text
stringlengths 6
976k
| token_count
float64 677
677
| cluster_id
int64 1
1
|
|---|---|---|
Costs
Course Cost:
$299.00
Materials Cost:
None
Total Cost:
$299
Special Notes
State Course Code
02125Students do best when they have an understanding of the conceptual underpinnings of calculus. This course stresses the dual concepts of conceptual understanding of calculus and fluency in the procedures that accompany those concepts. If students can grasp the reasons for an idea or theorem, they can usually figure out how to apply it to the problem at hand. We will study four major ideas during the year: limits, derivatives, indefinite integrals, and definite integrals. Students practice the skills of calculus while they solve real-world problems with calculus concepts | 677.169 | 1 |
Math
Pre-Algebra
This course provides students with a survey of preparatory topics for high school mathematics, including foundations for high school Algebra and Geometry.
Algebra I
This course expands on basic mathematical skills while developing the student's knowledge of the properties of the real number system and algebraic concepts. Throughout this course students also develop critical logical thinking skills. Topics include solving equations and inequalities, performing various operations with polynomials, factoring polynomials, algebraic fractions, graphing equations and inequalities, solving systems of linear equations, exponents and radicals, and quadratic equations.
Geometry
This course requires students to develop logical reasoning skills in order to use the properties of geometric figures to solve problems and write proofs. Algebraic concepts are reinforced throughout the course. Students explore the various topics with reference to realistic and relevant applications. Topics include points, lines, planes and angles, reasoning and proofs, line types, congruent triangles and relevant applications, quadrilaterals, connecting proportion and similarity, right angles, analyzing circles, polygons, surface area and volume, and coordinate geometry.
Algebra II
This course expands on topics covered in the Algebra I course. This course challenges students to continue development of logical thinking skills through a study of advanced algebraic concepts. Topics include problem solving through relations and functions (linear, polynomial, rational, quadratic, exponential and logarithmic) and graphing (linear functions, conic sections, exponential and logarithmic.
Calculus
Calculus is an elective course that covers the topics of first semester college calculus. This course covers various topics in differential and integral calculus and their applications.
AP Statistics
The purpose of this course is to introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes:
Students who successfully complete the course and examination may receive credit and/or advanced placement for a one-semester introductory college statistics course. This does not necessarily imply that the high school course should be one semester long.
Pre-calculus
The purpose of this course is to adequately prepare students for calculus by exposing students to the following material: Piecewise Functions, Defined Functions (Even and Odd Functions),.Polynomials, Rational Functions, Geometric Transformations of Functions, Algebra of Functions, Composition of Functions, Trigonometric Functions, Exponential Functions, Inverses of Functions, Logarithms, Parameters and Functions, Parametric Equations, Polar Coordinates, Graphing with Technology, Solving Equations, Curve Fitting and Conic Sections | 677.169 | 1 |
is a classic analysis written by French mathematician Edouard Goursat. This book covers such topics as integration, differential equation and multiple integral and etc. The proof are strict, and the development of proofs are much more make sense than today's delta-epsilon proofs. The theorems in the book are proved in a much more natural and intellectual way.
This is a study book devoted to the subject of differential and integral calculus. Although the study book was published for the first time in 1869, it has been very popular since then among readers who study mathematics. The study book contains very good explanations and wonderful examples of different kinds of differential and integral calculus | 677.169 | 1 |
This book provides a pedagogical and comprehensive introduction to graph theory and its applications. It contains all the standard basic material and develops significant topics and applications, such as: colorings...
47,99 $
Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical,...
149,99 $
A theft and a hold-up, an impostor trying to collect an inheritance, the disappearance of a lab mouse worth several hundred thousand dollars, and a number of other cases : these are the investigations led by...
109,99This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics,...
76,79 $
The P-NP problem is the most important open problem in computer science, if not all of mathematics. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications...
27,79 $
In the wrong hands, math can be deadly. Even the simplest numbers can become powerful forces when manipulated by journalists, politicians or other public figures, but in the case of the law your liberty—and...
19,79This book provides a detailed study of Financial Mathematics. In addition to the extraordinary depth the book provides, it offers a study of the axiomatic approach that is ideally suited for analyzing financial...
219,99 $
It is one of the wonders of mathematics that, for every problem mathematicians solve, another awaits to perplex and galvanize them. Some of these problems are new, while others have puzzled and bewitched thinkers... | 677.169 | 1 |
Success in your calculus course starts here! James Stewart's CALCULUS: EARLY TRANSCENDENTALS texts are world-wide best-sellers for a reason: they are clear, accurate, and fil [more].[less] | 677.169 | 1 |
Specification
Aims
The course unit will deepen and extend students' knowledge and understanding of algebra.
By the end of the course unit the student will have learned more about familiar
mathematical objects, will have acquired various computational and algebraic
skills, will have seen how the introduction of structural ideas leads
to the solution of mathematical problems and will have built a solid
foundation for any further study of algebra and algebraic structures.
Brief Description of the unit
Polynomials are familiar mathematical objects which play a part in virtually every branch of the
subject, e.g. solution of quadratic equations, the use of quadratic forms
to study maxima and minima of functions, approximation of functions by
Taylor or Chebyshev polynomials, the characteristic polynomial of a matrix,
etc. In algebra you have probably met problems involving factoring polynomials
and finding the gcd of two polynomials (in one variable) using the Euclidean
algorithm.
Historically the study of
solutions of polynomial equations (algebraic geometry) and the study of
symmetries of polynomials (invariant theory) were a major source of
inspiration for the vast expansion of algebra in the 19th and 20th centuries.
In this course the algebra of polynomials in n variables over a field of
coefficients is the basic object of study. The course covers recent advances
in the subject with important applications to computer algebra, together
with a selection of more classical material.
Learning Outcomes
On successful completion of this course unit students will be able to demonstrate
facility in dealing with polynomials (in one and more variables);
understanding of some basic ideal structure of polynomial rings;
ability to compute generating sets and Gröbner bases for such ideals;
ability to relate work with polynomials to the context of rings, ideals, and other
algebraic structures;
in particular, ability to solve problems relating to the factorisation of polynomials,
irreducible polynomials and extension fields;
facility in dealing with symmetric and alternating polynomials;
ability to relate work with symmetric functions to the context of invariants of finite
groups.
Future topics requiring this course unit
None.
Syllabus
Computing with Polynomials:
Polynomials in two or more variables, ideals in polynomial rings,
monomial
ideals, orderings on monomials, reduction and remainders, Gröbner
bases, Hilbert's basis theorem, S-polynomials and Buchberger's
algorithm.
Teaching and learning methods
Two lectures and one examples class each weekts. In addition students should expect to spend at least four hours each
week on private study for this course unit.
Course notes will be provided, as well as examples sheets and solutions. The notes will be
concise and will need to be supplemented by your own notes taken in lectures, particularly
of worked examples. | 677.169 | 1 |
This course is an introduction to the basic ideas of ordinary differential equations. Topics include linear differential equations, series solutions, simple non-linear equations, systems of differential equations, and applications.
Expected Educational Results
As a result of completing this course, the student will be able to do the following:
1. Analyze problems using critical thinking skills.
2. Use functions and their derivatives to construct mathematical models.
3. Solve application problems for which differential equations are mathematical
4. Solve the following kinds of first order, ordinary differential equations:
a. separable
b. homogeneous
c. exact
d. linear, and
e. Bernoulli.
5. Solve second order linear ordinary differential equations:
a. Homogeneous and non-homogeneous equations with constant coefficient
b. Power series solutions about ordinary and regular singular
6. Solve initial value problems using Laplace transforms.
7. Solve systems of linear differential equations.
8. Approximate a solution to a differential equation with a numerical method
9. Use some basic commands of a computer algebra system, and solve differential equations with them.
10. Determine the stability of linear systems.
11. Analyze almost linear systems.
12. Use the Energy Method to describe nonlinear systems.
13. Be able to identify the basic forms of bifurcation.
General Education Outcomes
I. This course addresses the general education outcome relating to communication by additional support as follows:
A. Students develop their listening and speaking skills through participation and through group problem solving.
B. Students develop their reading comprehension skills by reading the text and the instructions for text exercises, problems on tests, or on projects. Reading mathematics text requires recognizing symbolic notation as well as problems written in prose.
C. Students develop their writing skills through the use of problems requiring written explanations of concepts.
I. This course addresses the general education outcome of demonstrating effective individual and group problem-solving and critical thinking skills as follows:
A. Students must apply mathematical concepts previously mastered to new problems and situations.
B. In applications, students must analyze problems and describe problems with their pictures, or diagrams, or graphs, then determine the appropriate strategy for solving the problem.
I. This course addresses the general education outcome of using mathematical concepts to interpret, understand, and communicate quantitative data as follows:
A. Students must demonstrate proficiency in problem-solving skills including applications of differential equations and systems of differential equations.
B. Students must write differential equations to describe real-world situations and interpret information from the solution of differential equations and systems of differential equations.
C. Students must solve equations and systems of equations (both linear and which often arise in modeling numerical relationships.
I. COURSE GRADE
Exams, assignments, and final exam prepared by individual instructors will be used to determine the course grade.
II. DEPARTMENTAL ASSESSMENT
This course will be assessed every three years. The assessment instrument will consist of a set of open-ended questions, which will be included as portion of the final exam for all students taking the course.
A committee appointed by the Academic Group will grade the assessment material.
III. USE OF ASSESSMENT FINDINGS
The MATH 2652 committee, or a special assessment committee appointed by the Academic Group will analyze the results of the assessment and determine implications for curriculum changes. The committee will prepare a report for the Academic Group summarizing its finding.
Effective date of offering: Summer 2002
CCO completed 12/06/01
Reviewed by committee April 2005 | 677.169 | 1 |
Brand new. We distribute directly for the publisher. Winner of the CHOICE Outstanding Academic Book Award for 1997! The purpose of this book is to teach the basic principles [more]
Brand new. We distribute directly for the publisher. Winner of the CHOICE Outstanding Academic Book Award for 1997! The purpose of this book is to teach the basic principles of problem solving, including both mathematical and nonmathematical problems. This book will help students to...* translate verbal discussions into analytical data. * learn problem-solving methods for attacking collections of analytical questions or data. * build a personal arsenal of internalized problem-solving techniques and solutions. * become "armed problem solvers", ready to do battle with a variety of puzzles in different areas of life. Taking a direct and practical approach to the subject matter, Krantz's book stands apart from others like it in that it incorporates exercises throughout the text. After many solved problems are given, a "Challenge Problem" is presented. Additional problems are included for readers to tackle at the end of each chapter. There are more than 350 problems in all. This book won the CHOICE Outstanding Academic Book Award for 1997. A Solutions Manual to most end-of-chapter exercises is available.[less] | 677.169 | 1 |
Hailed by The New York Times Book Review as "nothing less than a major contribution to the scientific culture of this world," thisTable of Contents for Mathematics: Its Content, Methods and Meaning
Volume 1. Part 1
Chapter 1. A general view of mathematics (A.D. Aleksandrov)
1. The characteristic features of mathematics
2. Arithmetic
3. Geometry
4. Arithmetic and geometry
5. The age of elementary mathematics
6. Mathematics of variable magnitudes
7. Contemporary mathematics
Suggested reading
Chapter 2. Analysis (M.A. Lavrent'ev and S.M. Nikol'skii)
1. Introduction
2. Function
3. Limits
4. Continuous functions
5. Derivative
6. Rules for differentiation
7. Maximum and minimum; investigation of the graphs of functions
8. Increment and differential of a function
9. Taylor's formula
10. Integral
11. Indefinite integrals; the technique of integration
12. Functions of several variables
13. Generalizations of the concept of integral
14. Series
Suggested reading
Part 2.
Chapter 3. Analytic Geometry (B. N. Delone)
1. Introduction
2. Descartes' two fundamental concepts
3. Elementary problems
4. Discussion of curves represented by first- and second-degree equations | 677.169 | 1 |
Properties: Comprehend/Apply The learner will be able to
comprehend and apply the distributive, associative, commutative, inverse, identity, and substitution property to evaluate algebraic expressions.
Expressions: Procedures/Apply The learner will be able to
apply procedures for operating on algebraic expressions, commutative, associative, identity, zero, inverse, distributive, substitution, multiplication over addition.
Functions: Linear/Equations/Inequalities The learner will be able to
create equations and/or inequalities that are based on linear functions, apply many different methods of solution, and/or study the solutions in the context of the situation.
Figures: Two-/Three-Dimensional Objects The learner will be able to
precisely explain, classify, and comprehend relationships among types of two- and three-dimensional objects by applying their defining properties.
Math Concepts: Identify The learner will be able to
recognize concrete and/or symbolic illustrations of vertical, supplementary, complementary, and straight angles, parallel and perpendicular lines, transversals, and/or special quadrilaterals, and apply them to obtain solutions to problems.
Mathematical Reasoning: Explain The learner will be able to
apply many different methods to describe mathematical reasoning such as words, numbers, symbols, graphical forms, charts, tables, diagrams, and/or models.
Area/Volume/Length: Differences The learner will be able to
identify the differences and relationships between perimeter, area, and volume (capacity) measurement in the metric and U.S. Customary measurement systems.
Surface Area/Volume: Compute/Solve The learner will be able to
compute the surface area and volume of pyramids, cylinders, cones, and spheres and obtain solutions to problems involving volume and surface area.
Units: Choose/Metric/Customary The learner will be able to
choose suitable customary and metric measurement units for length (include perimeter and circumference), area, capacity, volume, weight, mass, time, and temperature.
Magnitude: Illustrate/Understanding The learner will be able to
illustrate an understanding of magnitudes and relative magnitudes of real numbers (integers, fractions, decimals) using scientific notation and exponential numbers.
Strategies: Daily life/Apply The learner will be able to
apply various methods, including common mathematical formulas, to obtain problem solutions of routine and non-routine problems drawn from everyday life. | 677.169 | 1 |
This collection of more than 55 activities compiled specifically for Algebra 1 including updated activities from Exploring Algebra with The Geometer's Sketchpad and many new ones cover topics such as fundamental operations; ratios and exponents; algebraic expressions; solving equations and inequalities; coordinates, slope, and distance; variation and linear equations; and quadratic equations. This curriculum module includes teacher's notes; activity prerequisites; time requirements; detailed answers; demonstration sketches enabling teachers to present the activities to the entire class; Explore More sections; Project Ideas; and a CD containing activity, demonstration, and supplemental sketches and other resources. Click here to download free sample activities from the book!
Available only in UK and Europe. Not available to US or other international customers
Price:
£36.00 excl Vat
Price:
£36.00 inc Vat
All required fields are marked with a star (*). Click the 'Add To Cart' or 'Add To Wish List' button at the bottom of this form to proceed. | 677.169 | 1 |
The first edition of this book (1965; Zbl 0193.34701) consisted of three parts: basic concepts, field theory and linear algebra, and as a modern down-to-earth approach with a personal touch it attained great popularity. The second edition (1984; Zbl 0712.00001) added some topics, mainly on commutative algebra and homological algebra.\par The current third edition has grown again, the additions dealing with topics close to the author's heart from number theory, function theory and algebraic geometry. For the math graduate who wants to broaden his education this is an excellent account; apart from standard topics it picks out many items from other fields: Bernoulli numbers, Fermat's last theorem for polynomials, the Gelfond-Schneider theorem and (as an exercise, with a hint) the Iss'sa-Hironaka theorem. This makes it a fascinating book to read, but despite its length it leaves large parts of algebra untouched. Semisimple algebras get a very cursory treatment (no mention of crossed products or the Brauer group) and there is only the merest trace of Morita theory; there are no Ore domains, Goldie theory or PI-theory. Graphs, linear programming and codes, constructions like ultraproducts and Boolean algebras are also absent, and lattices are only of the number-theoretic sort (reseaux, not treillis).\par Bearing these limitations in mind, the reader will nevertheless find a very readable treatment of many modern mainline topics as well as some interesting out-of-the-way items.\par Editorial comment: Note that there is also a 3rd ed. published by Addison-Wesley 1993 reviewed in Zbl 0848.13001. [Paul M.Cohn (London)] | 677.169 | 1 |
Maths Tuition
TUITION INFORMATION
Tutors 4 GCSE Mathematics Tuition
Adult Numeracy programmes are available at a number of different levels starting right at the basics running through to Level 2 (equivalent to Grade C at GCSE) so whatever your skill level, there is an Adult Numeracy programme which is right for you.
The Primary years are fundamental in the development of building blocks for all subjects, but particularly Maths and English. Children often find the regular repetition of times tables tedious and carry feelings of insecurity regarding their Maths education, well into adulthood.
Functional maths develops those practical, real life skills required in everyday situations. Problem solving skills, whilst closely related to logical mathematics skills, are different in the way they are developed.
There have been a number of changes to the GCSE Maths specifications and assessment practices over recent years, but the content and topics studied have remained fairly static.
Whether you are studying a Linear or Modular course at school at either Foundation or Higher tier, you will study: Number, Algebra, Geometry and Measure and Statistics both with and without a calculator. | 677.169 | 1 |
Precalculus Essentials, CourseSmart eTextbook Essentials' table of contents is based on learning objectives and condensed to cover only the essential topics needed to be successful in calculus. Using the text with MyMathLab, students now have access to even more tools to help them be successful including "just-in-time" review of prerequisite topics right when they need it.
This text offers a fast pace and includes more rigorous topics ideal for students heading into calculus.
Table of Contents
P. Basic Concepts of Algebra
P.1 The Real Numbers; Integer Exponents
P.2 Radicals and Rational Exponents
P.3 Solving Equations
P.4 Inequalities
P.5 Complex Numbers
1. Graphs and Functions
1.1 Graphs of Equations
1.2 Lines
1.3 Functions
1.4 A Library of Functions
1.5 Transformations of Functions
1.6 Combining Functions; Composite Functions
1.7 Inverse Functions
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Exercises for Calculus
Chapter 1 Practice Test A
Chapter 1 Practice Test B
2. Polynomial and Rational Functions
2.1 Quadratic Functions
2.2 Polynomial Functions
2.3 Dividing Polynomials and the Rational Zeros Test
2.4 Zeros of a Polynomial Function
2.5 Rational Functions
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Exercises for Calculus
Chapter 2 Practice Test A
Chapter 2 Practice Test B
3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Rules of Logarithms
3.4 Exponential and Logarithmic Equations and Inequalities
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Exercises for Calculus
Chapter 3 Practice Test A
Chapter 3 Practice Test B
4. Trigonometric Functions
4.1 Angles and Their Measure
4.2 The Unit Circle; Trigonometric Functions
4.3 Graphs of the Sine and Cosine Functions
4.4 Graphs of the Other Trigonometric Functions
4.5 Inverse Trigonometric Functions
4.6 Right-Triangle Trigonometry
4.7 Trigonometric Identities
4.8 Sum and Difference Formulas
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Exercises for Calculus
Chapter 4 Practice Test A
Chapter 4 Practice Test B
5. Applications of Trigonometric Functions
5.1 The Law of Sines and the Law of Cosines
5.2 Areas of Polygons Using Trigonometry
5.3 Polar Coordinates
5.4 Parametric Equations
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Exercises for Calculus
Chapter 5 Practice Test A
Chapter 5 Practice Test B
6. Further Topics in Algebra
6.1 Sequences and Series
6.2 Arithmetic Sequences; Partial Sums
6.3 Geometric Sequences and Series
6.4 Systems of Equations in Two Variables
6.5 Partial-Fraction Decomposition
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Exercises for Calculus
Chapter 6 Practice Test A
Chapter 6 Practice Test B
Appendix: Answers to Practice | 677.169 | 1 |
Offers an approach to introductory analysis with a constructive approach as opposed to the classical approach. There is no comparable book on the market.
Constructivism proves a chain of results and shows, ultimately, that the quantity can be constructed. This approach is gaining appreciation as an increasingly large number of computer science and related fields are encouraging a real analysis course for students.
Provides a unique look at the construction of real numbers as "consistent and fine families of rational intervals"
Includes hundreds of examples throughout the book, in all ranges of difficulty and length
Supplemented by a related web site that contains summaries of results with linked commentaries and references. Also includes links to web sites containing supplementary material and historical background.
Authored with a friendly voice, the book encourages and helps readers to conquer difficult points. | 677.169 | 1 |
Galvin Physics mastering reading comprehension, we learn to identify the main elements of story, talk about the story problems and how they get resolved, and draw conclusions. Predicting outcomes, talking about cause and effect relationships, and writing our own stories is part of the fun. Learning to use
...I use the book Algebra and Trigonometry with Analytic Geometry, by Swokowski and Cole, 10th edition. This is a college level book and I am confident it will help with learning the concepts of the course. High school algebra 2 requires students to dig deeper than the basic principles introduced ... | 677.169 | 1 |
Materials
Text The text book will be Precalculus by Stitz and Zeager. This
is an excellent, free book avalaible via a
Creative Commons
license. You can download the entire book for free from the
Stitz-Zeager website and you can purchase the first half of the book from
Lulu for $16. Here are direct links to the PDF
and Lulu pages:
Technology A graphing calculator is nice to have, but not a necessity
for this class. Some quizzes and some exams will require a simple (or better)
calculator. We'll have a few quizzes where calculators are not permitted.
Advice
Learning mathematics I expect that you wouldn't be in calculus
if you didn't already know that
mathematical study is a challenging, yet worthwhile endeavor. Mathematics
is the most natural language with which we describe the world around us and,
I believe, this this helps us better comprehend and enjoy the world.
However, understanding this deep language has a price - it's hard and takes
loads of work! I suggest that you spend at least 1.5 hours between classes
and at least 3 hours over the weekend studying each math class. Remember
that college is a full time job!
The Typical Week Typically, Monday and Wednesday will be
devoted to lecture over new material. I will assign a bit of homework
both of these days and you should do it as soon as you can. Thursdays
will usually be devoted to problem sessions. After I briefly answer a
couple of questions, you will work on a problem sheet in groups. This
is a great opportunity for you to learn material and to get feedback.
Furthermore, quizzes, (typically on Friday) will take problems right
off of these sheets.
Exam Week The exams are all on Friday. Problems will
be taken from homework, in class sheets, and a small collection of
review problems. We will typically review on the day before the
exam.
Help You are not undertaking this challenging task alone. Here
are a few sources of assistance.
Me I like to talk to people about mathematics! That's why I
chose this profession. Please feel free to approach me any
time you have questions.
Your classmates Most people learn mathematics best by talking it
through with others. You will find that you can both learn from and help
your fellow classmates. In particular, if your classmate is explaining a fine
point to you, then you are helping them!
The Math Lab We all know the Math Lab rocks! It's open long hours
and is located right across the hall from my office. You will welcome there and
will definitely find people to talk to about mathematics.
Grading
Exams There will be three exams during the term worth about 100
points apiece. The tentative dates for those exams are Friday February 3,
Friday March 2, and Friday April 6. There will be a comprehensive final exam worth
around 150 points on Friday April 27 at 8:00 AM for the early section and at 11:30 AM
for the later section.
Quizzes There will be quizzes worth 10 to 20 points
apiece almost every Friday.
In class work We will work problem sheets together most Thursdays.
You will earn a class participation grade of up to 40 points for this work.
Homework Homework will be assigned daily but not generally
collected. You will not be able to do well in the class without
doing the homework.
Final Grades I will determine final grades using
a scale not more stringent than the standard 90-80-70-60 scale.
You will be apprised of your standing as the term
progresses.
Late Work In general, I do not accept late work. I
understand, of course, that emergencies do arise. If so, please
contact me as soon as possible.
Cheating I trust students implicitly. I give take home exams
(in proof based courses)
and frequently leave the room during in class quizzes and exams. I
won't watch you like a hawk. However, it is surprisingly evident to
most instructors when cheating has occurred. I take cheating very
seriously, as I believe it undermines the objectives of academia and
the casual atmosphere I attempt to instill. If I have reason to
believe that cheating has occurred, I will not hesitate to inform the
provost and assign the offender a failing grade for the class. In
blatant or repeat offenses, my recommendation to the provost will be
dismissal from the university. Note that in the vast majority of
incidents of academic dishonesty, the potential rewards are very small
and the potential penalties are very high. | 677.169 | 1 |
Software Popular
In Mathematics there are having various different kind of the maths problems which are giving a valuable knowledge and we should give a strong foundation to the children in the mathematics , you may hear this word " Mathematic is the language of Science" so the kids need to do lot of the
This is a mathematics teaching software to the kids,are created to keep in mind about the teaching mathematics to the kids.this is a Arcade Based maths learning application which are very useful for the parents to teach the mathematics fact thorough a fun with effecive learning in mathematics.the
R is a Language and enviroment to statistical computing as well as graphics.this is equal to the S Language and Enviroment it was developed under the at Bell Laboratories (formerly AT&T, now Lucent Technologies) by John Chambers and colleagues.R are considering as a different
University and Colleage Students are looking a good advance Statistical Anaysis software for the learning purpose and it can be download fully and use it for your education use.this Free Statistical software are provding from the United Nations Educational Scientific and Cultural Organization and
This is Simply Scientific Calculating software for the Enginnering and Schools going Students surely can use this free application to calculate various problem and easyly find the soultion of that maths problem.it is used to evalutate the various engineering mathematics computation by using
This Numerical Calculation software are used for the engineering students who are looking to advanced mathematics learning software to performs the advacne maths performs and getting the correct solution .this maths application are primarily intended for numerical computations and it's
The Software Major Microsoftware provides a good educational tools for students at free of charge these application can be use for the mathematics calcuation,this software realy very useful to the schools or colleage students even in the classroom , this software brings a interest on the
This is the one of the best opensource environment Numerical Comutation math software for free for the engineering and the schools students can be use this software to calculate and know the solution of the numerical mathematics problem easy without making to invest the big amount.
A Open Source Mathematics application which is very useful for the all kind of the people they may be a students in shcools aro university ,Article writer or media and professor even scientist can able to use application for the maths writing purpose.
This is open source software application for calculating the Statistical Analysis and Matrix Algebra calculation for the students can use to calculate and find the solution of the problem of Statistical Analysis and Matrix Algebra.this software are developing on the support both of the School of | 677.169 | 1 |
Courses
Course Details
MATH 034A Basic Mathematics and Study Skills
4
hours lecture,
4
units
Letter Grade or Pass/No Pass Option
Description: This course is an introduction to fundamental concepts of arithmetic. Emphasis is placed on
addition, subtraction, multiplication, division and exponentiation on whole numbers, fractions, and decimals. Topics also include simple percents and ratios, systems of measurement, and applications of these topics. Students learn basic study skills necessary for success in mathematics courses. This course is intended for students preparing for Prealgebra. | 677.169 | 1 |
Introduction to Reasoning and Proof Prek - 2
9780325011158
ISBN:
032501115X
Pub Date: 2007 Publisher: Heinemann
Summary: "In Introduction to Reasoning and Proof, Karren Shultz-Ferrell, Brenda Hammond, and Josepha Robles familiarize you with ways to help students explore their reasoning and support their mathematical thinking. They offer an array of entry points for understanding, planning, and teaching, including strategies for encouraging children to describe their reasoning about mathematical activities and methods for questioning st...udents about their conclusions and their thought processes in ways that help support classroom-wide learning."--BOOK JACKET.[read more] | 677.169 | 1 |
Book Description: Matrix Algebra is a vital tool for mathematics in the social sciences, and yet many social scientists have only a rudimentary grasp of it. This volume serves as a complete introduction to matrix algebra, requiring no background knowledge beyond basic school algebra. Namboodiri's presentation is smooth and readable: it begins with the basic definitions and goes on to explain elementary manipulations and the concept of linear dependence, eigenvalues, and eigenvectors -- supplying illustrations through fully-worked examples.
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it | 677.169 | 1 |
FAQ
Why use freemathresource.com?
This site has been created to help you understand math better than you do right now. The information on the site will always be free for you to access at your convenience at any time of the day or night.
How can I get the most out of the site?
Getting the most out of the site depends on your goals. If your goal is to get help with a single question, then going through one article, lesson, or definition is what it required. If your goal is to improve your performance in math class, then regular use of the site can help you toward that goal.
I can't find the lesson I am looking for. Where is it?
The lessons are divided into courses on this site, so find the course you are taking and look at the menu of available lessons. If you can't find what you are looking for, the next best option is the search feature. Type in your lesson topic, keyword, or important definition in the search box to see what is available.
How do I leave a comment?
You must sign in to be able to leave comments on an article or lesson. If you are new to the website, then create a username and password
Why should I leave comments?
In math class, active participants usually do better than students who do the minimum. Becoming an active member of freemathresource.com will give you a chance to explain your thinking or give your opinion. Others may learn from the information provided in your comment just as you may benefit from reading someone else's comment. All participants win when there is active participation. | 677.169 | 1 |
While we understand printed pages are helpful to our users, this limitation is necessary
to help protect our publishers' copyrighted material and prevent its unlawful distribution.
We are sorry for any inconvenience.
The Elements of a Theory and a Report on the Teaching
of General Mathematical Problem-Solving Skills1
Alan H. Schoenfeld
INTRODUCTION
Can students be taught general strategies that truly enhance their abilities to
solve mathematical problems? Or are the heuristics described by Polya and
others merely a description of the actions of accomplished problem solvers? Are
they essentially valueless as prescriptions for problem solving? While many
mathematicians are convinced that they employ heuristics, there is little evidence that general problem-solving skills can be taught.I offered a course based on the applications of heuristics to mathematics majors at the University of California, Berkeley. This article presents the rationale
for heuristics and notes some questions about their effectiveness in the teaching
of problem solving. I offer some suggestions regarding these questions, and
describe the course I used to implement these suggestions. I discuss what we can
and cannot expect students to assimilate--heuristics they can learn to use and
obstacles that prevent them from employing others effectively.
SECTION 1. Problem Solving in Perspective: Theory and Practice
George Polya How to Solve It was published in 1945. That and his subsequent work laid the foundations for the study of general strategies for problem
solving in mathematics, focusing on the broad strategies he called "heuristics."
Definitions vary, but the following is compatible with Polya's usage:
A heuristic is a general suggestion or strategy, independent of subject matter,
that helps problem solvers approach, understand, and/or efficiently marshal
their resources in solving problems.
Examples of heuristics are: "draw a diagram if possible," "try to establish
subgoals," and "exploit analogous problems"; a more complete list is given in Section 3. A rationale for the study and teaching of heuristics is the following:
1.
Through the course of his career, a problem solver develops an idiosyncratic
style and method of problem solving. A systematic use of these strategies
may take years to develop fully.
2.
In spite of these idiosyncracies, there is a surprising degree of homogeneity in
the approaches of expert problem solvers. | 677.169 | 1 |
An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. It analyzes the idea of a generalized limit and explains sequences and functions to those for whom intuition cannot suffice. ... read more
Customers who bought this book also bought:
Our Editors also recommend:ics for the Nonmathematician by Morris Kline Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problemsMathematician's Delight by W. W. Sawyer "Recommended with confidence" by The Times Literary Supplement, this lively survey was written by a renowned teacher. It starts with arithmetic and algebra, gradually proceeding to trigonometry and calculus. 1943 edition.
Calculus: A Short Course by Michael C. Gemignani Geared toward undergraduate business and social science students, this text focuses on sets, functions, and graphs; limits and continuity; special functions; the derivative; the definite integral; and functions of several variables. 1972 edition. Includes 142 figuresMathematical Fallacies and Paradoxes by Bryan Bunch Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition Red Book of Mathematical Problems by Kenneth S. Williams, Kenneth Hardy Handy compilation of 100 practice problems, hints, and solutions indispensable for students preparing for the William Lowell Putnam and other mathematical competitions. Preface to the First Edition. Sources. 1988 edition.
Challenging Problems in Algebra by Alfred S. Posamentier, Charles T. Salkind Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, and more. Detailed solutions, as well as brief answers, for all problems are provided.
Challenging Problems in Geometry by Alfred S. Posamentier, Charles T. Salkind Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and more. Arranged in order of difficulty. Detailed solutionsProduct Description:
An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. It analyzes the idea of a generalized limit and explains sequences and functions to those for whom intuition cannot suffice. Many exercises with solutions. 1966 | 677.169 | 1 |
The best selling 'Algorithmics' presents the most important, concepts, methods and results that are fundamental to the science of computing. It starts by introducing the basic ideas of algorithms, including their structures and methods of data manipulation. It then goes on to demonstrate...
For departments of computer science offering Sophomore through Junior-level courses in Algorithms or Design and Analysis of Algorithms. This is an introductory-level algorithm text. It includes worked-out examples and detailed proofs. Presents Algorithms by type rather than application.
Designed for use in a variety of courses including Information Visualization, Human—Computer Interaction, Graph Algorithms, Computational Geometry, and Graph Drawing. This book describes fundamental algorithmic techniques for constructing drawings of graphs. Suitable as either a textbook ... | 677.169 | 1 |
Description
For freshman/sophomore, 1- or 2-semester/2—3 quarter courses covering finite mathematics for students in business, economics, social sciences, or life sciences departments.
This accessible text is designed to help students help themselves excel in the course. The content is organized into two parts: (1) A Library of Elementary Functions (Chapters 1—2) and (2) Finite Mathematics (Chapters 3—11). The book's overall approach, refined by the authors' experience with large sections of college freshmen, addresses the challenges of teaching and learning when students' prerequisite knowledge varies greatly. Student-friendly features such as Matched Problems, Explore & Discuss questions, and Conceptual Insights, together with the motivating and ample applications, make this text a popular choice for today's students and instructors.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.
Table of Contents
Part One: A Library of Elementary Functions
Chapter 1: Linear Equations and Graphs
1-1 Linear Equations and Inequalities
1-2 Graphs and Lines
1-3 Linear Regression
Chapter 1 Review
Review Exercise
Chapter 2: Functions and Graphs
2-1 Functions
2-2 Elementary Functions: Graphs and Transformations
2-3 Quadratic Functions
2-4 Polynomial and Rational Functions
2-5 Exponential Functions
2-6 Logarithmic Functions
Chapter 2 Review
Review Exercise
Part Two: Finite Mathematics
Chapter 3: Mathematics of Finance
3-1 Simple Interest
3-2 Compound and Continuous Compound Interest
3-3 Future Value of an Annuity; Sinking Funds
3-4 Present Value of an Annuity; Amortization
Chapter 3 Review
Review Exercise
Chapter 4: Systems of Linear Equations; Matrices
4-1 Review: Systems of Linear Equations in Two Variables
4-2 Systems of Linear Equations and Augmented Matrices
4-3 Gauss-Jordan Elimination
4-4 Matrices: Basic Operations
4-5 Inverse of a Square Matrix
4-6 Matrix Equations and Systems of Linear Equations
4-7 Leontief Input-Output Analysis
Chapter 4 Review
Review Exercise
Chapter 5: Linear Inequalities and Linear Programming
5-1 Inequalities in Two Variables
5-2 Systems of Linear Inequalities in Two Variables
5-3 Linear Programming in Two Dimensions: A Geometric Approach
Chapter 5 Review
Review Exercise
Chapter 6: Linear Programming: Simplex Method
6-1 A Geometric Introduction to the Simplex Method
6-2 The Simplex Method: Maximization with Problem Constraints of the Form ≥
6-3 The Dual; Minimization with Problem Constraints of the form ≥
6-4 Maximization and Minimization with Mixed Problem Constraints
Chapter 6 Review
Review Exercise
Chapter 7: Logic, Sets, and Counting
7-1 Logic
7-2 Sets
7-3 Basic Counting Principles
7-4 Permutations and Combinations
Chapter 7 Review
Review Exercise
Chapter 8: Probability
8-1 Sample Spaces, Events, and Probability
8-2 Union, Intersection, and Complement of Events; Odds
8-3 Conditional Probability, Intersection, and Independence
8-4 Bayes' Formula
8-5 Random Variables, Probability Distribution, and Expected Value
Chapter 8 Review
Review Exercise
Chapter 9: Markov Chains
9-1 Properties of Markov Chains
9-2 Regular Markov Chains
9-3 Absorbing Markov Chains
Chapter 9 Review
Review Exercise
Chapter 10: Games and Decisions
10-1 Strictly Determined Games
10-2 Mixed Strategy Games
10-3 Linear Programming and 2 x 2 Games--Geometric Approach
10-4 Linear Programming and m x n Games--Simplex Method and the Dual
Chapter 10 Review
Review Exercise
Chapter 11: Data Description and Probability Distributions
11-1 Graphing Data
11-2 Measures of Central Tendency
11-3 Measures of Dispersion
11-4 Bernoulli Trials and Binomial Distributions
11-5 Normal Distributions
Chapter 11 Review
Review Exercise
Appendixes
Appendix A: Basic Algebra Review
Self-Test on Basic Algebra
A-1 Algebra and Real Numbers
A-2 Operations on Polynomials
A-3 Factoring Polynomials
A-4 Operations on Rational Expressions
A-5 Integer Exponents and Scientific Notation
A-6 Rational Exponents and Radicals
A-7 Quadratic Equations
Appendix B: Special Topics
B-1 Sequences, Series, and Summation Notation
B-2 Arithmetic and Geometric Sequences
B-3 Binomial Theorem
Appendix C: Tables
Table I Area Under the Standard Normal Curve
Table II Basic Geometric Formulas
Answers
Index
Applications Index
A Library of Elementary Functions | 677.169 | 1 |
Mathematics is a subject that entails counting, computing and calculating of numbers and at times even variables. Earlier, abacus was used by man for the purpose of mastering the skill of counting but with the passage of time more sophisticated calculators were developed. Thanks to technological advancement now there are various types of electronic calculators which are available for purchase, a percentage calculator being one of them. These calculators can be extremely handy in many situations. For instance, if you had to calculate some percentages then it is advisable to use a percent calculator.
Using the technology of a percentage calculator or any other kind of calculator for that matter has its own advantages and disadvantages. Calculators are considered as a normal tool these days, which can prove to be indispensable at times. There are two kinds of calculators: handheld calculators and online versions and an example of the latter would be the percent calculator. Online calculators are different from handheld calculators in the sense that they are far more superior because they provide a lot more functions. Some of these net calculators can even plot an equation into a graphical form.
Popular math calculators such as the percent calculator or other types of calculators are used by people from different walks of life such as technicians, students, engineers and teachers. Online calculators, including the percentage calculator, equip the user with a superior understanding of mathematical operations. These calculators assist them in the process of verifying their knowledge of mathematical formulae and theory. With the help of such a tool, they will be able to visualize a possible value of an unknown answer. Technicians and engineers rely on online calculators heavily because their line of work calls for the use of such devices.
A lot of people have prejudices against mathematics and they are just scared of what the subject entails. On the contrary, mathematics is a subject that is very logical and unless the individual understands the logic behind it, he/she would always find it hard to figure things out. Online calculators like percentage calculator can remove some of the prejudices against mathematics to a certain extent. If you are wondering how a percent calculator or any calculator can help one understand mathematics, then the answer lies in the tendency of such calculators to provide explanations to its workings.
In order to understand how such calculators can help you understand math, make use of a high quality and ultra efficient percentage calculator. This can easily be located online in various websites and you just have to ensure that the option which you have chosen provides explanation of how the answer or solution was obtained. Now use the percent calculator to solve a sum that you do not understand. Once you verify the accuracy of the answer, you can then access the explanation part and see the step-by-step instructions on how the answer was calculated.
If you combine online calculators with online self-tutor resources then you will get the ultimate "dream team" to help you combat all your math problems. Using an online percent calculator is not at all difficult – you just have to enter some information from the sum that you are looking to solve. After this, you just have to click on a mouse button and the percentage calculator would do all the hard work for you and display the answer on your computer screen. So the next time when you are having difficulty with your mathematics homework or anything related to mathematics then make use of free online calculators as these magnify the beauty of mathematics.
Given the rising popularity of the Internet it is but natural for people to shift to an online percentage calculator to assist them in their work. Amongst the many advantages of a percent calculator one of the foremost is its convenience which adds to the fun of solving | 677.169 | 1 |
Griffin, GA CalRadicals Here we will define radical notation and relate radicals to rational exponents. We will also give the properties of radicals. Polynomials We will introduce the basics of polynomials in this section including adding, subtracting and multiplying polynomials | 677.169 | 1 |
COLLEGE ALGEBRA >CUSTOM<
Book Description: New Features
* Objective Based Learning: Introductory section objectives have been expanded to include the "what and why" of the objectives, followed by icons within the text identifying the specific areas of focus. A summary of chapter objectives will now be featured in the chapter summary material.
* Mathematical Modeling and Data Analysis: A focus on mathematical modeling and data analysis, specifically establishing a step by step process for understanding word problems and gathering the data from said problems.
* Graphical Interpretation:
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it | 677.169 | 1 |
Specification
Aims
To introduce students to representations of groups over the
field of complex numbers.
Brief Description of the unit
In the second and third year course units on group theory we have
seen that abstract groups are quite complicated objects. One of the most fruitful
approaches to studying these objects is to embed them into groups of matrices (to
"represent" the elements of an abstract group by matrices). The advantage of
this approach lies in the fact that matrices are concrete objects, and explicit
calculations can easily be performed. Even more importantly, the powerful methods of
linear algebra can be applied to matrices. The course is devoted to representations of
finite groups by matrices with entries in the field of complex numbers.
Learning Outcomes
On successful completion of this course unit students will
know the basic properties of complex
representations of finite groups and be able to use them in examples;
understand the relationship between a representation and its character;
know the basic properties of characters and use them in examples;
know the basic properties of a character table and be able to calculate character tables for certain small
groups. | 677.169 | 1 |
Math Class--Have You Seen the Preview?
H. Louise Amick, Washington College
I've always suggested to students that they read ahead in the text to have
some idea of what is to be discussed in class, but that suggestion hasn't
always been successful. Some students have ignored my advice knowing they
will survive by coming to class, while others have struggled to comply, but
found that the text really wasn't readable. My wish for previews that
students could really read and work through came true for one class when we
revised our Precalculus course.
When our department decided to require graphing calculators for
Precalculus, we were concerned about the financial burden that this
(together with the purchase of a text) would place on our students. We
decided that we could generate our own handouts for the course so that we
wouldn't need a text. A colleague and I agreed to collaborate on this
project. As we outlined and discussed the format of our handouts, our
summer project expanded into a summer spent writing a text.
Each chapter of the text is composed of three parts: a preview, a lesson,
and a problem set. The preview discussion and problems are to be done by
study groups prior to the presentation of the chapter in class. These
previews act as levelers---everyone comes to class with some knowledge to
contribute to the development of the chapter. The lesson section of the
chapter is very concise. Examples are included only when essential,
avoiding templates from which students can model their solutions to
problems. The problem sets contain a variety of problems, including
applications whenever possible.
We are not suggesting that it is necessary to write one's own text to
initiate class discussion and collaboration. While we are pleased with the
entire text and the changes it has produced in our classes, we believe the
previews are the key to our success. Consequently, we are advocating that
carefully developed previews can be used in any math class to foster
collaborative learning.
The nature of the previews we've developed for Precalculus varies over a
wide spectrum from reviews of prerequisite material to guided development of
formulas and identities. As we began to write each preview, we first asked
ourselves what prerequisite knowledge we would assume for the chapter and
how we could guide students to recall and review it. Then we focused on
how much of the chapter's content could be discovered by students through
experimentation with the graphing calculator, by applying geometry and
algebra, or through guided step-by-step examples that could be generalized.
One of the most successful previews has been the one shown below, which
introduced the chapter on composite and inverse functions. In developing
this lesson in class, I only had to provide the definition of a composite
function and the notation for an inverse function. Everything else sprang
from the students' discussion of their work on the preview.
Plot manually the three pairs of points and the line
y=x on the same coordinate system.
Describe as explicitly as possible the relationship of the
paired points to the line y=x.
If the coordinate system is folded using y=x as
a fold line, what relationship can be observed between the
paired points?
Show that the line segments
and are
perpendicular to the line y=x.
Show that y=x is the perpendicular bisector of
the line segments , and .
Show that , and in the
above problem satisfy the equation .
Show that , , and
in the above problem satisfy the equation .
Show that is
equivalent to .
Use your graphing calculator to sketch the graphs of , , and
y=x on the same viewing window without erasing.
These previews have allowed us to change our classes from lecture classes
into classes focusing on problem-solving and discussion. They have allowed
us to ``flesh out'' the lessons in class and develop our own examples.
Having done this, both the development of the lesson and the solving of the
problems in the problem sets become collaborative ventures. In addition to
the change in the atmosphere of our classes, we have seen measurable
success in another sense. Prior to the use of this approach, each year we
had approximately 25% of our Precalculus students either withdraw from
the course at midterm or fail at the end. Now only 14% do so. | 677.169 | 1 |
MAA Review
[Reviewed by Peter Olszewski, on 12/11/2012]
William Briggs, Lyle Cochran, and Bernard Gillett have written, in my opinion, a successful Calculus text. The true success of this text is that it reflects how today's college Calculus students learn: beginning with the exercises and referencing back to the worked out examples within the text.
The book has well thought out examples that will be clear to the student. Many pictures are given through out the text to aid students' understanding of the concepts. While reading the text, it was as though I was sitting in a Calculus class and my instructor was talking to me. In addition, there was a lot of handholding, but not overbearing handholding. The text is to the point! I fully enjoyed the pure mathematical examples with the well thought out pictures; they show the years of teaching experience of each author.
One of the first things I noticed in Chapter 1 was the way domain and range were treated from a graphical perspective, by taking any point on the curves and mapping it back to the x and y axes. The use of color is also helpful. In addition, I liked how the authors introduced the concept of secant lines early. In most other texts, they aren't introduced until the following chapter, which is typically about limits.
What I also really enjoyed about Chapter 1 was the review of trigonometry in Section 1.3. Many of my calculus students have forgotten the basic concepts of trigonometry, so it is a wonderful idea to have a review available, to be used at the instructors' choice.
As the title states, this text is for Scientists and Engineers, so it is fitting for secant lines to be quickly connected to velocity. The motivation for considering the slope of secant lines is very well done and the diagrams on page 41 are excellent. This is what the students need to see.
Jumping to the middle of the book, I strongly believe students are overwhelmed when it comes down to sequences and series. In most other texts I've read, sequences and series and all related topics are contained in one big chapter. Having these concepts broken into two chapters is more digestible for the students.
Of course, there are places where the book can be improved. I only mention a few.
In Chapter 1, the authors discuss domains and ranges of functions but not for compositions of functions. I would like to see examples of these, with graphics to support the solutions. In addition, having examples of finding domains and ranges of piecewise defined functions and domains and ranges of transformations of functions would further enhance this section. It has been my experience that students need extra guidance in finding domains and ranges.
After Theorem 2.2, I would recommend stating another theorem about using direct substitution of a polynomial and rational function followed by examples. In addition, I would like to see more examples following Example 6 on "other techniques" for finding limits analytically.
Many times, students forget simple algebraic concepts needed for Calculus. In the exercise set for Section 2.3, I believe the authors should limit the amount of problems where the limits of functions are tending towards a number a. I believe it would be more useful for students to see the direct numerical results as this is what they are more likely to see in their careers.
For Section 2.4, as an aid to help students understand the logic of when functions tend to zero and to infinity, it's useful to have an informal statement that 1/large tends to 0 and 1/small tends to infinity. This will help students quickly recall these two critical facts.
In Section 2.6, I feel as though there should be an example using the Intermediate Value Theorem involving a function before proceeding to the financial application.
The section on higher order derivatives in Section 3.2 is out of place. I strongly believe higher order derivatives need a section all their own, as there are many examples students need to see.
My suggestion for Sections 3.5 and 3.6 is that they be flipped. If the Chain Rule is learned first, many Chain Rule applications problems can be woven into the section on derivatives as rates of change.
I believe the statement of the Second Derivative Test in Section 4.2 will confuse students. Instead of saying, "If f′′(c) = 0, the test is inconclusive; f may have a local maximum, local minimum, or neither at c" I would suggest, "In such a case, the First Derivative Test can be used to determine if f is a local maximum, minimum, or neither."
While Example 3 is excellent in Section 4.3, I believe another example is needed before Example 3 involving a rational function that contains both vertical and horizontal asymptotes and a hole in the graph. In addition, Section 2.5 should be inserted in Chapter 4 before this section since the important connection to limits at infinity can now be made with the summary of curve sketching.
I was hoping to see more examples in Sections 4.5–4.7. I also feel as though Section 4.7, L'Hôpital's Rule, is out of place with the rest of the text. I believe this section should be either contained in Section 7.6 or be a new section before Section 7.6.
Reading further into the text, I believe there could be many more applications presented. For example, in Chapter 13, there are too many proofs in the homework set for dot products and the section on cross products ends very quickly with not enough applications. Section 13.7 is much better as the authors give many more applications. I especially enjoyed reading through Examples 5 and 6 in this section. So many times, students are told to ignore friction and air resistance. Here is a problem were the angle must be found to adjust the flight of a ball.
Moving to Section 13.9, once again, I believe there are too many proofs and not enough applied problems. After all, part of the title of the book is "for Scientists and Engineers"!
In the past, when I have taught engineering students, they wish to see how the mathematics they learn, whether it be calculus or matrices, will be used. Perhaps having student projects at the end of each chapter or section, specifically for the Sciences and Engineers could further enhance the text. The teaching and writing style of this text is excellent but I believe more applications would further student's motivation, creativity, and problem solving skills.
Peter Olszewski is a Mathematics Lecturer at Penn State Erie, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He can be reached at [email protected]. Webpage: Outside of teaching and textbook editing, he enjoys playing golf, playing guitar, reading, gardening, traveling, and painting landscapes. | 677.169 | 1 |
Secondary Mathematics II [2011]
Analyze functions using different representations. For F.IF.7b, compare and contrast absolute value, step and piecewisedefined functions with linear, quadratic, and exponential functions. Highlight issues of domain, range and usefulness when examining piecewise-defined functions. Note that this unit, and in particular in F.IF.8b, extends the work begun in Mathematics I on exponential functions with integer exponents. For F.IF.9, focus on expanding the types of functions considered to include, linear, exponential, and quadratic.
Extend work with quadratics to include the relationship between coefficients and roots, and that once roots are known, a quadratic equation can be factoredForming Quadratics
This lesson unit is intended to help educators assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representationGeoGebra
GeoGebra is dynamic online geometry software. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards Completing the Square Factoring | 677.169 | 1 |
A course designed to develop basic arithmetic and algebra skills to prepare for courses covering secondary school algebra, the first of which is MATD 0370. Content includes operations on whole numbers, integers, fractions, decimals, ratio and proportions, percent, solving linear equations in one variable applications, and relating simple algebra concepts to geometry.
Course Rationale
The Basic Math Skills course is designed to be the first course in a 3-course sequence for Developmental Math. The other two courses are Elementary Algebra and Intermediate Algebra. Students who pass Basic Math Skills will have a solid foundation in arithmetic of rational numbers, solving linear equations, and the beginnings of polynomial arithmetic.
A pre-test may be given upon request within the first week of class. If you do very well, and think that you might belong in the next-higher level course, Elementary Algebra (MATD 0370), you should discuss this with your instructor as soon as possible. In order to move up a level you will need to take the pre-test for MATD 0370 and do reasonably well on that test. A review for that pre-test is available on line at (or ask your instructor for a copy.) This will help you prepare and also give you an idea of the material that we cover in this course (MATD 0330) and that we will expect you to know as you begin MATD 0370. After looking at the review, you might decide that you actually need to stay in your current class. If, however, you are still interested in switching to the higher class, arrange to take that Elementary Algebra Pre-test as quickly as possible.
Attendance and Dropping:
There are 19 class meetings plus a final. I reserve the right to dropstudents who miss 4 or more classes. If you miss a lot of classes, you are ultimately responsible for withdrawing yourself to avoid a failing grade. Attendance is required for TSI mandated students, and so I will keep roll.
August 1st: Last Day to Withdraw.
Daily Lecture Schedule
Week
Mon
Sections
Wed
Sections
1
5/30
Intro: 1.1 - 1.3
2
6/4
1.4 - 1.6
6/6
1.7 - 1.9
3
6/11
2.1 - 2.3
6/13
2.4 - 2.6
4
6/18
3.1 - 3.4
6/20
4.1 - 4.3
5
6/25
4.4 - 4.6
6/27
5.1 - 5.4
6
7/2
5.5 - 5.7
7/4
no class
7
7/9
6.1 - 6.3
7/11
7.1 - 7.3
8
7/16
7.4 - 7.5
7/18
no class
9
7/26
8.1 - 8.3
7/25
8.4 - 8.7
10
7/30
8.9, 9.1 - 9.2
8/1
10.1, 10.3
11
8/6
10.5 - 10.7
8/8
Review
12
8/13
Final
8/15
Office Hours:
Current classroom if available 30 minutes before class, 4216a if classroom is not available.
Homework Assignments
Quizzes will be given at the end of every class over the previous class assignment. The quizzes will be closed book, but open homework. You must show work to receive credit. Many of the problems will be questions from the homework, on these questions it is expected you copy work from your completed homework. Quizzes will be returned the next classConcepts and skills associated with whole numbers
write the standard form of a whole number
round whole numbers and use rounding to estimate values involving whole number arithmetic
know the appropriate vocabulary and facts about angles, triangles, rectangles, squares, and circles
find perimeters of rectilinear figures
use standard formulas to find perimeters and areas of triangles, rectangles, squares and circles
find complementary and supplementary angles
find angles associated with parallel lines cut by a transversal
Statement on Scholastic Dishonesty
Acts prohibited by the college for which discipline may be administered include scholastic dishonesty, including but not limited to, cheating on an exam or quiz, plagiarizing, and unauthorized collaboration with another in preparing outside work. Academic work submitted by students shall be the result of their thought, work, research or self-expression. Academic work is defined as, but not limited to, tests, quizzes, whether taken electronically or on paper; projects, either individual or group; classroom presentations; and homework.
Statement on Scholastic Dishonesty Penalty
Students who violate the rules concerning scholastic dishonesty will be assessed an academic penalty that the instructor determines is in keeping with the seriousness of the offense. This academic penalty may range from a grade penalty on the particular assignment to an overall grade penalty in the course, including possibly an F in the course. ACC's policy can be found in the Student Handbook under Policies and Procedures or on the web at:
Statement on Academic Freedom
and a respect for a diversity of ideas and opinions. This means that students must take turns speaking, listen to others speak without interruption, and refrain from name-calling or other personal attacks.
Statement on Students with Disabilities
Each ACC campus offers support services for students with documented physical or psychological disabilities. Students with disabilities must request reasonable accommodations through the Office of Students with Disabilities on the campus where they expect to take the majority of their classes. Students are encouraged to do this three weeks before the start of the semester.
It is also recommended that instructors add the following:
Students who are requesting accommodation must provide the instructor with a letter of accommodation from the Office of Students with Disabilities (OSD) at the beginning of the semester. Accommodations can only be made after the instructor receives the letter of accommodation from OSD. developmental registration | 677.169 | 1 |
User dmitry - MathOverflowmost recent 30 from of Analytic geometry in modern undergraduate curriculumDmitry2011-03-28T07:20:12Z2011-03-29T22:52:41Z
<p>Hello.
I am a freshmen student in mathematics at Moscow State University (in Russia) and I'm confused with placing the subject called "analytic geometry" into the system of mathematical knowledge (if you will). </p>
<p>We had an analytic geometry course in fall; now we are having a course in linear algebra and it seems like most of the facts from "analytic geometry" are proved in a much more systematic and easier manner (quote from <a href=" rel="nofollow">wikipedia</a> "Linear algebra has a concrete representation in analytic geometry"). Many of our progressive professors also think that analytic geometry should be eliminated from the curriculum to clear more space for a linear algebra course. </p>
<p>So I'm confused:
1) if analytic geometry is a "concrete representation" of <em>linear algebra</em>, then why is it studied along with <em>calculus</em> (and not along with linear algebra) in US universities? (e.g. textbooks like <a href=" rel="nofollow">Simmons</a> )</p>
<p>There were, however, interesting parts of the course that were not covered in linear algebra: synthetic high-school-style treatment of beautiful topics like non-Euclidian and projective geometries.
Then
2) why <em>is not there a separate course</em> for such topics in US curricula? As I understand US freshman math majors study 2 basic subjects - real analysis and (abstract+linear) algebra (math 55 at Harvard, 18.100 and 18.700-702 at MIT). Are these geometric topics <em>integrated</em> into one of these courses or <em>are not they considered worth studying</em> for a modern math major?</p>
<p>Thank you</p>
<p>PS. This question is also important for me because it helps a lot to browse through US top universities for textbooks they use and notes. Unfortunately, Russian mathematical school is now in tatters and US textbooks are often significantly better. And since in high school geometry was among my favorite subjects I am particularly concerned about our geometry sequence and want to browse through best geometry syllabi.</p> | 677.169 | 1 |
This course provides students with a combined foundation in introductory and intermediate algebra topics that are NECESSARY skills for the study of a college-level mathematics course. Topics include real numbers, equations and inequalities, coordinate grid topics, exponents and polynomials, factoring, rational expressions, roots and radicals, systems of equations and quadratic equations. | 677.169 | 1 |
stella2java - Shodor Education Foundation, Inc.
Use Stella2java to make Java applets out of the modeling software package Systems Thinking Experimental Learning Laboratory with Animation (STELLA). Copy and paste your equations from Stella into a web form, answer a few questions, and download your applet.
...more>>
STELLA - isee systems
A model building and simulation software package. Read about STELLA-based materials such as Lessons in Mathematics: A Dynamic Approach. Get help with STELLA training, seek live support building a model, see tutorials, purchase supporting books and videos,
...more>>
Stella: Polyhedron Navigator - Robert Webb
"Small Stella" is a program for viewing polyhedra and printing their nets so you can build your own. It has over 150 built-in models, plus their duals. Models include Platonic solids, Archimedean, Kepler-Poinsot, Johnson solids, "Near Misses," and Stewart
...more>>
Stella's Stunners - Rudd CrawfordSteven Strogatz - The New York Times Company
Mathematics from an adult perspective -- from the basics of math to the baffling -- by Steven Strogatz, a professor of applied mathematics at Cornell University. This New York Times series is not meant to be remedial, but rather to give readers a better
...more>>
Stock-Trak - Stock-Trak
Stock-Trak is a virtual stock exchange simulator and fantasy stock market game. It allows its users to practice online stock trading within all of the major securities. Browse the site for information on stock investing research and fantasy stock market
...more>>
Strawberry Macaw's Puzzle Page
Although simple, this collection of four logic puzzles provides a challenge for students of any age. The interactive puzzles are: The Fox, the Duck, and the Bag of Corn; The Three Gallon and Five Gallon Cans; The Twenty-Three Matches Game; and The Game
...more>>
Stressed Out: Slope as Rate of Change - Cynthia Lanius
It's the night of the big game. You're in the locker room. The coach is pumping the team up. "Now, I know you people are nervous. That's okay, in fact, that's what we want. You're going to perform better on the court (stage) if you're a little nervous."Studying Mandelbrot Fractals - Suzanne Alejandre
What is a fractal? A definition and a Java applet to help in exploring the Mandelbrot set, redrawing small areas to fill the fractal screen and noticing how the images compare. Also links to other sites with fractal information for middle-schoolers.
...more>>
Studying Polyhedra - Suzanne Alejandre
What is a polyhedron? A definition and a Java applet to help in exploring the five regular polyhedra to find how many faces and vertices each has, and what polygons make up the faces. Also links to a page of information about buckyballs, stories written
...more>>
Study Island
Internet-based standards-mastery products, based on state standards. Subscriptions are available for single classes through districts, with individual subscriptions available for GED products.
...more>>
studymaths.co.uk - Jonathan Hall
Free help on your maths questions. See also the bank of auto-scoring GCSE maths questions, games, and resources such as revision notes, interactive formulae, and glossary of terms.Stupid Calculations - Josh Orter
Repository "where practical facts get rendered into utterly useless ones." Posts, which date back to May, 2013, have included "Monophone," musing on the size of the screen made from ripping the displays out of every iPhone ever sold and combining them
...more>>
subtangent.com - Duncan Keith
With Flash, explore interactive investigations such as Number Stairs and Diagonal Differences. Play Mathionaire, based on the popular TV game, but with maths questions. Quizzes include Function Machines, Number Properties, Pythagoras, and Quadratics 1.udoku
Flash-based game: enter a 9x9 grid so that every column, every row and each of the nine 3x3 segement contains the numbers 1 to 9. The game provides hints when you are stuck and has different levels.
...more>>
Sudoku - Pappocom, aka Wayne Gould
Finish filling in the 9x9 grid so that every row, every column, and each of the nine 3x3 boxes contains the digits 1 through 9. Different from a magic square, this puzzle requires no arithmetic, only reasoning and logic to deduce which digit to put where.
...more>>
A Su Doku solver
Solvers for sudoku puzzles, with documentation, source code, and binaries. Frequently asked questions about this numeric puzzle include "Su Doku" or "Sudoku"? How does the solver work? How do I compose a Su Doku problem? How few cells could appear on
...more>>
Sudoku Widget - Brian DeBoer
Macintosh OS X users familiar with Dashboard use its mini-applications to perform common tasks and get fast access to information. The Sudoku Widget by Brian DeBoer generates random puzzles with four different levels of difficulty, has the option to showSumdog - Peter Beckham, Crocodile Clips Ltd.
Free multi-player maths games designed to improve numeracy for students aged
9-13. Players compete either against the computer or other students around the world. The one hundred available games, which adapt to the skill level of each student, range
...more>>
Sumizdat Home Page - Sumizdat
Website of the publisher "Sumizdat", currently featuring the English translation of a classical Russian geometry textbook: Kiselev's Geometry/Book I. Planimetry, Kiselev's Geometry/Book II. Stereometry, and Arithmetic for Parents, translated from the
...more>> | 677.169 | 1 |
- Get to grips with converting your mathematics teaching over to Moodle - Engage and motivate your students with exciting, interactive, and engaging online math courses with Moodle, which include mathematical notation, graphs, images, video, audio, and more - Integrate multimedia elements in math courses to make learning math interactive and fun - Inspiring, realistic examples and interactive assessment exercises to give you ideas for your own Moodle math courses
In Detail Moodle is a popular e-learning platform that is making inroads into all areas of the curriculum. Using moodle helps you to develop exciting, interactive, and engaging online math courses. But teaching math requires use of graphs, equations, special notation, and other features that are not built into Moodle. Using Moodle to teach Mathematics presents its own challenges.
The book will show you how to set-up a Moodle course to support the teaching of mathematics. It will also help you to carefully explore the Moodle plugins that allow the handling of equations and enable other frequently used mathematical activities.
Taking a practical approach, this book will introduce you to the concepts of converting mathematics teaching over to Moodle. It provides you with everything you need to include mathematical notation, graphs, images, video, audio, and more in your Moodle courses. By following the practical examples in this book, you can create feature-rich quizzes that are automatically marked, use tools to monitor student progress, employ modules and plugins allowing students to explore mathematical concepts. You'll also learn the integration of presentations, interactive math elements, SCORM, and Flash objects into Moodle. It will take you through these elements in detail and help you learn how to create, edit, and integrate them into Moodle.
Soon you will develop your own exciting, interactive, and engaging online math courses with ease.
What you will learn from this book? - Convert mathematics teaching over to Moodle - Enhance your course with interactive graphs, images, videos, and audio - Integrate interactive presentations and explore different ways to include them in your course - Create your own SCORM activities using both free and commercial tools - Add rich animation and fun games by incorporating Flash games and activities for engaging your students - Build feature-rich quizzes and set online assignments - Monitor student progress and assess your teaching success - Configure Moodle to display the complete set of mathematical symbols and objects
Approach The book presents the reader with clear instructions for setting up specific activities, based around an example maths course (Pythagorean Theorem) with plenty of examples and screenshots. No Moodle experience is required to use the book, but the book will focus only on activities and modules relevant to teaching mathematics. We will assume that the reader has access to a working installation of Moodle. The activities will be appropriate for teaching math in high schools and universities.
Who this book is written for? The book is aimed at math teachers who want to use Moodle to deliver or support their teaching. The book will also be useful for teachers of "mathematical sciences", or courses with a significant mathematical content that will benefit from the use of some of the tools explored in the book. No Moodle experience is required to use the book.
Moodle 1.9 Math | 677.169 | 1 |
The videos on this page relate to topics from Section 2.3 of our current text. The section title is arithmetic combinations of functions. In this section, the authors address to a small extent how to sketch the graph of a function that is an arithmetical composition of a pair of functions | 677.169 | 1 |
New Syllabus Mathematics (6th Edition) Specific Instructional
On this page you can read or download New Syllabus Mathematics (6th Edition) Specific Instructional 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 keywords.
Before plotting graphs of functions, revise with the pupils the general method on the choice of scales for the straight line graph and the quadratic graphs that they had learned in Secondary 2 and the plotting of travel graphs and conversion graphs that they learned in SecondaryRemind them to label the graphs clearly. Pupils should be encouraged to draw the curves free hand as well as to use curved rules to assist them. There are many opportunities for teachers and pupils to explore this chapter using softwares such as Graphmatica, Winplot and others. | 677.169 | 1 |
This book guides students as they construct and manipulate geometric figures, and discover relationships and theorems on their own. It features over 100 activities covering virtually every concept st... More: lessons, discussions, ratings, reviews,...
These activities provide students with the opportunity to explore geometric concepts such as symmetry, transformations, and even fractal geometry in a way no other teaching tool can. The dynamic ca... More: lessons, discussions, ratings, reviews,...
This book guides students through a variety of proofs and applications of the Pythagorean theorem. By constructing and dynamically manipulating figures, students visualize the theorem and gain insight... More: lessons, discussions, ratings, reviews,...
Author Michael Battista has built what he calls the Shape Makers computer microworld, a series of explorations in which students develop dynamic mental models for thinking about geometric shapes an... More: lessons, discussions, ratings, reviews,...
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,...
Cabri 3D is interactive solid geometry software based on 3rd generation Cabri technology. It enables users to build and manipulate figures in 3D. It is entirely designed and developed by Cabrilog, and... More: lessons, discussions, ratings, reviews,...
Geocadabra is dynamic geometry software that supports students learning 2D and 3D geometry, functions and curves (with analysis), and probability.
The software was developed in Holland, and is avai...Students explore the relationship between equations and their graphs in this hands-on learning environment where they investigate, manipulate, and understand linear, quadratic and other graphs. They ...A test and worksheet generator for Pre-Algebra teachers. Create exactly the types of questions you are looking for. Lay out the questions on the page with automatic or manual spacing. Over 90 Pre-A... More: lessons, discussions, ratings, reviews,...
Tutorial fee-based software for PCs that must be downloaded to the user's computer. It covers topics from pre-algebra through pre-calculus, including trigonometry and some statistics. The software pos... More: lessons, discussions, ratings, reviews,...
QuickMathFacts is a tool that can be used at school or at home to increase proficiency in math fact memorization. It presents problems, within a selected set and a selected operator (addition, sub... More: lessons, discussions, ratings, reviews,...
Small Stella is the ideal entry-level polyhedron program for schools or anyone interested in geometry, with hundreds of polyhedra provided. Print out the nets required to build your own paper model... More: lessons, discussions, ratings, reviews,...
Cram is test preparation software to use on a mobile device. It allows you to create, import, share, and study for tests. Cram is suited for studying for job training, certifications, homework help, t | 677.169 | 1 |
A Potpourri of Graphical Solutions Using the TI-82
Alex Bezjak and David A. Young
The TI-82 Graphics Calculator, Texas Instrument's latest entry in the graphing calculator fields, can be quite useful in enhancing the teaching and learning of a wide range of mathematical topics.
This article will offer detailed instructions on the key-strokes necessary to analyze and illustrate problems dealing with
1. iterations with tables of values
2. graphing the orbits of iteration
3. descriptive statistics
4. inferential statistics
The authors will assume that the reader is vaguely familiar with appropriate function, editing, window, and mode setting keys. Make sure that the calculator is in the default mode - for this accept the entire left side of all menu choices when pressing the [ We will use the convention that a word in a represents a key on the TI-82, a word in BOLD represents an option from a menu listing, and I talics indicates a function key, which is accessed by the blue key in the first column.] key.
I. Iteration With Tables Of Values
We will look at two methods of iterating a function. They are
1. using theANS key
2. using the seq mode found in the menu of the key.
Method One
Let's produce six iterations of f(x) = x2 using the ANS key. Also let's start with a "seed" value of 0.5. Now enter these key-strokes:
These successive strokes produce an outcome of .25 which is the value of f(.5) = (.5)2. Now to generate the other five iterations, try these strokes:
. These steps set up an iterative algorithm that will generate the remaining iterations by pressing four consecutive times, resulting in a value of 5.42101086 E-20. The reader should note that pressing takes each f(x) value and places it in the domain and squares it.
Method Two
Let's attempt to iterate f(x) = x2 six times using the sequence mode. Press and use the arrow keys to highlight the seq option and press . These strokes place the calculator in the sequence mode. Now press which is the QUIT option that returns you to the home screen. Now enter and the screen should read:
" Un = "
" Vn = "
With the cursor blinking at " Un = " and any previous function cleared, key in these steps: . These steps place the function f(x) = x2 in the sequence mode which can be iterated by establishing the appropriate values in the window settings. For the window settings for this problem in the sequence mode try these numbers by pressing and using these values:
Un Start = 0.5, Vn Start = 0, n Start = 0,
n Min = 0, n Max = 6, Xmin = 0, Xmax = 6,
Xscl = 0, Ymin = 0, Ymax = 0.5, Yscl = 0
After setting these values press which lists the "Table" values for the first six iterations. You can confirm your values from the previous method.
II. Graphing the Orbits of Iteration
We will look at two methods of graphing an iterated function. They are
1. using the Time graph
2. using the Web graph.
Method One
If the reader wants to look at the relationship for f(x) = x2, (Un = Un-1 2), in terms of the number of iterations (n ) and the value of the function (Un ) on a graph, she will need to set the "Window" and "Format" to appropriate values. The current setting in the "Window" from part I will suffice for the "Time" graph, if you set the "Format", accessed from the key by high-lighting the FORMAT with the cursor keys and selecting the Time option. Now press to see the graph. You may press and use the cursor keys to see your values along the graph.
Method Two
To look at the Web plot of the function f(x) = x2 while in the seq mode, you will need to change the FORMATin the menu and change the values for x and y.
First press toggle right to FORMAT and press . This will place the blinking cursor on the word Time in the FORMAT menu. Now toggle right to the word Web and press . Press again to change the values for x and y. Select x to range from -1 to 1 and y the same so that you will see your function and the line f(x) = x. This will work if your seed "Un Start" is appropriate. Now press and and repeatedly press the right arrow, to create the Web, until you reach a cycle, a point of attraction, or it blows up. When you return to the Time plot make sure you reset your window values for x and y.
III. Descriptive Statistics
Statistical Analysis
Descriptive statistics and a histogram can be shown on the TI-82 as in the following example. Before entering these data, you might clear out the list remaining from a former problem. To clear old list, press and high-light 4:ClrList and press . The screen shows ClrList and a blinking cursor.
Key in then press toggle left one space, press . These strokes clear all data in list one and list two. Now press and with 1:Edit... high-lighted press . In the L1column, key in these 25 test scores, press after each. The scores are:
The bottom left of the screen should show that L1(25) = 72 which means that 25 data items have been entered with the last being 72.
To sort these data in L1 and L2 in a descending manner try these steps: and toggle down to 2:SortD( andpress . Complete this option by typing in . These steps arrange all items in L1 and L2 as pairs from the largest to the smallest for values in L1 since it was listed first in the sort command. In this problem we choose to give each individual score, so we will use a frequency of one. Use the arrow keys to get the cursor in cell L2(1) and key in and and repeat this process until all cells from L2(1) to L2(25) have the value of one. The reader should know that the TI-82 will default to a frequency of one in the plot mode, if selected.
For the univariate statistical analysis of these data press , toggle over to CALC and press twice. The screen shows six items including the mean, =73.6 and a sample standard deviation, = 18.196 (rounded off to three decimal places).
Histogram
To get a frequency chart (Histogram) of these items, press which activates the STAT PLOTmenu. Select 1:Plot1 by pressing . In plot 1 select the following settings: On, and for Type select the 4th icon which is the image of the histogram. For the Xlist choose L1 and for the frequency choose L2.
Screen settings for this graph are accessed through the window key. Press and try these values: Xmin = 25, Xmax = 95, Xscl = 10, Ymin = -5, Ymax = 10, Yscl = 10. Make sure all the functions in are turned off. Press and high-light the 9th choice 9:ZoomStat and press . A histogram of these given data appears on the screen and using the key, with the arrows, you can see the corresponding ranges of scores and their frequencies.
IV. Inferential Statistics
Linear Regression
To explore linear regression, lets look at these following data which relates temperature in degrees Celsius to a number that measures viscosity in a certain petroleum product. We chose L1 to contain the temperature and L2 for the measure of the corresponding viscosity. There are 8 pairs of data. L1 is the list {15, 20, 25, 27, 35, 40, 43, 47}. Toggle over to L2(1) and enter these numbers: {12, 13, 17, 19, 23, 26, 30, 31} and remember to press after each entry.
To get a scatter graph of these data, key in and select 2:Plot2 by pressing . Make sure plots 1 and 3 are turned off. In plot 2 select the following settings: On, and for Type select the 1st icon which is the image of the scatter plot. For the Xlist choose L1 and for the Ylist choose L2 and for the Mark choose the box. Key strokes should give a scatter plot of these data.
To get a regression line for these data, go to the select the CALC menu. Toggle down to 4:Med-Med press twice. This will do a regression analysis on the lists selected in the SetUp ( we assume L1 and L2). To place the regression equation in the function window, press , clear off Y1, make sure all other functions are off or cleared. Now enter these strokes: toggle to 5:Statistics... and press . Toggle right to EQ and down to 7:ReqEQ and press . The corresponding values will now appear on the function screen as a regular equation. Press and see the Med-Med regression line with the scatter plot of your data.
Non-Linear Regression
When your data are non-linear you can use the TI-82 to examine the relationship by placing it in a linear form. Consider these following data collected from an experiment:
X Y
1
2.0
2
7.0
3
15
4
27
5
42
6
61
7
83
First we need to plot the data to get a feel for the general shape of the relationship. Place the data in a list by pressing and selecting option 1:Edit by pressing . This places you in the first cell of the list L1. Move up into the heading of the list by pressing the up arrow key. This will place you in the heading of the list. Press if the list is not empty, or if it has more than 7 data points in it, since that is what you are working with. This step is not necessary if you fill the list by using the key or if you use a sequence. Now enter the data for X in list L1and the values for Y in list L2 . This is done by placing the cursor in the appropriate cell, keying in the values, and pressing , then repeating the data entry, since your cursor will move down in the list each time. Once you have the data entered in the two lists you will want to look at their plot.
To plot a set of data select the STAT PLOT by pressing the keys. This will give you a menu of three plots to work with, as well as the possibility of turning all plots on or off. Since you want only one plot, select 1:Plot1 by pressing when it is high-lighted with the cursor. Press to highlight the On choice, move down by pressing thearrow key, and select the scatter plot, the automatic option for this line, by pressing . Now move down to the Xlist line and select, as the independent variable, L1 by pressing . Then move down again to the Ylist line and move right to place the cursor on the L2 option. Press to select this. The last line on this menu is for the type of mark to be used in the plot. Since we have only one plot to work with the previously selected option will suffice. Exit this menu by pressing the key (you should be in the function mode). Make sure all of your functions in the menu are turned off and that the other plots are off. Press and select option 9, 9:ZoomStat , by pressing . You will then get a plot of your data.
As you look at the plot, you should try to recognize the type of graph it is, linear, quadratic, cubic, exponential, logarithmic, etc. In this case, let us say that we think it is quadratic. If this is the case, we could take the square root of the Y values in L2 and compare them to X, expecting a linear relationship. To do this we would like to place into the third list, L3. This can be done from the home screen by pressing: . Now you want to do a linear regression on list 1 and 3. To do this you will need to press: move to the right to high-light CALC press . If you look at the value of r, you should see .9999026873. This is the regression coefficient and, since it is close to 1.0000, you can see you have a good fit. To look at this in greater detail, press and clear off Y1 by pressing . Then place the regression equation into Y1by pressing , the right arrow twice to EQ and then press to select 5:Statistics..., EQ, 7:RegEQ. Now, with all your functions off - except Y1, set up another plot, on STAT PLOT , using 2:Plot2 . Make sure you turn off plot 1, and repeat your zoom adjustment. This graph will be of your linear regression equation and of the data (X, ). If this looks good, and it should, you have a fit (i.e., it was a quadratic).
You must now convert your linear equation Y=aX+b into the form y=Ax2 + Bx + C. To do this take your linear equation and square it, so that you have (1.2866219332929X+.07215863765871)2 as the function that is connected to the data you collected. This would be approximately: f(x) = 1.66x2 + 0.186x + 0.005. If you look at this function plotted against L1 and L2 from your plot 1, you will see the fit.
However, as a matter of accuracy of fit for f(x) = 1.66x2 + 0.186x + 0.005, the reader is advised that the residuals for this function and the actual data be extracted. Explanations of residuals and their use in determining the accuracy of a linearized function can be found in a variety of books on data analysis. Time and space constraints prevent the authors from describing a detailed set of instructions about residuals using the TI-82.
A program for the TI-82 that will give the residuals of a set of data approximated by a function, stored in Y1 is given without explanation. | 677.169 | 1 |
Welcome to the Math Lab Home Page
Purpose
The purpose of the Math Lab at WWCC is to provide a comfortable, quality, learning environment. Tutoring services are offered free of charge to all currently enrolled WWCC students. We help with mathematics while encouraging student independence and responsibility.
Services
Experienced and knowledgeable math tutors available throughout the day to help with all math courses offered at WWCC
Apple and Windows computers with math and science software
Calculators and textbooks
The Math Lab is a peer-led service that is primarily staffed by WWCC students.
You do not need an appointment. We work on a drop-in basis only.
Best Practices
Many students find the most successful way to use the Lab is on a daily basis as an addition to their classroom experience.They find that completing their homework in the lab serves the dual purpose of getting the work done and having their questions answered by a knowledgeable tutor.
We have a few things we expect of those who use the Tutoring and Learning Center.
Be respectful of others studying.
Cell phone ringers must remain off.
Talking on a cell phone is prohibited.
Eating or drinking at the computers is not allowed.
Excessive noise is not allowed.
Noise from headphones is not allowed (headphones are allowed, but must not be audible to others). | 677.169 | 1 |
Concepts in Geometry DVD Discover the role that math plays in the design, technology, and construction of modern skyscrapers, as it did in ancient Greek architecture.
9 - 12
DVD
$59.95
Patterns and Trends DVD From recognizing patterns of repeating events to determining rules for extending patterns, introduce young students to basic properties of functions and algebra.
K - 2
DVD
$39.95
Geometry Skills DVD Introduce elementary students to more advanced properties and concepts of geometry.
3 - 8
DVD
$39.95
Patterns, Symmetry, and Beauty DVD Beauty is in the eye of the beholder they say. So what do people find beautiful and why? Philosophers and mathematicians from the past and modern-day artists and scientists ponder this question.
6 - 12
DVD
$59.95
Coordinate Geometry DVD This video shows how coordinate grid systems have been used throughout history for navigation, archaeology, and space exploration. | 677.169 | 1 |
This introduction to probability theory transforms a highly abstract subject into a series of coherent concepts. Its extensive discussions and clear examples, written in plain language, expose students to the rules and methods of probability. Suitable for an introductory probability course, this volume requires abstract and conceptual thinking skills and a background in calculus. Topics include classical probability, set theory, axioms, probability functions, random and independent random variables, expected values, and covariance and correlations. Additional subjects include stochastic processes, continuous random variables, expectation and conditional expectation, and continuous parameter Markov processes. Numerous exercises foster the development of problem-solving skills, and all problems feature step-by-step solutions
Table of Contents for Introduction to Probability Theory with Contemporary Applications | 677.169 | 1 |
We don't try to teach you everything there is to know about calculus–only the strategies and information you'll need to get your highest score.
In Cracking the AP Calculus AB & BC Exams, we'll teach you how to·Use our preparation strategies and test-taking techniques to raise your score·Focus on the topics most likely to appear on the test·Test your knowledge with review questions for each calculus topic coveredThis book includes 5 full-length practice AP Calculus AB & BC tests: 3 for AB and 2 for BC.
All of our practice questions are just like those you'll see on the actual exam, and we explain how to answer every question..
For more information about the title Cracking the AP Calculus AB and BC Exams, 2006-2007 Edition (College Test PrepA "Unified Theory" For Calculus(January 29, 2003) — A University of Missouri-Rolla mathematician's research into a "unified theory" of continuous and discrete calculus is gaining the attention of mathematicians worldwide for numerous ... > read more
Math Goes Viral in the Classroom(December 11, 2009) — At least a dozen Alberta high-school calculus classrooms were exposed to the West Nile virus recently. Luckily, it wasn't literally the illness. Educators used the virus as a theoretical tool when ... > read more
Soap Films Help to Solve Mathematical Problems(January 27, 2011) — Soap bubbles and films have always fascinated children and adults, but they can also serve to solve complex mathematical calculations. This is shown by a study carried out by two professors who have ... > read more
Atoms Under The Mantle(March 14, 2007) — French CNRS scientists have succeeded in modeling the defects of the earth's mantle responsible for its deformation. These results, obtained using a novel approach which combines numerical calculus ... > read more | 677.169 | 1 |
II. COURSE DESCRIPTION
This course places as much emphasis on the modern mathematical ideas and their meaning as on computation. Topics included are set theory, logic, systems of numeration, mathematical systems, counting theory, probability, statistics, and geometry.
III. RATIONALE OF COURSE
The purpose of the course is to give insight into some of the more uncommon areas of mathematical thought. As many of these areas require the learning of methods of investigation rather than memorization, the main goal is that the student should be able to transfer his knowledge of logical investigation of mathematics to other fields of study.
IV. COURSE COMPETENCIES
Interpret mathematical language.
Judge an argument as to whether it follows the rules of deductive reasoning. | 677.169 | 1 |
TI Interactive Student Version
Student Edition TI Interactive Studio...Integrated learning software for math and science. A user-friendly, integrated computer learning environment that combines the functionality and familiarity of the TI83 graphing calculator with the desktop publishing capability of the computer.
TI InterActive! is the user-friendly, interactive computer software designed for teachers and students. TI InterActive! enables high school and college teachers and students to easily explore mathematics and science concepts on a computer. Teachers can enhance students' learning through interactive lessons that encourage exploration, visualization, data analysis and writing.
With over 125,000 items and parts in stock daily, TheNerds.net is sure to meet all your computer and electronics needs. This TI Interactive Student Version is factory fresh: We never sell refurbished products. The retail list price on this product is $60.89 | 677.169 | 1 |
2007{"itemData":[{"priceBreaksMAP":null,"buyingPrice":50.02,"ASIN":"0387257659","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":70.12,"ASIN":"0387961712","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":53.2,"ASIN":"088385807X","isPreorder":0}],"shippingId":"0387257659::I7rPM7tSXJQC9Vl%2BXBQRCgiJuWVPm2rsYE%2Fx08%2BVFQk17FkbybHYIMoemUJ8xO%2BfAY%2BguGZTwkvMc%2BQ8oMk%2F3Q1NEF4VzzIcJWNTgzRJfFM15FUZNJh%2F1A%3D%3D,0387961712::djqJ%2FKTU349YD4m%2FAyNU6jbWYtyKS7fV5cAVy%2F697X5RP1H7CGHyLkKg6xbAPHWM3LEv7qoChTCe4Odetcdf7lXsZE5iIxViAgFBKrjExmM%3D,088385807X::BC6r4PCb3sHvDI49xr2wB9umsBbC%2FFVXKYeCTKZfPDzOGH203Ge%2BVLr2qSmdnbNCqsFHgZapdRfQe3eTbOUFMy9xAbNnRx6lCkEMsqJJH work contains carefully selected problems in Algebra, Real Analysis, Geometry and Trigonometry, Number Theory and Combinatorics and Probability. … The book is mainly intended to offer the principal skills and techniques for solving problems in elementary Mathematics. … The reviewer recommends this book to all students curious about the force of mathematics, especially those who are bored at school and ready for a challenge. Teachers would find this book to be a welcome resource, as will contest organizers." (Teodora-Liliana Radulescu, Zentralblatt MATH, Vol. 1122 (24), 2007) "I enjoyed this book … . Not just because of the collection of problems, but also because of their sheer scope and depth. This is a great collection which is extremely well-organized! … This extraordinary book can be read for fun. However, it can also serve as a textbook for preparation for the Putnam … for an advanced problem-solving course, or even as an overview of undergraduate mathematics. … it could certainly serve as a great review for senior-level students." (Donald L. Vestal, MathDL, December, 2007) "A 935-problem and almost 800-page super-problem book with solutions, whose reading would certainly challenge, attract, and keep really busy any undergraduate student interested in acquiring various problem-solving techniques. … the array of remarkable problem books has gained a new addition that could be really useful to undergraduate students. … a book about excellence in mathematics, coming from a long cultural tradition whose history and experience can only help us deepen our understanding of how mathematics could be taught in a more attractive and inquisitive way." (Bogdan D. Suceavă and Jack B. Gaumer, The Mathematical Intelligencer, Vol. 33 (2), 2011)
From the Back Cover Key features of Putnam and Beyond * Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. * Each chapter systematically presents a single subject within which problems are clustered in every section according to the specific topic. * The exposition is driven by more than 1100 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. * Complete solutions to all problems are given at the end of the book. The source, author, and historical background are cited whenever possible. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for self-study by undergraduate and graduate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.
There are many books on problem solving. The majority are aimed at junior high and high school students preparing for either the International Mathematical Olympiad or national IMO selection tests (the American Mathematics Contests in the United States, such as the USAMO). A select few, such as Problem Solving through Problems by Loren Larson, are aimed at university students preparing for university competitions. This book, as the title suggests, belongs to this latter category, and it has a particular emphasis on the sorts of problems that occur on the Putnam exams.
This book is generally written at a higher level than most other problem solving books. Many problem solving books place a great emphasis on geometry. Just as the Putnam exam generally replaces synthetic geometry with analysis and abstract and linear algebra (although there are exceptions), so this book replaces the traditional focus on geometry with a focus on analysis and algebra. That said, there is an entire chapter on geometry, but it does not discuss synthetic geometry, instead focusing on vectors, the geometry of the complex plane, analytic geometry, and some special topics that are especially relevant to college mathematics (integrals in geometry, some higher-level results such as the fact that all conics are rational curves, and a brief but still substantive survey of trigonometric substitutions).
Putnam and Beyond discusses many areas of college mathematics that are likely to appear on the Putnam exam but would never appear on the IMO, such as abstract algebra, linear algebra, and real analysis (with a very tiny bit of complex analysis).
That said, this book still does overlap a bit with many other problem solving books. It opens with a chapter on general problem solving strategies, but I feel that these sections are written with students who have encountered the basic methods before. For example, most introductions to induction demonstrate it by summing some series, but the authors here show that if finitely many lines divide the plane into regions, the regions can be colored with two colors in such a way that no two neighboring regions receive the same color. Another example they offer is a particularly difficult inequality from a past Putnam exam. So in a way the opening chapter is appropriate more as a *second* introduction to problem solving techniques than as a first introduction. This leads to my next point.
The book's exposition is generally written at a high level, and I'd say that to fully appreciate it would impose somewhat high prerequisites, including a good amount of mathematical maturity and a good knowledge of basic college mathematics up through first courses in algebra and analysis. For example, a problem in the very first section of the very first chapter on argument by contradiction requires one to be familiar with the density of rationals in the reals.
To anyone interested in beautiful proofs or in competition math, I would heartily recommend this book along with Problem Solving through Problems by Larson. I think Putnam and Beyond is written at a slightly higher level than Larson's book and many of the problems here are more difficult than those in Larson, but together both books provide a very thorough and strong review of undergraduate mathematics through problem solving.
Finally, full solutions to every single problem (and by "full" I mean complete proofs written out in detail, often with accompanying figures) are in the back of the book (in fact, a little more than half of the pages are devoted to these solutions).
This book consists of a very useful collection of Putnam-like math problems. Putnam and Beyond is organized for self-study by undergraduate and graduate students who wish to try a lot of competitive math problems.It is also useful for teachers who are preparing their bright students for IMO type (or higher) math competitions. However the book assumes a level of mathematical maturity and prior mathematical knowledge that not many college students possess. Another very useful book for math competitions is The IMO Compendium. | 677.169 | 1 |
Each student will receive a concept list and assignment sheet for each unit. We will cover a conceptevery day or so. Students will be:
expected to complete the practice problems as directed
given opportunities to ask questions and gain additional clarification on concepts
given the answers to the practice problems on the day the problems are assigned
given the opportunity daily to show me what they have completed of the practice problemsand I will note this appropriately
given a quiz after approximately 3 concepts are taught
given an opportunity to evaluate their understanding of the concepts and given feedback as totheir grasp of the concept using the scale below:No answer orno work shownI know youdont know itI think youdont know itI think youknow itI know youmostly know itI know youknow it0 1 2 3 4 5We will repeat this process (teach a few concepts, quiz, and get feedback) until we reach the end of aunit. At the end of each unit, each student will receive scores for each concept that was tested usingthe same scale from the quizzes. These scores for each concept will be entered into the gradebook asfollows:No answer orno work shownI know youdont know itI think youdont know itI think youknow itI know youmostly know itI know youknow it0 1 2 3 4 55/10(50%)6/10(60%)7/10(70%)8/10(80%)9/10(90%)10/10(100%)Understand that these are the only scores that will be entered into the gradebook. There will be noscores entered for practice problems and quizzes I will note what practice problems have beencompleted and I will use the information from the homework and quizzes to help determine whattopics the class needs more time and help learning. Students are expected to use the practiceproblems to help them to grasp the concepts and to use the feedback from the quizzes to gauge wherethey are at in their understanding and prepare accordingly for the test.If a student is not satisfied with his or her understanding of a concept, he or she may choose toreassess that concept. In order to reassess, the following must occur:
The student must have completed the practice problems for the concept prior to the unit test. Iwill have already noted what was completed as mentioned above.
After the unit test, the student needs to have done some additional practice or gotten helpfrom either myself or another student or tutor. | 677.169 | 1 |
The Admissions Magazine
Popular Classes
History of Mathematics
In Math 112 we trace the evolution of mathematics from its earliest roots to the invention of the calculus in the 17th century. We examine the major mathematical ideas of each era by focusing on the character and achievements of the different civilizations... | 677.169 | 1 |
Survey of Mathematics with Applications, A (9th Edition)
9780321759665
ISBN:
0321759664
Edition: 9 Pub Date: 2012 Publisher: Addison Wesley
Summary: This textbook serves as a broad introduction to students who are looking for an overview of mathematics. It is designed in such a way that students will actually find the text accessible and be able to easily understand and most importantly enjoy the subject matter. Students will learn what purpose math has in our lives and how it affects how we live and how we relate to it. It is not heavy on pure math; its purpose ...is as an overview of mathematics that will enlighten students without an intense background in math. If you want to obtain this and other cheap math textbooks we have many available to buy or rent in great condition online.
[read more]
Rating:(0)
Ships From:Greenville, TxShipping:Standard, Expedited, Second Day, Next DayComments:Text may contain some highlighting. Order shipped same day if if rec'd by 1PM CST, otherwise ship... [more]Text may contain some highlighting. Order shipped same day if if rec'd by 1PM CST, otherwise ships the next business day. Great Customer Service. Upgrade shipping available. [less] | 677.169 | 1 |
Learn More!
For each chapter, this section provides a step-by-step worked-out example of
a computational problem from the book. Be sure that you understand each step before
moving on, and don't be afraid to take your time with each problem. | 677.169 | 1 |
test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts.
Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means.
Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts.
Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods.
Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op
Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log
Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information.
Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base 'p r . 'and the area of the curved surface ' p r l'. The student will also be able to find the slant height 'l' given the perpendicul
Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume.
Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume.
Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately.
Objective: On completion of the lesson the student will be able to use the Sine rule to find the length of a particular side when the student is given the sizes of 2 of the angles and one of the sides.
Objective: On completion of the lesson the student will understand how to find the first derivative of various functions, and use it in various situations to identify increasing, decreasing and stationary functions.
Objective: On completion of the Calculus lesson the student will be able to find a second derivative, and use it to find the domain over which a curve is concave up or concave down, as well as any points of inflexion.
Objective: On completion of the Calculus lesson the student will be able to use the first and second derivatives to find turning points of a curve, identify maxima and minima, and concavity, then use this information to sketch a curve.
Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit
Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication.
Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix.
Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane | 677.169 | 1 |
Mathematical Excursions - 3rd edition
Summary: MATHEMATICAL EXCURSIONS, Third Edition, teaches students that mathematics is a system of knowing and understanding our surroundings. For example, sending information across the Internet is better understood when one understands prime numbers; the perils of radioactive waste take on new meaning when one understands exponential functions; and the efficiency of the flow of traffic through an intersection is more interesting after seeing the system of traffic lights represented in a math...show moreematical form. Students will learn those facets of mathematics that strengthen their quantitative understanding and expand the way they know, perceive, and comprehend their world. We hope you enjoy the journey. ...show less
1111578494 | 677.169 | 1 |
25
Total Time: 3h 37m
Use: Watch Online & Download
Access Period: Unlimited
Created At: 12/02/2008
Last Updated At: 07/20/2010
Taught by Professor Edward Burger, these lessons were really helped me work with Complex Rational Expressions. I was really lost when dealing with these buggers but I watched the video 5 times before I really began to understand these expressions. Everything was explained clearly in the video. I will be looking for a part 2 to this topic.
I was struggling to grasp this concept when reviewing for an exam, as the examples in my text were not sufficient enough. This video was able to articulate the concept in a very clear manner and I can finally exhale and feel confident going into my exam. Thanks!
I love how animated his style is; it makes his teaching style even more engaging. Even when you thought it couldn't get more interesting, his bright orange tie makes it that much more fun to watch his lessons.
But to rate his lesson based on knowledge and ability to teach, I would give it a 10. It's so much easier to learn from a video tutorial than it is for me to read a textbook or sit through a lecture. I can start and stop whenever I want and take breaks without interrupting a class, etc. It's so much easier for me to learn at my own pace! Having these videos on integral algebra online makes me very happy.
Very happy indeed.
Below are the descriptions for each of the lessons included in the
series:
Int Algebra: Solving a Mixture Problem
In this lesson, you will learn how to approach word problems that involve equalities and ratios or fractions percentages, ratios, recipes, mixes, etc an Average
In this lesson, you will learn how to approach word problems that involve averages or means averages or means (many of which include grades or scores Factor Sums and Differences of Cubes
In this lesson, you will learn how to factor the difference of two cubes and how to factor the sum of two cubes. Neither of these are simple factorizations, so Professor Burger will show you what the factorization is and then explain where it comes from. Additionally, he'll show you some ways to remember what these factorizations are. (x^3 - y^3) = (x - y)(x^2+xy+y^2) and (x^3+y^3) = (x+y)(x^2-xy+y^2) Long Division with Polynomials
You know how to use long division to divide two numbers; you can also use long division when dividing polynomials. In this lesson, Professor Burger will review with you how to long divide and then show you how to use long division with polynomials (to evaluate things like (x^4+3x^2-5x-10)/(X^2+3x-5) ). When long dividing, you often end up with a remainder, and this will be the case when using long division on polynomials, as well. This lesson will show you how to find both the quotient and the remainder when dividing two polynomials using long division Synthetic Division with Polynomials
You know how to use long division to divide two numbers; you can also use long division when dividing polynomials. In this lesson, Professor Burger will show you how to eliminate several of the steps in long division by u sing synthetic division. Synthetic division only works when you are dividing by (x + ?) or (x - ?) where ? is a number. In synthetic division, you start by using the coefficients of the polynomial in the numberator with switched signs. In the end, you will end up with the same answer for both the quotient and remainder as you would using long division, but it will be a less harrowing path to get there Multiply-Divide Rational Expressions
In math, a rational expression or rational function is any function which can be written as the ratio of two polynomials. These are inevitably expressed as fractions. In this lesson, you will learn how to multiply and divide rational functions. Rational expressions can be multiplied or divided just like fractions. In walking you through examples of this type of multiplication and division, Professor Burger will highlight things to watch out for and shortcuts that can help you along the way. He will also show you why dividing is the same thing as multiplying by the reciprocal Add-Subtract Rational Expressions
In math, a rational expression or rational function is any function which can be written as the ratio of two polynomials. These are inevitably expressed as fractions. In this lesson, you will learn how to add and subtract rational functions. As with any fractions, to do this, you'll need to find a common denominator. In walking you through examples of this type of addition and subtraction, Professor Burger will highlight things to watch out for and shortcuts that can help you along the way Rewriting Complex Fractions
In math, a rational expression or rational function is any function which can be written as the ratio of two polynomials. These are inevitably expressed as fractions. Dealing with complex rational expressions is the same basic thing as dealing with other rational functions. In a complex rational expression, you generally end up with a variable within a fraction that's with another fraction that also includes another variable. The approaches to addition, subtraction, multiplication and division that are used with simple rational expressions all work the same here. You will need to invert and multiply in order to divide and you will need to find common denominators and least common multiples, etc. In this lesson, you will see a series of examples to see how these complex rational expressions are handled (things like (1/(1/x))/(1/(1/x)^2)). Containing Radicals
When working with equations, you often end up with a radical of some sort (like a square root) on one side of the equation. These type of equations are called radical equations because they contain a square root. To evaluate this type of equation, you'll want to get rid of the radical. This lesson will show you how to approach and solve this type of equation by getting rid of the radical (by isolating the radical alone on one side of the equals sign and then squaring both sides of the equation). When evaluating this type of equation, you will always want to check your solutions in the original equation to make sure that you don't end up with an extraneous root as a solution. Even if the equation solves to give you an extraneous root, it is not a valid solution. An extraneous root is something that is a root to the quadratic but not to the original equation with Two Radicals
In this lesson, Professor Burger will show you how to solve equations that contain two radicals (roots). When you have an equation with two square roots, you'll want to have them on opposite sides of the equal sign. Then, you'll square both sides of the equation. If there is still a radical remaining, you'll have to isolate it on one side of the equation and then square both sides once again. There will be several examples included in this lesson that will show you how to approach this type of problem and then how to check your work Functions and the Vertical Line Test
A function is basically a machine that takes an input value (x) and processes it to produce an output value (y). With a function, if an x value is known, you can find the y value. When graphed, a curve is a function if it passes the vertical line test. In this lesson, Professor Burger will show you how the vertical line test means and how to recognize when a curve does not pass the vertical line test. The vertical line test looks to verify that, for every value of x, only one y value is produced. If something doesn't pass the vertical line test, it is called a relation and not a function Function Notation and Values
In this lesson, Professor Burger will show you how to correctly denote functions and values. By definition, a function has only one value of y for each value of x. A function can always be expressed using the term f(x) instead of y. This lesson will walk through when to use this notation and how to use it correctly to indicate what you want it to be. Additionally, Professor Burger will show you how to verbally say the new notation in addition to how to write it. Last, he'll walk you through a few examples involving functions and their notation and evaluation Domain and Range
While a function always satisfies the vertical line test (for any value of x there is only one value of y), there are functions in which the domain of the function does not include all values of x. In this lesson, we look at the domain of a function (all of the values of x for which we can evaluate the function and find a value of y) and the range of a function (all the values of y that may be generated by evaluating the function for some value of x). In addition to learning about evaluating a function to find the domain and range, Professor Burger will graphically show you how to identify the domain and range Satisfying the Domain of a Function
In this lesson, you will learn how to find all of the allowable x values for a particular function (the function's domain). An allowable x value is one in which you can evaluate the function. There are certain types of numbers which are not allowable, like square roots of negative numbers, numbers with 0 in the denominator, etc. If you evaluate a function and end up with one of these types of numbers, then the x value is deemed to be outside of the domain for the function. Professor Burger will also show you how to correctly denote the domain of a function once you determine what it is Composite Functions
In this lesson, you will learn about a method that you can use to combine functions. The composition of two functions is the way to combine two functions. In this lesson, you will learn how to combine functions (for example, to find f(g(x)) ). There are specific ways to denote these types of composite functions, and you will also learn how to correctly write composite functions (f(g(x)) or (f o g)(x) ). To compose a function (find the composition of functions), you'll have to take the answer of one function and plug it into the other function (to find something like, 'g composed of f of 3'. Professor Burger will also highlight why g(f(3)) is not always equal to f(g(3)). Substitution
In this lesson, Professor Burger will show you how to solve systems of equations using a technique known as substitution. In this approach, you will solve one equation for one of the variables (eg y) and then plug the value (what y is equal to) into into the other equation (anywhere a y appears). This substitution will allow you to solve for x and then in turn solve for y. In order to fully explain how this works, Professor Burger will walk you through several different types of examples Elimination
While you can often solve systems of equations using substitution, you may also find that elimination is a simple approach for some systems of equations. When evaluating a system of linear equations with two linear variables using elimination, you will look for ways to combine the equations (or multiples of the equations) such that the sum of the equations will eliminate one of the variables. Once you eliminate one variable, it should be easy to deduce the value of the other equation. Once you have this, you should be able to plug it in to one of the original equations to solve for the eliminated value by Completing the Square This lesson will teach you how to find solutions by completing the square. In this technique, you'll start by isolating all constants on one side of the equation and all variable terms on the other side. Then, you'll add or subtract something to both sides to complete the square. In this case, you'll end up with x^2+6+9 = 9-1. This equation will be easier to evaluate given that you can simplify it to (x+3)^2 = 8. When you finally get to a solution value for x using this approach, you may need to rationalize a denominator (take radicals out of it), and Professor Burger will review this in the lesson, too Completing the Square: An Example In this lesson, you will learn more advanced techniques to use when solving an equation by completing the square. This lesson will cover what to do when the initial x^2 term contains a coefficient, how to solve problems that involve fractions, how to handle denominators with fractions, etc. This technique is the basis for the quadratic formula, which can always been used to solve quadratic equations Find Vertex by Completing the Square
In this lesson, you will learn how to find the vertex of a parabola given the formula for the parabola. To do this, you will complete the square. By completing the square of the parabola equation, you will be able to get the equation into a standard form that can be more easily evaluated. A parabola is a conic section in which the locus of points constructing it are equidistant from the focus and the directrix. Once we've identified the vertex of a parabola, we can get a good sense for how the parabola is positioned on the Cartesian coordinate plane the Quadratic Formula
The quadratic formula is used to solve for x in quadratic equations, which come in the form ax^2+bx+c=0. This formula is most commonly used when the expression can't be easily factored for evaluation. Oftentimes, this is because the two solutions to the equation are not real numbers. In this lesson, Professor Burger will walk you through when to use the formula, what the alternatives to the formula are and how to apply the formula. He will also explain how and why the formula can give imaginary numbers as solutions and what that means Predict Solution Type by Discriminant
When working with quadratic equations and the quadratic formula, there is a way to determine what type of solutions you will find and how many there will be (2 real solutions or 2 complex solutions or 1 solution) by looking at the coefficients of the quadratic formula. In this lesson, you will learn how to do this by calculating and evaluating the discriminant (d) of the quadratic formula (equal to b^2-4ac, which is a component of the quadratic formula The Pythagorean Theorem
The Pythagorean Theorem describes the relationship between the sides of a right triangle. It asserts that if the hypotenuse is length c and the other two legs are a and b, then a^2+b^2=c^2. This formula has a number of applications, and you will go through many of them in this lesson. Professor Burger will show you how to find one leg of a right triangle if you know the other two or if you know the length of one side and have two polynomials to express the lengths of the other two sides (e.g. if you know the three sides are c=x+2 and a=x and b=x+2 Quadratic Inequalities
In this lesson, Professor Burger will teach you how to solve quadratic (non-linear) inequalities. In a quadratic inequality, there are things like x^2 included. To evaluate these inequalities, we once again start by factoring. Next, you'll find the values for x, for which the quadratic inequality is positive such that you will be able to make a sign chart and then determine the sign (positive or negative) for ech interval delineated on the sign chart. Once you have identified the intervals that satisfy the equation, Professor Burger will show how to properly denote the answer using correct notation Writing an Equation for a Parabola
A parabola is a conic section in which the locus of points constructing it are equidistant from the focus and the directrix. To find the formula of this equation when given the vertex (h,k) and the distance from the focus (p), this lesson will show you how to find the equations for the parabola described by these criteria. There will be two formulas depending on whether p is positive or p is negative (which should indicate whether the parabola opens up or down). | 677.169 | 1 |
Because individual students have different needs, interests and abilities, there are three different courses in mathematics: Mathematical Studies SL, Mathematics SL and Mathematics HL.
These courses are designed for different types of students: those who wish to study mathematics in depth, either as a subject in its own right or to pursue their interests in areas related to mathematics; those who wish to gain a degree of understanding and competence better to understand their approach to other subjects; and those who may not as yet be aware how mathematics may be relevant to their studies and in their daily lives. | 677.169 | 1 |
In this year long course, students develop algebraic fluency by learning the skills needed to solve equations and perform manipulations with numbers, variables, equations, and inequalities. They also learn concepts...
Algebra I A: This course covers such key concepts as variables, function patterns, and graphs. Students learn operations with rational numbers and properties of rational numbers. Students
solve linear equations and...
The purpose of this Algebra I course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics in a year long course. Topics included are real...
Class.com Algebra 1 is a traditional two semester middle or high school algebra course that equates to approximately 80 hours of instructional time per semester. Numerous interactive and multimedia components within each...
Publisher: Class.com (Cambium Learning)
Also published by Class.com (Cambium Learning)
Algebra I is a full-year, high school credit course that is intended for the student who has successfully mastered the core algebraic concepts covered in the prerequisite course, Pre-Algebra. Within the Algebra I course,...
Algebra I begins with a review of algebraic properties, integers, exponents, and roots. Students will then build on that knowledge as they study rational numbers, solving equations, proportions, and absolute values,... | 677.169 | 1 |
Cliffs Quick Review for Geometry - 01 edition
Summary: When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core geometry concepts -- from perimeter, area, and similarity to parallel lines, geometric solids, and coordinate geometry -- and get the best possible grade.
At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented wri...show moreters who know how to cut to the chase -- and zero in on the essential information you need to succeed. ...show less
Ed Kohn, MS is an outstanding educator and author with over 33 years experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at Sherman Oaks Center for Enriched Studies.
2001 Paperback Good Our goal with every sale is customer satisfaction, so please buy with confidence. Orders are shipped same or next day. This is a used book and may show some signs of use or wear...show more. ...show lessVeryGood
Coas Books, Inc. NM Las Cruces, NM
2001 | 677.169 | 1 |
Algebra II: Polynomials and Radicals
Find study help on polynomials and radicals for algebra II. Use the links below to select the specific area of polynomials and radicals you're looking for help with. Each guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn polynomials and radicals for algebra II. | 677.169 | 1 |
The Mathematics Department offers twelve courses which give students the opportunity for a full four-year course of study. Three units of credit are required for graduation. The Advanced Program is offered to accelerate students' study by allowing them to register for AP Calculus in their senior year. All students will be required to purchase a specific graphing calculator at the beginning of their freshman year. This calculator will be used in mathematics and science classes.
318 Advanced Algebra 1
for freshmen with special placement
1 credit
Prerequisites: Placement test and department approval
This accelerated course in Algebra is available to the student who has had an introduction to Algebra in the eighth grade. Advanced Algebra 1 covers the content of the Algebra 1 course in more depth and with more emphasis on applications. In addition, some Algebra 2 topics are covered, including exponential functions, piecewise functions, matrices, linear programming, solving linear equations in three variables, and graphing radical and rational equations.
321 Geometry
required for sophomores
1 credit
Prerequisites: Algebra 1 or Advanced Algebra 1
This course uses undefined terms, definitions, constructions, postulates, theorems and some trigonometry to help students prove statements about geometric figures and relationships between those figures. Additional topics could include coordinate geometry and transformations.
328 Advanced Geometry
Sophomores or freshmen, with special placement
1 credit
Prerequisites: Advanced Algebra 1 with no semester grade lower than a B, or special placement, and department approval
This accelerated course in Geometry is available only to students with strong algebra skills and strong reasoning ability. Advanced Geometry covers the content of the Geometry course in more depth and with more emphasis on analysis. Additional topics include right triangle trigonometry, vectors, law of sines and cosines, and parametric equations and projectile motion.
331 Algebra 2
Juniors
1 credit
Prerequisites: Geometry and department approval
This course extends the study of Algebra 2 through two semesters. The course strengthens Algebra 1 skills and develops the concepts of Algebra 2. Topics studied include linear and quadratic equations and inequalities, graphing, polynomial functions, rational expressions, exponents, radicals, irrational and complex numbers. Optional topics include exponential and logarithmic functions, and the binomial theorem.
Algebra 2
Juniors
1 credit
Prerequisites: Geometry or Advanced Geometry, with no semester grade lower than a C in all previous math classes and department approval
This course includes a review of skills from Algebra 1 and all the essential topics for an Algebra 2 course. It also includes the study of Trigonometry. Topics included are quadratic relations, exponential and logarithmic functions, radical expressions, and analytic geometry.
Advanced Algebra 2 with Trigonometry
Juniors or sophomores, with special placement
1 credit
Prerequisites: Advanced Algebra 1 and/or Advanced Geometry, with no semester grade lower than a B in all previous math classes and department approval
This accelerated course is available only to the very capable student intending to enroll in AP Calculus. The course encompasses Algebra 2 with Trigonometry and material from the Pre-Calculus course. Topics included are Quadratic, Polynomial, and Rational Functions; Exponential and Logarithmic Functions; Analytic Geometry; Sequences and Series; Probability and Statistics; Trigonometry, Vectors and Polar Coordinates. Emphasis is placed on applications of the topics covered.
341 Trigonometry
Elective for seniors
½ credit
Prerequisites: Algebra 2 and department approval
This is a first semester course. The students are introduced to the study of trigonometry using triangle trigonometry. Topics covered include solving right triangles, solving general triangles, and applications. The unit circle, radian measurement, basic trigonometric identities, and graphing trigonometric equations are also covered.
343 Topics in Discrete Mathematics
Elective for seniors
½ credit
Prerequisites: Algebra 2 and department approval
This is a second semester course. The students are introduced to the study of probability and statistics and series and sequences. Additional topics may be covered.
342 Pre-Calculus
This course is designed to broaden the student's grasp of mathematics and to provide an ample preparation for the study of college level courses. The following topics are included: complex numbers, polynomial functions, exponential and logarithmic functions, sequences and series, trigonometric functions, and matrices.
345 AP Statistics
Elective for seniors; juniors with special placement
1 credit
Prerequisites: Algebra 2/Trig or Advanced Algebra 2/Trig, no grade below a C in previous math and English classes, a brief writing assignment and department approval.
This accelerated course teaches students the major concepts and tools for collecting, analyzing and drawing conclusions from data and covers the advanced placement curriculum. The four conceptual themes covered are: Exploring Data; Sampling and Experimentation; Probability and Simulations; Statistical Inference.
349 AP Analytic Geometry and Calculus
Elective, 12; 11 with special placement)
1 credit
Prerequisites: Advanced Algebra 2/Trig or Precalculus, no grade lower than a B in all previous math classes and department approval
This course continues the development of advanced mathematics and encompasses a first course in the differential and integral calculus of functions of a single variable. Topics covered are real numbers, analytic geometry and functions, limits and continuity, the derivative and applications of the derivative, the differential, antidifferentiation, and the definite integral. | 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 |
Do your students have difficulty understanding math terms??Remembering the steps of algorithms in sequence? Interpreting data in displays? Our math study skills program will help you teach them math and how...
9,79 $
"It is only when we forget our learning that we begin to know," Thoreau wrote. Ideas about education permeate Thoreau's writing. Uncommon Learning brings those ideas together in a single volume for the first...
6,99 $
This practical guide, written by a chief examiner, gives you the tools and planning techniques for making light work of assignments, essays, reports and dissertations. It covers: * Thoroughly understanding the...
6,49 $
Successful study is dependent on effective study skills. Yet many students are never taught how to study, and many are anxious about their ability to develop the necessary skills required to complete their course....
9,79 $
Most advanced educational courses now include a dissertation or research project of some kind. For many students this can be a terrifying experience. Although colleges and universities may have different systems,...
7,49 $
Critical Thinking is a core skill needed to make all your studies more effective. This totally revised and updated book is a must if you want to find out how to develop your own arguments and evaluate other...
9,79 $
Now in its 9th edition, this extensively revised and updated handbook explains how you can write reports that will be: * Read without unnecessary delay * Understood without undue effort Accepted, and where applicable,...
9,79 $
This friendly and accessible workbook takes you through a series of activities that will help you to gather information about your self and condense it into the format required to complete your UCAS personal...
7,49 $
This practical and easy-to-use guide shows students how to easily master core essay skills in just one hour. With advice, useful checklists and exercises to help develop essential writing and planning skills...
5,29 $
This practical and jargon-free guide shows students how to easily master essential study skills in just one hour. With advice, useful checklists and exercises covering every key area, from developing crucial...
5,29 $
This practical and jargon-free guide shows students how to easily master the key revision and exam strategies for study in just one hour. With advice, useful checklists and exercises covering every key area,...
5,29 $
This practical and easy-to-use guide allows students to master essential dissertation skills in just one hour. With advice, useful checklists and exercises to help develop the core skills required to successfully...
5,49 $
If your child is beginning life in college, there's a surprise around every corner... But that doesn't mean you can't be prepared! The Happiest Kid on Campus is a witty and wise guide to everything you need...
9,99 $
This first book in a series of four books; includes the success stories of business and professional women who won the title of "South Australian Executive Woman of the Year". These women are the founders of...
1,49 $
Brace yourself for a magical adventure beyond what you ever thought possible. Experience a journey that will propel you to want "more" out of life and understand through the words of Napoleon Hill, "... that...
6,79 $...
9,99 $
Taking a thematic approach to learning that employs seeing, hearing, reading, and writing, these books outline three four-week, cross-curricular units that develop the competencies children need to become fluent,... | 677.169 | 1 |
Course Description: This course emphasizes the principles of Algebra 1 at a rigor and pace reflective of an Honors program.
Teacher's Goals, Expectations, and Student Participation: Students are expected to be on time to class and prepared for the class activities. Class will usually start with a "Do Now" problem which is to be completed at the start of class. I expect classroom rules, as well as school wide rules to be followed in class. There will be homework almost every night, and you should expect a quiz every 2 to 3 sections. A test will be given at the end of each Chapter.
Course Materials:You will need a notebook with 3 sections; one for classwork and "Do Now " problems, one for notes, and one for homework. You should bring this notebook to class every day along with a writing utensil and any homework due that day. You should also have your own scientific calculator as it is difficult to provide a full class set and I cannot guarantee that I will have enough to go around.
Assessment Procedures and Policies:
MP1:
Summer Assignment and First Test - 20%
Tests – 50%
Quizzes – 20%
Homework/ Class work/Class Participation – 10%
MP2, MP3, MP4:
Tests – 60%
Quizzes – 30%
Homework/Class work/Class Participation – 10%
Each Marking Period is 22% of your Y1 grade, the other 12% is the Final Exam.
Contact Information:
Email Address: [email protected]
Extra Help is available by appointment before and after school as well as during the day if arranged ahead of time. See me if you need help!!! | 677.169 | 1 |
Preface
Preface
This book is a result of feedback from many readers of the book Engineering with Mathcad: Using Mathcad to Create and Organize your Engineering Calculations.
The goal of Engineering with Mathcad was to get readers using Mathcad's tools as quickly as possible. This was accomplished by providing a step-by-step approach that enabled easy learning. As a result of reader feedback, Essential Mathcad makes it even easier to learn Mathcad. We added a new Chapter 1 that quickly introduces many useful Mathcad concepts. By the end of Chapter 1 you should be able to create and edit Mathcad expressions, use the Mathcad toolbars to access important features, understand the difference between the various equal signs, understand math and text regions, know how to create a user-defined function, attach and display units, create arrays, understand the difference between literal subscripts and array subscripts, use range variables, and plot an X-Y graph. Readers felt that the discussion of Mathcad settings and templates in Part 1 slowed down their learning of Mathcad. As a result of this feedback, the chapters Mathcad Settings, Customizing Mathcad, and Templates have been moved to Part IV. These chapters will have more meaning after readers have a greater understanding of Mathcad. Most of the material from Engineering with Mathcad is included in this book, but it has been rearranged in order to allow quicker access to Mathcad's tools.
Readers asked for more applied examples of using Mathcad from various disciplines. Essential Mathcad provides many additional examples from fields such as: Chemistry, water resources, hydrology, engineering mechanics, sanitary engineering, and taxes. These examples help illustrate the concepts covered in each chapter.
A challenge with any book is to hit a balance between too little material and too much material. Based on feedback from Engineering with Mathcad, I feel that we have achieved a good balance in Essential Mathcad. Some have said that the first edition did not cover enough advanced topics for their math, physics or advanced engineering courses. Others asked for coverage of some essential engineering topics. On the other hand, some said that the book was too long and covered too much material. Essential Mathcad is an attempt to achieve an even better balance. By adding the new Chapter 1, An Introduction to Mathcad, and rearranging other chapters, I think we have helped make learning Mathcad even easier. By adding discussion of some requested topics, I think we have satisfied the desires of many readers who wanted discussion of more topics. This book cannot and does not include a discussion of all the many Mathcad functions and features. It does attempt to focus on the functions and features that will be most useful to a majority of the readers.
Book Overview
This book uses an analogy of teaching you how to build a house. If you were to learn how to build a house, the final goal would be the completed house. Learning how to use the tools would be a necessary step, but the tools are just a means to help you complete the house. It is the same with this book. The ultimate goal is to teach you how to apply Mathcad to build comprehensive project calculations.
In order to begin building, you need to learn a little about the tools. You also need to have a toolbox where you can put the tools. When building a house, there are simple hand tools and more powerful power tools. It is the same with Mathcad. We will learn to use the simple tools before learning about the power tools. After learning about the tools, we learn to build.
This book is divided into four parts:
Part I—Building Your Mathcad Toolbox. This is where you build your Mathcad toolbox—your basic understanding of Mathcad. It teaches the basics of the Mathcad program. The chapters in this part create a solid foundation upon which to build.
Part II—Hand Tools for Your Mathcad Toolbox. The chapters in this part will focus on simple features to get you comfortable with Mathcad.
Part III—Power Tools for you Mathcad Toolbox. This part addresses more complex and powerful Mathcad features.
Part IV—Creating and Organizing Your Project Calculations with Mathcad. This is where you start using the tools in your toolbox to build something—project calculations. This part discusses embedding other programs into Mathcad. It also discusses how to assemble calculations from multiple Mathcad files, and files from other programs.
Additional Resources
This book is written as a supplement to the Mathcad Help and the Mathcad User's Guide. It adds insights not contained in these resources. You should become familiar with the use of both of these resources prior to beginning an earnest study of this book. To access Mathcad Help, click Mathcad Help from the Help menu, or press the F1 key. The Mathcad User's Guide is a PDF file located in the Mathcad program directory in the "doc" folder.
In addition to the Mathcad Help and the Mathcad User's Guide, the Mathcad Tutorials provide an excellent resource to help learn Mathcad. The Mathcad Tutorials are accessed by clicking Tutorials from the Help menu. Take the opportunity to review some of the topics covered by the tutorials.
This book (if sold in North America) includes a CD containing the full, non-expiring version of Mathcad v.14. The software is intended for educational use only. The book along with CD provides a complete introduction to learning and using Mathcad. A companion website is provided along with the text and includes links to additional exercises and applications, errata, and other updates related to the book. Please visit
Teminology
There are a few terms we need to discuss in order to communicate effectively.
The terms, "click," "clicking" or "select" will mean to click with the left mouse button.
The terms "expression" and "equation" are sometimes used interchangeably. "The term "equation" is a subset of the term "expression." When we use the term "equation," it generally means some type of algebraic math equation that is being defined on the right side of the definition symbol ":=". The term "expression" is broader. It usually means anything located to the right of the definition symbol. It can mean "equation" or it can mean a Mathcad program, a user-defined function, a matrix or vector or any number of other Mathcad elements. | 677.169 | 1 |
098 Developmental Arithmetic (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is less than 15 or COMPASS Math score of 30 or less. Fundamental topics in arithmetic, geometry, and pre-algebra.
099 Developmental Algebra (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is at least 15 but less than 19 or COMPASS Math score of 31 to 58. Fundamental topics in algebra for students with insufficient knowledge of high school level mathematics. PR: ACT Mathematics Main score of 15 or grade of "S" in MATH 098.
109 Algebra (3-0-3). Real numbers, exponents, roots and radicals; polynomials, first and second degree equations and inequalities; functions and graphs. PR: ACT Mathematics main score of 19 or grade of "S" in MATH 099.
211 Informal Geometry (3-0-3). Theorems are motivated by using experiences with physical objects or pictures and most of them are stated without proof. Point approach is used with space as the set of all points; review elementary geometry, measurement, observation, intuition and inductive reasoning, distance, coordinate systems, convexitivity, separation, angles, and polygons. No field credit for math majors/minors. PR: MATH 101 or higher.
220 Calculus I (4-0-4). A study of elements of plane analytical geometry, including polar coordinates, the derivative of a function with applications, integrals and applications, differentiation of transcendental functions, and methods of integration. PR: MATH 109 and MATH 110, or GNET 116, or ACT Mathematics main score of 26 or COMPASS Trigonometry score of 46 or above.
250 Discrete Mathematics (3-0-3). Treats a variety of themes in discrete mathematics: logic and proof, to develop students' ability to think abstractly; induction and recursion, the use of smaller cases to solve larger cases of problems; combinatorics, mathematics of counting and arranging objects; algorithms and their analysis, the sequence of instructions; discrete structures, e.g., graphs, trees, sets; and mathematical models, applying one theory to many different problems. PR: MATH 109 and MATH 110 or GNET 116.
290 Topics in Mathematics (1-4 hours credit). Formal course in diverse areas of mathematics. Course may be repeated for different topics. Specific topics will be announced and indicated by subtitle on the student transcript. PR: Consent of instructor.
400 Introduction to Topology (3-0-3). A study of set theory; topological spaces, cartesian products, connectedness; separation axioms; convergences; compactness. Special attention will be given to the interpretation of the above ideas in terms of the real line and other metric spaces. PR: MATH 240.
490 Topics in Mathematics (1-4 hours credit per semester). Advanced formal courses in diverse areas of mathematics. Courses may be repeated for different topics. Specific topics will be announced and indicated by subtitle on transcript. PR: Consent of instructor. | 677.169 | 1 |
Word problems for systems of linear equations are troublesome for most of the
students in understanding the situations and bringing the word problem into
equations. We tried to explain the trick of ...
Solving Math Word problems is not easy! A lot of students have difficulty with Math problems but employing some basic techniques will help you. Math word problems are nothing but numerical functions ...
Get answers to all Algebra word problems online with TutorVista. Our online Algebra tutoring program is designed to help you get all the answers to your Algebra word problems giving you the desired ...
Solving Help With Math Word Problems is not easy! A lot of students have difficulty with Math problems but employing some basic techniques will help you. Math word problems are nothing but numerical
problems but employing some basic techniques will help you. Math word problems are
nothing but numerical functions ... | 677.169 | 1 |
Mathematics, Grade 12. (MAP4C or MTT4G or a mathematics with a similar content.) | 677.169 | 1 |
You will be completing math assignments pertaining to the probability and statistics. Tasks will include watching videos, playing math games online, writing journals, completing discussions, and performing math computation and application skill problems. | 677.169 | 1 |
This Tutorial, intended for mature students, covers the Algebra Topics taught in School and required for College. It makes Algebra easy by carefully explaining the Algebra Rules with examples of how to apply them. Many people have trouble with Algebra because when it was taught in school, they weren\'t ready to absorb the abstract Rules. Now, with maturity, the Algebra Rules are simple to learn and Algebra becomes easy | 677.169 | 1 |
Mathematics 2
[ LFSAB1102 ]
Functions of several real variables ; vector analysis ; linear algebra ;
linear differential equations with constant coefficients ; introduction to
data analysis and reasoning in a context of random uncertainty.
Study and handling of the above-mentioned concepts for their use in later
courses. Training in the domains of rigor and abstraction by studying
important proofs in calculus or algebra, and by constructing proofs
featuring interaction between several different concepts or notions.
Resolution of problems or exercises requiring the use of several
mathematical tools.
Aims
After completing this course, students will be able to:
Handle functions of several real variables.
Master advanced notions in linear algebra.
Conduct mathematical reasoning and write short proofs in a rigorous manner.
Understand and use different proof techniques.
Deal with problems, exercises and proofs for which not all data is provided
explicitly.
Interpret a problem, exercise or statement from various points of view
(e.g. algebraic point of view or geometric point of view).
Model mathematical situations involving random elements.
Solve exercises and understand results whose difficulty warrants formal
definitions and advanced theorems.
Approach theories whose formalism exceeds the framework of intuitive
examples and which require abstraction. | 677.169 | 1 |
Description
The Rockswold/Krieger algebra series uses relevant applications and visualization to show students why math matters, and gives them a conceptual understanding. It answers the common question "When will I ever use this?" Rockswold teaches students the math in context, rather than including the applications at the end of the presentation. By seamlessly integrating meaningful applications that include real data and supporting visuals (graphs, tables, charts, colors, and diagrams), students are able to see how math impacts their lives as they learn the concepts. The authors believe this approach deepens conceptual understanding and better prepares students for future math courses and life.
Table of Contents
1. Introduction to Algebra
1.1 Numbers, Variables, and Expressions
1.2 Fractions
1.3 Exponents and Order of Operations
1.4 Real Numbers and the Number Line
1.5 Addition and Subtraction of Real Numbers
1.6 Multiplication and Division of Real Numbers
1.7 Properties of Real Numbers
1.8 Simplifying and Writing Algebraic Expressions
2. Linear Equations and Inequalities
2.1 Introduction to Equations
2.2 Linear Equations
2.3 Introduction to Problem Solving
2.4 Formulas
2.5 Linear Inequalities
3. Graphing Equations
3.1 Introduction to Graphing
3.2 Linear Equations in Two Variables
3.3 More Graphing of Lines
3.4 Slope and Rates of Change
3.5 Slope-Intercept Form
3.6 Point-Slope Form
3.7 Introduction to Modeling
4. Systems of Linear Equations In Two Variables
4.1 Solving Systems of Linear Equations Graphically and Numerically
4.2 Solving Systems of Linear Equations by Substitution
4.3 Solving Systems of Linear Equations by Elimination
4.4 Systems of Linear Inequalities
5. Polynomials and Exponents
5.1 Rules for Exponents
5.2 Addition and Subtraction of Polynomials
5.3 Multiplication of Polynomials
5.4 Special Products
5.5 Integer Exponents and the Quotient Rule
5.6 Division of Polynomials
6. Factoring Polynomials and Solving Equations
6.1 Introduction to Factoring
6.2 Factoring Trinomials I (x + bx + c)
6.3 Factoring Trinomials II (ax2 + bx + c)
6.4 Special Types of Factoring
6.5 Summary of Factoring
6.6 Solving Equations by Factoring I (Quadratics)
6.7 Solving Equations by Factoring II (Higher Degree)
7. Rational Expressions
7.1 Introduction to Rational Expressions
7.2 Multiplication and Division of Rational Expressions
7.3 Addition and Subtraction with Like Denominators
7.4 Addition and Subtraction with Unlike Denominators
7.5 Complex Fractions
7.6 Rational Equations and Formulas
7.7 Proportions and Variation
8. Radical Expressions
8.1 Introduction to Radical Expressions
8.2 Multiplication and Division of Radical Expressions
8.3 Addition and Subtraction of Radical Expressions
8.4 Simplifying Radical Expressions
8.5 Equations Involving Radical Expressions
8.6 Higher Roots and Rational Exponents
9. Quadratic Equations
9.1 Parabolas
9.2 Introduction to Quadratic Equations
9.3 Solving by Completing the Square
9.4 The Quadratic Formula
9.5 Complex Solutions
9.6 Introduction to Functions
Appendix A: Using the Graphing Calculator
Appendix B: Sets
Answers to Selected Exercises
Glossary
Bibliography
Photo Credits | 677.169 | 1 |
prominent. In some approaches, students are engaged in using the tools of algebra to model situations and problems, while, in others, algebra as an abstract language is stressed. While much controversy surrounds the worth and merit of these different perspectives on the subject, additional debates center on the contribution of calculators and other technology, the structure of lessons, and the role of the teacher. Because curricula have already been developed that represent these different perspectives on the subject and on how it might best be taught, one important initiative of SERP might be to design comparative studies of how these curricula are taught in classrooms and what and how diverse students learn algebra over time.
In this initiative, cohorts of students could be followed longitudinally. Studies could gather information about the instruction they receive, exposure to curriculum, information on the teachers, and their use of the curriculum and other tools. This initiative will depend on the development of effective assessments (see Initiative 3).
As with elementary mathematics, however, knowing why particular curricular interventions produce particular outcomes will require companion controlled experiments at the level of particular program features to test for causality. This kind of research is necessary not only to advance scientific understanding, but also because it provides critical knowledge for teachers who adapt curricula and allows developers to improve curricula or design alternatives that are responsive to research findings.
Simultaneous with this effort, SERP can support curriculum development that extends existing curricula in promising directions. The Algebra Cognitive Tutor, for example, emphasizes highly contextualized problem solving. While many fewer students drop out and students master the material covered more quickly and effectively, the curriculum may not achieve the fluency in symbol manipulation and abstract analysis expected for high-achieving students. The developers suggest that the curriculum could quite easily be strengthened in this respect, and a separate accelerated algebra course is likely to yield even better results for high-achieving students. In studying the set of curricula as they are being implemented, SERP as a third-party entity would be well positioned to identify and support promising areas like this for further development. | 677.169 | 1 |
Visual Mathematics Full Description
Visual Mathematics is a highly interactive visualization software (containing -at least- 67 Visual Mathematics, a member of the Virtual Dynamics Mathematics Virtual Laboratory, is an Intuitively-Easy-To-Use software.
Visual Mathematics modules include the theory necessary to understand every theme, they include very many solved examples. Every student should have this powerful tool at home.
Teachers use Visual Mathematics to prepare homeworks and tests in a short time.
With Visual Mathematics the student solves homework problems while he/she really learns and enjoys mathematics. Visual Mathematics may be used (1) in the classroom, to very easily make clear the topics the teacher covers, (2) in the school library, as reference to review themes covered in classes (3) at home, for the student to study at his own pace and understand while solving and visualizing hundreds of problems. Teachers may use Visual Mathematics to prepare classes. <>
Software related to Visual Mathematics
Calc 3D Pro 2.1.10
Calc 3D is a collection of mathematical tools for highschool and university. | 677.169 | 1 |
In a differential equations course, students learn to use integrating factors to solve first order linear differential equations, and in the process reinforce learning of key concepts from their calculus courses. This capsule offers some differential equations solved by the originators of the technique of using an integrating factor, though they did not use that expression. Solving differential equations via integrating factors is difficult for some students, particularly those who try to memorize a formula. We advocate that students learn to derive the method and solve differential equations using the product rule and the fundamental theorem of calculus, as advocated in a number of modern texts [2, 3]. Memorizing the formula would not be in the spirit of the originators of the method, Johann Bernoulli (1667–1748) and Leonhard Euler (1707–1783), nor does formula memorization lead to deep learning of fundamental mathematical processes. Understanding why integrating factors work, as offered in this historical perspective, can deepen student understanding of calculus topics such as the product rule, the fundamental theorem of calculus, and basic integration techniques. This capsule provides some historical information about the work of Bernoulli and Euler, and we offer student activities that will connect that history to enable more thorough learning of the method of integrating factors.
Historical preliminaries
Johann Bernoulli was a colleague of Gottfried Leibniz (1646–1716) and is acknowledged as one of the foundational figures in the development of the calculus. In the early 1690's he prepared lectures in the nascent calculus for Guillaume de l'Hôpital (1661–1704), who is credited with writing the first text on the calculus | 677.169 | 1 |
Take it step-by-step for pre-calculus success! The quickest route to learning a subject is through a solid grounding in the basics. So what you won't find in Easy Pre-calculus Step-by-Step is a lot of… | 677.169 | 1 |
Math Program Desciption:
It is a simple math program that tests your math capabilities in any level of difficulty and in the basic areas of math (addition, subtraction, division and multiplication).It also provides immediate feedback when you answer questions.
UMS Math Editor is the program used for typing plain text and mathematical formulas. The distinctive feature of UMS Math Editor is that it not only allows you a simple way to enter mathematical formulas in a regular word processing environment, but
Undoubtedly, mathematics is one of the most important subjects taught in school. It is thus unfortunate that some students lack elementary mathematical skills. An inadequate grasp of simple every-day mathematics can negatively affect a person's life....Envisioneer Express is the easiest to use residential design program available. This program was designed specifically to introduce clients to the simple creation of floor plans, 3D models, and interior design concepts.
Envisioneer uses real world...... | 677.169 | 1 |
Fields and Geometry III
Description
This first part of this course generalizes the real numbers to a mathematical structure called a field. Finite fields have many applications, particularly in Information Security where the understanding of finite fields is fundamental to many codes and cryptosystems. Properties and constructions of fields will be investigated in detail. The second part of the course considers projective geometries. Projective geometry is one of the important modern geometries introduced in the 19th century. Projective geometry is more general than our usual Euclidean geometry, and it has useful applications in Information Security, Statistics, Computer Graphics and Computer Vision. The focus of this course will be primarily on projective planes.
Objective
To provide an introduction to the areas of Fields and
Projective Geometry with particular emphasis on the links between the
two areas. At the end of this course students should:
have a knowledge of the structure of finite fields and be able to
perform basic calculations in finite fields.
understand the ideas in projective geometry, and how projective
geometry relates to Euclidean geometry.
have enough tools to study objects and transformations in
projective planes corresponding to fields.
Graduate attributes
Linkage past
Prerequisite is MATHS 1007A/B Mathematics I (Pass
Div I) or both MATHS 1007A/B Mathematics I (Pass Div II) and MATHS
2004 Mathematics IIM (Pass Div I). It will be an advantage to have
done PURE MTH 2002 Algebra II, although the necessary material is
revised at the start of the course.
Linkage present
This course complements the first semester
course PURE MTH 3007 Groups and Rings III. It also contains
concepts that are useful for the course PURE MTH 3006 Coding and
Cryptology III
Linkage future
This course is one of the core Pure Mathematics
courses, and provides a strong foundation for further study in the
areas of Algebra and Projective Geometry. Finite fields have many
applications, and an understanding of their structure is essential
to students who want to further their knowledge of codes and
cryptosystems. | 677.169 | 1 |
David Lay, author of the currently used Linear Algebra
textbook, has provided a convenient way for faculty and students to access the
data in homework problems. With the Lay Linear Algebra toolbox installed, at
the command line you type "c2s3" for chapter 2, section 3. MATLAB responds with
a list of homework problems with data and prompts for an exercise number. After
entering the number, MATLAB responds by defining a matrix or matrices
containing the data. In addition, the Lay toolbox has various tools which
manipulate matrices in a way parallel to the presentation in the book. For
example, there are commands for each of the elementary row operations. The
author has included boxed MATLAB subsections in the Study Guide which
demonstrate how to use these tools. To get a hard copy of the Study Guide, you
may contact the publisher. The electronic version is on the CD-ROM that comes
with the book. I can provide you with an electronic copy if you do not have the
CD. I have made use of the slides provided by the publisher. Depicting examples
in 3 dimensions is difficult and the author has done a reasonably good job.
In the MATLAB toolbox folder (e.g.,
C:\MATLAB7\toolbox), create a new folder "Lay"
Extract the files from the zipped file (about 50, all
ending with .m) and put into the "Lay" folder
Open up MATLAB. Go to Set Path under the File menu and
add the "Lay" folder.
Go to the command line window in MATLAB and enter
"c1s1". You should get the following response and prompt: "Exercise number
(1-4,7-18,29-32,34)?"
In addition to the author's tools,
there is an extensive set of material online for creating labs, illustrating
concepts or as places for students to explore. A good place to start is MAA's
Digital Library
[Thomas Hern was a coauthor of a seminal article that I handed out
to attendees a week after the seminar: "Viewing Some Concepts and
Applications in Linear Algebra" from Visualization in Teaching and
Learning Mathematics (1991) of the MAA Notes Series.]
Most tools on the MAA Digital
Library site are stand alone, meaning that they do not need costly software
such as MATLAB, Maple or Mathematica. However, since
we do have access to this software, we may explore what is available for any or
each of them. A good start is the ATLAST project:
The files can be downloaded here
and documentation is available. However, there is a lab manual and guide
published by Prentice Hall. Since Prentice Hall has merged with Addison-Wesley,
we may get them to bundle the guide with the Lay text. I have asked Pearson
(Fred Speers) to send us a review copy or 2. | 677.169 | 1 |
Search form
Addressing the Common Core with Fathom
Common Core Statistics and Probability standards are easily addressed with Fathom.
With Fathom, modeling comes alive.
For 40 years, Key Curriculum has created tools and curriculum that incorporate problem solving, real-world applications, conceptual understanding, and mathematics as sensemaking. These pedagogical approaches are at the heart of our dynamic mathematics software, and central to the Mathematical Practice Standards of the Common Core State Standards.
Additionally, the Common Core State Standards include a strong and coherent data analysis, statistics, and probability strand, which starts in kindergarten with basic graphical representations of categorical data. This evolves into deeper concepts in grades 9–12, such as calculating (with technology) and interpreting correlation coefficients, and understanding, calculating, and modeling conditional probability. And, the modeling strand emphasizes the value of technology in building mathematical models.
The current version of Fathom is 2.13—read release notes here. To update for free from an earlier version of Fathom 2, choose Check for Updates from Fathom's Help menu.
Note that Fathom 2.13 is the latest version of Fathom 2L, which is a downloadable version of Fathom that must be registered with a License Name and Authorization Code. Users who have installed Fathom 2 from a CD need to call McGraw-Hill Digital Technical Support at 800-437-3715 and register their software in order to upgrade to Fathom 2.13. | 677.169 | 1 |
Beginning and Intermediate Algebra, 5th Edition
Description all the tools they need to achieve success.
With this revision, the Lial team has further refined the presentation and exercises throughout the text. They offer several exciting new resources for students that will provide extra help when needed, regardless of the learning environment (classroom, lab, hybrid, online, etc)–new study skills activities in the text, an expanded video program available in MyMathLab and on the Video Resources on DVD, and more!
Table of Contents
Chapter 1 The Real Number System
1.1 Fractions
Study Skills: Reading Your Math Textbook
1.2 Exponents, Order of Operations, and Inequality
Study Skills: Taking Lecture Notes
1.3 Variables, Expressions, and Equations
1.4 Real Numbers and the Number Line
Study Skills: Tackling Your Homework
1.5 Adding and Subtracting Real Numbers
Study Skills: Using Study Cards
1.6 Multiplying and Dividing Real Numbers
Summary Exercises on Operations with Real Numbers
1.7 Properties of Real Numbers
1.8 Simplifying Expressions
Study Skills: Reviewing a Chapter
Chapter 2 Linear Equations and Inequalities in One Variable
2.1 The Addition Property of Equality
2.2 The Multiplication Property of Equality
2.3 More on Solving Linear Equations
Summary Exercises on Solving Linear Equations
Study Skills: Using Study Cards Revisited
2.4 An Introduction to Applications of Linear Equations
2.5 Formulas and Applications from Geometry
2.6 Ratio, Proportion, and Percent
2.7 Further Applications of Linear Equations
2.8 Solving Linear Inequalities
Study Skills: Taking Math Tests
Chapter 3 Linear Equations in Two Variables
3.1 Linear Equations in Two Variables: The Rectangular Coordinate System | 677.169 | 1 |
MATHEMATICS DEPARTMENT
A minimum of two years of mathematics is required for graduation from Santa Monica High School (30 units). A minimum of 1 year (10 units) must be taken in grades 10-12. However, students are encouraged to take as many math courses as they wish, while attending Samohi.
Samohi's college prep sequence includes the following; Algebra, Geometry (P & HP), Algebra II (P & HP), and Pre-Calculus (P & HP). Successful completion of these courses prepares students for admission to the UC/CSU system as well as other universities.
For those who want to continue their studies in mathematics, Samohi offers the following; Calculus A/B, B/C, and D/E, Statistics and Statistics AP.
Prior to enrollment transfer students whose previous mathematics course does not clearly communicate an equivalent math level will be administered a math placement test. | 677.169 | 1 |
Introductory & Intermediate Algebra for College Students Plus NEW MyMathLab with Pearson eText Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum appeal. Blitzer's personality shows in his writing, as he draws readers into the material through relevant and thought-provoking applications. Every Blitzer page is interesting and relevant, ensuring that students will actually use their textbook to achieve success!
The Blitzer Algebra Series combines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum appeal. Blitzerís personality shows in his writing, as he draws readers into the material through relevant and thought-provoking applications. Every Blitzer page is interesting and relevant, ensuring that students will actually use their textbook to achieve success!
7.3 Adding and Subtracting Rational Expressions with the Same Denominator
7.4 Adding and Subtracting Rational Expressions with Different Denominators
Mid-Chapter Check Point Section 7.1–Section 7.4
7.5 Complex Rational Expressions
7.6 Solving Rational Equations
7.7 Applications Using Rational Equations and Proportions
7.8 Modeling Using Variation
Chapter 7 Group Project
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Test
Cumulative Review Exercises (Chapters 1–7)
8. Basics of Functions
8.1 Introduction to Functions
8.2 Graphs of Functions
8.3 The Algebra of Functions
Mid-Chapter Check Point Section 8.1–Section 8.3
8.4 Composite and Inverse Functions
Chapter 8 Group Project
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Test
Cumulative Review Exercises (Chapters 1–8)
9. Inequalities and Problem Solving
9.1 Reviewing Linear Inequalities and Using Inequalities in Business Applications
9.2 Compound Inequalities
9.3 Equations and Inequalities Involving Absolute Value
Mid-Chapter Check Point Section 9.1–Section 9.3
9.4 Linear Inequalities in Two Variables
Chapter 9 Group Project
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Test
Cumulative Review Exercises (Chapters 1–9)
10. Radicals, Radical Functions, and Rational Exponents
10.1 Radical Expressions and Functions
10.2 Rational Exponents
10.3 Multiplying and Simplifying Radical Expressions
10.4 Adding, Subtracting, and Dividing Radical Expressions
Mid-Chapter Check Point Section 10.1–Section 10.4
10.5 Multiplying with More Than One Term and Rationalizing Denominators
10.6 Radical Equations
10.7 Complex Numbers
Chapter 10 Group Project
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Test
Cumulative Review Exercises (Chapters 1–10)
11. Quadratic Equations and Functions
11.1 The Square Root Property and Completing the Square; Distance and Midpoint Formulas
11.2 The Quadratic Formula
11.3 Quadratic Functions and Their Graphs
Mid-Chapter Check Point Section 11.1–Section 11.3
11.4 Equations Quadratic in Form
11.5 Polynomial and Rational Inequalities
Chapter 11 Group Project
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Test
Cumulative Review Exercises (Chapters 1–11)
12. Exponential and Logarithmic Functions
12.1 Exponential Functions
12.2 Logarithmic Functions
12.3 Properties of Logarithms
Mid-Chapter Check Point Section 12.1–Section 12.3
12.4 Exponential and Logarithmic Equations
12.5 Exponential Growth and Decay; Modeling Data
Chapter 12 Group Project
Chapter 12 Summary
Chapter 12 Review Exercises
Chapter 12 Test
Cumulative Review Exercises (Chapters 1–12)
13. Conic Sections and Systems of Nonlinear Equations
13.1 The Circle
13.2 The Ellipse
13.3 The Hyperbola
Mid-Chapter Check Point Section 13.1–Section 13.3
13.4 The Parabola; Identifying Conic Sections
13.5 Systems of Nonlinear Equations in Two Variables
Chapter 13 Group Project
Chapter 13 Summary
Chapter 13 Review Exercises
Chapter 13 Test
Cumulative Review Exercises (Chapters 1–13)
14. Sequences, Series, and the Binomial Theorem
14.1 Sequences and Summation Notation
14.2 Arithmetic Sequences
14.3 Geometric Sequences and Series
Mid-Chapter Check Point Section 14.1–Section 14.3
14.4 The Binomial Theorem
Chapter 14 Group Project
Chapter 14 Summary
Chapter 14 Review Exercises
Chapter 14 Test
Cumulative Review Exercises (Chapters 1–14)
Appendices
A. Mean, Median, and Mode
B. Matrix Solutions to Linear Systems
C. Determinants and Cramer's Rule
D. Where Did That Come From? Selected Proofsís his Developmental Algebra Series, Bob has written textbooks covering college algebra, algebra and trigonometry, precalculus, and liberal arts mathematics, all published by Pearson Education. When not secluded in his Northern California writerís cabin, Bob can be found hiking the beaches and trails of Point Reyes National Seashore, and tending to the chores required by his beloved entourage of horses, chickens, and irritable roosters. | 677.169 | 1 |
XX10198: Mathematics 1
This unit is only available to students in the Department of Electronic & Electrical Engineering.
Description:
Aims: This is the first of two first year units intended to lead to confident and error-free manipulation and use of standard mathematical relationships in the context of engineering mathematics. The unit will consolidate and extend topics met at A-level, so that students may improve their fluency and understanding of the basic techniques required for engineering analysis.
Learning Outcomes: After successfully completing this unit the student should be able to:
Handle circular and hyperbolic functions, and sketch curves. Differentiate and integrate elementary functions, products of functions etc. Use complex numbers. Employ standard vector techniques for geometrical purposes. Determine the Fourier series of a periodic function. | 677.169 | 1 |
Toolbar
Search Google Appliance
Mathematics, BS
What Is the Study of Mathematics?
Mathematics reveals hidden patterns that help us understand the world around us. Now much more than arithmetic and geometry, mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, of human behavior, and of social systems.
As.
-From Everybody Counts: A Report to the Nation on the Future of Mathematics Education (c) 1989 National Academy of Sciences
Why Should I Consider this Major?
The special role of Mathematics in education is a consequence of its universal applicability. The results of Mathematics-theorems and theories-are both significant and useful; the best results are also elegant and deep. Through its theorems, Mathematics offers science both a foundation of truth and a standard of certainty.
In addition to theorems and theories, Mathematics offers distinctive modes of thought which are both versatile and powerful, including modeling, abstraction, optimization, logical analysis, inference from data, and use of symbols. Experience with mathematical modes of thought builds mathematical power-a capacity of mind of increasing value in this technological age that enables one to read critically, to identify fallacies, to detect bias, to assess risk, and to suggest alternatives. Mathematics empowers us to understand better the information-laden world in which we live.
-From Everybody Counts: A Report to the Nation on the Future of Mathematics Education (c) 1989 National Academy of Sciences
Empowered with the critical thinking skills that Mathematics develops, recent Mathematics graduates from Western have obtained positions in a variety of fields including actuarial science, cancer research, computer software development, business management and the movie industry, among many others. The skills acquired in our program have prepared graduates for further academic studies in Mathematics, Computer Science, Physics, Biology, Chemistry, Oceanography and Education.Coursework
Requirements
MATH 204 Elementary Linear Algebra
MATH 224 Multivariable Calculus and Geometry I
MATH 225 Multivariable Calculus and Geometry II
MATH 226 Limits and Infinite Series
MATH 304 Linear Algebra
MATH 312 Proofs in Elementary Analysis
Note: The pair MATH 203 and 303 may be substituted for MATH 204 and 331.
Choose either:
MATH 124 Calculus and Analytic Geometry I
MATH 125 Calculus and Analytic Geometry II
or
MATH 134 Calculus I Honors
MATH 135 Calculus II Honors
or
MATH 138 Accelerated Calculus
One course from:
MATH 302 Introduction to Proofs Via Number Theory
MATH 309 Introduction to Proofs in Discrete Mathematics
No fewer than 31 approved credits in mathematics or math-computer science, including at least two of the following pairs:
One course from:
MATH 303 - Linear Algebra and Differential Equations II
MATH 331 - Ordinary Differential Equations
Together with one of:
MATH 415 - Mathematical Biology
MATH 430 - Fourier Series and Applications to Partial
Differential Equations
MATH 431 - Analysis of Partial Differential Equations
MATH 432 - Systems of Differential Equations
Only one of the pairs from the above group can be used
The following pair:
MATH 341 - Probability and Statistical Inference
MATH 342 - Statistical Methods
The following pair:
MATH 401 - Introduction to Abstract Algebra
MATH 402 - Introduction to Abstract Algebra
The following pair:
MATH 421 - Methods of Mathematical Analysis I
MATH 422 - Methods of Mathematical Analysis II
The following pair:
MATH 441 - Probability
MATH 442 - Mathematical Statistics
The following pair:
M/CS 335 - Linear Optimization
M/CS 435 - Nonlinear Optimization
The following pair:
M/CS 375 - Numerical Computation
M/CS 475 - Numerical Analysis
Supporting Courses
At least 19 credits from 400-level courses in mathematics or math-computer science except MATH 483, and including at most one of MATH 419 or MATH 420.
One of:
CSCI 139 Programming Fundamentals in Python
CSCI 140 Programming Fundamentals in C++
CSCI 141 Computer Programming I
MATH 207 Mathematical Computing
Note: If the supporting sequence from CSCI below is chosen, this requirement is fulfilled.
One of the following sequences:
PHYS 161 - Physics with Calculus I
PHYS 162 - Physics with Calculus II
PHYS 163 - Physics with Calculus III
OROR
CSCI 141 - Computer Programming I
CSCI 145 - Computer Programming & Linear Data Structures
CSCI 241 - Data Structures
CSCI 301 - Formal Languages and Functional Programming
And one of:
CSCI 305 - Analysis of Algorithms and Data Structures I
CSCI 330 - Database Systems
CSCI 345 - Object Oriented Design
CSCI 401 - Automata and Formal Language Theory
OR
ECON 206 - Introduction to Microeconomics
ECON 207 - Introduction to Macroeconomics
ECON 306 - Intermediate Microeconomics
And one of
ECON 375 - Introduction to Econometrics
ECON 470 - Economic Fluctuations and Forecasting
ECON 475 - Econometrics
Language competency in French, German or Russian is strongly recommended for those students who may go to graduate school.
Students who are interested in the actuarial sciences should complete: MATH 441 and 442, M/CS 335 and 435, M/CS 375 and 475 as part of their major programs.
GURs:
The courses below satisfy GUR requirements and may also be used to fulfill major requirements.
QSR: CSCI 139, 140, 141, 145; MATH 124, 125, 134, 135, 138
SSC: ECON 206, 207
LSCI: CHEM 121, 122, 123, 125, 126, 225; PHYS 161, 162, 163
"The Department of Mathematics has very highly qualified faculty who excel as both teachers and scholars. We have expertise in both pure and applied mathematics as well as statistics and math education. Our instructional focus is to establish a sound understanding of the fundamental concepts as well as mastery of the related analytical and computational skills. We have small classes and strive for active involvement of students in their learning. Our graduates are extremely well prepared for the workplace and for more advanced studies in math and related fields."
- Tjalling Ypma, Faculty
"The focus of the math department is to give students a strong background in problem solving and applying those skills. There is a wide range of mathematicians at Western, making it easy to find professors who share your interests and help you maximize your potential. They take teaching and advising very seriously; my advisor was always available for help with my resume' and planning my courses and my future. I am confident that Western has prepared me for success in graduate school and beyond. Whether your goals are professional or academic, being a Math major at Western will help you to succeed."
- Malcolm Rupert, Student
Notable Alumni
Jeanie Light
Software engineer, Google
Software engineer, Google
Charles Clark
Co-Director, Joint Quantum Institute, National Institute of Standards and Technology | 677.169 | 1 |
Algebra Tutor
AlgebraTutor is a set of books and videos designed to help you get through Algebra class. Covering most of the topics found in college and high school algebra, its like having a "dummies" book with video help but without the fluff. Includes a book with 200 pages of material and hundreds of solved examples plus 6 video tutorials - all showing solved examples. The emphasis is on showing you how to solve algebra problems in a step-by-step fashion. Plus - each chapter includes an end of chapter quiz complete with answers so you can test your learning progress.
****************** PACKED WITH SOLVED EXAMPLES ******************
Algebra tutor makes algebra easy for anyone to learn. Using a teach by example approach you get these tutorial books: | 677.169 | 1 |
The Oxford Users' Guide to Mathematics is one of the leading handbooks on mathematics available. It presents a comprehensive modern picture of mathematics and emphasises the relations between the different branches of mathematics, and the applications of mathematics in engineering and the natural sciences. The Oxford User's Guide covers a broad spectrum of mathematics starting with the basic material and progressing on to more advanced topics that have come to the fore in the last few decades. The book is organised into mathematical sub-disciplines including analysis, algebra, geometry, foundations of mathematics, calculus of variations and optimisation, theory of probability and mathematical statistics, numerical mathematics and scientific computing, and history of mathematics. The book is supplemented by numerous tables on infinite series, special functions, integrals, integral transformations, mathematical statistics, and fundamental constants in physics. It also includes a comprehensive bibliography of key contemporary literature as well as an extensive glossary and index. The wealth of material, reaching across all levels and numerous sub-disciplines, makes The Oxford User's Guide to Mathematics an invaluable reference source for students of engineering, mathematics, computer science, and the natural sciences, as well as teachers, practitioners, and researchers in industry and academia.
Reviews
"With so much mathematics in compact form, this book will be useful as a quick reference for those working in such fields as physics, engineering, and economics, as well as for mathematicians."--CHOICE
You can earn a 5% commission by selling Oxford User's Guide to Mathematics | 677.169 | 1 |
Algebra II picks up, of course, where Algebra I leaves off. And now we have the benefit of a years worth of geometry to provide further insight into some algebraic topics.
A quick and speedy review of some previously learned algebra leads to intensive work with polynomial functions and their distant cousins, the rational functions. The transcendental functions of exponentiation and the logarithm are covered in detail as well.
Expect some things that look familiar, but questions and applications that do not. Expect to be pushed to really THINK about what these functions do, how they do it, and how they behave. Expect to leave this course with a better understanding of why some functions make better real life models for a particular situation than others.
Looking forward to meeting each of you and successfully working our way through the course!
Visit our Class Edmodo site for announcements, handouts, and other useful information related to Algebra 2: | 677.169 | 1 |
78915052
ISBN-13:
9780878915057
Publisher:
Research & Education Association
Release Date:
January, 1998
Length:
1104 Pages
Weight:
Unavailable
Dimensions:
10.1 X 6.8 X 2.1 inches
Language:
English
Calculus Problem Solver (REA) (Problem Solvers Solution Guides) tex... Read moreDETAILS- The PROBLEM SOLVERS are unique - the ultimate in study guides.- They are ideal for helping students cope with the toughest subjects.- They greatly simplify study and learning tasks.- They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding.- They cover material ranging from the elementary to the advanced in each subject.- They work exceptionally well with any text in its field.- PROBLEM SOLVERS are available in popular subjects.- Each PROBLEM SOLVER is prepared by supremely knowledgeable experts.- Most are over 1000 pages.- PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly.
Customer Reviews
Excellent
Posted by Robert T Carroll on 09/16/2003
I was recently offered a high school teaching job, so I needed to brush up on my calc, and this book did the trick. Unlike other books, this one "teaches by example". I always found that too many college professors & textbooks spend too much time trying to "explain" the concept. My experience has been to skip the lecture part, do the problems, and in doing so, the concept will come to you. The fact that the problems are all solved in detail is also a plus. A lot of texts simply list the answer to the problem, so you're often left wondering how they got it. This won't be an issue with this text.
Great for University Students!
06/16/2000
The Calculus Problem Solver is an excellent book for University students or even high school students taking Calculus. This book is clearly organized with a table of contents and an index. It provides an explanation on each topic, followed by tons of practice problems with full solutions. It beats regular textbooks because the solutions are fully explained using words and calculations so the reader understands exactly how to solve each problem. It is also low on wear and tear, I bought my book used and have trucked it to school and back and it has remained in tact. I would recommend this book to every Calculus student and or Physics student as this book also provides topics ranging from first year Physics to Advanced.
Calculus: Oh how i love it
Posted by Calc Lover on 04/18/2000
This book is a great solution guide to ANY Calculus I,II,III textbook. Basically contains all problems which are solved out in a sytematic approach. Lets you follow the solution from beginning to end with comlpete understanding. I recommend this book for people who need help with Calculus and for people who just cant get enough problems, ITS GREAT.
Step by Step
01/09/2004
I have been out of college for 7 years. I began Grad school last quarter. This book gave me the basic steps to relearn and remember Calculus. It takes you through each kind of problem without skipping steps or assuming you already know what you are doing. A big crutch for understanding single and multivariable calculus. -I passed the placement exam and then used the book to assist in other engineering classes.
This is exactly what the title says
Posted by ophelia99 on 01/03/2005
Even if you understand the principles, the handful of problems in the average textbook are too few to really drill you on the procedures. It's a little like the difference between understanding some music theory and being able to play an instrument. Practice, for those of us who are not math prodigies, is essential. If you are willing to put in the hours and hours, this hugh collection of solved problems is well worth the price. | 677.169 | 1 |
Summary
In this Spreadsheets Across the Curriculum activity, students are guided step-by-step to build a spreadsheet that estimates the real cost of driving out of the way for less-expensive gasoline. To better illustrate the modeling process, the module begins with the simplest case of factoring in only the extra gas consumed and is then expanded to consider not only the additional wear-and-tear expense, but also the non-monetary cost of travel time. This module should demonstrate both the power of basic mathematics to analyze authentic relevant scenarios as well as the ease at which this can be accomplished using spreadsheets.
Gain experience with using numbers and mathematical calculations to examine their opinions.
Context for Use
I wrote the module out of dismay with how the media hypes their "cheap gas price" reports and yet continually fails to provide any context as to when and how this information will actually serve its intended purpose, namely to save the consumer money. However, without an audience of own, my thoughts would all be for naught. Luckily, a module exploring the trade-offs involved in driving some distance to get cheaper gas is perfect for Davenport University's College Mathematics course (MATH120). A major focus of this class is to develop the students' ability to apply the concepts learned in basic algebra to both the content of their major as well as their daily life. .
The module is meant to be the first step into real modeling (i.e., thinking beyond the basic textbook story problem). The module is given around the fifth week of classes after the students have completed sessions on applying linear, quadratic, logarithmic and exponential functions as well as systems of linear equations. The reason for the later placement is so students will have time to complete a series of short Excel skill-building assignments. This way, students can start on the module with full confidence in their spreadsheeting abilities. Alternatively, the module could be given to correspond with coverage of linear functions, but then additional time would need to be dedicated to the Excel portions of the module.
I prefer to have a discussion about gas prices and the cheap-gas reports prior to showing the students the module. I open the discussion by showing the students a cheap-gas website or a cheap-gas report from a recent copy of the local newspaper, and then I ask them if they've seen these reports and if anyone actually follows up on them (and how). Typically the conversation stalls with students either believing there is value in making a trip for cheaper gas or that the trip isn't worthwhile; significantly, students in the latter group are unable to provide evidence as to why it isn't worthwhile except for "I don't want to take the time." At this point, I give them the overview of modeling that appears on Slide 2 of the module and immediately follow that up by asking the students to identify everything they think may be relevant to making this decision (Students who already have a strong opinion regarding what they would do in this situation can be coaxed back to "neutral" by asking them to put this in business context where their boss would like actual data before making a choice).
After that introduction, I start to walk the students through the actual module. (They seem to like the fact that they have already brought up most if not all or more of the variables mentioned in the module). As we sort through the variables, the most natural question that arises is what information is actually available to us, which then leads us right into what assumptions are we going to make. For example, the fuel cost to make the trip is the first variable most people consider. Finding this cost depends on the distance we need to travel, the price we pay for the gas, and the fuel efficiency of the vehicle we're driving; hence, we need to establish values for each of these. I chose the numbers I used because (a) they are believable and (b) they work out nicely - which we then proceed to do. The great thing about this is that if students don't like my numbers, they can run their own numbers later.
As is often done in real-world problem solving, we have started our considerations with a simple case. So next we increase the complexity by incorporating the other variables. We discover that gathering the relevant information can become difficult (and possibly impractical) to find, thus requiring additional assumptions if we wish continue. We also find that the scale of the problem may render some variables irrelevant. Lastly, and building on the idea that this may not be worth our time, we take a look at the non-monetary costs (for many scenarios this road can easily lead to a discussion of ethics).
Although we only change gas prices in this module, I have set up the spreadsheet in a manner that allows one to alter distance traveled and wear-and-tear costs.
Description and Teaching Materials
The module is a PowerPoint presentation with embedded spreadsheets. IfThe module is constructed to be a stand-alone resource. It can be used as a homework assignment or lab activity. It can also be used as the basis of an interactive classroom activity.
Assessment
The last slide of the module is a set of questions that can be used for assessment.
The instructor version includes a slide of questions that can be used as a pretest. | 677.169 | 1 |
Mathematics - AS/A2 Levels
Entry Requirements
Five GCSEs at Grades A* - C including English Language and Mathematics at Grade B Higher Tier.
Further Mathematics is available through attendance at one twilight session per week at The University of Northampton and revision classes at the University of Warwick.
Course Content
A Level Mathematics is one of the most useful subjects you can study, as the successful mathematician possesses a problem-solving ability that is valuable in many occupations. This course builds on the algebra, trigonometry and geometry you learned at GCSE Level and develops the topics of calculus into Pure Mathematics. Modules also include Statistics (the identification of patterns in data) and Mechanics (developing mathematical models of physical forces). You should enjoy problem-solving, have a tenacious, disciplined approach and be prepared to practise between lessons the skills you have acquired | 677.169 | 1 |
OOC: Can't help there I'm afraid - I dropped maths first chance I got XD you could try Student room? There's normally a lot of people there who can help if you're stuck with something :)
ooc: A lot of people do XD I barely chose it myself. Student room?
It's a forum thing where people can go and get help with work stuff and discuss things - a lot of people in my year used it and they said it was helpful so… :P It should turn up on google if you look for it there.
I shall definitely give it a look, it sounds like it may help a lot :D Thank you! | 677.169 | 1 |
Middle School Mathematics
About Middle School Mathematics
The FCPS Mathematics Program of Studies (POS) define the instructional programs that must be implemented in mathematics in the middle school. Each POS describes the curriculum content and identifies the essential knowledge and skills taught in the instructional program.
Mathematics Course Sequence
Mathematics courses, from Grade 6 through Grade 12, should be completed in sequence since each course provides the prerequisite knowledge and skills for the follow-on course. | 677.169 | 1 |
An Introduction to Optimization, 2nd Edition
This authoritative book serves as an introductory text to optimization at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization, Second Edition helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization.
Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked examples to illustrate both theory and algorithms, this book also provides: * A review of the required mathematical background material * A mathematical discussion at a level accessible to MBA and business students * A treatment of both linear and nonlinear programming * An introduction to recent developments, including neural networks, genetic algorithms, and interior-point methods * A chapter on the use of descent algorithms for the training of feedforward neural networks * Exercise problems after every chapter, many new to this edition * MATLAB(r) exercises and examples * Accompanying Instructor's Solutions Manual available on request An Introduction to Optimization, Second Edition helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business | 677.169 | 1 |
This new edition of a classic American Tech textbook presents
basic mathematic concepts typically applied in the industrial,
business, construction and craft trades. By combining
comprehensive text with
illustrated examples of mathematics problems, this book
offers easy-to-understand instructions for solving math-based
problems encountered on the job. Many different trade areas are
represented throughout the book.
Each of the twelve chapters contains an Introduction providing an
overview of the chapter content. Examples of specific mathematic
problems are displayed in illustrated, step-by-step formats.
Following visual as well as written processes provides the reader
with a sequenced opportunity to learn each concept. Learned
knowledge is then applied in Practice Problems, which immediately
follow Examples in the book. Students are encouraged to use the
space provided in the margins to answer these questions.
Tips located throughout the text assist in the development of
mathematics skills.
Calculator tips are also provided in each chapter to offer an
alternative method of solving problems and equations. Points
to Know are included to enhance the learner's understanding of how
mathematics principles are applied to the trade professions.
Additionally, photographs provide visual examples of how these
principles relate to on-the-job skills.
Practical Math is designed to be a basis for a mathematics course
or as a supplement to many other American Tech books and training
products. | 677.169 | 1 |
The Mathematics Survival Kit
The Mathematics Survival Kit
Professor Jack Weiner taught at the University of Guelph from 1974 to 1976. He spent the next five years at Parkside High School in Dundas, Ontario. In 1982, he was re-recruited by Guelph and has been happily teaching and writing there ever since. He has won both the University of Guelph Professorial Teaching Award and the prestigious Ontario Conderation of University Faculty Associations Teaching Award. He has been listed as ...
How to get an 'A' in Math!
1) After class, DON'T do your homework! Instead, read over your class notes. When you come to an example done in class...
2) DON'T read the example. Copy out the question, set your notes aside, and do the question yourself. Maybe you will get stuck. Even if you thought you understood the example completely when the teacher went over it in class, you may get stuck.
And this is GOOD NEWS! Now, you know what you don't know. So, consult your notes, look in the text, see your teacher/professor. Do whatever is necessary to figure out the steps in the example that troubled you.
From the Best of Our Knowledge
ALBANY, NY (2007-11-12) THE MATHEMATICS SURVIVAL KIT ,
Pt. 1 of 2 -
If you listen to public radio on the weekends, you have likely heard a university math professor who is also the Math Guy. But if your tastes run more to television, you may have also seen the Friday night CBS show, Numbers, in which a curious young math wiz named Charlie, solves crimes using mathematics. Regardless of your viewing or listening habits, it's apparent more emphasis is being placed on math.
Now, comes The Mathematics Survival Kit. It's written by Professor Jack Weiner from the University of Guelph in Ontario, Canada. Weiner has partnered with education software provider, Maple, to produce an interactive e-book version of his math survival book. The University of Guelph has taken the lead introducing e-books , intelligent assessment systems, and podcasts nto its math curriculum. This next generation of educational technology provides teachers with ore time to motivate students and improve their comprehensive retention. | 677.169 | 1 |
Applied mathematics (minor subject)
An applied mathematician works with solving problems which lie beyond the realm of regular mathematics, and therefore Applied mathematics is the programme for you if you want to work with mathematics and still keep in mind how mathematics can be of use in your future career.
Applied mathematics is not a particular branch of mathematics, but rather a way of working with mathematics. In the Applied mathematics programme, you will learn to create models of and solve problems from the practical world by utilising advanced mathematical tools.
The Applied mathematics programme gives you the opportunity to solve complex problems and to create new insight and recognition. Applied mathematics is for you if you want to learn to utilise advanced mathematical tools and computers to model, analyse and solve complex problems in the business sector or in research. An applied mathematician masters and is able to further develop the mathematical tools which have contributed to the development of the modern society of information. | 677.169 | 1 |
chapter we looked at first order
differential equations. In this chapter
we will move on to second order differential equations. Just as we did in the last chapter we will
look at some special cases of second order differential equations that we can
solve. Unlike the previous chapter
however, we are going to have to be even more restrictive as to the kinds of
differential equations that we'll look at.
This will be required in order for us to actually be able to solve them.
Here is a list of topics that will be covered in this
chapter.
Basic Concepts Some of the basic concepts and ideas that are
involved in solving second order differential equations.
Mechanical Vibrations An application of second order differential
equations. This section focuses on
mechanical vibrations, yet a simple change of notation can move this into
almost any other engineering field. | 677.169 | 1 |
Exploring, Investigating and Discovering in Mathematics
May 23, 2011 - 22:52 — Anonymous
Author(s):
V. Berinde
Publisher:
Birkhäuser
Year:
2003
ISBN:
3-7643-7019-X
Price (tentative):
€34
MSC main category:
00 General
Review:
The book is a collection of problems from elementary mathematics. It can be of substantial help in work with gifted secondary school students. On the other hand, it also contains problems on determinants, special sequences, functional equations, primitive functions, difference and differential equations, so that it will be useful for work with students of basic courses on analysis and algebra. The collection is divided into 24 groups. Over 100 problems are presented with solutions, and another 150 are accompanied by hints and clear ideas how to proceed on the way to a solution. Using included material, the author leads readers from active problem solving to exploration of methods to obtain new problems and to an active use of the gained inventive skills. The book is based on the author's personal long lasting cooperation with the Romanian journal Gazeta Matematica. | 677.169 | 1 |
Customers who bought this book also bought:
Our Editors also recommend:Test Your Logic by George J. Summers Fifty logic puzzles range in difficulty from the simple to the more complex. Mostly set in story form, some problems involve establishing identities from clues, while others are based on cryptarithmetic.
Amusements in Mathematics by Henry E. Dudeney One of the largest puzzle collections — 430 brainteasers based on algebra, arithmetic, permutations, probability, plane figure dissection, properties of numbers, etc. More than 450 illustrations.
Sam Loyd's Book of Tangrams by Sam Loyd This classic by a famed puzzle expert features 700 tangrams and solutions, plus a charming satirical commentary on the puzzle's origins, its religious significance, and its relationship to mathematics.
Product Description:
160 math teasers and 40 alphametics will provide hours of mind-stretching entertainment. Accessible to high school students. Solutions. Four Appendices | 677.169 | 1 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.