pupils in generating and explaining non-standard formulae, for example, for
composite shapes. | 677.169 | 1 |
Calculus For Biologists: A Beginning - Getting Ready for Models and Their Analysis
This book tries to show beginning biology majors
how mathematics, computer science and biology can
be usefully and pleasurably intertwined.
After the necessary start up costs to develop some
essential calculus tools, we use a few select models to illustrate how these three fields influence each other in interesting and useful ways. Indeed, we believe that the three must be considered as part of a larger whole and that the use of these ideas is perhaps best described as an emergent phenomena! And we must always be careful to make sure our use of mathematics gives us insight. This fourth edition again adds a bit more biology and polishes the mathematical and numerical discussions. In addition,more exercises have been added and additional typographical errors have been found and corrected. | 677.169 | 1 |
The chapter begins with an exploratory problem designed to introduce the concept of linear programming with an objective function to maximize profits by optimizing a company's product mix. The problem context involves assembling two types of computers with different profit margins and labor requirements. Students are led through a graphical solution to a two decision variable problem involving two constraints.The second product mix example involves a detailed totally worked-out example involving the manufacture of skateboards. Students are shown step-by-step how to formulate and solve this two decision variable problem graphically. A third decision variable is then added to motivate the need for EXCEL to solve larger problems. Students are taught how to use SOLVER as standard add-in to EXCEL to solve linear programming problems. This section also discusses how to use the linear programming output to perform sensitivity analysis. There is also an optional section that discusses the Simplex algorithm that is the basis for computational solution of LP problems. The third example is a sports shoe company and focuses on interpretation of results. The text presents a fully formulated and solved problem involving six decision variables and six constraints. The emphasis is on interpreting the output from SOLVER and answering a variety of what-if questions.
Binary programming is a form of integer programming. The word "binary" refers to the decision variables. When decision variables are binary, this means that they can only take on the values of either 0 or 1. That might seem overly restrictive, but there are many situations that can easily be modeled using binary decision variables. For example, the following decisions could be modeled with binary decision variables:
- Should we located a new automobile dealership at this location?
- Should I choose to apply to this college?
- Should I invest in this stock?
We all make decisions everyday in our lives that involve uncertainty. Decision Trees is the first chapter in the Probabilistic material and introduces the concept of making decisions under uncertainty and risk. The decision tree methodology involves accounting for every possible decision and random event. The best alternative generally maximizes the expected value of profit or minimized the expected cost, however, other non-financial variables are also considered. Expected value does not also capture an individual's risk tolerance. This risk aversion is the foundation for the insurance industry. The final problem in this chapter follows Jee Min a high school junior as he tries to determine how much collision insurance he needs. | 677.169 | 1 |
Computers and math are a natural, after all, computers
were developed to solve complex math problems for the military,
industry, and academia. Spreadsheets, such as Microsoft
Excel, help organize and analyze information, especially information involving numbers.
We can use this technology to review and apply algebra.
There is also a great amount of information on the
Web. The "Quick Links" on the right all contain more
information about any topic we discuss in class. Below are
links to some of the resources I have created for this class. Each
reviews important concepts and recommends useful Web resources.
Interactive
Activity: Number Types. I created this MS Excel
spreadsheet to review different number types (Natural, Whole, Integer,
Rational, Irrational, and Real). To use it, you will need to have
EXCEL 2000 or greater. The spreadsheet will pop up in a new browser
window. Simply close that window when you are done.
Interactive
Activity: Divisibility Rules. Let's review when
numbers are divisible by 2, 3, 4, 5, 6, 9, & 10. The rules are
listed. The first 3 are done for you as an example. The spreadsheet will pop up in a new
browser window. Simply close that window when you are done.
Interactive
Activity: Beginning Algebra Vocabulary. The
algebraic terms and concepts from each chapter are presented here is a
"matching" format. Read the short definitions and select
the appropriate term for each from pull-down menus. The spreadsheet will pop up in a new
browser window. Simply close that window when you are done.
Integrated Math Projects
Fall
Semester MS Excel Review This interactive presentation introduces the
basics of spreadsheets and MS Excel. Please follow the navigation
directions at the bottom of each slide.
Spring
Semester MS Excel Review Another interactive presentation, with
a springtime theme, introduces the
basics of spreadsheets and MS Excel. Please follow the navigation
directions at the bottom of each slide.
Algebra
and Excel. Working with a math teacher, I created this
handout to introduce the concept of formulas in Excel and review some
basic algebraic concepts. We use the formula for the perimeter of
a rectangle to illustrate this. (Click HERE
for printable, .pdf version)
Story Problems: Percents. Problem solving is all about
understanding a situation and systematically setting up a strategy to
provide a solution. We will use MS Excel to set up a spreadsheet
to solve different types of percentage problems. (Click HERE
for printable, .pdf version)
Mile Per
Gallon. I try to keep all of my computer activities
focused on problem solving and "real-world" skills. (Click
HERE for
printable, .pdf version)
Virtual
Dice. I wrote this activity to introduce basic concepts of
probability, review Excel functions, and have some fun in class.
(Click HERE for
printable, .pdf version)
Free Web Space -
StuStorage. I want my students to take advantage of the
technology support that is available on campus. Here are
directions for signing up for and using the student storage accounts at
UW-Whitewater. (Click HERE for
printable, .pdf version) | 677.169 | 1 |
Natural Science Division
Course Descriptions: Math (MATH)
MATH 99. Intermediate Algebra (4) A study of the algebraic operations related to polynomial, exponential, logarithmic, rational and radical functions, systems of equations, inequalities, and graphs. Designed for students who have had from one to two years of high school algebra, but who are unprepared for MATH 103/104 (College Algebra/Trigonometry). Grades are A, B, C, NC. The course grade is not calculated into the student's GPA and does not count toward fulfilling any requirements for a degree, including total units for the degree.
MATH 103. College Algebra (3) A study of the real number system, equations and inequalities, polynomial and rational functions, exponential and logarithmic functions, complex numbers, systems of linear and nonlinear equations and inequalities, matrices, and introduction to analytic geometry. The emphasis of this course will be on logical implications and the basic concepts rather than on symbol manipulations. Prerequisite: MATH 99 or appropriate score on math placement exam.
MATH 120. The Nature of Mathematics (3) An exploration of the vibrant, evolutionary, creative, practical, historical, and artistic nature of mathematics, while focusing on developing reasoning ability and problem-solving skills. Core material includes logic, probability/statistics, and modeling, with additional topics chosen from other areas of modern mathematics. (GE)
MATH 130. Colloquium in Mathematics (1) Designed to introduce entering math majors to the rich field of study available in mathematics. Required for all math majors during their first year at Pepperdine. One lecture period per week. Cr/NC grading only.
MATH 140. Calculus for Business and Economics (3) Derivatives: definition using limits, interpretations and applications such as optimization. Basic integrals and the fundamental theorem of calculus. Business and economic applications such as marginal cost, revenue and profit, and compound interest are stressed. Prerequisites: Two years of high school algebra and appropriate score on math placement exam, or Math 103. (GE)
Math 270. Foundations of Elementary Mathematics I (4) This course is designed primarily for liberal arts majors, who are multiplesubject classroom teacher candidates, to study the mathematics standards for the Commission on Teacher Credentialing. Taught from a problem-solving perspective, the course content includes sets, set operations, basic concepts of functions, number systems, number theory, and measurement. (GE for liberal arts majors.)
Math 271. Foundations of Elementary Mathematics II (3) This course includes topics on probability, statistics, geometry, and algebra. The course is part of the liberal arts major in continuing study to meet mathematics standards for the Commission on Teacher Credentialing. (Students who have previous approved math courses or who select the math concentration must check with the liberal arts or math advisor for course credit.)
MATH 317. Statistics and Research Methods Laboratory (1) A study of the application of statistics and research methods in the areas of biology, sports medicine, and/or nutrition. The course stresses critical thinking ability, analysis of primary research literature, and application of research methodology and statistics through assignments and course projects. Also emphasized are skills in experimental design, data collection, data reduction, and computer-aided statistical analyses. One two-hour session per week. Corequisite: MATH 316 or consent of instructor. (PS, RM)
MATH 320. Transition to Abstract Mathematics (4) Bridges the gap between the usual topics in elementary algebra, geometry, and calculus and the more advanced topics in upper division mathematics courses. Basic topics covered include logic, divisibility, the Division Algorithm, sets, an introduction to mathematical proof, mathematical induction and properties of functions. In addition, elementary topics from real analysis will be covered including least upper bounds, the Archimedean property, open and closed sets, the interior, exterior and boundary of sets, and the closure of sets. Prerequisite: MATH 151. (PS, RM, WI)
MATH 325. Mathematics for Secondary Education. (4) Covers the development of mathematical topics in the K-12 curriculum from a historical perspective. Begins with ancient history and concludes with the dawn of modern mathematics and the development of calculus. Considers contributions from the Hindu-Arabic, Chinese, Indian, Egyptian, Mayan, Babylonian and Greek people. Topics include number systems, different number bases, the Pythagorean Theorem, algebraic identities, figurate numbers, polygons and polyhedral, geometric constructions, the Division Algorithm, conic sections and number sequences. Course also covers the NCTM standards for K-12 content instruction and how to build mathematical understanding into a K-12 curriculum. Prerequisite: MATH 320 or concurrent enrollment.
MATH 335. Combinatorics (4) Topics include basic counting methods and theorems for combinations, selections, arrangements, and permutations, including the Pigeonhole Principle, standard and exponential generating functions, partitions, writing and solving linear, homogeneous and inhomogeneous recurrence relations and the principle of inclusion-exclusion,. In addition, the course will cover basic graph theory, including basic definitions, Eulerian and Hamiltonian circuits and graph coloring theorems. Throughout the course, learning to write clear and concise combinatorial proofs will be stressed. Prerequisite: MATH 151 and MATH 320 or concurrent enrollment in MATH 320 or consent of the instructor.
MATH 355. Complex Variables (4) An introduction to the theory and applications of complex numbers and complex-valued functions. Topics include the complex number system, Cauchy-Riemann conditions, analytic functions and their properties, complex integration, Cauchy's theorem, Laurent series, conformal mapping and the calculus of residues. Prerequisite: MATH 250 and MATH 320 or concurrent enrollment in MATH 320 or consent of the instructor.
MATH 370. Real Analysis I (4) Rigorous treatment of the foundations of real analysis; metric space topology, including compactness, completeness and connectedness; sequences, limits, and continuity in metric spaces; differentiation, including the main theorems of differential calculus; the Riemann integral and the fundamental theorem of calculus; sequences of functions and uniform convergence. Prerequisites: MATH 250 and MATH 320 or consent of the instructor.
MATH 470. Real Analysis II (4) Convergence and other properties of series of real-valued functions, including power and Fourier series; differential and integral calculus of several variables, including the implicit and inverse function theorems, Fubini's theorem, and Stokes' theorem; Lebesgue measure and integration; special topics (such as Hilbert spaces). Prerequisite: MATH 370.
MATH 490. Research in Mathematics (1-4) Research in the field of mathematics. May be taken with the consent of a selected faculty member. The student will be required to submit a written research paper to the faculty member.
In The News
Pepperdine Named to the 2013 President's Higher Education Community Service Honor Roll: Pepperdine University was recently named to the President's Higher Education Community Service Honor Roll for... more | 677.169 | 1 |
Feeling free by Mary Beth Sullivan(
Book
) 4
editions published
between
1979
and
1985
in
English
and held by
405
libraries
worldwide
Children with learning problems and physical disabilities talk about their handicaps.
Against all odds inside statistics(
Visual
) 6
editions published
between
1988
and
1989
in
English
and held by
241
libraries
worldwide
Twenty-six programs on 13 videocassettes, each cassette running ca. 30 minutes, explain the principles of statistics using real-world situations. Originally developed as a public television series.
For all practical purposes(
Visual
) 3
editions published
in
1986
in
English
and held by
129
libraries
worldwide
A series which stresses the connections between contemporary mathematics and modern society. Presents a great variety of problems that can be modeled and solved by quantitative means.
College algebra in simplest terms(
Visual
) 4
editions published
in
1991
in
English
and held by
125
libraries
worldwide
Presents the role of algebra in daily life and demonstrates practical applications in the workplace. Uses symbols, charts, pictures, and state-of-the-art computer graphics to illustrate basic algebraic techniques. Reviews problems step-by step, focusing on the methods students find most difficult to grasp.
Statistics(
Visual
) 5
editions published
between
1987
and
1988
in
English
and held by
57
libraries
worldwide
Sol Garfunkel takes the viewer on an exploration of statistics and their related display and interpretative disciplines. Methods of gathering useable reliable data, such as randomization, and sampling are discussed. Methods of graphical displaying data from histograms to three dimensional computer arrays are shown. Statistics are shown to be useful when patterns of events are more important than individual events themselves. Finally the methods for stating the reliability of the results are explored.
Race for the top(
Visual
) 4
editions published
between
1990
and
1993
in
English
and held by
50
libraries
worldwide
Shows the competition between Fermilab in the United States and CERN in Europe to discover the "top quark" (the predicted, but not yet detected fundamental subatomic particle).
Normal calculations ; Time series(
Visual
) 1
edition published
in
1989
in
English
and held by
50
libraries
worldwide
Normal calculations covers standardization and calculation of normal relative frequencies from tables and assessment of normality by normal quantile plots. Time series deals with distribution of a single variable, change over time, seasonal variation, inspecting time series for trends, and smoothing by averaging. Uses animated graphics, on-location footage, and interviews.
An Astronaut's view of earth(
Visual
) 4
editions published
between
1991
and
1992
in
English
and held by
49
libraries
worldwide
Film footage on the earth shot aboard the Space Shuttle.
What is statistics? ; Picturing distributions(
Visual
) 1
edition published
in
1989
in
English
and held by
45
libraries
worldwide
Presents the why as well as the how of statistics using computer animation, colorful on-screen computations, and documentary segments.
Algebra in simplest terms(
Visual
) 3
editions published
in
1991
in
English
and held by
43
libraries
worldwide
This is an instructional series of 26 half-hour programs for high school, college, and adult learners, or for teachers seeking to review the subject matter. Host Sol Garfunkel explains concepts that may baffle many students, while graphic illustrations and on-location examples demonstrate how algebra is used for solving real-world problems. Algebra is important in today's world, used in such diverse fields as agriculture, sports, genetics, social science, and medicine. This series helps students connect algebra's mathematical themes and applications to daily life.
For all practical purposes. Statistics(
Visual
) 5
editions published
in
1988
in
English
and held by
31
libraries
worldwide
These five programs from the series For All Practical Purposes explore the nature and use of statistics in the modern world.
For all practical purposes. Social choice : #15 prisoner's dilemma(
Visual
) 1
edition published
in
1986
in
English
and held by
26
libraries
worldwide
Program 15 discusses the human problem of making decisions, such as in business and politics. Partial conflict results in these situations and cooperation for mutual benefit is shown to be the best solution for these games of partial conflict.
For all practical purposes. Statistics : #8 organizing data. #9 probability(
Visual
) 1
edition published
in
1986
in
English
and held by
24
libraries
worldwide
Program 8 focuses on exploratory data analysis, emphasizing that the human eye and brain are the best known devices to see and recognize patterns. Introduces histograms, medians, quartiles, scatterplots and boxplots. Program 9 analyzes how we can predict long-term patterns of chance events by looking at the operation of a gambling casino. Introduces elementary probability concepts along with an analysis of normal curves, standard deviation and expected value.
For all practical purposes. Statistics : #6 overview. #7 collecting data(
Visual
) 1
edition published
in
1986
in
English
and held by
23
libraries
worldwide
Program 6 introduces the major themes of statistics, collecting data, organizing and picturing data and drawing conclusions from data. Program 7 looks at data collection and explores how surveys and public opinion polls actually work. Discusses the difference between a survey and an experiment and considers why and how chance is used in random sampling to make our confidence in our findings more certain.
Overview(
Visual
) 10
editions published
between
1985
and
1987
in
English
and held by
22
libraries
worldwide
Introduces the major themes of statistics, collecting data, organizing and picturing data and drawing conclusions from data.
For all practical purposes. Computer science : #25 computer graphics / #26 conclusion(
Visual
) 1
edition published
in
1987
in
English
and held by
22
libraries
worldwide
Program 25 shows how computer art, graphics and animation is created. Explains pixels and how their collective image can represent a picture or any graphic symbol. Program 26 sums up the key points in the series and emphasizes the real-world applications of mathematics in today's society and the mathematical models that can be built from them. | 677.169 | 1 |
Discrete Mathematics And Its Application By Susanna S.epp Manual
On this page you can read or download Discrete Mathematics And Its Application By Susanna S.epp Manual in PDF format. We also recommend you to learn related results, that can be interesting for you. If you didn't find any matches, try to search the book, using another keywordsDiscrete Mathematics and Its Applications Fifth Edition Kenneth H. Rosen AT&T Laboratories Boston .. Much of discrete mathematics is devoted to the study of discrete structures, which are used to represent discrete objects. Many important discrete structures are built. study of discrete mathematics with an introduction to logic. In addition to its importance in understanding niathematical reasoning, logic has numerous applications in. the study of mathematics are: (1) When is a mathematical argument correct? (2) What methods can be used to construct mathematical arguments? This. include axioms or postulates, which are the underlying assumptions about mathematical structures, the hypotheses of the theorem to be proved, and. they are used to prove mathematical theorems, but also for their many applications to computer science. These applications include verifying that computer programs., understanding the techniques used in proofs is essential both in mathematics and in computer science. RULES OF INFERENCE We will now. | 677.169 | 1 |
Full-time Courses: A Level Mathematics
Mathematicians are always in demand to solve problems and help make the right decisions. That's why those with a Mathematics A level earn on average £5,000 more than those with other qualifications in each year of their career.
You will have access to the multitude of university courses which require an A level Maths qualification. You will continue to use and enjoy maths because it is the language we use to describe and model the world in physical and social science.
If you would like to add an A Level onto your Level 3 study programme, then please include this on your application form. | 677.169 | 1 |
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>> Sunday, January 23, 2011
When students get to the more advanced math classes in their high school careers, they are typically required to purchase a graphing calculator. These calculators are unlike any tool they have used before, and can truly be compared to handheld computers. Before it becomes too overwhelming, students should consider a few tips for using their graphing calculator. Before getting started with the graphing calculator, students should understand that this piece of equipment is far more advanced than what they have previously used. They will use it to solve entire problems and will spend a great deal of time staring at the screen. That is why they should first set the brightness and contrast settings to a level that will be comfortable for their eyes.
The most important thing a student can do to be successful with their new graphing calculator is to read the manual. There are many more keys on this calculator than the average model, and it is important to be familiar with them all. If this seems like too much to handle, they may want to make a cheat sheet with the most important key functions on it. All of the keys on the graphing calculator are very useful in math class, but there are a few that will be used on a regular basis. The first key to become familiar with is the exponent key, which quickly solves any number to any exponent. When a student first purchases a graphing calculator for math class, they may be overwhelmed by everything it is capable of doing. The best way to become comfortable with it is by reading the manual and understanding all of the functions. | 677.169 | 1 |
Algebra by Design Series: Algebra II Topics by Design
By Russell E. Jacobs
Employs a search-and-shade technique that rewards students for their efforts and allows for self-check. Each page contains exercises with shading codes that students use to shade a grid labeled with the answers. If the answers are correct, a symmetrical design emerges. Reproducible for classroom use. Answer key is provided. | 677.169 | 1 |
Compositions of Functions
In this lecture you will learn about Compositions of Functions in Calculus. Our instructor will walk you through Alternative Notation in Compositions as well as reviewing several functions before our five video examples.
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Compositions of Functions
This topic is very
important in preparation for the Chain Rule for differentiation!
You can informally
think of this as involving an "outer function" and an "inner
function."
Some functions
involve a composition of three of more functions.
You will be using
function compositions throughout the rest of calculus!
Compositions of Functions
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. | 677.169 | 1 |
Mathematics Course Descriptions
MATH 0013
Pre-Intermediate Algebra - A course to teach the basic ideas in theory and
application of several areas of mathematics. The student will be prepared to
complete Intermediate Algebra. Course covers real numbers, simple algebraic
expressions, linear equations in one variable and consumer multiplication. This
course does not count as a degree requirement.
MATH 0123 Intermediate Algebra - A course designed to meet the curriculum
deficiency for beginning freshmen or transfer students. The course includes
elementary algebra to give the student an adequate mathematical background. This
course does not count as degree a requirement.
MATH 1313 Statistics - Designed to introduce the non mathematics student to the
techniques of experimental statistics, to furnish the background necessary to
conduct research, and to read and evaluate associated literature. Will not
satisfy general education requirements.
MATH 1403 Contemporary Mathematics - Offers an overview of traditional algebraic
topics using an applied format. An alternative to College Algebra, Contemporary
Mathematics will satisfy the general education mathematics requirement. Students
planning to take courses that have MATH 1513 College Algebra as a prerequisite
SHOULD NOT TAKE CONTEMPORARY MATHEMATICS since it WILL NOT SATISFY ANY
COLLEGE ALGEBRA PREREQUISITES.
MATH 1513 College Algebra - Designed to provide techniques and concepts
necessary to study applications in various fields. Course fulfills general
education requirement. Pre: Curricular requirements from high school.
MATH 2215 Analytic Geometry and Calculus I - Introduction to theory and
applications of elementary analytical geometry and calculus including theory of
limits, differentiation and integration. Pre: MATH 1613 or permission of the
mathematics department.
MATH 2315 Analytic Geometry and Calculus II - A continuation and extension of
2215 including techniques of integration, infinite sequences and series, and
parametric and polar coordinates. Pre: MATH 2215 or permission of the
mathematics department.
MATH 3013 Linear Algebra - Fundamental concepts of the algebra of matrices,
including the study of matrices, determinants, linear transformations, and
vector spaces. Pre: MATH 2315 and MATH 3513 or permission of the mathematics
department.
MATH 3033 Theory of Probability and Statistics I - Probability as a mathematical
system with associated applications to statistical inference. Pre: MATH 2315 or
permission of the mathematics department.
MATH 3041 Mathematics Technology - This course will introduce students to
several types of mathematics technology. In particular, students will be
introduced to the TI-92™ Graphing calculator and computer software such as
Mathematica, Derive, and Equation Editor. The course is designed to help
students learn and understand mathematics with the aide of technology. The
technology will be used to help illustrate various applications of mathematics,
including solving equations, graphing equations, trigonometry, elementary
statistics, and calculus. Prerequisites: MATH 2215 Calculus I or permission of
the department.
MATH 3323 Multivariable Calculus - A continuation and extension of Calculus I
and II to Euclidean 3-space. Pre: MATH 2315 or permission of the mathematics
department.
MATH 3353 Introduction to Modern Algebra - Fundamental concepts of the
structure of mathematical systems. Group, ring, and field theory. Pre: MATH 2315
and MATH 3513 or permission of the mathematics department.
MATH 4533 Mathematics Models and Applications - A study
of the foundations of model building. Applications of advanced mathematics.
Computer algorithms and practical evaluation of models. Pre: MATH 2315 or
permission of the department.
Mathematics Area of Concentration for
Elementary Teachers (These classes will NOT satisfy general education
requirements and will NOT count as electives for math majors)
MATH 2233 Structural Concepts in Arithmetic - A modern
introduction to the real number system and its subsystems.
MATH 3203 Structural Concepts in Mathematics - A modern
introduction to probability, statistics, geometry and other related topics. Pre:
MATH 2233 or permission of the mathematics department.
MATH 3223 Geometry for Elementary Teachers - Introduction to geometric concepts to provide a superior mathematical
background for elementary teachers. A generalization and extension of intuitive
Geometry studied in MATH 2233 and MATH 3203. Pre: MATH 3203 or permission of the
mathematics department. | 677.169 | 1 |
Book Description: Ensure top marks and complete coverage with Collins' brand new IGCSE Maths course for the Cambridge International Examinations syllabus 0580. Provide rigour with thousands of tried and tested questions using international content and levels clearly labelled to aid transition from the Core to Extended curriculum. * Endorsed by University of Cambridge International Examinations * Ensure students are fully prepared for their exams with extensive differentiated practice exercises, detailed worked examples and IGCSE past paper questions. * Stretch and challenge students with supplementary content for extended level examinations and extension level questions highlighted on the page. * Emphasise the relevance of maths with features such as 'Why this chapter matters' which show its role in everyday life or historical development. * Develop problem solving with questions that require students to apply their skills, often in real life, international contexts. * Enable students to see what level they are working at and what they need to do to progress with Core and Extended levels signalled clearly throughout. * Encourage students to check their work with answers to all exercise questions at the back (answers to examination sections are available in the accompanying Teacher's Pack). | 677.169 | 1 |
Book Description: This brief book presents an accessible treatment of multivariable calculus with an early emphasis on linear algebra as a tool. Its organization draws strong analogies with the basic ideas of elementary calculus (derivative, integral, and fundamental theorem). Traditional in approach, it is written with an assumption that the student reader may have computing facilities for two- and three-dimensional graphics, and for doing symbolic algebra. Chapter topics include coordinate and vector geometry, differentiation, applications of differentiation, integration, and fundamental theorems. For those with knowledge of introductory calculus in a wide range of disciplines including—but not limited to—mathematics, engineering, physics, chemistry, and economics.
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Math Lab
What is the Math Lab?
The purpose of the Math lab is to aid students in developing their mathematical abilities. The lab is staffed by a director and several student tutors who are available to help students in their calculus and statistic courses. Instruction in the Math Lab is very informal. Students are welcome to come to the lab with questions whenever they need help in understanding math course work. The lab has a Hewlett Packard workstation which students may use. Our goal in the lab is to increase each student's understanding of her or his course material. This takes time and active participation on the student's part. Please do not expect the lab to provide quick answers for the purpose of completing homework assignments. This does you a disservice. If we can help you understand the material so you can complete your assignment, we will be glad to do so. Many of the math professors are now assigning special problem sets from The Real Calculus Problems. Since these problems are graded by the professors and count substantially in a student's final grade, the lab does not routinely give assistance on these problems. Instead we have set up special problem-solving sessions with tutors who have been trained by the professors to give appropriate help on these special problem sets.
Director
Jim Lawrence is Director of the Math Lab. He sees students by appointment. If you would like an appointment or if you have other questions, stop in the lab or call x3060. | 677.169 | 1 |
feedback. Prerequisites: High school calculus | 677.169 | 1 |
Teacher makes maths-changing discovery – watch TVNZ Breakfast interview with author, Philip Lloyd – August 2010, click here
The Calculus Workbook NCEA Level 3 offers students the tools they need for success in Calculus.
In the first part there are exercises at Achieved, Merit and ExcellGrammar for Starters is an entertaining book that will have immediate appeal to students. It takes them on a Journey of discovery that will help them understand the nature of the language that they already use. It aims to stimulate curiosity about the way language works and encourage an interesting ... | 677.169 | 1 |
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Learning Matlab - Essentials Skills (2012) - FREE SHIPMENT
The advertisement posted in this page is already inactive and it is possible that the details here are already invalid. Content posted in this page is only provided for reference and does not constitute fact. Please be guided accordingly.
In this video series 7 Hour, Jason Gibson Teaches you How to use this Software package with Step-by Step video tutorials. The lessons begin with Becoming familiar with the user interface and Understanding How to interact with Matlab. Then you'll learn about variables, Functions, and How to Perform Basic Calculations. Next, Jason Will guide you in Learning How to do Algebra, trigonometry, and Calculus computations Both numerically and symbolically. The course wraps up with basic plotting in Matlab. Take the mystery out of Matlab and improve your productivity with the software immediately!
1. Introduction Sect 1: Overview of the User Interface - Part 1 Sect 2: Overview of the User Interface - Part 2 Sect 3: Overview of the User Interface - Part 3 Sect 4: Using the Help Menus
2. Basic Calculations Sect 5: Basic Arithmetic and Order of Operations Sect 6: Exponents and Scientific Notation Sect 7: Working with Fractions and the Symbolic Math Toolbox - Part 1 Sect 8: Working with Fractions and the Symbolic Math Toolbox - Part 2 | 677.169 | 1 |
Book Description: This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers students at both high school and college levels an excellent mathematics workbook. Filled with rigorous problems, it assists students in developing and cultivating their logic and probability skills. 1974 edition | 677.169 | 1 |
Wolfram Mathematica for Students 7.0 is a program to perform mathematical calculations. This program has the same features than the professional version, the only difference is the cost of the license. The...
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Supplement your learning and reinforce key concepts with the companion volume to Internal Medicine Essentials for Clerkship Students 2! Newly reorganized and fully updated, MKSAP for Students 4 is designed...
Plan6 is a web based tool for K12 school districts that allows each student in 9-12 grade to plan 4 years of high school and at least two more. The site provides a space for Students to answer questionsImprove your playing by improving your ears! Auralia is comprehensive ear training software for beginners, Students and professionals! Suitable for all ages, Auralia has thousands of questions, across 41License:Shareware | Price: $34.95 | Size: 10.4 MB | Downloads (129 )
French-English Dictionary by Ultralingua for Windows Download
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Mathematics of the Securities Industry
Numbers, ratios, and formulas are the lifeblood of the financial markets. Mathematics of the Securities Industry uses straightforward math and examples to explain every key number used on Wall Street, from the calculation of each number to why it is important and how best to use it. Completely up-to-date to include three-day settlement, decimalization, new tax laws, and more, it is today's easiest-to-use reference for measuring investment potential and accurately monitoring stock and bond performance.
How does a market globalize? How do antitrust and trade policies speed up or slow down the process? How do firms take part in it? This book offers a comprehensive appraisal of the phenomenon from a ...
This text analyzes the development and causal factors behind the geography of the commercial Internet industry. It presents an accurate map of Internet domains in the world, by country, by region, by ... | 677.169 | 1 |
Guys, I am having a very tough time with my homework on Algebra 1. I thought this would be easy and hence didn't care to check till now. When I sat down to work on the problems today, I found it to be rather unsolvable. Can any one guide me by offering information on the existing tools that can guide me with brushing up my basics on , topic-kwds and topic-kwds.
I have no clue why God made algebra, but you will be happy to know that a group of people also came up with Algebra Buster! Yes, Algebra Buster is a program that can help you solve math problems which you never thought you would be able to. Not only does it solve the problem, but it also explains the steps involved in getting to that solution. All the Best!
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Number
The students will develop an algebraic expression from geometric representations and ultimately graph quadratic equations with understanding. The students will also develop a better understanding of algebraic expressions by comparing with geometric, tabular, and graphical representationsThis lesson unit is intended to help teachers assess how well students are able to solve quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation. | 677.169 | 1 |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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CS034Intro to Systems ProgrammingDoeppner & Van HentenryckLab 6Out: Wednesday 9 March 2005 What youll learn.Modern C+ comes with a powerful template library, the Standard Template Library, or STL. The STL is based on the independent concepts
MAT125.R92: QUIZ 0SOLUTIONSNo score will be assigned for this quiz. The graph of the function f (x) is given below:11(a) Determine the domain and range of f (x). Domain: 4 < x < 1 and 1 < x < 4 (or, in other notations, (4, 1) and (1, 4). We
Chemistry 112B: Organic Chemistry Winter 2008 Professor Rebecca Braslau Assigned Homework Problems The following problems are required, and must be turned in. Problems are to b e done without looking at the answers as much as possible, then corrected
1 Problem 37 section 4.1. We have the situation shown in the gure, where v is the velocity, (xb , yb ) are the coordinates of the runner, xa is the x-coordinate of the runners friend (we do not show the y -coordinate of the runners friend since it is
MAT123 - Introduction to calculus Second Practice Midterm The Second Midterm will be on Tuesday 11/11 at 8:30pm at Harriman 137. Important: check the webpage to get a copy of Second Midterm of Fall 2007! Question 1. Compute: (a) log2 (16) (b) ln e3 +
Math 127 - S2008 Practice Test for the Final Examination1. Show that the function y =Ccos(x) x2is a solution of the dierential equationx2 y + 2xy = sin(x). For what value of C does the solution satisfy the initial condition y(2) = 0? 2. Find th
Answers for HW 9 3. Usually, one may compute the 1st, 2nd and 3rd derivatives of f at to get the 6 T3 . For this problem, one may also use sin(y + z ) = sin y cos z + cos y sin z to get the whole Taylor series of f. Just take y = x and z = .(Sinc
Math 127 - Spring 2008 Practice for Second Examination1. Find the interval of convergence for the power series(1)n+1n=2(x 6)2n . n12 3n2. Find the MacLaurin series for the function ex 1 f (x) = . x3 3. Find the sum of the innite series 2 3
Calculus Early Exam February 5, 2003Instructions: The exam consists of 15 multiple choice questions. You have 90 minutes to answer all fteen questions. Be sure to record your answers on the opscan form. You are not allowed to use any books, notes, o
MAT131 Spring 2003 Midterm II SolutionProblem Score Max 21 12 8 1 2 3 4 5 6 TotalUse of calculators, books or notes is not allowed. Show the all steps you made to find the answers. Write carefully, points may be taken off for meaningless stateme
MAT 331: Mathematical Problem Solving with ComputersStony Brook, Fall 2008General Information: This course serves as an introduction to computing for the math student. After a general introduction to the use of the computers, we will turn to more
Natasha Tuskovich Friday, June 12, 2009E. coli Bio-ThermometerIntroduction A biological thermometer would ideally be a simple, accurate and easily observable register of the organisms environment. A basic version is comprised of E. coli cells that
Math 331, Fall 2008, Problems1. Compute IFS parameters and the similarity dimension of the following fractal.1.00.750.50.250.0 0.0 0.25 0.5 0.75 1.02. (a) Find the IFS parameters to generate atractor of the Picture: a right gasket of side
Chapter 5 A turtle in a fractal garden1 Turtle GraphicsImagine you have a small turtle who responds to certain commands like move forward a step, move back a step, turn right, and turn left. Imagine also that this turtle carries a pen (or just lea
MAT331 Exercises, Fall 0812.4Write a procedure in Maple that counts the frequency of letters in a string of text. For example, here is what it looks like when I use mine: freqs("time flies like an arrow, fruit flies like a bananna."); [" ",9], [ | 677.169 | 1 |
Master of Science:
Master of Science:
Mathematics for Elementary Education
The MATH 140-141 sequence is designed for preservice elementary school teachers. These courses
are required for admission to the Elementary Education Program in the College of Education.
The courses emphasize a problem-solving, calculator-based, activity-oriented approach to the study
of mathematics. Arithmetic, algebraic, geometric, and statistical interpretations of topics are
integrated. The classes are offered in a laboratory setting to encourage interaction between
students in a cooperative learning atmosphere. Course work includes not only tests and homework
but also group projects and independent investigations.
Success in these courses requires a mastery of precollegiate mathematics, including algebra.
Students who do not demonstrate sufficient mathematical strength are placed into algebra courses.
Transfer students who have taken math for teachers courses may be able to receive credit for Math 140
or Math 141. We recommend looking at the sample proficiency exams in order to gauge your preparedness.
To confirm your readiness to take one of the courses, we encourage you to contact
Janice Nekola (312-413-3750) in the Office of Mathematics Education. You can arrange
to take a practice exam that we can grade and then counsel you appropriately. | 677.169 | 1 |
CMATH for Delphi 7 makes fast complex-number math functions (cartesian and polar) available in three precisions. This comprehensive library was written in Assembler for superior speed and accuracy. | 677.169 | 1 |
61461
Catalog Number
10-804-107
Class Title
College Mathematics course is designed to review and develop fundamental concepts of mathematics pertinent to the areas of: 1) arithmetic and algebra; 2) geometry and trigonometry; and 3) probability and statistics. Special emphasis is placed on problem solving, critical thinking and logical reasoning, making connections, and using calculators. Topics include performing arithmetic operations and simplifying algebraic expressions, solving linear equations and inequalities in one variable, solving proportions and incorporating percent applications, manipulating formulas, solving and graphing systems of linear equations and inequalities in two variables, finding areas and volumes of geometric figures, applying similar and congruent triangles, converting measurements within and between U.S. and metric systems, applying Pythagorean Theorem, solving right and oblique triangles, calculating probabilities, organizing data and interpreting charts, calculating central and spread measures, and summarizing and analyzing data. PREREQUISITE: Successful scores on placement test or 10834109 Pre-Algebra | 677.169 | 1 |
Accommodating Disabilities: Lehman College is committed to providing
access to all programs and curricula to all students. Students with disabilities
who may need classroom accommodations are encouraged to register with the
Office of Student Disability Services. For more info, please contact the
Office of Student Disability Services, Shuster Hall, Room 238, phone number,
718-960-8441.
Course Calendar:
We will try to cover the material in Chapters 1-6 of the book at a speed
appropriate for maximal understanding and retention.
Introduction to Linear Algebra before Ch 1
I will try to give a preview of important concepts in a little different
way than Strang. We will redo it his way in Ch1
problems from class and
pg 8: 2,3,4,7,15 due Jan 30
pg19: 1,2,3,4 due Feb 4
Hopefully this session wont take more that 1.5 weeks
Due Feb 11
pg 8-9: 8,16,17,18,19
pg 19 7a,c,d;9,10,12,18,19
HW from class
Show addition by vectors is the same as addition by algebra for
vectors. Consider obtuse angles.
Show that the dot product (inner product) is the same vectorially
and algebraically when one of the vectors is along the x axis. Consider obtuse
angles.
Show that if A,B are two by two matrices and v is
a 2X1 matrix
then A(Bv) = (AB)v where we are
using matrix multiplication (associativety) (extra
credit)
HW due Feb 18
Read through Ch 1 and first two sections Ch2
pg 40,41 1,2,4,9-12,15-20,22
HW due Feb 25
read 2.3
pg pg 51 1-5; pg 53 11, In 12,13,14 do what book asks but then
work with Gauss-Jordan to solve by row reducing to identity. Can
you see what the inverses are when they exist?
HW due March 6
Read to page 70
p51 1,3,5,11a,12,13
p63 1,2,3,4,12,13,16,18
p75 1,2,3,4,5.6.7d
Consider the equations
x+2y=4; 3x+5y=7
-2x-3y=5; 4x-7y=8
x+y=5; -x-y=3
In each equation try use the method of Gauss-Jordan keeping
track of the matrices that do row operations to find the inverse
of the appropriate matrix to solve the equations. If the method
fails explain why. Once you can find the inverse solve the equations
just using matrix multiplication when the right hand side is
a general 2x1 vector.
Before the test Read to pg 88
pg 77-78 13,16,17,20
p89 6,10,12 (use that if there is a right inverse then there is
a left inverse and hence an inverse),13 (use same thm),22,23,27
HW due April 22: Read 3.1,3.5
pgs127-129 1,2,3a,4,5,6,9,10,11
p178: 1,2,3,5,6,8,11,12,13,14
HW due May 1
p 129-130: 19,20,22,23,26
p178: 15,16,18,20,21,22
Final Exam: The Final Exam will be given during Finals
Week on Wed May 22 from 11:00 to 1:00 in Gi205 (regular room).
Department of Mathematics and Computer Science, Lehman College, City University
of New York | 677.169 | 1 |
If you haven't tried WolframAlpha, you really need to head over there immediately after reading this post.
The great thing about this site is its ease of finding computational data. Do you have an algebraic equation you need solved? Type it in the search box and watch the magic happen. Ask for the population of France and get both the number and a chart of population growth for the last 30 years. Just for fun, type in the following formula:
Taylor series of sin^3(x)
No, I don't know what it means either, but Wolfram Alpha does!
Here is the question. Would your math students benefit from using this site? Maybe not if you have a typical math class. If you expect your kids to sit down and do their homework in the confines of their room armed only with a calculator and their wits, you aren't paying attention. Kids today sit down with their laptop, mobile phone, calculator, iPod, and television all at the ready. They are connected. They are social.
So maybe to use this site you might have to rethink what you want from your students for their homework. Maybe you want them to find the answer here and then explain in class how the answer was solved. Yes, they will get step-by-step instructions for algebra problems. Here is an example of a linear equation I just made up:
If you assign a problem and then have the students discuss how it is solved so that they can teach others in the class, then Wolfram Alpha would be a great resource. It would ensure that the student is getting immediate, positive, correct feedback on how to solve problems.
Of course, there are a ton of other ways to use Wolfram Alpha. You just need to check them out for yourself. OK, you don't have to go all the way over to the Wolfram Alpha site. You can search right here and see for yourself.
Comments
I agree with you wholeheartedly… WolframAlpha is an AMAZING tool. I am currently working on it to submit science content (on an elementary level)… I would love some feedback as to what questions and information you would like to see on the site/project! You can also email Robert with information too!! (you must love mathforum too??!!! Am I right??) | 677.169 | 1 |
What is a Clarifying Lesson?
A model lesson teachers can implement in their classroom. Clarifying Lessons combine multiple TEKS statements and may use several Clarifying Activities in one lesson. Clarifying Lessons help to answer the question "What does a complete lesson look like that addresses a set of related TEKS statements, and how can these TEKS statements be connected to other parts of the TEKS?"
TEKS Addressed in This Lesson
Foundations for functions: 2A.1.A, B
Quadratic and square root functions: 2A.6.A, B, C; 2A.8.A, B, C, D
Materials
EDITED Resources. The resources on this page have been aligned with the
revised K-12 mathematics TEKS. Necessary updates to the resources are in
progress and will be completed Fall 2006. These revised TEKS were adopted by
the Texas State Board of Education in 2005–06, with full implementation
scheduled for 2006–07.
Clarifying Lessons
Algebra II: Quadratic Functions
Lesson Overview
Students use quadratic functions to describe the relationship of the height of a football thrown in a parabolic path to its distance from the goal line.
Mathematics Overview
Students collect and organize data, make a scatterplot, fit a curve to the appropriate parent function, and interpret the results. Students translate among the various representations of the quadratic function, formulate equations, use a variety of methods to solve the quadratic equations, and analyze the solutions in terms of the situation.
Set-up (to set the stage and motivate the students to participate)
If necessary, have students discuss the layout of a football field before beginning the problem on the worksheet.
Have students work in pairs. If appropriate, pair students so that at least one of them has a working knowledge of football.
Use the guiding questions to direct students in working through the worksheet.
Teacher Notes (to personalize the lesson for your classroom)
Guiding Questions (to engage students in mathematical thinking during the lesson)
What data are you using to determine the function that best describes the relationship of the height of the ball to its distance from the goal line? (2A.1.B, 2A.6.C, 2A.8.A)
How is the graph related to the actual path of the ball? (2A.1.B)
What values would not make sense to use for x in this situation? (2A.1.A, 2A.6.A, 2A.8.C)
Teacher Notes (to personalize the lesson for your classroom)
Summary Questions (to direct students' attention to the key mathematics in the lesson)
How can you use the equation to determine the height of the ball at a given
position on the field? (2A.1.B)
How can you use the graph to determine the
height of the ball at a given position on the field? (2A.1.B)
How is using
the graph like using the equation? How are they different? (2A.8.C)
How
can you use the equation to determine the distance of the ball from the
goal line at a given height? (2A.8.D)
How can you use the graph to determine
the distance of the ball from the goal line at a given height? (2A.8.B)
How is using the graph like using the equation? How are they different? (2A.8.C)
Teacher Notes (to personalize the lesson for your classroom)
Assessment Task(s) (to identify the mathematics students have learned in the lesson)
After discussing the Football Problem in class, give a similar problem for students to complete working independently or working together in small groups.
Teacher Notes (to personalize the lesson for your classroom)
Extension(s) (to lead students to connect the mathematics learned to other situations, both within and outside the classroom)
Have students write their own problems involving situations that can be represented by quadratic functions and share their problems with the class. | 677.169 | 1 |
Standards in this domain:
Understand the concept of a function and use function notation.
F-IF.1.-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Interpret functions that arise in applications in terms of the context.
F-IF.4. For.★
F-IF.5. Rel.★
F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★
Analyze functions using different representations.
F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
F-IF.8.Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
F-IF.9. Compare | 677.169 | 1 |
{"itemData":[{"priceBreaksMAP":null,"buyingPrice":11.69,"ASIN":"0486277097","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":3.99,"ASIN":"0486270785","isPreorder":0}],"shippingId":"0486277097::T2kU%2FutiwHe0Kgd9%2BqQwMcxxGzzZTv3BhvpHZFtLGkVF41wy5gt7mVaz1Gu49gET5RoYgncdqwb72D%2FIKvAkykVuAmQZt2SFTVBnpD7NIWk%3D,0486270785::oKWzOfHt82Tii4kBfxDKKlBfLYSXYgds0v4TxCfIZihKnxCT5LCpOcyjMTVGJttPZ6nDFPH8iRDtoTWKwWtNVTStAx1sD%2BJTD60k5ojmK "320 unconventional problems in algebra, arithmetic, elementary number theory and trigonometry." The problems are mathematically accessible to students at the high school level or higher, as they call more upon analytical thinking than upon advanced mathematical techniques. There is a range of difficulties, with harder problems marked with stars in the book. (The hardest problems are marked with double stars.) The problems are divided into twelve sections: "Introductory Problems," "Alterations of Digits in Integers," "The Divisibility of Integers," "Some Problems from Arithmetic," "Equations Having Integer Solutions," "Evaluating Sums and Products," "Miscellaneous Problems from Algebra," "The Algebra of Polynomials," "Complex Numbers," "Some Problems of Number Theory," "Some Distinctive Inequalities," and "Difference Sequences and Sums." Much of the book is devoted to providing hints and solutions, which are both thorough and clear. This is a great resource for preparing for competition, for developing your analytical thinking, or just for having fun (that is, if you are the sort of person who finds solving math problems fun).
The reason I am giving 5 stars to this book is for its unique collection of problems. It has been very entertaining reading the book so far (I have not completed the book). There however are a few errors which can be easily figured out by the reader. The treatment of each problem is unique.
This is a great resource for challenging math problems. After getting annoyed with newspaper "problem of the week" type books, this was a refreshing find. Don't let the "high school level" disclaimer fool you - there are some seriously difficult problems in here.
If you're the type to find logic and math problems fun, I would recommend dropping $15 for this text. It's well worth the time.
I found this book very interesting, because it deals with many many problems of algebra and number theory. You can find many interesting and tough theorems (not all of them are widely known nor taught) with their demonstration. I particularily liked the section about "distinctive inequalities": it deals with a great number of inequalities and you can learn some new techniques for solving them. The book lacks of geometry, that's true (only some trig somewhere), but it gives (in my opinion) really a strong preparation on topics concerning algebra... try it!
This books is what every book on math olympiads should be, it deals with high level problems in a way that readers can easily follow; I also liked it because there are some problems who have many interesting solutions and generalizations
It is a problem and solution type of book. The organization is not ideal. The problems are not ordered by difficulties. There are some very difficult problems. The solutions are quite rigorous and mostly well explained. Probably nice for a teacher to use, not good for self study.
Almost all the problems are for algebra, which seems narrow for preparation for high school math Olympiad. From the forward, it is stated that they are for 8th and 9th graders in USSR, which probably explain the lack of Euclidean geometry.
If you like challenging math problems then this book is for you. It's ideal if you want to prepare for a national math olympiad or if you just like hard math problems. Get this book and you won't regret it !!! | 677.169 | 1 |
Specification
Aims
To introduce students to matrix analysis through the development of
essential tools such as the Jordan canonical form, Perron-Frobenius
theory, the
singular value decomposition, and matrix functions.
Brief Description of the unit
This course unit is an introduction to matrix analysis,
covering both classical and more recent results that are useful in
applying
matrix algebra to practical problems.
In particular it treats eigenvalues and singular values, matrix
factorizations,
function of matrices, and structured matrices.
It builds on the first year linear algebra course.
Apart from being used in many areas of mathematics,
Matrix Analysis has broad
applications in fields such as engineering, physics, statistics,
econometrics
and in modern application areas such as data mining and pattern
recognition.
Examples from some of these areas will be used to
illustrate and motivate some of the theorems developed in the course.
Learning Outcomes
On successful completion of this course unit students will
be familiar enough with matrix analysis and
linear algebra that they can effectively use the tools and ideas of
these
fundamental subjects in a variety of applications, | 677.169 | 1 |
This course is that portion of Abstract Algebra that studies elementary
group theory. It considers the properties of groups, subgroups, and functions;
this leads to groups of permutations and groups isomorphic to them. Homomorphisms
of groups along with the induced quotient groups culminate in the Fundamental
Homomorphism Theorem; this rounds out the course. Either Math 232 or
this course fulfills the requirement for Modern Algebra by the Indiana
State Department of Education for Secondary Teacher Education students
of mathematics.
REQUIREMENTS AND GRADING
The course will cover sequentially the first sixteen chapters of
the text. Understanding rigorous mathematical proofs is an essential part
of this course.
Your course grade will be based on four criteria: Examinations (two
during the semester, plus the final exam), written homework assignments,
a class presentation, and attendance. Attendance will be taken each class
period and will affect your grade by a maximum of two percentage points
in either direction. The criteria will be weighted in the following manner:
Examinations:
50%
Homework:
30%
Presentation:
20%
Attendance:
+/-2%
NOTES ON GRADING CRITERIA
There will be an assignment from each chapter covered in the text. I
will always announce when an assignment is due, however, in case for any
reason you don't hear me give the due date, the game plan will always be
as follows: Assignments should be attempted by the next class period
(so that questions may be asked in class) and are due at the end
of the second class period after the appropriate chapter is finished. E.g.,
if I complete Chapter 4 on Tuesday September 19, the assignment for Chapter
4 is due at the end of the Tuesday September 26 class. Late assignments
will not be accepted except under extreme circumstances.
I cannot stress enough the importance that doing your homework has to
your success in an advanced math course such as this. Math is not a "spectator
sport". Even though class attendance and participation will help you a
great deal in keeping up with the material, you cannot adequately learn
math without practicing it on your own.
Your assignments must be NEATLY DONE, and all work must be shown.
Multiple pages must be STAPLED, and each page must have a smooth edge -
pages torn out of spiral binders are NOT ACCEPTABLE.
The first two exams will be given during the regular class period (approximately
September 28 and November 9), and the third will be given in finals week.
They will consist mostly of short proofs and definitions, with an occasional
computational problem. If you keep up with class notes and do all homework
assignments in a timely manner you will be adequately prepared for the
exams.
Your class presentation can be either a detailed explanation of a proof
from the text (or elsewhere) or lecture about some aspect of the history
or current state of abstract algebra. The presentations should be at least
ten minutes long, and we'll start these sometime in late September - early
October. | 677.169 | 1 |
Resources:
Description of the Lake Braddock Middle School MATH program:
The LBSS Middle School math program is comprised of six different math courses; Mathematics 7, Mathematics 7 Honors, Algebra I Honors, Mathematics 8, Algebra I, and Geometry Honors. Math 7 and 8 is a two-year program designed to prepare students for Algebra I in the 9th grade. Content is composed of four primary mathematical strands, the Language of Algebra, Proportional Reasoning, Quantitative Literacy and Space and Shapes. For advanced math students Algebra I is offered in the 7th grade for those students who have passed a county defined set of prerequisites. Algebra I is also offered in the 8th grade. For students who took Algebra I in the 7th grade and earned an A or B, Geometry Honors is offered in the 8th grade. Algebra I and Geometry Honors are high school courses and as such, will be placed on a students final high school transcript. For the students not quite ready for Algebra I in the seventh grade, the middle school offers a "Mathematics 7 Honors" course with a strong enrichment-based curriculum branching into upper level mathematics. | 677.169 | 1 |
RELATED LINKS
4 credits, Spring, 2000
Professor Larry Krajewski
Office: Murphy Center 526
Office Phone: 796-3658
Home Phone: 782-1648 [No calls between 10 p.m. and 7 a.m. please]
Hours: 3M, 11W, 12F & by appointment
E-mail: [email protected]
[email protected] Prerequisite: C or better in Math 255 Text: Mathematics for Elementary School Teachers by Tom Basserear,Houghton Mifflin, 1997 Final Exam: 1:10 class Wednesday, May 10, 7:40-9:40 a.m.
2:10 class Thursday, May 11, 9:50-11:50 a.m. Description: This course is designed to introduce the preservice K-9 teacher with ideas, techniques and approaches to teaching mathematics. Manipulatives, children's literature, problem solving, diagnosis and remediation, assessment, equity issues, and the uses of the calculator are interwoven throughout the topics presented. The math content areas are rational numbers and geometry. The Viterbo College Teacher Education Program has adopted a Teacher As Reflective Decision Maker Model. Each course is designed to contribute to the development of one or more of the knowledge bases in professional education. This course contributes to the development of the knowledge bases: Knowledge of the Learner, Curriculum Design, Planning and Evaluation, and Instructional and Classroom Management.
Goals:
To Resources
You may qualify for free tutoring in the Learning Center.
Methodology: Lecture, class discussion, small group work, student presentations.
Todd Wehr Library The following books are on reserve:
Solutions Manual
Selected Bibliography for Gender Equity in Mathematics and
Technology Resources Published in 1990-1996 ,Women & Mathematics Education
Objectives
Upon successful completion of this course, the student will be able to:
1. ..explore, conjecture, reason logically and use a variety of mathematics methods
effectively to solve nonroutine problems.
2. ..establish classroom environments so that his or her students can explore, conjecture,
reason logically and use a variety of mathematics methods effectively to solve
3. ..nonroutine problems and develop a lifelong appreciation of math in their lives;
4. ..design and use several forms of assessment, such as portfolios, journals, open-ended
problems, tests, and projects
5. ..become familiar with educational research on effective teaching of mathematics. Student Responsibilities As teachers you should appreciate the importance of class participation. Your active participation makes the course go. Math is not a spectator sport. Assigned problems and textbook exercises are ways for you to develop problem solving skills and reflect on your learning.
Requirements
Six summaries of articles on the following topics (include a copy of the
article in your summary; article must be at least two pages long.)
Fractions
Geometry
Equity and mathematics
Measurement
Technology
Assessment
The purpose of this assignment is to acquaint you with some resources outside of the textbook and to introduce you to some ideas or activities that you may want to share with the class when we are investigating the appropriate topic.
Please follow these guidelines:
Include a copy of the article with your summary.
Use the reporting form included in your packet.
Articles must be at least two pages long in the original citation.
Articles taken from the internet must be complete (No missing pictures,
diagrams, or equations.)
A problem notebook with assigned problems from the text and class.
You must work out the solutions. Copying answers from the solutions manual is not appropriate.
Completion of a minimum of 12 hours of field experience working with an elementary student on mathematics
A journal of your sessions with an elementary student. [NOTE: you
MUST MEET WITH YOUR STUDENT AND FULFILL THIS REQUIREMENT IN ORDER TO PASS THIS COURSE.]
Two math activities, one on geometry and one on fractions
Five investigations
Two in-class exams
Evaluation
Percentage
Problem notebook 15%
Readings 3%
Student journal 15%
Investigations (5) 25%
Math activities 2%
Tests (2) 40% Topics
I. Geometry
A. Spatial Reasoning
B. Van Hiele levels
C. Two dimensional geometry
D. Three dimensional geometry
E. Translations, Reflections and Rotations
F. Symmetry
G. Similarity
II. Measurement
A. Length
B. Area
C. Volume
III. Extending the number system
A. Integers
B. Rational numbers and fractions
1. Models for rational numbers
2. Comparing rational numbers
3. Renaming rational numbers
4. Addition and subtraction
5. Multiplication and division
C. Decimals
D. Proportions and ratios
E. Percents
A Note: Some
Hopefully you will see mathematics as an open- ended,
So I ask your help in establishing a mathematical community where one uses logic and mathematical evidence as verification rather than the teacher, where mathematical reasoning replaces the memorization of procedures, and where conjecturing, inventing, and problem solving are encouraged and supported.
persons actively involved in problem solving.
To nurture a mathematical idea in the mind of a child might be easier if it first thrived in the mind of the child's teacher.
Americans with Disabilities Act
If you are a person with a disability and require any auxiliary or other accommodations
for this class, please see me and Wayne Wojciechowski, the Americans With
Disabilities Act Coordinator (MC 320 - 796- 3085 ) within ten days to discuss your
accommodation needs. BIBLIOGRAPHY | 677.169 | 1 |
Algebra 2 Help.pdf...
[More] that
you understand the subject and score well in it. | 677.169 | 1 |
Search Course Communities:
Course Communities
Lesson 13: Completing the Square
Course Topic(s):
Developmental Math | Quadratics
This lesson introduces completing the square as a means of expanding the set of quadratic equations that may be solved beyond the extraction of roots and factoring. Simpler cases are first presented and then towards the end of the lesson a procedure for completing the square of (ax^2 + bx + c = 0) is given. | 677.169 | 1 |
Euclid's Elements
Description
Euclid's Elements is a remarkable geometry course centered around the propositions of Euclid's Elements.
In the first half of each class students will present prepared talks to explain and demonstrate a geometric proof to the group. Students will learn to make presentations, critically think, and build their confidence as they go through this yearlong course. Students become the teachers of other students!
The second half of each class will have students work through QED™ designed activities to
Euclid's Elements was the first logical presentation of mathematics as designed from a set of first principles. Until publication of modern text books in the 20th century, the Elements was the standard geometry text for all advancedmathematics students. Our course reintroduces this tradition striving to foster excellence in geometry, logic, critical thinking, and public speaking.
Sequence
The Fundamentals
An exciting introduction to Euclid's classic "The Elements". Students will learn logical flow, presentation skills, and the fundamentals of geometry from Euclid's first and second book.
science: students will work with a range of physical problems to determine ideas of measurement, accuracy, and precision.
Information
Each course in Euclid's Elements is a 30-hour workshop for a total of 90 hours of in-class material. Academic year sequences are held in 10 week classes each 3 hours long. Summer camps are held in a single week and cover 30 hours of material.
Each student will receive a full copy of Euclid's Elements. Students are expected to be prepared each week to make a presentation to their classmates.
Classes consist of hands-on activities, lecture, and practice problems. Academic year students are required to complete a minimal amount of practice problems.
Prerequisites
Students should have completed Algebra and should be reading at an 8th grade level. | 677.169 | 1 |
European Partners
The European graduate program (Europäisches Graduiertenkolleg) will be interdisciplinary combining aspects from discrete mathematics and computer science. Its scientific program ranges from more theoretical areas like combinatorics and discrete geometry via algorithmics and optimization to application areas like computer graphics or geographic information systems. The program is split into four basic research areas, namely combinatorics, geometry, optimization, and algorithms and computation. The major scientific goal of the program is to intensify the cooperation and interaction between discrete mathematics, algorithmics, and application areas. | 677.169 | 1 |
Product Description
The final stop for Saxon's middle school math, Math 8/7 continues teaching students the way they learn best...through incremental development of new material and continual review of the old. Following Math 7/6, concepts such as arithmetic calculation, measurements, geometry and other skills are reviewed, while new concepts such as pre-algebra, ratios, probability and statistics are introduced as preparation for upper level mathematics. Lessons contain a warm-up, introduction to new concepts, lesson practice where the new skill is practiced, and mixed practice, which is comprised of old and new problems.
Product Reviews
Math 87, Third Edition
4.7
5
34
34
Great Math Series!
I purchased Saxon Math 8/7 for my 4th grader after she finished Saxon Math 7/6. We use it as part of our homeschool curriculum. I love that Saxon Math has such great explanations of new concepts, and constant repetition of those concepts throughout the book. The result is that when a child finishes a Saxon book, they thoroughly know all the concepts taught in that book. Great series!
March 28, 2013
Best Math text for middle school!!
Saxon Math 8/7 is the best I have seen for teaching middle school math students. The lessons flow at a comfortable pace; while the Mixed Practice keeps past lessons fresh in students minds during the introduction of new facts and procedures.
September 18, 2012
Solid math program with plenty of explanation and review. Student can use textbook to "self teach". Lots of drill practice which has been very helpful. Very little teacher prep required!
September 7, 2012
I LOVE the saxon program I am very happy with that. However it took over 2 weeks for it to get to my house. I should have bought it from amazon. And the book was not manufactured right when it was binded the pages were doubled over. And since I wanted this program before my son started school this year I carefully fixed it myself with some scissor's and tape. I am more unhappy with the time it took to get to me however that was riduclous.
July 27, 2012 | 677.169 | 1 |
Vector Calculus, CourseSmart eTextbook, 4th Edition
Description
For undergraduate courses in Multivariable Calculus.
Vector Calculus, Fourth Edition, uses the language and notation of vectors and matrices to teach multivariable calculus. It is ideal for students with a solid background in single-variable calculus who are capable of thinking in more general terms about the topics in the course. This text is distinguished from others by its readable narrative, numerous figures, thoughtfully selected examples, and carefully crafted exercise sets. Colley includes not only basic and advanced exercises, but also mid-level exercises that form a necessary bridge between the two. Instructors will appreciate the mathematical precision, level of rigor, and full selection of topics.
Table of Contents
1. Vectors
1.1 Vectors in Two and Three Dimensions
1.2 More About Vectors
1.3 The Dot Product
1.4 The Cross Product
1.5 Equations for Planes; Distance Problems
1.6 Some n-dimensional Geometry
1.7 New Coordinate Systems
True/False Exercises for Chapter 1
Miscellaneous Exercises for Chapter 1
2. Differentiation in Several Variables
2.1 Functions of Several Variables;Graphing Surfaces
2.2 Limits
2.3 The Derivative
2.4 Properties; Higher-order Partial Derivatives
2.5 The Chain Rule
2.6 Directional Derivatives and the Gradient
2.7 Newton's Method (optional)
True/False Exercises for Chapter 2
Miscellaneous Exercises for Chapter 2
3. Vector-Valued Functions
3.1 Parametrized Curves and Kepler's Laws
3.2 Arclength and Differential Geometry
3.3 Vector Fields: An Introduction
3.4 Gradient, Divergence, Curl, and the Del Operator
True/False Exercises for Chapter 3
Miscellaneous Exercises for Chapter 3
4. Maxima and Minima in Several Variables
4.1 Differentials and Taylor's Theorem
4.2 Extrema of Functions
4.3 Lagrange Multipliers
4.4 Some Applications of Extrema
True/False Exercises for Chapter 4
Miscellaneous Exercises for Chapter 4
5. Multiple Integration
5.1 Introduction: Areas and Volumes
5.2 Double Integrals
5.3 Changing the Order of Integration
5.4 Triple Integrals
5.5 Change of Variables
5.6 Applications of Integration
5.7 Numerical Approximations of Multiple Integrals (optional)
True/False Exercises for Chapter 5
Miscellaneous Exercises for Chapter 5
6. Line Integrals
6.1 Scalar and Vector Line Integrals
6.2 Green's Theorem
6.3 Conservative Vector Fields
True/False Exercises for Chapter 6
Miscellaneous Exercises for Chapter 6
7. Surface Integrals and Vector Analysis
7.1 Parametrized Surfaces
7.2 Surface Integrals
7.3 Stokes's and Gauss's Theorems
7.4 Further Vector Analysis; Maxwell's Equations
True/False Exercises for Chapter 7
Miscellaneous Exercises for Chapter 7
8. Vector Analysis in Higher Dimensions
8.1 An Introduction to Differential Forms
8.2 Manifolds and Integrals of k-forms
8.3 The Generalized Stokes's Theorem
True/False Exercises for Chapter 8
Miscellaneous Exercises for Chapter 8
Suggestions for Further Reading
Answers to Selected Exercises | 677.169 | 1 |
Precalculus
9780321531988
ISBN:
0321531981
Edition: 4 Pub Date: 2008 Publisher: Pearson
Summary: - By Judith A. Penna - Contains keysroke level instruction for the Texas Instruments TI-83 Plus, TI-84 Plus, and TI-89 - Teaches students how to use a graphing calculator using actual examples and exercises from the main text - Mirrors the topic order to the main text to provide a just-in-time mode of instruction - Automatically ships with each new copy of the text | 677.169 | 1 |
Price
Specifications
StudyWorks! Middle School Deluxe Math delivers colorful, interactive lessons, animations and activities that reinforce all the fundamentals needed before entering high school. This package delivers over 120 complete lessons, covering all the major topics in sixth, seventh and eighth grade math - in greater depth than any other package! Each unit is comprehensive, interactive and motivational so that middle school students can absorb key concepts step - by - step, master each and move on. Middle School Deluxe Math covers what middle school students need for success on the math portion of almost every state's standardized exams, with correlations to the majority of state curriculum standards. ??Designed to be always up - to - date and useful every day - because it includes unlimited access to deluxe Web services at StudyWorksOnline! This includes online testing, live online homework help, and integrated access to rich Web resources and learning activities. | 677.169 | 1 |
Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films.
The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics.
Through the Maple® applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames.
The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. | 677.169 | 1 |
Synopses & Reviews
Publisher Comments:
This edition of Swokowski's text is truly as its name implies: a classic. Groundbreaking in every way when first published, this book is a simple, straightforward, direct calculus text. It's popularity is directly due to its broad use of applications, the easy-to-understand writing style, and the wealth of examples and exercises which reinforce conceptualization of the subject matter. The author wrote this text with three objectives in mind. The first was to make the book more student-oriented by expanding discussions and providing more examples and figures to help clarify concepts. To further aid students, guidelines for solving problems were added in many sections of the text. The second objective was to stress the usefulness of calculus by means of modern applications of derivatives and integrals. The third objective, to make the text as accurate and error-free as possible, was accomplished by a careful examination of the exposition, combined with a thorough checking of each example and exercise | 677.169 | 1 |
1. Use basic matrix operations and the algebra of matrices in practical problems. Possible applications may be drawn from areas such as Kirchoff's laws, Leontieff model of an interacting economy, Markov chains, method of least squares, singular value decomposition and fourier coefficients of a function. 2. Understand the concepts of vector spaces, subspaces, basis, independence and dependence, dimension, coordinates, rank of a matrix, inner product. 3. Use the dependency relationship algorithm and the Gram-Schmidt orthogonizational process. 4. Understand linear transformations, range and null space of a linear transformation, the correspondence principle and similarity. 5. Understand properties of the determinant function and the cofactor expansion of determinants. 6. Understand the concepts of eigenvalues and eigenvectors. 7. Understand the concepts of quadratic formsMethods of presentation can include lectures, discussion, experimentation, audio-visual aids, small-group work and regularly assigned homework. Calculators/computers will be used when appropriate. Mathematica, Derive and TI-92 calculators are available for use at the College at no charge. Course may be taught as face-to-face, media-based, hybrid or online course.
VIII. Course Practices Required
(To be completed by instructor)
IX. Instructional Materials
Textbook information for each course and section is available on Oakton's Schedule of Classes. Within the Schedule of Classes, textbooks can be found by clicking on an individual course section and looking for the words "View Book Information".
Textbooks can also be found at our Mathematics Textbooks page.
A computer algebra system is required.
X. Methods of Evaluating Student Progress
(To be determined and announced by the instructor)
Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or group projects, calculator/computer projects and a final examination | 677.169 | 1 |
Provide students with practice in skills areas required to understand pre-algebra conceptsBasic skills review in the first part of the book and more specific algebra topics introduced throughout the bookEachInstructional Fair Pre-Algebra Resource BookGrades 5 - 8Provide students with practice in skills areas required to understand pre-algebra conceptsBasic skills review in the first part of the book and more specific algebra topics introduced throughout the bookInstructional Fair Pre-Algebra Resource Book Fair Pre-Algebra Resource Book0.00 | 677.169 | 1 |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
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Ocean 423 Vertical circulation1When we are thinking about how the density, temperature and salinity structure is set in the ocean, there are different processes at work depending on where in the water column we are looking. If we are considering | 677.169 | 1 |
up-to-date, broad scope textbook suitable for undergraduates starting on computational physics courses. It shows how to use computers to solve mathematical problems in physics and teaches a variety of numerical approaches. It includes exercises, examples of programs and online resources at | 677.169 | 1 |
Just in Time Algebra for Students of Calculus in Management and the Lifesciences
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Mymathlab Mystatlab Student Access Kit For Ad Hoc Valuepacks
Summary
Strong algebra skills are crucial to success in applied calculus. This text is designed to bolster these skills while students study applied calculus. As students make their way through the calculus course, this supplemental text shows them the relevant algebra topics and points out potential problem spots. the table of contents is organized so that the algebra topics are arranged in the order in which they are needed for applied calculus. | 677.169 | 1 |
Within each curriculum organizer, students will be graded by learning outcome and assessed through tests, quizzes, assignments, and projects. Check my website for a list of the learning outcomes. If needed, students can retest certain learning outcomes provided they have completed all work for the unit and sought extra help. In the event of a retest, the second test will count for your grade. Retests must be arranged at a time of mutual convenience as soon as possible after the initial test. Failure to show up for a retest will result in the loss of the privilege. Students with unexcused absences will not be permitted to retest.
There will be a midterm exam worth 10% of the final grade, and a final exam worth 20% of the final grade.
Daily assignments will be assigned. Homework must be done regularly to be successful.
Topics Covered
o Rational Numbers
o Powers and Roots
o Equations and Inequalities (Algebra)
o Polynomials
o Linear and Non-Linear Relations (Graphing)
o Geometry
o Transformations
o Statistics and Probability
o Trigonometry (time permitting)
How to Succeed
1) Attendance: Be punctual! If you are late please knock once and wait to be let in.
2) Come prepared! Please bring a pen, pencil, paper, ruler and a calculator to every class.
3) Review your class notes. This will help you retain the information and help your performance on tests. It is also easier to stay up to date instead of trying to catch up. | 677.169 | 1 |
Practical Problems in Mathematics for Welders, 6th Edition
ISBN10: 1-111-31359-8
ISBN13: 978-1-111-31359-3
AUTHORS: Chasan
Discover how this highly effective, practical approach to mathematics can prepare you with the math skills most important for success in today's welding careers. PRACTICAL PROBLEMS IN MATHEMATICS FOR WELDERS, 6E combines an inviting, comprehensive introduction to math with an emphasis on the latest procedures, practices, and technologies in today's welding industry. You'll see how welders rely on mathematical skills to solve both everyday and more challenging problems, from measuring materials for cutting and assembling to effectively and economically ordering materials. Highly readable, inviting units emphasize both basic procedures and more advanced mathematics formulas welders must regularly use.
Clear, uncomplicated explanations, new practice problems, and real-world examples emphasize some of the industry's latest developments. New, more dimensional illustrations throughout this edition help you further visualize concepts with an approach that's ideal for learners at all levels of math proficiency. A new homework solution and dynamic online website help reinforce the math skills most important for success in welding | 677.169 | 1 |
2249937 / ISBN-13: 9780582249936
Introduction to graph theory
In recent years graph theory has emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as ...Show synopsis mathematics, computer science and economics, and as a readable introduction to the subject for non-mathematicians. The opening chapters provide a basic foundation course, containing definitions and examples, connectedness, Eulerian and Hamiltonian paths and cycles, and trees, with a range of applications. This is followed by two chapters on planar graphs and colouring, with special reference to the four-colour theorem. The next chapter deals with transversal theory and connectivity, with applications to network flows. A final chapter on matroid theory ties together material from earlier chapters, and an appendix discusses algorithms and their efficiency.Hide synopsis
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject582249937 Brand New Paperback Overseas International...New. 0582249937 | 677.169 | 1 |
Calculus Text Puzzles
This is the home page for Calculus Text Puzzles: An interactive way of
reading scrambled calculus definitions, examples and proofs. Some
parts of the text on these dynamic webpages can be rearranged easily,
and the reader is given automatic feedback on whether the original
correct form of the text has been
reconstructed.
Click on some of the links below and see how this approach
allows you to (re)discover concepts. This can help with understanding
calculus, and it is more interesting than simply reading the textbook.
It is meant as an intermediate step between studying existing
definitions and proofs versus writing your own. You are encouraged to print out
the unscrambled version of a completed puzzle and keep it as a
study-aid. The pages below require a fairly recent web
browser such as Internet Explorer 5.5+ or Netscape 6+. If you have an
older browser, you may be able to view the previous version of
Calculus Text Puzzles.
Instructions: Some pieces of the definitions and results below
have been shuffled, and your task is to sort them into the logically
correct order (if there seem to be several correct orders, choose one
that produces the 'most sensible' result).
Click a puzzle piece
to select it,
then click another puzzle piece
to move (or swap) the selected piece to
that particular position. When you think you are done,
click on the Check button.
If you are happy with your grade, you can enter your name and
print the page. Don't worry, the grade and your name are not recorded
anywhere on the web (the Text Puzzles run locally in your browser).
Chapter 4: Applications of Derivatives
Definitions:
Concepts of derivatives related to finding maxima and minima.
(for Netscape 7 or IE+MathPlayer)
Results:
The Mean Value Theorem and some of its consequences.
(for Netscape 7 or IE+MathPlayer) | 677.169 | 1 |
MERA search of MERLOT learning exercisesCopyright 1997-2013 MERLOT. All rights reserved.Sat, 18 May 2013 21:08:42 PDTSat, 18 May 2013 21:08:42 PDTMER4434Finding the Domain of a Function Online Lesson
This lesson was created by Jennifer Anders and Nicole McGlashan of Huron High School, Huron, South Dakota. It is designed to help a student use the associated applet, and then extend the ideas it develops. | 677.169 | 1 |
We bought it for our daughter and it seems to be helping her a whole bunch. It was a life saver. Margaret, CA
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I never bought anything over the internet, until my neighbor showed me what the Algebra Buster can do, and I ordered one right away. It was a good decision! Thank you. Mark Fedor, MI07-06 :
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A video that focuses on the TI-Nspire graphing calculator in the context of teaching algebra. In this program the TI-Nspire is used to explore the nature of linear functions. Examples ranging from ... More: lessons, discussions, ratings, reviews,...
Zoom Algebra is a Computer Algebra System App for TI-83 Plus and TI-84 Plus graphing calculators. Its patent-pending interface is visual and easy to use, with many little shortcuts. For example, ...This lesson involves a useful applet from the National Library of Virtual Manipulatives (NLVM). It is a good introduction to solving two-step equations for grade 6 or 7 or an effective review lesson f... More: lessons, discussions, ratings, reviews,...
Student page for the classroom activity (also called the Masonry Problem; a variation on polyominoes) to be explored through manipulatives (dominoes). Students explore different possibilities of makin... More: lessons, discussions, ratings, reviews,...
Use this activity yourself or with students, to guide them through online math experiments. In the process, you'll get comfortable interpreting graphs
of time vs. distance, and gain insight into your... More: lessons, discussions, ratings, reviews,...
Gives students experience in manipulating graphs by changing domain and range values for the viewing window, which can easily be carried over to more powerful tools such as graphing calculators. Allow... More: lessons, discussions, ratings, reviews,...
A classroom activity (also called 1000 Lockers) to be explored through the use of manipulatives and a ClarisWorks spreadsheet. Students then look for patterns and write the answer algebraically. More: lessons, discussions, ratings, reviews,...
This eModule presents sequences of geometric patterns and encourages students to generate rules and functions describing relationships between the pattern number and characteristics of the pattern. S... More: lessons, discussions, ratings, reviews,...
A classroom activity, to be explored through large movement experience, manipulatives, and an interactive Java applet. Students then revisit the activity, look for patterns, and write the answer algeb... More: lessons, discussions, ratings, reviews,...
Compare different representations of motion: a story, a position graph, and the motion itself. Create a graph that matches a story, or write a story to match a graph, and check either by watching Mell... More: lessons, discussions, ratings, reviews,...
The primary goal of this lesson is to understand that the costs associated with buying on credit and that making only minimum payments are problematic to long-term financial health. The secondary goal... More: lessons, discussions, ratings, reviews,...
This collection of activities is intended to provide middle and high school Algebra I students with a set of data collection investigations that integrate mathematics and science and promote mathematiThis activity focuses on:
* graphing an ordered pair, (a, f(a)), for a function f
* the connection between a function, its table, and its graph
* the interpretation of the horizontal coordinate | 677.169 | 1 |
Math made easier: advice from experts
Many students struggle with various kinds of math, including positive and negative number signs, fractions, factoring, graphing and word problems, instructors in the department of mathematics and statistics said.
In fall 2011, the success rate for college algebra, a core math course, was 59 percent, said Mellisa Hardeman, senior instructor in the department. The success rate dropped anther percentage point the following year, she said.
In fall 2012, 50 to 60 percent of pre-core math students had difficulties solving math problems, said Denise LeGrand, director of the Mac I math lab.
Ike McPhearson, math tutor, explained why students may have trouble comprehending math. One reason is that students may come from a home where education is not valued, he said.
A bad experience with an instructor can also change students' attitudes about math.
"You can't take yourself too seriously as a teacher," said Hardeman. Instructors can never give a student too much help passing math, she said.
Students who took a math course in high school before going to college are less likely to struggle with math, Hardeman said. Some students go to college years after graduating high school, however, and may forget everything they learned in their math classes.
Fortunately, there are a number of strategies that can help students overcome these challenges and develop a better understanding of math.
"In order to make math easy for students, show different ways of how to understand it," said McPherson, who has tutored high school and college students. Another way of making math fun for students is to create different games, he said.
According to LeGrand, the most important way to become better at math is to practice math exercises for 20 to 30 minutes.
"They won't see the results right away," said LeGrand, " but if they go to class and focus on work required, they will be successful and they will build confidence."
In addition, students can get help from tutors at the math lab. Each semester, the lab hires 12 tutors, LeGrand said.
For the math-impaired, there is a new math course called Quantitative and Mathematical Reasoning. The course was designed for students who are not science, technology, engineering or mathematics majors. It focuses on practical math, for example, currency exchange rates. The course fulfills the core math requirement, in place of college algebra.
Pre-core math courses, developmental math courses students take if they do not have the prerequisites for college math classes, are becoming more successful, said Tracy Watson, coordinator for pre-core math. The success rate for those courses rose to 77 percent in fall 2012, she said. Previously, the success rate was 37 percent for a 4-year period, she said.
This semester, there are 80 math majors at the university.
"We all like how math works because it all fits together," Watson said.
"Students who major in math develop a sense of thinking and solving problems," said Thomas McMillan, department chair.
Once students better understand math, they will have the confidence to solve not only math problems, but problems in everyday life as well | 677.169 | 1 |
Mathematics for the Trades, CourseSmart eTextbook, 8th Edition
Description
For Basic Math, Math for the Trades, Occupational Math, and similar basic math skills courses servicing trade or technical programs at the undergraduate/graduate level.
THE leader in trades and occupational mathematics, Mathematics for the Trades: A Guided Approach focuses on fundamental concepts of arithmetic, algebra, geometry, and trigonometry. It supports these concepts with practical applications in a variety of technical and career vocations, including automotive, allied health, welding, plumbing, machine tool, carpentry, auto mechanics, HVAC, and many other fields. The workbook format of this text makes it appropriate for use in the traditional classroom as well as in self-paced or lab settings. For this revision, the authors have added over 150 new applications, new chapter summaries for quick review, and a new chapter on basic statistics. Student will find success in this clear and easy to follow format which provides immediate feedback for each step the student takes to ensure understanding and continued attention.
Table of Contents
Chapter 1 Arithmetic of Whole Numbers
Chapter 2 Fractions
Chapter 3 Decimal Numbers
Chapter 4 Ration, Proportion, and Percent
Chapter 5 Measurement
Chapter 6 Pre-Algebra
Chapter 7 Basic Algebra
Chapter 8 Pratical Plane Geometry
Chapter 9 Solid Figures
Chapter 10 Triangle Trigonometry
Chapter 11 Advanced Algebra
Chapter 12 Statistics
Answers to Previews
Answers | 677.169 | 1 |
How is that you can walk into a classroom and gain an overall sense of thequality of math instruction taking place there? What contributes to gettingthat sense? In Math Sense, Chris Moynihan explores some of the componentsthat comprise the look, sound, and feel of effective teaching and learning.Does the landscape of the classroom feature such items... more...
This book (along with vol. 2)... more...
A collection of lectures presented at the Sixth International Conference, held at the University of Ioannina, on p-adic functional analysis with applications in the fields of physics, differential equations, number theory, probability theory, dynamical systems, and algebraic number fields. more...
While computational technologies are transforming the professional practice of mathematics, as yet they have had little impact on school mathematics. This pioneering text develops a theorized analysis of why this is and what can be done to address it. It examines the particular case of symbolic calculators (equipped with computer algebra systems) in... more...
The Hindu?Arabic numeral system (1, 2, 3,...) is one of mankind's
greatest achievements and one of its most commonly used
inventions. How did it originate? Those who have written about the
numeral system have hypothesized that it originated in India; however,
there is little evidence to support this claim.
This book provides considerable evidence... more...
This text presents an up-to-date treatment of fuzzy automata theory and fuzzy languages. The authors also discuss applications in a variety of fields, including databases, medicine, learning systems and pattern recognition. more...
Thirty-three papers from the July 2003 conference on non-associative algebra held in Mexico present recent results in non-associative rings and algebras, quasigroups and loops, and their application to differential geometry and relativity. The contributors investigate alternating triple systems with simple Lie algebras of derivations, simple decomp more... | 677.169 | 1 |
Cheat Sheets and Tables. Here is list of cheat sheets and tables that Iu0027ve written. Most of these are pdf files and so you will need the Adobe Viewer to view them.
tutorial.math.lamar.edu/../cheat_table.aspx
AQA GCSE Specification, 2010 - Mathematics A 5 Background Information 1 Introduction Following a review of the National Curriculum requirements, and the establishment of the ...
store.aqa.org.uk/../AQA-4306-W-SP-10.PDF
Page 5 Introduction The GCSE awarding bodies have prepared revised specifications to incorporate the range of features required by GCSE and subject criteria.
AQA GCSE Specification, 2011 - Mathematics A 5 Background Information 1 Introduction Following a review of the National Curriculum requirements, and the establishment of the ...
store.aqa.org.uk/../AQA-4306-W-SP-11.PDF
23 Areas outside the box will not be scanned for marking 25 The table shows information about two types of light bulbs, Standard and Energy Saving. Both types of light bulb give ...
Dear Mathematics Colleague We are proud to introduce you to the new accredited GCSE Mathematicsspecification from Edexcel, ready for first teaching in September 2010.
B_Issue 2_WEB.pdf | 677.169 | 1 |
Product Description
Review
R. Hartshorne Algebraic Geometry "Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions."—MATHEMATICAL REVIEWS
This book is one of the most used in graduate courses in algebraic geometry and one that causes most beginning students the most trouble. But it is a subject that is now a "must-learn" for those interested in its many applications, such as cryptography, coding theory, physics, computer graphics, and engineering. That algebraic geometry has so many applications is quite amazing, since it was not too long ago that it was thought of as a highly abstract, esoteric topic. That being said, most of the books on the subject, including this one, are written from a very formal point of view. Those interested in applications will have to face up to this when attempting to learn the subject. To read this book productively one should gain a thorough knowledge of commutative algebra, a good start being Eisenbud's book on this subject. Also, it is important to dig into the original literature on algebraic geometry, with the goal of gaining insight into the constructions and problems involved. The author of this book does not make an attempt to motivate the subject with historical examples, and so such a perusal of the literature is mandatory for a deeper appreciation of algebraic geometry. The study of algebraic geometry is well worth the time however, since it is one that is marked by brilliant developments, and one that will no doubt find even more applications in this century.
Varieties, both affine and projective, are introduced in chapter 1. The discussion is purely formal, with the examples given unfortunately in the exercises. The Zariski topology is introduced by first defining algebraic sets, which are zero sets of collections of polynomials. The algebraic sets are closed under intersection and under finite unions. Therefore their complements form a topology which is the Zariski topology. The properties of varieties are discussed, along with morphisms between them. "Functionals" on varieties, called regular functions in algebraic geometry, are introduced to define these morphisms. Rational and birational maps, so important in "classical" algebraic geometry are introduced here also. Blowing up is discussed as an example of a birational map. A very interesting way, due to Zariski, of defining a nonsingular variety intrinsically in terms of local rings is given. The more specialized case of nonsingular curves is treated, and the reader gets a small taste of elliptic curves in the exercises. A very condensed treatment of intersection theory in projective space is given. The discussion is primarily from an algebraic point of view. It would have been nice if the author would have given more motivation of why graded modules are necessary in the definition of intersection multiplicity.
The theory of schemes follows in chapter 2, and to that end sheaf theory is developed very quickly and with no motivation (such as could be obtained from a discussion of analytic continuation in complex analysis). Needless to say scheme theory is very abstract and requires much dedication on the reader's part to gain an in-depth understanding. I have found the best way to learn this material is via many examples: try to experiment and invent some of your own. The author's discussion on divisors in this chapter is fairly concrete however.
The reader is introduced to the cohomology of sheaves in chapter 3, and the reader should review a book on homological algebra before taking on this chapter. Derived functors are used to construct sheaf cohomology which is then applied to a Noetherian affine scheme, and shown to be the same as the Cech cohomology for Noetherian separated schemes. A very detailed discussion is given of the Serre duality theorem.
Things get much more concrete in the next chapter on curves. After a short proof o the Riemann-Roch theorem, the author studies morphisms of curves via Hurwitz's theorem. The author then treats embeddings in projective space, and shows that any curve can be embedded in P(3), and that any curve can be mapped birationally into P(2) if one allows nodes as singularities in the image. And then the author treats the most fascinating objects in all of mathematics: elliptic curves. Although short, the author does a fine job of introducing most important results.
This is followed in the next chapter by a discussion of algebraic surfaces in the last chapter of the book. The treatment is again much more concrete than the earlier chapters of the book, and the author details modern formulations of classical constructions in algebraic geometry. Ruled surfaces, and nonsingular cubic surfaces in P(3) are discussed, as well as intersection theory. A short overview of the classification of surfaces is given. The reader interested in more of the details of algebraic surfaces should consult some of the early works on the subject, particularly ones dealing with Riemann surfaces. It was the study of algebraic functions of one variable that led to the introduction of Riemann surfaces, and the later to a consideration of algebraic functions of two variables. A perusal of the works of some of the Italian geometers could also be of benefit as it will give a greater appreciation of the methods of modern algebraic geometry to put their results on a rigorous foundation.
33 of 36 people found the following review helpful
5.0 out of 5 starsTHE book for the Grothendieck approach16 Mar 2004
By Davis C. Doherty - Published on Amazon.com
Format:Hardcover
This is THE book to use if you're interested in learning algebraic geometry via the language of schemes. Certainly, this is a difficult book; even more so because many important results are left as exercises. But reading through this book and completing all the exercises will give you most of the background you need to get into the cutting edge of AG. This is exactly how my advisor prepares his students, and how his advisor prepared him, and it seems to work.
Some helpful suggestions from my experience with this book: 1) if you want more concrete examples of schemes, take a look at Eisenbud and Harris, The Geometry of Schemes; 2) if you prefer a more analytic approach (via Riemann surfaces), Griffiths and Harris is worth checking out, though it lacks exercises.
43 of 49 people found the following review helpful
5.0 out of 5 starsTerrific, if you want it.24 Sep 2000
By Colin McLarty - Published on Amazon.com
Format:Hardcover
This book hardly needs a review on Amazon, because if you have as much math background as it needs, then you must already know it is indispensible for learning about schemes in algebraic geometry. The book is clear, concise, very well organized, and very long. If you do not already know the Noether normalization theorem, and the Hilbert Nullstellensatz, then you do not want this book yet--you want an introduction to commutative algebra. | 677.169 | 1 |
Calculus I (Math 207) can have a strong impact on
how one looks at many situations.To make calculus a valuable class, there is one constant reminder a
student needs to believe:"I
have the potential." In
other words, one must assure oneself of their ability to make a success out of
Calculus I.Success is not the
grade you receive but rather the understanding and applying of the acquired
knowledge to life.
To achieve this success, I will mention what I wish
I knew the first week of class.I
wish I knew that calculus does pertain to everyday life.It will help the student with problem
solving, analysis, thinking skills, and (needless to say) patience.Also, calculus can be related to things
one encounters everyday—frogs approaching the ends of diving boards,
volumes of tulip petals, airplane descent, food product structure, and
economics.In addition to everyday
experiences, this class will provide a challenge and require
self-discipline—so keep a good attitude.
Besides maintaining a good outlook on the class, one
might want to review some math fundamentals—trigonometry and
algebra.As a suggestion, one
might ask the professor for a past Math 151 exam in order to review key
pre-calculus concepts.One should
also practice graphing skills.In
a majority of calculus, the graph will help with the understanding of many
problems and test questions.
For me, I have found difficulty at times to
understand some concepts. Calculus may at times seem exotic and foreign; and
sometimes the professor's doctorate-understanding definition does not
seem clear to the student.However, there is a solution:write down the professor's definition, try some problems in the
homework, and even read the book.Then, once you understand the concept, write the definition in your own
words in your notes.This will
help a lot when one gets to the tests.
Understanding
is essential in a smooth transition to college mathematics, and even in
everyday college life. It is just as important to persist at calculus until one
understands the concepts as it is to understanding that your roommate might get
upset if one accidentally locks his or her roommate out when you leave not
remembering he or she if just down the hall.In a new experience, mistakes happen. But to improve, one
needs to remember certain things.However, in college mathematics one can no longer memorize
formulas.One must understand how
to use formulas. To attain this understanding I suggest practice, practice, and
more practice.So, when one
becomes discouraged, take a break.Don't give up mid way through the semester!You can always get help from tutors and
the professor.Tutors help
students to talk out the problem and find out where the error was.Asking the professor for help is a
great way to establish a one-on-one relationship with him or her.All the effort from homework and help
is sure to pay off in one's ability to understand calculus.
From what I have mentioned, calculus may seem
overwhelming.To aid in retaining
the great accumulation of calculus knowledge along with two to four other
classes, one should make a smooth transition into college life.One should eat and sleep well as well
as find ways to relieve stress and allow for some rewarding free time.All of these will help with one's
patience, motivation, and happiness—essentials in making college a
success!
Calculus I has offered me a challenge.I assure that myself and other Calculus
I students will use the acquired understanding in problem solving and
situational analysis; and one does learn some interesting things.After all, I have acquired the ability
to find the volume of a triple-scoop waffle cone.And if I don't understand the problem at first, I can
figure out the rate at which the waffle cone is decreasing! | 677.169 | 1 |
MATH E-3 Quantitative Reasoning: Practical Math
This course reviews basic arithmetical procedures and their use in everyday mathematics. It also includes an introduction to basic statistics covering such topics as the interpretation of numerical data, graph reading, hypothesis testing, and simple linear regression. No previous knowledge of these tools is assumed. Recommendations for calculators are made during the first class. Prerequisite: a willingness to (re)discover math and to use a calculator.
(4 credits) | 677.169 | 1 |
HOMEWORK QUICK START
This book is straightforward and easy-to-read review of arithmetic skills. It includes topics that are intended to help prepare students to successfully learn algebra, including: * Working with fractions * Understanding the decimal system * Calculating percentages * Solving linear equalities * Graphing functions * Understanding word problems | 677.169 | 1 |
Theme of Conference:
This workshop will give an introduction to Painleve
equations and monodromy problems suitable for postgraduate students and
postdoctoral researchers. Topics to be covered include:
Speaker:
Philip Boalch (ENS Paris)
Title:
"Algebraic solutions of the Painleve equations" (2 lectures)
Speaker:
Thanasis Fokas (Cambridge)
Title:
TBA (on asymptotic analysis of the Painleve equations) (2 lectures)
Speaker:
Nalini Joshi (Sydney)
Title:
"Asymptotics of Painleve equations" (2 lectures)
Speaker:
Jon Keating (Bristol)
Title:
"Random matrices and Painleve equations" (2 lectures)
Speaker:
Marta Mazzocco (Manchester)
Title:
"Hamiltonian structure of the Painleve equations" (2 lectures)
Speaker:
Frank Nijhoff (Leeds)
Title:
"Discrete Painleve equations" (2 lectures)
Speaker:
Kazuo Okamoto (Tokyo)
Title:
"Introduction to the Painleve equations" (4 lectures)
Speaker:
Hiroshi Umemura (Nagoya)
Title:
"Differential Galois theory and the Painleve equations" (4 lectures)
Speaker:
Yousuke Ohyama (Osaka)
Title:
"Classical solutions on the Painleve equations: from PII to PV" (2 lectures)
PAINLEVE EQUATIONS AND MONODROMY PROBLEMS: RECENT DEVELOPMENTS
in association with the Newton Institute programme entitled "The Painleve
Equations and Monodromy Problems" (4-29 SEPTEMBER 2006) and is
an activity of the Marie Curie FP6 RTN ENIGMA (European Network In
Geometry, Mathematical Physics and Applications) | 677.169 | 1 |
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Test or improve reading, writing critical thinking and problem
solving skills with the leading
logic chapters in Volume 2. Logic mastery may ease or avoid
learning difficulties, and so make further studies easier - just add
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Improve the quality of written work in mathematics with this
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signs shows how to do and record evaluation steps, so that they can
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work" makes the domino effects of care and mistakes easier to
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Why do we study slopes, factored polynomials and the max-min analysis
of functions in high school? Answer are given by this light calculus
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Volume 3, Why Slopes and More Math.
Check basic arithmetic skills with the
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here?"
"That depends a good deal on where you want to get to," said the Cat.
"I don't much care where--" said Alice.
"Then it doesn't matter which way you go," said the Cat.
"--so long as I get SOMEWHERE," Alice added as an explanation.
"Oh, you're sure to do that," said the Cat, "if you only walk long
enough." (Alice's Adventures in Wonderland, Chapter 6)
--
Different ends and values for instruction leads to disagreement on what
should be met, how and why. No position on mathematics education will
please all. The site position is based on a technical view of how later
concepts and skills depend on earlier ones, and in particular on what
mastery of calculus requires from earlier studies at the high school and
even primary school level. However, preparation for calculus should not
be the only aim for earlier schooling. For more context and motivation
and for less student alienation, ideas and methods with take-home value
clear to students and their parents may provide another focus, a maximal
one, for early instruction. Clear ends and values may focus and motivate
mathematics education and in the process lead to fewer topics. Then skill
and concept development may proceed with quality first and quantity
second.
Site Origins & Limitations
Writing began offline in the last few days of 1990 to address two
mathematics education obstacles:
First, common fears and difficulties may be explained by
concept and skill development steps to big for most, not all.
Second, student alienation from mathematics mastery may be
explained by those fears and difficulties, combined with an
absence of reasons or context for mastery of concepts and
skills, one at a time, one after another.
Since 1990 or so in Canada, the UK and the USA, many teacher
education programs advocate pychological theories of learning in
which instruction aimed at student mastery of given ideas and
methods is regarded as substandard and unreliable end for
instruction. Unreliability may be reduced by addressing the two
obstacles just mentioned. However in practice for decades before
and after 1990, educational authorities have set final
examinations which hope for mastery of ideas and methods in
mathematics and other disciplines in a repeatable and
reproducible manner. If the conflict seen here between
educational theory and practice leads to course design and
delivery with little or no respect for how later ideas and
methods depend on earlier ones, then we have a third obstacle to
student mastery of higher level ideas and methods in mathematics.
While holding student back a grade or two will harm their
self-esteem, the continual promotion of students in schools
without respect for how mastery of later ideas and methods stands
on mastery of earlier ones will eventually undermine and destroy
student skills and confidence. Site material in providing lessons
and lesson ideas, and in offering ends and values below may,
albeit not all certain, ease the foregoing problems in logic and
mathematics education.
The composition of ideas and methods, offline in 1990 and online
since summer 1995, was and remains an iterative affair. It was
guided by inductive
principles for instruction aimed at student mastery of given
skills and concepts. met in 1981 outside of mathematics.
Every master of mathematics knows how mathematical induction
may fail, and by analogy how such instruction may fail. In
particular, Common fears and difficulties may be explained by
steps missed and by steps too big, not for all, but for most.
Remedies may follow from smaller or alternative steps to make
mastery of key skills and concepts easier and quicker. Site
technical and wordy remedies for common fears and difficulties
will fail when and where students and schools do not respect
how later skills and concepts depend on earlier ones.
The student or school wanting algebra be taught well without a
previous mastery of exact arithmetic with decimals, fractions
and signs is setting the stage for a mastery of algebra too
weak for strong courses in mathematics at the college and
senior high school level. Skill and concept development to
succeed has to respect how later ideas and methods stand on
earlier ones.
While no amateur nor professional has the right to impose a
mathematics education program on students, parents and
educational authorities, today any one may propose one online.
The reforms or remedies here like those elsewhere need to be
tried and tested before general use. Incomplete ideas for reform
rushed into service may disrupt education more than it helps.
Principles for instruction no matter how good need to be fully
supported by lessons and lesson plans likely to work in a
repeatable and reproducible manner for more.
By fall 2011, site lessons and lessons ideas for addressing
content, that is concept and skill, mastery difficulties were
essentially online in full but in some need of editing and
pruning. Between spring 2012 and 2013, the issue of why and what
to learn or teach in logic and mathematics was addressed first in
a first phase program for mathematics and logic instruction, and
then in the ends and values outlined below. Here again, there is
some work to be done in identifying and presenting skills and
concepts with take-home value for daily or adult life in ways
that may also serve further instruction. While the site author
has a doctorate in mathematics with ten plus years of experience
in instruction, the composition of site material in the last two
decades has been generally without further classroom experience.
So the composition of site ends, values and lesson ideas has
mostly been a post-classroom experience driven by inductive
principles and standards for concept and skill development,
and by kind reviews.
For students, which way to go in mathematics and how far depends on the
motivation found in school or which they bring to school. High marks
provides motivation for those who like to perform for themselves or for
parents and teachers. Further motivation of a social nature comes if a
student likes a teacher, belongs to a group of students who are competing
academically, or has parent who favours hard work in school and college.
But the apart from that, the short- and long-term end and values below
offer sounder context for skill and concept development.
Courses in mathematics and science are in part like movies or books. What
a course covers, how and why, is often a mystery before its end and to
often after. For most students, the question why learn or study a subject
or a topic appears. The appearance is a sign of intelligence. Some
students have parents who say mathematics mastery is important. But nany
have parents who in recalling their experience express a dislike for
mathematics after primary school. But if we combine ends and values from
earlier times, we may arrive at overlapping sets of ends and values for
learning and teaching primary and high school mathematics. These ends and
values are easily understood and repeated, and likely to be just right
for some. The first two ends reflect the actual or potential needs of
adult or daily life, and in trades and activities that do not require
common studies. The third end reflect the needs of calculus-based college
programs and of advanced, senior high school science courses. The first
two ends are more immediate than the third end. For the first two ends,
if not the third, over-preparation is better than under-preparation to
students and their families earn their livelihoods and to rationally
defend their interests in a world where daily behaviour, and contracts
involving money matters or income have huge consequences for individuals
and their families.
For mathematics and logic instruction, preparing children and teenagers
to earn income as adults may meet the need of employers, but more
importantly, it may and should meets the needs of students and their
families for earning income in employment or self-employment, and
defending their own interests while changing jobs or being fired from a
long-term post. While high school, trade school, undergraduate
university programs and graduate university programs may open doors for
gainful employment, education too long or too much may also distract
from gainful employment. Showing students early how to handle money
matters in daily and adult life from not going into debt while buying
or selling to evaluating the immediate or long-term value of a
mortgage, a pension plan or the income stream and benefits of a job
with or without benefits may help them face or avoid common situations
and difficulties.
Early mathematics skill development may serve common arithmetic and
geometric needs in daily and adult life. That may include say the
common needs of precollege trades and professions. Preparation for
daily or adult life at home, at work and in travel requires us to
count, measure and calculate with money, time, length, area, volume,
speed and rates of change on paper or with the geometric help of
maps, plans and diagrams carefully drawn to scale. Arithmetic mastery
may include formula evaluation. Early skill development should make
us want to avoid the domino effects of errors. That has value for all
multistep methods in- and out-side of mathematics. Early skill
development, well done, may make mastery of routine skills and
concept common, while providing a partial base for college studies.
Focus mostly on method and ideas with actual and then take-home value
may lead students and their families to value and want mathematics
and logic in early instruction.
The scout motto "be prepared" for what may come applies. For better
and worse, numerical and logical skills and concepts are needed in
daily and adult life to understand others, to read and write
instructions precisely, and to correct yourself or others. There is
a great risk of making incorrect decisions if you do not fully
understand the numerical and logic reasoning used in arguments and
agreements between yourself and others. Mastery of logic and basic
mathematics, the more the better, will help you quietly recognize
faulty decision making, yours or that of others.
In early or later development of mathematics, or of reading and
writing abilities, logic mastery leads to more or full precision in
reading, writing, speaking and listening. This precision will ease or
avoid confusion in following and giving instructions in many arts and
disciplines at home, in school and in the workplace. Logic mastery
sooner rather than later is best for its take-home value. But when
may depend on each student. Before or beside logic mastery, early
skill development may emphasize how to do and record measurement and
arithmetic steps precisely, so that the steps can be seen and
verified, and so that students become aware of the need to avoid the
falling domino effect of errors. In this falling domino effect, a
mistake in one step leads the following steps to being in error,
except in the lucky case where a second or further mistake cancels
the effect of the earlier ones. For that, there should be no credit.
Plug: The leading math-free chapters of online Volume Three
Skills for Algebra on implication rules and their use in
deductive reason may lead the not too young to logic mastery.
Mid- and senior- high school mathematics and logic skill development
may build on early development to serve the needs of senior high
school science and technology courses, and the needs of
calculus-based college programs in commerce, science, engineering and
technology. Calculus in the first instance consists of calculation of
slopes for linear and nonlinear curvers y =f(x). The key role of
slopes in calculus explains why slopes and rates of change need to be
mastered in earlier studies. Hint, Hint Site volume 3 with its
light calculus previews offer a context for the study of slopes,
factored polynomials and function maxima and minima may amuse and
inform students in courses leading to calculus and in the first weeks
of calculus.
Students heading for calculus-based, college programs in business, if
they avoid demanding high school science courses, will not see senior
high school mathematics used before arriving in college. To compensate,
long-term value needs to be emphasized - the calculations and logic of
college level programs requiring calculus will be more difficult to use
and bend to our future requirements with a weak mastery of mathematics.
Site volumes 2 and 3 in forming and reforming the views of students and
teachers in senior high school mathematics as indicated above may inform
and amuse, and in the process provide some context and motivation for the
study of slopes, factored polynomials, function maxima and minima, and
calculus too.
All the ideas described briefly below are explained in more detail in
site algebra starter lessons and in site Volume 2, Three Skills and
Algebra. The arithmetic related ideas could have been placed with site
arithmetic lessons instead.
Arithmetic and algebraic expressions are often to complicated to
read aloud, term term by term. Diagrams too are better seen than "read
aloud". Outside of mathematics, a picture is worth a thousand words. In
mathematics, a symbol, an expression or a diagram better seen and
grasped in silence may also be worth a hundred to a thousand words.
There has been a great silence in arithmetic, algebra, geometry and
calculus because mathematical ideas and methods are often better
written and drawn in silence instead of being expressed and explained
aloud. Yet we may deliberately use more words to introduce skills and
concepts clearer, to talking unifying themes, and to improve
communication in circumstances where writing or drawing is not
possible. While demonstration how appears in site material, we will
identify where the greater use of words is possible. There is more to
mathematics than be given a formula, and numbers to use in it. But
remember, pictures and diagrams too can be employed alone and besides
words to make skills and concepts easier to learn and teach.
Before and besides the role of letters and symbols in algebra, we may use
words and numerical examples to talk about about and show how to
calculate totals and products by adding and multipling subtotals and
subproducts. We may also talk informally but precisely about counts and
measures as being known or not, constant or not, forgotten or not, and
variable or not. Many technical terms may be introduced and understood
before and besides the letters and symbols. Moreover, to gossip or talk
about people, places and activities, we need names, labels and phrases to
identify them. In mathematics, names and descriptive phrases such as the
compound growth formula, the rectangular area calculation, the
distributive law and the Chinese Square Proof of the Pythagorean Theorem
allow us to gossip and talk about calculations and further ideas in
situations where symbols and diagrams cannot be formed nor read. Most
formulas, methods and practices in mathematics and logic are named. For
people wanting and able to talk about what they learning with others,
learning the names becomes an asset and not a burden.
In describing how to calculate averages and how to compute the
perimeter of a polygon, word descriptions of how may be simpler or
not to understand and explain than formulas. As a first example,
the average of a set or sequence of numbers is given by their total
divided divided by the number (count) of set or sequence elements. As a
second example, the perimeter of a polygon is given by the sum of the
lengths of it sides, or more briefly by the instruction: add the sides.
As a third example, the total area of a region consisting of
non-overlapping subregions is given by a sum of subareas. In early
mathematics instruction, how to compute this or that may be easier to
understand and explain with words with the use of letters or symbols
being more complicated. But for the compound interest or growth
formula, for the quadratic formulas and later for the chain rule - do
not worry what computations these phrases name or identify, the the
letters and symbols in them are worth a thousand words. The greater use
of words advocated for earlier instruction here is not possible in
later instruction. So the silence will return.
Using rules and formulas forwards and backward, and talking about it
may end a further silence. Talking and writing about the forward and
backward use of rules and formulas provides a unifying verbal theme for
the study of logic, mathematics and science in school and college
studies. Most if not all rules and formulas are not only used directly in
a forward sense but also indirectly or backwards. Determing the constant
in a proportionality relation uses the relationship, an equation,
backwards. Once it is found, the proportionality relations may then be
used or rewritten forwards and backwards to compute or express the value
of one number or quantity in terms of others. The example here may not be
familar to you if you have not seen them, but by talking about the
forward and backward use of rules, formulas and proportionality
relations, the backward use will be expected and not be another surprise
for students weak and strong of mathematics, logic and science. This
forwards and backwards use is common pattern previously met and mastered
case by case in silence. Talking and writing about it introduces or
extends the oral dimension of skill and concept development.
Site algebra starter lessons and the online chapters of Volume 2, Three
Skills for Algebra, material, show how to learn and teach skills and
concepts with words, forwards and backwards. Algebra starter lessons
include a geometric, stick diagram introduction for solving linear
equations in a way that visually proves or improves fraction skills and
sense. Here fractional operations on stick diagrams are suppose to make
the algebraic solution of linear equations easier to grasp. However, in
entertaining a group of students during a one hour, substitute teaching
assignment, one keen student could not make the transition from solving
with stick diagrams to solving algebraically. It was not my place to give
him extra instruction. He may have been better served by more stick
diagram examples, or by a leap to the algebraic method. I cannot say.
Geometry too can help with the introduction of calculus and in providing
motivation or context for the study of slopes (remember the domain name
is whyslopes.com) and the study of factored polynomials alone and in
ratios (rational expressions). See site Volume 3, Why Slopes and More
Mathematics, online in full with a fall 1983 why slopes prequel. Volume 3
in a preview of calculus provide geometric motivation for the study of
slopes and factored polynomial to the location of maxima and minima of
functions.
The site introduction of complex numbers is geometric instead of
algebraic. It follows or re-invents a path in a 1951 book on Secondary
Mathematics (possibilities) by Howard Fuhr, a mathematician who
masqueraded as a mathematics education professor at Columbia University
and who as part of the NCTM leadership in the 1960s help develop and
implement the college-oriented Modern Mathematics Programs for skill and
concept development in primary and high school mathematics from counting
to calculus. The level of rigour in this geometric introduction of
complex numbers is not less than that in the geometric introduction of
trigonometry using triangles and/or the unit circles drawn in a Cartesian
plane.
The big steps in modern mathematics programs were too hard for
many to follow. Site material offer smaller steps to compensate. Before
modern mathematics programs, instruction had a greater focus on skills
and concepts with value for daily and adult life - work, mortgages and
investments included. The discussion of ends and values above suggests
preparation for daily and adult life as much as possible first and
foremost, and on preparation for college second while emphasing
anything in the latter that could have take-home value.
Site composition was driven by a search to remedy the skill and concept
development difficulties stemming from steps too big and steps without
clear value for students and their families in earlier programs in
mathematics and logic education - programs which aimed for student
mastery of selected skills and concepts. In consequence, site lessons and
lesson ideas include many expositional innovations to aid skill and
concept development. Most, if not all, are mathematically correct, with a
few small departures from earlier views to make instruction simpler.
In calculus and secondary mathematics, late primary mathematics too,
there are many different starting points for instruction.
For example, the site development of prime numbers begins with a
definition that is not the most general but with a definition that is
likely the easiest for students to understand and apply. For a second
example, the site essay on what is a variable, by talking or writing
about numbers and quantities varying in one sense or another, we
provide a prequel to the later, more formal and more algebraically
advanced view of what is a variable, a prequel that is easily
understood because it is wordy and pre-algebraic. For more examples,
see the site geometric development of complex numbers before trig, and
see light calculus preview in Volume 3, Why Slopes and More Math, and
see, still in Volume 3, the decimal prequel to the epsilon-delta view
or definitions of limits and continuity.
The choice of starting point need not reflect the conventions of higher
mathematics, conventions that may be arbitrary despited being widely
accepted. Instead, the choice of starting point may reflect the objective
of making skill and concept development simpler for students and their
teachers. The harder starting points may be left to advanced studies
involving fewer students and teachers.
Mathematics Literacy: Since students may leave school early,
we need to show them and give them mastery of reading, writing,
arithmetic and geometry with actual or potential take-home value for
their daily and adult life in local and distant communities. While
learning mathematics with comprehension is best, the take-home value
of basic and routine skills needed for daily and adult to important
to insist upon mastery with comprehension. In this course design and
delivery should emphasize the domino effect of errors in multistep
methods, numerical or geometric. And in arithmetic, students should
be shown how to do and record steps in a manner that their skills can
be seen and checked as done or later. In practical, skill-based arts
and disciplines from cooking to mathematics, skills needs to be
demonstrated to be believed, and indeed to be both taught and
mastered. In general, there are too many skills for a student to find
them or their refined form by discovery. The challenge for early
mathematics instruction is to identify and provide observable and
thus verifiable skills with take-home value that serves common or
routine needs while seamlessly preparing students for late
instruction.
Geometry with Proportionality First: To quickly support the
common, actual or potential, geometric use of maps, plans and
diagrams drawn to scale in daily and adult life, and in precollege
trades and professions, the site webvideo exposition of geometry may
include SAS, ASA and SSS methods or practices for the construction of
similar or proportional triangles, and in general assume that in
maps, plans and diagrams drawn to different scales that corresponding
angles are equal and corresponding lengths are proportional. So the
similarity or proportionality present in maps, plans and diagrams
drawn to scale may be exploited to indirectly measure angles and
lengths, and quantities computed from them. Trigonometry may then be
introduced as a way to calculate angles and lengths instead of
obtaining them direct from measurements, actual or of the
corresponding angles and lengths on maps, plans and diagrams drawn to
scale. The early mastery of common, and easily understood and
repreated practices with maps, plans and diagrams drawn to scale
provides a context for and even implies the assumptions and axioms of
Euclidean Geometry.
Geometry with Congruence or Isometery Second: For simpler or
more accessible account of Euclidean geometry, the site account does
not include a proof of the Pythagorean thereom. The Chinese Square
Dissection proof provides a more accessible alternative. The latter
is presented online in Volume 2, Three Skills for Algebra. Without
the Pythagorean thereom, Euclidean geometry may be easy enough to
return to the North American classroom in a way that shows high
school or college students how logic in the form of implication rules
alone and in direct deductive chains of reason appears in
mathematics.
Counting and Arithmetic with Decimals: Decimal place value is
the key to counting. We assume every set of fewer than 10, 100, 1000
and 10000, etc, can be divided into a group of upto 9 units, a group
upto 9 groups of ten, upto 9 groups of 100 and upto 9 groups of 1000
in manner that the count between 0 and 9 of units, 10s, 100s and
1000s are unique, albeit the division of set elements into groups of
units, 10s, 100s and 1000s is not unique. The foregoing division or
partition gives a unique, multidigit decimal way to write and record
the count or number of set elements in which each unit has a place
value. The concept of place value leads to and easily justifies
arithmetic counting shortcuts involving the addition, comparision,
subtraction and multiplication and even division of decimals. The
details are given in the site arithmetics section along with North
American, metric (or SI) and UK-German methods for writing and
reading aloud with words multidigit decimals without and then with a
decimal point. Comprehension of operations with decimals enriches
early instruction and may help some master these operations. Others,
most others perhaps, may find full explanation of why some operations
work too complicated for their liking. For them skill and confidence
in decimal methods may follow learning how to use the methods to
obtain repeatable and reproducible results via steps observable and,
if need-be correctable.
Counting and Arithmetic with Fractions: The fraction three
quarters when written or read aloud means three times a quarter. A
quarter ¥ is a unit fraction. Proper and improper fractions with the
same denominator all give a number or count of a unit fraction, that
associated with the same denominator. With the aid of decimal
representations forms of numerators, it is an easy matter to count,
add, compare, subtract and even divide multiples of a single unit
fraction. It also an easy matter to multiply a multiple of a single
fraction by a whole number - to form a multiple of a multiple. By
long division and regrouping, each improper fractions is equivalent
to a mixed numbers. In primary and secondary school, students may be
shown how to add and subtract fractions with unlike denominators by
raising terms to convert each fraction to another equivalent
fraction, so after conversion, each has a common denominator and so
is a multiple of a common unit fraction. Following this, students may
be shown how to compare, multiple and divide fractions by rote. Site
fraction lessons in contrast show how raising terms to obtain like
denominators explains and justifies methods to compare and divide
fractions while raising terms to ensure the numerator of the
multiplicand is a multiple of the denominator of the multiplier
explains and justify methods for fraction multiplication. The
justification of arithmetic with fractions sets the stage for the
justification of arithmetic with decimal fractions (multiples of
one-tenth, one hundredth, one thousandths) that usually denoted by
multidigit decimals with digits after and even before a decimal
point.
Comprehension of operations with fractions agains enriches early
instruction and may help some master these operations. Others, most
others perhaps, may find full explanation of why some operations work
too complicated for their liking. For them skill and confidence in
decimal methods may follow learning how to use the methods to obtain
repeatable and reproducible results via steps observable and, if
need-be correctable.
Prime Numbers and Fractions: For algebra alone or as part of
calculus, and for operations with complex numbers, students need an
efficient command of arithmetic with fractions where the denominators
are say less than 200. Prime factorization of whole numbers less than
200 is useful here. The development of prime number factorization
methods in the site arithmetic section shows how to use time tables
to recognize small primes, and how to use an olde square rule method
to quickly and efficiently obtain prime number factorization of whole
number less than 289 = 172, and to recognize primes less
than 289 as well. The foregoing path as demostrated in site
arithmetic section may be easier for people to learn and teach.
Prime factorization is also useful for a "simplification" of roots
involving whole numbers or their fractions, a simplification often
seen in trig and calculus. Mastery of exact arithmetic in high
mathematics requires mastery of some cosmetic standards or
conventions for the expression of fractions, roots and radicals.
Arithmetic with units and denominate Numbers - missing. Units
of measure and counting appear directly in daily and adult life, and
also in science and technology. Units of measure also appear in the
description of speed, acceleration and other first and second order
rates - rates that may be described as derivatives in calculus.
Modern mathematics programs did not mention nor sanction the use of
units and their multiples (denominate numbers) in high school and
college studies, albeit this use appear in science courses and in
some practical examples met in mathematics courses in trigonometry
and before. The site account of arithmetic and fractions with units
compensates for this. Albeit, the compensation is given in a do this,
do that manner, because of a lack of words on my part to provide
greater comprehension. Readers are invited to provide remedies. Early
algebra courses today may introduce monomials (products of letters or
"variables" to various powers) and operations on them alone and in
fractions before students understand the computational significance
of monomials and operations on them. Site algebra starter lessons
explanation of equivalent computation rules may provide a remedy for
that. But before or besides algebra, The same exercises with
monomials given by numerical multiple of products of units to various
powers may be more meaningful to students, while be a prerequisite to
the numerical description of rates and proportionality constants.
Algebra Starter Lessons. Showing students how to do and record
numerical and algebraic steps in ways that can be seen and checked when
done or later makes their mastery of multistep methods observable, and
hence verifiable or correctable. Showing should also make students
aware of the domino effects of mistakes, and the care needed to avoid
or correct such errors. The introduction and assumption of methods to
compute totals and products using subtotals and subproducts employs
practices that are too complicated in high school instruction to derive
from the usual axioms for arithmetic with real numbers. But the
assumption of these methods or practices extends the usual axioms and
from the perspective of advance mathematics gives a very redundant set
of axioms. But the same redundancy is justified as it makes early
instruction easier and more effective, and the extra assumptions have
immediate take-home value for daily and adult life not present in the
usual axioms. Now the usual axioms are best understood besides or after
a math-free mastery of logic. The usual axioms for the distributive,
commutative and associative law are algebraically described. Many
students find the algebraic description too remote or abstract. But if
we introduce the concept that each algebraic expression give a unique
computation rule, one that that be evaluated on paper or with the aid
of a program on a calculator or computer, we may observe from numerical
examples that different computation rules appear to be equivalent in
the sense that they give the same result. This small step of
introducing the concept of equivalent computation rules provides
another context, a different starting point, for understanding and
explaining distributive, commutative and associative laws in arithmetic
with many kinds of numbers, and eventually with numbers being replaced
by computation rules - those with numerical values.
Arithmetic without Calculators: To be over-prepared is better
and less risky than being under-prepared. A written, calculator-free
mastery of arithmetic with signs, decimals, fractions; with units of
measures; and with number theory practices is needed for a full,
traditional, mastery of algebra, trigonometry, complex numbers and
calculus. A full mastery of arithmetic with units of counting and
measures also has value for adult and daily life, and for further
studies in commerce, science, engineering and even mathematics
itself.
In modern urban life we depend on machines to simplify our daily
life. But calculators usage both simplifies and weakens mathematics
mastery, or that needed to understand decimals, fractions, algebra,
trigonometry and calculus. As a master of my subject with standards
for skill and concept development, I see the student who can only do
arithmetic with the aid of a calculator as being handicapped from
being too spoilt in earlier instruction. Any expectation that
quantitative skills and disciplines can be well-taught without a
written mastery of arithmetic with decimals and fractions is false.
Again, manually learning how to do and record work in steps that can
be seen and corrected as done or later may begin with evaluation of
arithmetic expressions and algebraic formulas. While calculators are
useful, failure to require manual student mastery of arithmetic
removes a starting point for observable skill and concept
development. In particular, mastery of observable steps that can
be seen and confirmed or corrected as done or later is also is key
part of showing and demonstrating abilities in problem solving, in
writing proofs and employing multistep methods at home, at work and
in studies in many arts and disciplines.
Mathematics after primary school has been difficult and without immediate
value for many generations of students. While some students have parents
who did well or who encourage skill and concept development, other
students have parents who may say mathematics after arithmetic is a waste
of time. High school and college students may attend courses because
those courses are required. In high school and college, students who base
their efforts only on whether or not their teachers are pleasing have a
shallow context and motivation for learning. Students for whom doing well
in tests and finals is the only motivation also have shallow reason for
learning. Cultural values for learning may appeal to some. But practical
ends and values may appeal to more.
In primary school, students and their families may see the 4Rs (reading,
writing, reasoning and arithmetic) as being useful in adult and daily
life. There-in lies content and motivation. But at the junior- and
mid-high school level, some mathematics and logic lessons are of actual
or potential service to daily and adult life for decision-making and
money-matters at home and the work place. Other lessons only have
long-term value for college programs that some students may never enter
or complete. Instruction may lean to the first kind of lessons initially
to provide ends and values easily understood and appreciated by students
and their families. Emphasizing the more useful methods and concepts
first may help retain student motivation and also help those who have
leave school early. But eventually, high school and college mathematics
has less and less take-home value besides more and more value for future
studies or courses that students may not see. Here again, instruction may
focus on the take-home value, when present to provide motivation.
At the precalculus level, instruction should focus on two kinds of skills
and concepts, those that have actual or potential take-home value for
daily & adult life, and for precollege trades and activities; and
those that prepare students for a light and then deeper command of
calculus. In the former, I would include a set-based development of
probability theory. In both streams, I might include matrix operations
but not linear programming. The latter can be left to college programs in
commerce, science, engineering and technology. I would restrict high
school mathematics to computations and proofs that are lead to repeatable
and reproducible results, and to the computation of averages useful in
small business for estimating demand for products and services being
sold. Further elements of descriptive statistics, I would leave to
college studies, or to high school courses on critical thinking.
The recommended focus may mean fewer topics are taught. For students not
heading for calculus-based studies, less with a focus of skills and
concepts with take-home value may be best. In the preparation of students
for calculus and senior high school mathematics, multiple topics with no
short-term value may be met. That short-term value will vary between
students. Students in courses required to prepare for calculus who do
take mathematically demanding, senior high school courses will see more
short-term value. In general, calculus and preparation for calculus is a
long demanding path which many find difficult or hard to complete. But,
here is a plug, site Volumes 2 and 3, make the path easier and throught
calculus preview make calculus and precalculus easier and more appealing.
To serve the skill and concept needs of the common person in the street,
we need to put first those skills and concepts with actual or potential
value for daily and adult life. Then students may attend school and go
home with methods that help themselves or their families in money and
other matters. Near the end of school coverage of arithmetic, geometric
and logic (or reading and writing) skills and concepts with actual or
potential service for daily and adult life, more algebra and higher level
geometry skills may be introduced to revisit and reinforce the foregoing
service while being of service to more trades and activities at the
precalculus level, and also being of service or preparation for senior
high school science courses and perhaps later studies in calculus. The
multiple ends and values in the foregoing need to be balanced. The
balance may depend on the local or immediate needs of students and their
families, that is, how long students are likely to remain in school; on
whether or not, they are likely to see all all ends and values served;
and on whether or not, the students are quick or slow learners.
The concept and skill development standards and principles for
instruction in results-oriented arts and disciplines, as espoused in site
material, seek to provide students with an observable and verifiable
know-how of the ideas and methods currently forming and characterizing
each art or discipline. The latter presents a moving targets as best
practices in each may vary over time and place. But in a moving target,
concept and skill mastery may be seen or empirically measured by student
response to questions. In each such art and discipline, students are
expected to retain know-how and build on it in a progressive manner, with
regression being a sign of weakness, or absence too long from practice in
an art or discipline. Each art or discipline comes with different
cultural and practical values, some more important than others in ways
that may justify its instruction or not in each school or school system.
Morover, course design and delivery needs to acknowledge that there are
multiple intelligences in learning and teaching styles. A style that is
suitable for instruction in the humanities where conclusions are highly
subjective is not suitable for instruction in mathematics and science
where the benefits, origins and limitations of ideas and methods need to
be indicated and mastered in all or part.
In modern mathematics programs for secondary mathematics
education, direct instruction aimed at student mastery of given
concepts and skills has been uncertain and unreliable due to steps too
big or hard for most to follow, and due a college-oriented choice of
concepts and skills with value too long-term for students and their
families. Those steps too big undermined course design and delivery.
However, direct instruction can address its own problems by serving
short- and long-term ends and values in the selection and arrangement
of course topics, and in offering smaller, more accessible and reliable
steps for concept and skill mastery. The key question is whether or not
remedies based on the smaller and alternative steps in site lessons and lesson ideas,
alone or with the proposed ends and values above, will be
effective..
Site lessons and lessons ideas from counting to calculus provide a
foundation for college level studies of modern mathematics. Site lessons
and lesson idea offer student and their teachers a mastery of concepts
and skills with comprehension, if that be wanted, based on a redundant
set of practices and axioms, whose redundancy can be explained and
removed in college course in or leading to modern mathematics. The ends
and value further offer reasons for mathematics and logic mastery that
students and their families are more likely to appreciate before
preparation for calculus becomes the main focus of instruction at the
senior high school level. For calculus, Chapter 14 of site Volume 3, Why
Slopes and More Mathematics, offers a decimal, error control development
of limit and continuity concepts that may stand alone, or be used to make
the epsilon-delta development much easier to understand and explain. Site
departures in early instruction from modern mathematics are intended to
provide TCPITS an more accessible view, but they are also intended to
develop the logical and algebraic maturity needed for college and senior
high school students to study modern mathematics if they choose or where
it appears in their programs of study.
Indirect Instruction Benefits and Limits
Indirect instruction has the advantage of enriching skills and concept
mastery in classes where there is time for individual and group
creativity. But the subjective nature of that enrichment means direct
instruction is needed to develop or at least consolidate mastery of core
skills and concepts, those on which later methods and ideas stand,
Moreover, for student mastery of skills and concepts of importance for
their take-home value, or importance for further mastery, direct
explanations seem more reliable and certain than indirect ones, and
easier to design and provide.
When and where direct instruction clear steps or lessons to
provide mastery of important skills and concepts, to aid student to
follow the steps and lessons as is or in briefer form, teachers may
provide circumstances and pose questions to indirectly lead student to
formulate ideas and skills and gain the experience on which direct
instruction may stand. But where direct instruction lacks those clear
steps and lessons, it is doubtful that indirect instruction will
provide a practical and clearer path to to student mastery of the given
skills and concepts. The ability to explain matters directly is likely
a prerequisites to the ability to provide skill and concept mastery
indirectly.
Each program of instruction aim at mastery of given ideas and methods has
varying degrees of success and failure, and of motivation and alienation
for students and their families. In the case of modern mathematics
programs for secondary and college studies, the very rigour that attract
some students repelled many more, and include steps too big and also, I
will missing, in course design and materials. Missing steps were missing
not only in modern mathematics programs for algebra alone and in advance
courses, but also in earlier methods or paths for concept development.
The missing steps represent old gaps inherited in the design and redesign
of mathematics instruction over many, many decades, if not a century or
two. Site material in providing smaller steps allows steps too big to be
recognized and gives remedies - full or not - to be tried and tested.
Given that students have multiple abilities levels, a situation inherited
from nature, how far students may go in mastery of mathematics depends on
their will and natural talent. Smaller steps should allow more to go
further | 677.169 | 1 |
A new model for graphing functions of complex numbers
4DLab plots complex functions in an integrated way: the domain and the range of a function are not shown apart. In fact, complex functions are plotted analogously as the real functions are plotted.
The traditional graphing procedure —in textbooks and in other plotting software— is to separate the function domain from the function range; this is because the domain is usually a plane region of a plane, and the range is usually a surface. But 4DLab follows the new transcomplex numbers approach, where the complex numbers are extended to 4–dimensional ordered pairs.
At last, the graphs of the functions of complex variables are meaningful!
The transcomplex numbers system is an extension of the complex numbers system to 4 dimensions. Complex variables are 2–dimensional while transcomplexs are 4–dimensional. There are other four entries numbers systems, like, for example, the quaternions. But only the transcomplexs combine the simplicity of the real numbers with the power of the complex numbers. But where the transcomplexs shine above all the others is in the graphs it produces: visually simple and beautiful; no more abstract "surfaces", no more dual and disintegrated plotting. 4DLab is the software made specially to plot transcomplex surfaces, but since mathematics is an integrated and unified field, 4DLab also follows this model. Thus, in the same way that 3–dimensional surfaces are plotted, the 2–dimensional real functions are also plotted: you use the same equation editor. Just write-in —the editor will check your syntax— and choose the type of rendering you wish.
Math can be inspirational!
4DLab was also a program made to produce aesthetically appealing images. There are many choices and parameters to choose or change. So, if you wish, your plots can be done over an appealing background, you can add your name, or the equation involved, etc.
4DLab is a new tool for learning math and a new tool for graphing 3D equations and 2D equations. This free software is a3D and 2D graphing software. Choose a picture —any picture; a texture, a landscape, a photograph— and plot it against a surface and you will visually grasp the concept of one-to-one (1–1) mapping. Complex math can be made simple by bringing some abstract concepts down to the point that it becomes personal.
Overall Features of 4DLab:
With 4DLab the function domain can be any rectangular shape; not necessarily square. Graphs can also be made of any rectangular sub domain of the main domain.
Surfaces can be shown in grid-only mode, or opaque with or without showing the grid mesh. Axes are shown exactly where they belong: intersecting the surface at the exact points.
For any function, the domain-to-range relation can be seen instantly by just moving the mouse over the the domain region. The corresponding point of a domain can be seen as a moving point, or as a line connecting the domain with the range. This is an useful tool, especially when a point in the space is relate to another point in the space far away, or not directly above, as with real functions plots.
The program incorporates a dedicated calculator to compute the coordinates of any point coordinates for any equation set, be them part of the equation domain or not.
The program can maintain a list of your favorite website links with editable comments. You can click on any of the saved links for immediate reference.
Decorate any of your math pictures with any background of your preference.
The coordinates axes names can be changed to adapt to your needs. So, instead of X, Y, or Z, the axes labels can be named: Ohms, or Degrees, or Distance, etc.
Surface or line pictures can be labeled as Fig.1, Fig. 2, etc, or the user can insert, his/her name or a copyright notice. Other labels are available. The notes are saved as part of the pictures.
Surfaces or line plots can be rotated and viewed from any angle. The program can show the surface plots intersection with the XY, or iZY planes. Pictures can be resized manually with the mouse, or can be resized exactly to any desired dimension with pixel precision.
The center of coordinates can be moved away from the center of the picture frame for better composition of those offset plots. | 677.169 | 1 |
(I previously reviewed the DVD tutorial for Algebra ½, and much of that information applies to Algebra I as well.)
In the past few years, our family has used the DVDs from Teaching Tape Technology to give additional instruction in Saxon Math for grade levels 4th through Advanced Math. We have been (and still are) extremely satisfied with these videos and the teacher, so when I had the opportunity to review the Algebra 1 (3rd edition) DVDs from Mastering Algebra "John Saxon's Way," I was intrigued--yet a bit hesitant. Could these videos measure up? Could I be objective? I can honestly answer "yes" to both questions.
These Algebra 1 DVDs come in a hard plastic case with clear sleeve protectors for each disc. There are 11 DVDs, covering over 20 hours of Saxon Math instruction (120 lessons) in a classroom setting. Each disc has about 12 lessons. To see the concepts that are covered in Algebra 1, visit the following link on the usingsaxonmath.com website: In addition, by using this outline of lessons covered in Saxon Algebra 1, you could correlate the DVDs to another pre-algebra curriculum.
Art Reed is a fantastic instructor. He is engaging and inspiring, but his approach is also straightforward and no nonsense--without a lot of fluff. But then again, he also has a great sense of humor. He is a professional through and through, and he knows his stuff. It is obvious that he enjoys teaching math and wants his students to master the material. I like his confident way of presenting each lesson, but he is also the first to say that he makes mistakes like everyone else. He expects students to take responsibility for their work and do what it takes to learn the material. He does not spoon feed, but he does explain each concept thoroughly and provide encouragement. He gives extra tips and information to make everything easier to understand, and I think his approach fosters a much-needed character-building "learning style." I also like the way he uses visual aids and manipulatives when needed to reinforce certain concepts.
Art Reed was a contemporary and friend of John Saxon, who passed away in 1996, so he has a firm grasp on how the program is to be used. Although now retired, Mr. Reed has over 12 years of classroom teaching experience using Saxon Math, and he has been a Saxon homeschool consultant during the last nine years. In addition, he is the author of the hands-on guide Using
John Saxon's Math Books, designed to help homeschool educators successfully use Saxon Math and save money too.
The cost of this DVD set for Algebra 1 (3rd Edition) is $49.95 with free shipping. You can visit the usingsaxonmath.com website for more information or to download sample lesson videos.
Overall, I think this is a wonderful set for homeschool families who use Saxon Math. The DVDs are the perfect solution for moms (or dads) who need a bit of assistance in teaching higher-level math. The students have access to an experienced instructor, and they can replay the videos as many times as they need to master the material. Personally, I was thrilled to find yet another great resource for Saxon Math instruction to add to our collection. I highly recommend Art Reed and the Mastering Algebra "John Saxon's Way" DVDs as a great investment in your child's mathematical education.
Product review by Amy M. O'Quinn, The Old Schoolhouse® Magazine, LLC, May 2010 | 677.169 | 1 |
This class is basically 3 mini courses of Matrix algebra/manipulation, Advanced Calculus, and Complex Variables. The matrix stuff is almost a rehash of what you leaned in undergrad math classes (341 maybe?). Advanced calc and complex variables gets a bit tougher, but with a good professor, these shouldn't be too bad.
Good teacher. Very friendly and encourages class interaction. Interjects a good bit of humor into his class as well. Explains stuff very clearly and speaks clearly. Homeworks and tests were always graded promptly and fairly. | 677.169 | 1 |
Basic Mathematics
Description
Basic Mathematics, by Goetz, Smith, and Tobey, is your students' on-ramp to success in mathematics! The authors provide generous levels of support and interactivity throughout their text, helping students experience many small successes, one concept at a time. Students take an active role while using this text through making decisions, solving exercises, or answering questions as they read. This interactive structure allows students to get up to speed at their own pace, while also developing the skills necessary to succeed in future mathematics courses. To deepen the interactive nature of the book, Twitter® is used throughout the text, with the authors also providing a tweet for every exercise set of every section, giving students timely hints and suggestions to help with specific exercises.
Features
The highly interactive approach combines concise instruction with a clean,innovative design to ensure that students are actively engaged in the material.
Guided Practice exercises are designed to sit alongside the examples in the text. Students navigate through finding a solution to a problem similar to the example they are shown.
Interactive Definitions accompany Examples and Guided Practice as appropriate to help students develop an understanding of a critical or difficult mathematical term.
"Do you Understand?" questions follow the Interactive Definitions, ensuring that students have absorbed the material. Students are then asked to determine if they've "Got it" or need to "Get Help."
The clean design includes a subtle yellow background on all pages to make reading easier on the eyes.
Topic-specificFlow Charts appear as appropriate throughout the book to walk students through the thought process needed to solve a particular type of problem.
Study tips are designed to reach today's students. Twitter® is used throughout the text, with the authors also providing a tweet for every exercise set of every section, giving students timely hints and suggestions to also help with specific exercises.
Vocabulary is heavily integrated in the exposition to reinforce comprehension.
Vocabulary Preview appears at the very beginning of each section. This familiarizes students with the key vocabulary for the section before they encounter it in context.
The second time the vocabulary is introduced is through Interactive Definitions; these appear with Examples and Guided Practice when students need to develop an understanding of a critical or difficult mathematical term. At the end of the feature, students see an additional "Do You Understand" question, followed by "Got It" or "Get Help."
Vocabulary Review appears at the start of every end-of section exercise set.
Students are given many opportunities to practice skills and reinforce concepts at every level of the text.
Objective Practice exercises appear after the examples, Guided Practice, and Concept Checks. Exercises are numbered, so they can easily be used as in-class work or assigned for homework.
End-of-Section Level:
Self Assessments appear at the end of the exercise set of the first section of every chapter after Chapter 1. Students are asked to evaluate how they did on their last test and how well they felt they had prepared for it.
Question Logs appear after the exercise set in each section. Students are provided an organized space to write down questions for their instructor.
Section Exercises are two-fold: they review all basic skills just learned and then incorporate those skills with higher-level thinking questions that include applications, analysis, and synthesis.
End-of-Chapter Level:
The Chapter Organizer appears at the end of the chapter. It serves as an additional review of key concepts, vocabulary, and procedures. Students are able to use this as a study aid for each chapter.
Chapter Review exercises follow the Chapter Organizer. Exercises are organized by section so students can refer back through the text for help.
Chapter Test follows every Chapter Review and covers the key topics within each chapter.
This text is available through the Pearson Custom Library. If your course does not cover all the chapters in this text, we encourage you to build a version that more closely matches your syllabus. Visit the Pearson Custom Library for more information.
Table of Contents
1. Whole Numbers
1.1 Understanding Whole Numbers
1.2 Adding Whole Numbers
1.3 Subtracting Whole numbers
1.4 Multiplying Whole Numbers
1.5 Dividing Whole Numbers
1.6 Exponents, Groupings, and the Order of Operations
1.7 Properties of Whole Numbers
1.8 The Greatest Common Factor and Least Common Multiple
1.9 Applications with Whole Numbers
Chapter 1 Chapter Organizer
Chapter 1 Review Exercises
Chapter 1 Practice Test
2. Fractions
2.1 Visualizing Fractions
2.2 Multiplying Fractions
2.3 Dividing Fractions
2.4 Adding and Subtracting Fractions
2.5 Fractions and the Order of Operations
2.6 Mixed Numbers
Chapter 2 Chapter Organizer
Chapter 2 Review Exercises
Chapter 2 Practice Test
3. Decimals
3.1 Understanding Decimal Numbers
3.2 Adding and Subtracting Decimal Numbers
3.3 Multiplying Decimal Numbers
3.4 Dividing Decimal Numbers
Chapter 3 Chapter Organizer
Chapter 3 Review Exercises
Chapter 3 Practice Test
4. Ratios, Rates, and Proportions
4.1 Ratios and Rates
4.2 Writing and Solving Proportions
4.3 Applications of Ratios, Rates and Proportions
Chapter 4 Chapter Organizer
Chapter 4 Review Exercises
Chapter 4 Practice Test
5. Percents
5.1 Percents, Fractions, and Decimals
5.2 Use Proportions to Solve Percent Exercises
5.3 Use Equations to Solve Percent Exercises
Chapter 5 Chapter Organizer
Chapter 5 Review Exercises
Chapter 5 Practice Test
6. Units of Measure
6.1 U.S. System Units of Measure
6.2 Metric System Units of Measure
6.3 Converting Between the U.S. System and the Metric System
Chapter 6 Chapter Organizer
Chapter 6 Review Exercises
Chapter 6 Practice Test
7. Geometry
7.1 Angles
7.2 Polygons
7.3 Perimeter and Area
7.4 Circles
7.5 Volume
7.6 Square Roots and the Pythagorean Theorem
7.7 Similarity
Chapter 7 Chapter Organizer
Chapter 7 Review Exercises
Chapter 7 Practice Test
8. Statistics
8.1 Reading Graphs
8.2 Mean, Median and Mode
Chapter 8 Chapter Organizer
Chapter 8 Review Exercises
Chapter 8 Practice Test
9. Signed Numbers
9.1 Understanding Signed Numbers
9.2 Adding and Subtracting Signed Numbers
9.3 Multiplying and Dividing Signed Numbers
9.4 The Order of Operations and Signed Numbers
Chapter 9 Chapter Organizer
Chapter 9 Review Exercises
Chapter 9 Practice Test
10. Introduction to Algebra
10.1 Introduction to Variables
10.2 Operations with Variable Expressions
10.3 Solving One-Step Equations
10.4 Solving Multi-Step Equations
Chapter 10 Chapter Organizer
Chapter 10 Review Exercises
Chapter 10 Practice Test
Appendices
A. Additional Practice and Review
Section 1.2 Extra Practice, Addition Facts
Section 1.3 Extra Practice, Subtraction Facts
Section 1.4 Extra Practice, Multiplication Facts
Mid Chapter Review, Chapter 1
Mid Chapter Review, Chapter 2
Mid Chapter Review, Chapter 9
B. Tables
Basic Facts for Addition
Basic Facts for Multiplication
Square Roots
U.S. and Metric Measurements and Conversions
Author
Brian Goetz has helped students of all levels achieve success in mathematics for sixteen years. As a curriculum specialist for the Grand Rapids Area Precollege Engineering Program, he created numerous materials to motivate and inspire underserved populations. Brian also ran a math learning center at Bay de Noc Community College, where he helped students exceed their expectations of success. Brian has been teaching at Kellogg Community College for eight years. A common thread throughout all his teaching experiences is that an active and supportive environment is needed for students to succeed. With this belief close to his heart, Brian finds working with the other authors to be one of the most rewarding experiences of his career. When he isn't working, Brian spends quality time with his family and friends, mountain bikes, and kayaks. He dreams of spending a summer kayaking around Lake Superior.
Graham Smith has spent his life immersed in education. He was raised in a family of six teachers, where dinner conversations often centered on public education. Since then, Graham has gained sixteen years of classroom experience, and spent the last 9 years teaching full-time at Kellogg Community College (KCC). The majority of Graham's professional life has been focused on the education and success of the under-prepared student, which he continues through this work as the Developmental Mathematics Coordinator at KCC. Graham's substantial training and experience in mathematics and education, as well as his training and certification in developmental education through the Kellogg Institute at Appalachian State University and the National Center for Developmental Education, provide a comprehensive understanding of developmental mathematics. This background and experience provide the author team with a well-developed perspective. In his spare time, Graham enjoys spending time with his wife Amy, catching big fish, playing the guitar, and tinkering with his car that runs on recycled vegetable oil.
Dr. John Tobey currently teaches mathematics at North Shore Community College in Danvers, MA where he has taught for thirty-nine years. Previously Dr. Tobey taught calculus at the United States Military Academy at West Point. He has a doctorate from Boston University and a Master's degree from Harvard. He served as the mathematics department chair for his college for five years. He has authored and co-authored eight college mathematics textbooks with Pearson. He is a past president of New England Mathematics Association of Two Year Colleges (NEMATYC) and is an active member of the American Mathematics Association of Two Year Colleges (AMATYC). In 1993 Dr. Tobey received the NISOD award for excellence in teaching. | 677.169 | 1 |
revolutionary text covers single-equation linear regression analysis in an easy-to-understand format that emphasizes real-world examples and exercises. This intuitive approach avoids matrix algebra and relegates proofs and calculus to the footnotes. Clear, accessible writing and numerous exercises provide students with a solid understanding of applied econometrics. This new approach is accessible to beginning econometrics students as well as experienced practitioners. "A. H. Studenmund's practical introduction... MORE to econometrics combines single-equation linear regression analysis with real-world examples and exercises. Using Econometrics: A Practical Guide provides a thorough introduction to econometrics that avoids complex matrix algebra and calculus, making it the ideal text for the beginning econometrics student, the regression user looking for a refresher or the experienced practitioner seeking a convenient reference."--BOOK JACKET. | 677.169 | 1 |
Where do I start?
Choosing a first course in math or computer science
Find your programming background across the top, and your math background
down the left hand side, of the following table. The table entry
where they cross will tell you what math course and what CS course to take
first.
Programming background
Little or none
Half a year
w/grade of B
or better
4 on AP CS AB,
or 5 on AP CS A
5 on AP
CS AB exam
Math background
"Hate math",
took very little
MTH 101/102
MTH 101/102
MTH 101/102
MTH 101/102
CSC 160
CSC 171
CSC 172
see advisor
Haven't taken
pre-calculus
MTH 110/140
MTH 110/140
MTH 110/140
MTH 110/140
CSC 160
CSC 171
CSC 172
see advisor
Took
pre-calculus
Under 15/25 on
dept. placement test
MTH 110/140
MTH 110/140
MTH 110/140
MTH 110/140
CSC 160
CSC 171
CSC 172
see advisor
At least 15/25 on
dept. placement test
MTH 141
MTH 141
MTH 141
MTH 141
CSC 171
CSC 171
CSC 172
see advisor
4 on AP Calculus BC
or 5 on AP Calculus AB
MTH 142
MTH 142
MTH 142
MTH 142
CSC 171
CSC 171
CSC 172
see advisor
5 on AP
Calculus BC exam
see advisor
see advisor
see advisor
see advisor
CSC 171
CSC 171
CSC 172
see advisor
MATH 101 and 102 are independent courses; you may take either or both,
in either order. They are not remedial courses on math skills, but
conceptual courses intended to demonstrate, through interesting real-world
applications, the usefulness of mathematics and mathematical notation,
particularly for students who "hate math". Those considering computer
science or physical science will find MATH 101 particularly useful.
MATH 110 and 140 are both referred to as "Pre-calculus", but MTH 140 goes
a little bit faster and includes trigonometry. Students planning
to major in math, computer science, or physics must take MTH 140; those
majoring in most other subjects may take either one.
Students planning to major or minor in math or computer science, as well
as those who have always liked math but don't like calculus, should also
take CSC/MTH 156 some time in their first few semesters.
CSC 160 is primarily for students who have never written a program before;
it uses the simpler Scheme language in order to concentrate on concepts of
programming rather than language syntax.
Those with a strong background in math or programming (e.g. in Java or C++)
may take it if they wish, or may skip it and go straight to CSC 171. | 677.169 | 1 |
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