text stringlengths 8 1.01M |
|---|
EuclideanSpace - Martin Baker
Introductions to algebra, geometry, calculus, discrete math, and statistics, particularly where relevant to 3D programming. In each subsection, Baker lays out notation and defines key terms to the right, in grey boxes with brown headers.
...more>>
The Euler Archive
The Euler Archive is an online resource for Leonhard Euler's original works and modern Euler scholarship. The searchable database provides access to his original publications, references to available translations, and current research. Also available
...more>>
The Euro - European Central Bank
On January 1, 2002, euro banknotes and coins were put into circulation. This site has sections for: euro banknotes and coins, getting ready for the euro, information for organizations, a children's zone, background to the euro, and news and events.
...more>>
Fibonacci - James Grant
Pages about Fibonacci the mathematician, the sequence that bears his name and its relationship to the Golden Ratio, as well as how the Fibonacci numbers occur in nature.
...more>>
Get Help With Your Math Homework - Cramster.com
Find homework solutions from text books, lecture notes, and solved exams written by college professors for their courses. Subscription fees required. Ask questions and answer other members' questions "for self practice, karma points and goodwill" on the
...more>>
A History of Mathematical Notations - Florian Cajori
"In this history it has been an aim to give not only the first appearance of a symbol and its origin, but also to indicate the competition encountered and the spread of the symbol among writers in different countries...." The first volume of Cajori's
...more>>
How Stuff Works
A site devoted to explaining the world in a way that is both informative and entertaining. Content is designed to be understandable for people of all ages and education levels.
...more>>
Institute for Learning - University of Pittsburgh
Research-based curriculum, tools, and professional development designed to build the capacity of teachers, administrators, and systems to provide students with high quality instruction and learning opportunities. See especially What We Know, Principles
...more>>
K-12th Grade Mathematics Textbook Analysis - Jim Kelly
An analysis of a number of elementary and secondary school mathematics textbook series, using 1000 commonly used conceptual, operational and notational terms, intended to help education professionals match curriculum needs to existing materials. Also
...more>>
Logical Laws - Alex Sakharov
This page contains a collection of logical laws of the first-order logic. The collection is based on Kleene's collection (from his books 'Introduction to Metamathematics' and 'Mathematical Logic') and contains a few additions. The laws holding in classical
...more>>
Mad4Maths - John Massey, Mad4Maths.com
A free fun animated website featuring games and puzzles for kids aged 6-10 yrs. Also features guides for parents on how maths in now taught in schools and explanations of current multiplication, division, and addition/subtraction methods.
...more>>
Mad Maths - Philippe Chevanne
Word problems, with short solutions and "details" that reveal steps in solving number theory, logic, geometry, and more. Scripts include original JavaScript about continued fractions, Apollonius circles, Pythagorean triples, decompositions of sums of Functions - Wolfram Research, Inc.
An encyclopedic collection of information about tens of thousands of mathematical functions. The site details the interrelationships between the special functions of mathematical physics and the elementary functions of mathematical analysis, as well as |
Mathematical Dictionary for School
9780521556576
ISBN:
0521556570
Publisher: Cambridge University Press
Summary: Bolt, Brian is the author of Mathematical Dictionary for School, published under ISBN 9780521556576 and 0521556570. Ninety six Mathematical Dictionary for School textbooks are available for sale on ValoreBooks.com, twelve used from the cheapest price of $0.01, or buy new starting at $9 [more Mathematical Dictionary for Schools contains contains over 500 definitions of technical terms found within GCSE syllabuses. Key words and phrases are explained in clear, si [more]
A Mathematical Dictionary for Schools contains contains over 500 definitions of technical terms found within GCSE syllabuses. Key words and phrases are explained in clear, simple language with illustrations to aid understanding of more difficult terms.[less]
160 pages. Softcover. Brand new book. MATHEMATICS. Contains definitions and examples of the mathematical words likely to be ncountered by students aged 11 to 16. Over 500 mat [more]
160 pages. Softcover. Brand new book. MATHEMATICS. Contains definitions and examples of the mathematical words likely to be ncountered by students aged 11 to 16. Over 500 mathematical words are defined, and there are plenty of examples and illustations to help with the concepts. (Key Words: Reference Books, Mathematics, Dictionaries, Brian Bolt, David Hobbs, Standard Deviation).[ |
Mathematics Honours 4210
Introduces students to the investigative and research aspects of mathematical knowledge. It prepares students for further postgraduate study in mathematics (PhD or Masters) either in Australia or overseas. Alternatively, it provides valuable additional training for those students wishing to enter the workforce. Employers particularly appreciate the communication, report writing, problem-solving and research skills developed in the Honours program. Honours is a coordinated programme spanning two semesters of full-time study or four semesters of part-time study. The Honours program requires students to study 6 advanced topics together with a project done under the supervision of an academic staff member. For administrative purposes students enrol in each of the 20 unit semester length subjects: MATH4110, MATH4120, MATH4210, MATH4220.
Not available in 2014
Previously offered in 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004
Objectives
1. To deepen understanding of a particular area of mathematics, while at the same time broadening knowledge of related areas 2. To develop the capability of understanding mathematical, and mathematically based technical literature 3. To develop writeen and oral communication skills 4.To develop research skills
Students intending to pursue Honours in Mathematics should consult with Head of School or the Mathematics Honours Coordinator prior to their commencement. In general a credit level average in a mathematics major at the 3000 level is required for entry into Honours.
Modes of Delivery
Internal Mode
Teaching Methods
Lecture Individual Supervision Student Projects
Assessment Items
Examination: Class
Essays / Written Assignments
Projects
Contact Hours
Lecture: for 4 hour(s) per Week for Full Term
Compulsory Components
Requisite by Enrolment
This course is only available to students enrolled in the Bachelor of Science (Honours), Bachelor of Science (Professional) (Honours) or Bachelor of Mathematics (Honours) programs. |
Algebra.help -- calculators, lessons, and worksheets, For students and parents, includes lessons, step-by-step calculators, worksheets, and other algebra resources..
Itslearning, Looking for our company website? itslearning.eu; head over to our global website to learn more about our great products.
Classzone, Classzone book finder. follow these simple steps to find online resources for your book..
Vdoe :: mathematics standards of learning resources, Mathematics standards of learning (sol) – adopted 2009. the standards of learning and curriculum framework comprise the mathematics content that teachers in.
Pearson successnet, Welcome to the new pearson successnet landing page this page will redirect you to the universal pearson sign in page where you should enter your username and password.
Homework help | chegg.com - raise your gpa w/ a free homework, Get homework help with math, calculus, algebra, physics, chemistry, science, accounting, english and more.. |
Getting Started with MATLABMATLAB (short for Matrix Laboratory) is a software tool used widely in engineering curriculum that provides high-performance numerical computational, graphical, and animation capabilities. Many of OUP's engineering titles, including Lathi's Modern Digital and Analog Communications, 4e, the forthcoming Uicker, Pennock and Shigley's Theory of Machines and Mechanisms, 4e, and Sadiku's Elements of Electromagnetics, 5e, incorporate MATLAB codes into the homework problems and chapter examples. The new edition brings the book up to date with MATLAB ve... MORErsion 2009a. This includes updating commands, examples, figure, and graphs. Chapter 8 also underwent a complete revamp to address the restructure of symbolic computation in the new version of MATLAB. The author is also taking this opportunity to add additional examples and new topics, including nested functions and PDEs. The book is supplemental in nature and is essentially an introductory user's guide, and is used in a variety of different engineering and science courses. MATLAB, a software package for high-performance numerical computation and visualization, is one of the most widely used tools in the engineering field today. Its broad appeal lies in its interactive environment, which features hundreds of built-in functions for technical computation, graphics, and animation. In addition, MATLAB provides easy extensibility with its own high-level programming language.
Enhanced by fun and appealing illustrations, Getting Started with MATLAB employs a casual, accessible writing style that shows users how to enjoy using MATLAB.
Features
* Discusses new features and applications, including the new engine of symbolic computation in MATLAB 7.8 (released March 2009) * Provides two sets of self guided tutorials for learning essential features of MATLAB * Includes updated commands, examples, figure, and graphs * Familiarizes users with MATLAB in just a few hours though self-guided lessons * Covers elementary, advanced, and special functions * Supplements any course that uses MATLAB * Works as a stand-alone tutorial and reference
Visit the companion website at for more information on updates to MATLAB software. |
Now in its Tenth Edition, this text once again lives up to its reputation as a clearly written, comprehensive finite mathematics book. In an engaging and accessible style, this book demonstrates how mathematics applies to various fields of study. The text is packed with real data and real-life applications to business, economics, social and life sciences. The new edition also features a new full color design and improved goal-oriented pedagogy to further facilitate understanding.
Chapter Opening and Chapter Project- Each chapter begins with a situation and ends with a related project.
A Look Back…A Look Forward- Each chapter begins with a discussion of the relationship between what has been learned earlier and what is coming next.
Objectives- Each section begins with a list of learning objectives. The objectives also appear in the text where the objective is covered and are repeated in the Chapter Review along with Review Exercises that relate to the objective.
Preparing For This Section- Most sections begin with a list of key concepts to review in preparation for the section. Page references are provided for easy access. Related "Are You Prepared?" problems are given at the beginning of the Exercise set to help students assess their understanding of these concepts. Answers to these problems are given at the end of the Exercise set.
Now Work Problems- Following most examples, the student is directed to a related problem in the exercises to assess understanding before going further in the text. |
The Math Learning Center, or MLC for short, was created to help FAU
students develop their math problem solving skills so they have the
confidence and ability to solve math problems on their own.
The MLC offers FREE walk-in group
tutoring any time the center is
open:
Monday - Thursday: 9am - 6pm
Friday: 9am - 4pm
The MLC offers FREE one-on-one tutoring for
most undergraduate courses in
mathematics. Please read the policy
for this service by clicking the
link in the left menu bar.
The MLC is beginning to offer
online "eTutoring" services during
the Fall 2013 semester. Please use
the link in the left menu bar to
visit the Remote MLC webpage. Here,
you can access the dates/times/URLs
for any etutoring being offered.
Tutoring is available for most
undergraduate mathematics courses: Intermediate and College Algebra, Math
for
Liberal Arts, Statistics, Pre-calculus, Trigonometry, and all Calculus
courses.
Exam review sessions are offered as well. You
can check out the schedules for tutoring and exam review sessions by
clicking on the related links in the left menu bar.
The Math Learning Center is
certified with the College Reading
and Learning Association (CRLA). See
more about the CRLA. |
MATHEMATICS
MATH-022
Basic Algebra (2)
Course Level: Undergraduate
An introduction to algebra. Includes a review of integer and rational numbers; solving linear equations in one or two variables; word problems; polynomials and rational expressions; radicals; the quadratic formula; and some graphing techniques. Usually offered every term. Note: Intended for students with inadequate preparation for other courses in mathematics. No academic credit is received for this course, nor does it fulfill the mathematics requirement for any degree program. Credit equivalent is listed only for the purpose of determining full-time student status. |
Welcome to the Math Page Summer Review Packets Students who will be taking Algebra 2, Honors Algebra 2, Honors PreCalc or AP Calculus will need to complete a review packet prior to the first day of class. If you did not receive a copy of the correct packet please download a copy using the links to the right.
Supplies:
Students should check the list below to see what supplies they will need to start the 2013 - 2014 school year.
Algebra 1with inches and centimeters)
· graphing calculator
Geometry and Honors Geometry
Supply list for class: (Have these items with you daily!)
·3 ring binder (1.5")
·Graph paper
·Notebook paper
·Pencils
·Erasers
·Dry erase markers
·Colored pencils (recommended for classroom use)
·Graphing or scientific calculator
Items for homework use: (We have these for classroom use)
·Ruler (inches and centimeters)
·Protractor
·Compass
·Graphing or scientific calculator
Algebra 2, Honors Algebra 2 and Bridge to Algebra 2inches and centimeters)
·graphing calculator
The school book store will carry AAA batteries and all items in the supply lists except calculators and ring binders.
Graphing Calculator Recommendations:
Starting with the 2013-2014 school year students will need a graphing calculator for Algebra 1, Algebra 2 and all fourth year courses. We are recommending either the Texas Instruments TI-83, TI-84 or the Casio 9750-GII, 9860-GII. Check the companies websites for product descriptions and where to purchase. |
A Tribute to Paul Erdős(
Book
) 5
editions published
between
1990
and
2008
in
English
and held by
320
libraries
worldwide
More sets, graphs, and numbers a salute to Vera Sós and András Hajnal(
Book
) 6
editions published
in
2006
in
English
and held by
284
libraries
worldwide
Discrete mathematics, including (combinatorial) number theory and set theory has always been a stronghold of Hungarian mathematics. The present volume honouring Vera Sos and Andras Hajnal contains survey articles (with classical theorems and state-of-the-art results) and cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers inspire further research. The volume is recommended to experienced specialists as well as to young researchers and students.
Set theory by A Hajnal(
Book
) 8
editions published
in
1999
in
English and Undetermined
and held by
278
libraries
worldwide
This is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems.
Combinatorics(
Book
) 12
editions published
between
1976
and
1988
in
English and Undetermined
and held by
270
libraries
worldwide |
Resources
For better or for worse, we hear this often, whether a student's last math class was a year ago or...well, longer.
We've identified resources from leading Math tutorial sites to target the specific math skills you need to suceed at Davenport. You can use these Math Skills Review pages to self-assess your current skills and find out what you might need to practice or re-learn.
KHAN ACADEMY®
More Resources
We have recommendations for books and videos (available for check-out if you are a Davenport student). Our Admissons and Advisors staff are always ready to answer questions about COMPASS Placement and the Math requirements at Davenport. You can also Ask a Librarian for help finding even more online and hard copy resources. |
Tom Carson engages students in the learning process by meeting them where they are and leading them to where they need to be through the determination of their individual learning style, the development of study skills, and the integration of learning strategies that help each student succeed. Elementary Algebra with Early Systems of Equations authors have framed three goals for Elementary Algebra: 1) reduce math anxiety, 2) teach for understanding, and 3) foster critical thinking and enthusiasm.
The authors' writing style is extremely student-friendly. They talk to students in their own language and walk them through the concepts, explaining not only how to do the math, but also why it works and where it comes from, rather than using the monkey-see, monkey-do approach that some books take.
Elementary Algebra with Early Systems of Equations, as the title implies, places the topic of Systems of Equations early in the text, in Chapter 5. This organization is ideal for those instructors who prefer to teach systems of equations immediately following the chapter on graphing, and the chapters prior to polynomials and factoring. For those who prefer to teach the topic later, Elementary Algebra, by the same author team, places Systems of Equations in Chapter 8
In Gilligan's Wake, Esquire columnist Tom Carson takes a shaky premise---20th-century American culture as seen through the characters of Gilligan's Island--and turns it into a feverishly imaginative jigsaw puzzle of a book. Each castaway has been given a bizarre, interconnected history, which they recount in the book's seven chapters.
This fateful trip begins with Gilligan, who tells of his days writing beat poetry with Lawrence Ferlinghetti, only to awaken in a Minnesota mental institution. The Skipper relates how he spent World War II drinking cheap beer on PT boats with McHale and Jack Kennedy, who had "a grin like autumn leaves with a pack of Chiclets in the middle." In later stories, "beaming, imbecilic" Thurston recommends former chum Alger Hiss for his first government job, while spoiled Lovey has a morphine-inspired fling with The Great Gatsby's Daisy Buchanan. Brilliant bombshell Ginger ("My hips could have started the Timex folks weeping") lands a B-movie career in L.A., and a memorable night at Frank Sinatra's house. In between building the A-bomb, inventing the CIA, and generally dictating world events with his pals Roy Cohn and "Hank" Kissinger, the Professor bestows sexual favors on invalids. Finally, cheerful Mary-Ann, "the personification of America," leaves her Kansas home to attend the Sorbonne, where she meets a handsome Frenchman and discovers she is unable to lose her virginity.
Along the way, Gilligan's Wake's elusive meta-narrator reveals himself through clues and exposition in his hallucinatory retelling of American history. Carson propels the novel with astute cultural criticisms and energetic prose, including rapid-fire wordplay and narrative echoes that recall Thomas Pynchon. The result is a multifaceted, uncertain, and dazzling voyage. --Ross Doll[via]
Intermediate Algebra students often have never developed nor applied a study system in mathematics. To address these needs, the authors have framed three goals for Intermediate Algebra: 1) reduce math anxiety, 2) teach for understanding, and 3) foster critical thinking and enthusiasm. The authors' writing style is extremely student-friendly. They talk to students in their own language and walk them through the concepts, explaining not only how to do the math, but also why it works and where it comes from, rather than using the "monkey-see, monkey-do" approach that some books take. [via]
Prealgebra, 2e, is a book for the student. The authors author has framed three goals for Prealgebra: 1) reduce math anxiety, 2) teach for understanding, and 3) foster critical thinking and enthusiasm.
The author's writing style is extremely student-friendly. He talks to students in their own language and walks them through the concepts, explaining not only how to do the math, but also why it works and where it comes from, rather than using the monkey-see, monkey-do approach that some books take. The second edition has been revised to include an increase in mid-level examples and exercises. In addition, the explanations and annotations are now more concise, yet keep the ever-important thoroughness that is the Carson style |
Chapter 7 Resource Masters | Keyword: chapter resource masters iv Teacheru0027s Guide to Using the Chapter 7 Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often.
Glencoe Texas Mathematics, Course 3 | Keyword: glencoe texas mathematics Chapter 2 54 Glencoe MAC 3 For Exercises 1 and 2, look for a pattern. Then use the pattern to solve the problem. 1. GEOMETRY Draw the next two angles in the pattern.
Skills Practice Workbook | Keyword: skills practice workbook Copyright by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be ... |
... read more
Customers who bought this book also bought:
Our Editors also recommend:Experiments in Topology by Stephen Barr Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.
Product Description:
in probability theory. The book's primary aim is not so much to impart new information as to teach an active, creative attitude toward mathematics. The sole prerequisites are high-school algebra and (for Multicolor Problems) a familiarity with the methods of mathematical induction. The book is designed for the reader's active participation. The problems are carefully integrated into the text and should be solved in order. Although they are basic, they are by no means elementary. Some sequences of problems are geared toward the mastery of a new method, rather than a definitive result, and others are practice exercises, designed to introduce new concepts. Complete solutions appear at the end |
Provides the theoretical underpinnings of calculus and the advanced study of functions. Emphasis is on precise definitions and rigorous proof. Topics include the real numbers and completeness, continuity and differentiability, the Riemann integral, the fundamental theorem of calculus, inverse function and implicit function theorems, and limits and convergence.
Grade
Based on problem sets (50%), midterm exam (20%), and final exam (30%). It is expected that you will work on the problem sets together; however, they must be written up separately. |
These pages contain information that I have put together on how to use Mathematica (a powerful symbolic mathematical computer program now available at ACC). It also contains animations I have put together and computer labs I have developed for my students. I am still working on this site, so it should grow over the next semester or two.
These are some notes I wrote for my online courses about how to prepare and study for a math test. You might want to read through this if you haven't done so well on math tests in the past or you get really nervous about taking math tests (or even if you have just been out of school for a while). |
Linear algebra is the study of vector spaces and linear mappings between them. In this course, we will begin by reviewing topics you learned in Linear Algebra I, starting with linear equations, followed by a review of vectors and matrices in the context of linear equations.
Numerical analysis is the study of the methods used to solve problems involving continuous variables. It is a highly applied branch of mathematics and computer science, wherein abstract ideas and theories become the quantities describing things we can actually touch and see.
Statistics is about extracting meaning from data. In this class, we will introduce techniques for visualizing relationships in data and systematic techniques for understanding the relationships using mathematics.
The main purpose of this course is to bridge the gap between introductory mathematics courses in algebra, linear algebra, and calculus on one hand and advanced courses like mathematical analysis and abstract algebra, on the other hand, which typically require students to provide proofs of propositions and theorems.
In this course you will examine real world problems -- rescue the Apollo 13 astronauts, stop the spread of epidemics, and fight forest fires -- involving differential equations and figure out how to solve them using numerical methods.
In this course, you will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes solving algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing linear equations.
This course is a continuation of "Beginning Algebra". Algebra allows us to formulate real-world problems in an abstract mathematical term or equation. These equations can then be solved by using techniques you will learn in this course.
During this four week course, instructors will learn how to create and teach an exciting new type of developmental math course known as a pathways course. These courses (e.g., Math Literacy for College Students, Quantway™, and Statway™) are becoming a popular way to redesign college math programs. |
Forum Memberships
conquistador
I respectfully disagree with this comment. To provide some background on my person, I am currently a junior in high school. Last year I took and got a 5 on both the AP BC Calculus and the AP Comp Science test; meaning that essentially I have passed already passed my first year of college math and an introductory college computer science class.
1) The concept is simple, if you do not understand mathematics, you will struggle with the TEM aspect of STEM. Based on my experience my accelerated math makes my life incredibly easy in more complex science and technological courses (ex. AP mechanical physics, AP computer science, AP statistics, AP chemistry and applied engineering). Therefore, I disagree with the notion that "math" isn't needed to excel in STEM courses. It may not be fundamentally necessary but without it you, like many of my peers, WILL struggle.
2) I believe that what Stephan Wolfram is doing, while superficially helpful, is actually detrimental to mathematics at a high school and college based level. wolfram as is used by most high school students does NOT help make math understandable. Graphing calculators and technology give answers, they do not teach mathematics. Many of my peers (even in upper level courses) use these tools to get answers, answers they neither understand, nor can apply properly. I understand that wolfram has aspects that go through how to solve specific problems(I have even used them myself for tricky integrals) but based on observation alone few people use those. Instead Wolfram, just as graphing calculators, is used to quickly "do" homework. Essentially they are tools for cheating.
3) Based on personal experience and statistical data from many European and Asian nations, I believe the solution to America's STEM educational difficulties stems from a delayed exposure to mathematics. I was exposed to Algebra 1 level mathematics at around 3rd grade and this allowed me to skip 3 grades in the public school system. In nations that excel at mathematics and STEM competitions by 6th grade most students are at Algebra 2 level. (it should be noted that I touched a graphing calculator for the first time sophomore year and likewise students from other nations do NOT use technology when doing mathematics) The solution is obvious. DO MATHEARLIER and all will succeed in STEM courses.
and that's my 2 cents for the day.
Starcraft BroodWars? Apparently it still has a very large following in Korea; as in if i remember right, the most played video-game following League of Legends. it is more played than SC II there |
An examination of the mathematical underpinnings of the elementary school curriculum with an emphasis on the understanding of mathematical concepts. Topics will include foundations of integer and rational arithmetic, notions of place-value and base, number sense and estimation, functions and their applications, Euclidean geometry, and mathematical problem-solving. This course is recommended as a second course in mathematics for prospective elementary teachers, and also satisfies the core curriculum requirement for the third course in the Natural Sciences and Mathematical and Quantitative reasoning requirement in the core curriculum. Prerequisite: MATH 100 and an EDUC course, or permission of the instructor |
Matrix Multiplication
In this lecture our instructor will walk you through Matrix Multiplication. First, you will understand the Dimension Requirement that is essential for Matrix Multiplication to produce the correct result. After going over the Properties of Matrix Multiplication such as the Associative Property, Distributive Property, and the Commutative Property.
This content requires Javascript to be available and enabled in your browser.
What is some applications of these to the real world? Iv'e been trying to associate these with an application in the real world, but I can't think of anything.
Matrix Multiplication
Matrix
multiplication is defined if and only if the number of columns of
the first matrix is equal to the number of rows of the second
matrix.
Matrix
multiplication is associative and satisfies the left and right
distributive properties.
Matrix
multiplication is not commutative.
Matrix Multiplication
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture. |
This Maths School Guide has Maths formulas for School Students & College Grade/Higher Grade Students. It lists out all the important formulas/topics in Algebra, Geometry, Trigonometry. Regular review of these formulas/concepts will definitely help improve your grades. |
Categories:
Description:
This book contains 500 problems that range over a wide spectrum of
mathematics and of levels of difficulty. Some are simple
mathematical puzzlers while others are serious problems at the
Olympiad level. Students of all levels of interest and ability will
be entertained by the book. For many problems, more than one
solution is supplied so that students can compare the elegance and
efficiency of different mathematical approaches. A special
mathematical toolchest summarizes the results and techniques needed
by competition-level students. Teachers will find the book useful,
both for encouraging their students and for their own pleasure.
Some of the problems can be used to provide a little spice in the
regular curriculum by demonstrating the power of very basic
techniques. The problems were first published as a series of
problem booklets almost twenty years ago. They have stood the test
of time and the demand for them has been steady. Their publication
in book form is long overdue |
Algebra is one of the main branches in mathematics. The book series of elementary algebra exercises includes useful problems...
see more
'Algebra is one of the main branches in mathematics. The book series of elementary algebra exercises includes useful problems in most topics in basic algebra. The problems have a wide variation in difficulty, which is indicated by the number of stars.'
According to The Orange Grove, "Written for high school students. CK-12 Foundation's Geometry FlexBook is a clear...
see more
According to The Orange Grove, "Written for high school students. CK-12 Foundation's Geometry FlexBook is a clear presentation of the essentials of geometry. Topics include: Proof, Congruent Triangles, Quadrilaterals, Similarity, Perimeter & Area, Volume, and Transformations'The Mathematics Department of the University of Washington designed its precalculus to concentrate on two goals:A review of...
see more
'The Mathematics Department of the University of Washington designed its precalculus to concentrate on two goals:A review of the essential mathematics needed to succeed in calculusAn emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical toolsThis text was written with those goals in mind. It does not look like the widely used precalculus texts on the market. The actual text is short and there are not a lot of routine drill exercises. Instead the book emphasizes multi-part story problems in a conscious attempt to engage students at a deeper level in order to prepare them the calculus, science, and engineering courses they will soon be taking. There are 20 problem sets, one set at the end of each chapter. The web site also has twenty years of exams (midterms and finals) and their solutions.' |
Online Math Homework Help
This tool provides more than 100 textbooks** via instant and free access to Hotmath—a subscription worth up to $49
per year. Students get help solving a specific problem from their textbook by selecting the:
Code:
Subject
Publisher
Chapter
Page
Specific problem number
A full-featured 2D and 3D graphing calculator
This powerful tool functions more efficiently than many stand-alone calculators costing up to $100. Work can be
saved to finish later, added to Word or PowerPoint documents, or shared with study groups.
Triangle Solver
This tool develops Geometry skills. Now students can easily input their own values.
The calculator:
Determines the missing information
Draws the triangle to scale
Provides the math rules it used to compute the missing values
Equation Library
Equation Library contains more than 125 interactive common math equations and formulas. Students can type in live
inputs and the Library will provide the missing variable—and in some cases even graph the equation!
Unit Conversion Tool
This tool is extremely useful in both math and sciences by making it easy for students to quickly convert units of |
50
Total Time: 6h 49m
Use: Watch Online & Download
Access Period: Unlimited
Created At: 05/18/2010
Last Updated At: 05/18/2010
In this 50-lesson algebra series, we'll look at equations and inequalities. We'll start out looking at word problems dealing with linear equations. Then, we'll move on to look deeply at quadratic equations and how to approach and solve them. Next up, we'll transition back to word problems to really cement our quadratic equation knowledg. After that, we'll look at radical equations and variation before starting a study of inequalities. Within the videos on inequalities, we'll look at basic and advanced techniques for manipulating and solving inequalities, including those that contain quadratics, rational numbers, radicals and absolute valueCollege Algebra: Introduction to Solving Linear Equations with Rationalsation with at Word Problems
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Beginning Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers linear equations, inequalities, polynomials, rational expressions, relations and functions, roots and radicals, quadratic equations and systems of equations. Perimeter Linear for Consecutive Numbers
Professor Burger walks you through a word problem to find consecutive numbers. First, you will read the problem and then define a variable for the numbers you need to find. Using this variable, you will write an equation to solve for the variable. Then, you can replace this variable in the equation and determine the consecutive numbers sum Finding an Average
In this lesson, you will learn how to approach word problems that involve averages or means that involve averages or means (many of which include grades or scores Constant Velocity Problem about Work Mixture Problem
In this lesson, you will learn how to approach word problems that involve equalities and ratios or fractions that involve percentages, ratios, recipes, mixes, etc an Investment Business Quadratics by Factoring
In this lesson, you will learn to solve quadratic equations by factoring. Quadratic equations involve factors that are now squared, which could give us more than one possible answer. To discover if an equation has more than one answer, you need to set the equation equal to zero and factor. You will discover that if your quadratic equation factors into a perfect square, it will have only one solutionInt Algebra: Solving 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 Proving the Quadratic Formula Using 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 a Squared Variable Finding Real Number Fancy Word Problems with Quadratic Pythagorean Theorem referees Motion Projectile Other Determining Extraneous Roots theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
Int Algebra: Solving Equations 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 Equations 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 Rational Exponent Vari systems Direct Proportion
In order to explain direct proportionality, Professor Burger uses a real-world example of a spring and Hooke's Law. Hooke's law states that the distance a spring stretches varies directly to the force applied. If force, f, is directly proportional to distance, d, then d~f or d=kf. This equation allows us to find the constant, k, of how much the spring stretches when force is applied. After we have found this number, we can determine the distance the spring will stretch with varying forces applied.
A lesson on inverse proportions can be found here Inverse Proportion
In this lesson, inverse proportionality is explained using light as a real-world example. The illumination of a light source varies inversely to the square of the distance from the source, or I=k/(d^2). So, to find the illumination of a particular light source, you will need to find the constant, k, of that source, and then divide by the distance squared.
An introduction to direct proportion can be seen here:
This lesson is perfect for review for a CLEP test, mid-term, final, summer school, or personal growth! Inequalities
Professor Burger discusses solving inequalities for one variable. He begins with reminders about adding, subtracting, multiplying, and dividing with both positive and negative numbers and the effect on the inequality sign. Then he demonstrates solving for a variable within an inequality, using the inequality 2(x + 3) < 4x + 10. You will then review interval notation (covered in a previous lesson) and three different ways to write the answer Mathematics More On Inequality Word 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 including Quadratic Domains of Radical Express Burger Number Lines & Absolute Values Equations
In this lesson, Professor Burger discusses solving problems with absolute values. Remember that the absolute value of a number includes both the positive and negative value of that number. This means that an equation involving an absolute value means that you will have to solve for two equations, one equal to a positive value, and one equal to the negative value Equations with 2 Absolute Values
In this lesson, you will learn how to solve an equation that has two absolute values. When beginning any equation with an absolute value, remember that, by definition, the absolute value of a number has both a positive and negative answer. You will also go over how to work an equation with a fraction inside an absolute value.
For a refresher on equations with one absolute value, see this lesson Inequalities
Reminding us of its definition, Professor Burger demonstrates how to work an inequality with an absolute value. You will need to convert the inequality from the absolute value to an inequality encompassing both the positive and negative points of that absolute value. This will look different, depending on whether the absolute value is < or >. Prof. Burger walks you through several examples.
For an introduction to inequalities, see this lesson:
And for more on absolute values:
functions Absolute Value Inequality |
Algebra Teacher's Activities Kit is a unique resource that provides 150 ready-to-use algebra activities designed to help students in grades 6-12 master pre-algebra, Algebra I, and Algebra II. The book covers the skills typically included in an algebra curriculum. Developed to motivate and challenge students, many of the activities focus on real-life applications. Each of the book's ten sections contains teaching suggestions that provide teachers with strategies for implementing activities and are accompanied by helpful answer keys. The activities supply students with quick feedback, and many of the answers are self-correcting.
Each activity stands alone and can be applied in the manner that best fits your particular teaching program. Algebra Teacher's Activities Kit can be used as a supplement to your instructional program, to reinforce skills and concepts you've previously taught, for extra credit assignments, or to assist substitute teachers.
For quick access and easy use, the activities are printed in a big 8 1/2" x 11" lay-flat format for photocopying and are organized into ten sections.
GRAPHING LINEAR EQUATIONS AND INEQUALITIES is packed with 15 activities, including Graphing Points on the Coordinate Plane . . . Finding the Slope of a Line . . . Solving Systems of Equations by Graphing.
BASIC OPERATIONS WITH MONOMIALS AND POLYNOMIALS offers 12 activities, such as Using the Terms of Polynomials . . . Finding Powers of Monomials . . . Finding Cubes of Binomials.
FACTORS OF MONOMIALS AND POLYNOMIALS features 12 exercises, such as Finding the Missing Factor . . . Factoring Trinomials . . . Factoring the Sum and Difference of Cubes.
Judith A. Muschla (B.A. Mathematics, K—12) has taught mathematics in South River, New Jersey, for over twenty-five years. She was a recipient of the 1990—91 Governor's Teacher Recognition Program award in New Jersey, and she was named the 2002 South River Public Schools District Teacher of the Year. Muschla has been a member of the state Standards Review Panel for the Mathematics Core Curriculum Content Standards in New Jersey.
Gary Robert Muschla (B.A. and M.A.T., Trenton State College) taught reading and writing for more than twenty-five years at Appleby School in Spotswood, New Jersey. He is the author of several practical resources for teachers.
This is the sixth math resource coauthored by Judith Muschla and Gary Muschla. Their earlier books include The Math Teacher's Book of Lists, Hands-on Math Projects with Real-Life Applications, Math Starters, The Geometry Teacher's Activities Kit, and Math Smart, all published by Jossey-Bass Publishers. |
Intermediate Algebra: Functions and Authentic Intermediate Algebra that incorporate a graphing calculator. Unique and enthusiastic in its approach, Lehmann's text is a rich combination of important skills, concepts, and applications. This text captivates students' and instructors' interest as they use curve fitting to model current, compelling, and authentic situations. The curve fitting approach emphasizes concepts related to functions in a natural, substantial way and encourages students to view functions graphically, numerically, and symbolically as well as to verbally describe concepts related to functions. The examples in the test demonstrate both how to perform skills and how to investigate concepts. Students learn why they perform skills to solve problems as well as how to solve the problems. Explorations deepen students' understanding as they investigate mathematics with graphing calculator and pencil and paper activities. |
Choose the algebra textbook that's written so you can understand it. ALGEBRA AND TRIGONOMETRY reads simply and clearly so you can grasp the math you need to ace the test. And with Video Skillbuilder CD-ROM, you'll follow video presentations that show you step-by-step how it all works. Plus, this edition comes with iLrn, the online tool that lets you sign on, save time, and get the grade you want. With iLrn, you'll get customized explanations of the material you need to know through explanations you can understand, as well as tons of practice and step-by-step problem-solving help. Make ALGEBRA AND TRIGONOMETRY your choice today313.95
Purchase Options
Hardcover $250.99
$250.99
Save $6262.49
from$62.49
Save up to $251.46!
Rent thru 02/09/14 for $62.49
$62.49
Save $251.46!
Rent thru 03/11/14 for $70.49
$70.49
Save $243.46!
Rent thru 04/20/14 for $77.99
$77.99
Save $235.96!
Rent thru 09/07/14 for $89.99
$89.99
Save $223.96!
Rent thru 06/04/15 for $97.99
$97.99
Save $215 ofChapter each $12.50
each$12.50
eChapter Options
FREE
Table of Contents (and additional FREE Content)
FREE
eChapter P: Prerequisites
eChapter 1: Equations and Inequalities
eChapter 2: Coordinates and Graphs
eChapter 3: Functions
eChapter 4: Polynomial and Rational Functions
eChapter 5: Exponential and Logarithmic Functions
eChapter 6: Trigonometric Functions of Angles
eChapter 7: Trigonometric Functions of Real Numbers
eChapter 8: Analytic Trigonometry
eChapter 9: Polar Coordinates and Vectors
eChapter 10: Systems of Equations and Inequalities
eChapter 11: Analytic Geometry
eChapter 12: Sequences and Series
eChapter 13: Counting and Probability |
eBook & Document Store
30 Mathematics Lessons Using the TI-15
Help learners grasp mathematical concepts and skills with lessons that integrate calculator use. These books provide step-by-step mathematics lessons that incorporate the use of the TI-10 and TI-15 calculators throughout the learning process. The 30 lessons present mathematics in a real-world context and cover each of the five strands including numbers and operations, geometry, algebra, measurement, and data analysis and probability. |
Arithmetic Reasoning Questions Study Guide for McGraw-Hill's ASVAB
The ASVAB Arithmetic Reasoning test measures your ability to solve the kinds of arithmetic problems that you encounter every day at home or on the job. All of the questions on the test are word problems. That is, each one presents a real-life situation with a problem that must be solved using an arithmetic operation, such as addition, subtraction, multiplication, or addition. Arithmetic Reasoning problems also involve other arithmetic concepts, such as fractions, decimals, percents, exponents, and square roots.
It is important to do well on the Arithmetic Reasoning test because it is one of the four ASVAB tests that are used to calculate the AFQT—your military entrance score. That's why it pays to spend time reviewing topics in basic arithmetic and tackling plenty of sample ASVAB Arithmetic Reasoning questions.
The following pages offer a quick but important overview of the basic arithmetic you need to know to score well on the ASVAB. Make sure that you carefully review and test yourself on every topic covered in this section. Also make sure that you learn how to use all of the problem-solving methods presented in the examples. There is much more to basic math, but if you master the core information presented here, you will be able to answer ASVAB Arithmetic Reasoning questions with relative ease. Note that your ASVAB arithmetic review should also include the next chapter of this book, which covers word problems. |
...
More About
This Book
assessing their test scores, and much more. The three-hole punched and perforated format allows students to insert all relevant pages into a 3-ring binder and organize them along with their class notes, homework, review sheets, and tests.
Product Details
ISBN-13: 9781133363910
Publisher: Cengage Learning
Publication date: 1/12/2012
Edition number: 5
Pages: 448
Product dimensions: 8.50 (w) x 10.90 (h) x 1.10 (d)
Meet the Author
: Alan Tussy teaches all levels of developmental mathematics at Citrus College in Glendora, CA. He has written nine math books-a paperback series and a hard-cover series. An extraordinary author, he is dedicated to his students' success, relentlessly meticulous, creative, and a visionary who maintains a keen focus on his students' greatest challenges. Alan received his Bachelor of Science degree in Mathematics from the University of Redlands and his Master of Science degree in Applied Mathematics from California State University, Los Angeles. He has taught up and down the curriculum from prealgebra to differential equations. He is currently focusing on the developmental math courses. Professor Tussy is a member of the American Mathematical Association of Two-Year Colleges.
R. David Gustafson is Professor Emeritus of Mathematics at Rock Valley College in Illinois and has also taught extensively at Rockford College and Beloit College. He is coauthor of several best-selling mathematics textbooks, including Gustafson/Frisk/Hughes' COLLEGE ALGEBRA, Gustafson/Karr/Massey's BEGINNING ALGEBRA, INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA, BEGINNING AND INTERMEDIATE ALGEBRA: A COMBINED APPROACH, and the Tussy/Gustafson and Tussy/Gustafson/Koenig developmental mathematics series. His numerous professional honors include Rock Valley Teacher of the Year and Rockford's Outstanding Educator of the Year. He has been very active in AMATYC as a Midwest Vice-president and has been President of IMACC, AMATYC's Illinois affiliate. He earned a Master of Arts from Rockford College in Illinois, as well as a Master of Science from Northern Illinois |
...
More About
This Book
Related Subjects
Meet the Author
Brita Immergut (Brooklyn, NY) taught mathematics for 30 years in middle schools, high schools, and at LaGuardia Community College of the City University of New York. She has conducted workshops and taught courses for math-anxious adults at schools and organizations. Professor Immergut received an Ed.D. degree in Mathematics Education from Teachers College, Columbia University. She is a co-author of two textbooks for adults: Arithmetic and Algebra...Again and An Introduction to Algebra: A Workbook for Reading, Writing and Thinking about Mathematics 29, 2005
Invaluable Resource for Parents
If you are like most parents in their late thirties and forties and you can't remember the math you learned in middle school and high school, this is an invaluable resource when your child asks you for help with his or her math homework. Can remember how to solve a problem with negative exponents? Look up 'Exponent' under 'E,' and there is the answer.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Anonymous
Posted January 12, 2002
Math's Martha Stewart (Only Fun!)
Introduced to this by a friend, I'm someone who barely passed geometry. I'm simply bad when it comes to numbers. If only this book had been around when I was back in school. Any parent and their child could be helped by Brita Imergutt's approach to math. She clearly loves her subject and makes it fun to learn. A time to enjoy rather than to be frustrated. Terrific teacher. If this book were about cooking, the author would be the star of the Food Channel. Somehow she makes math equally tasty.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. |
MAT101 - Why is it important to be able to identify sets and set theory as ...
math,algebra - why are function notations important, are they really that ...
biology - why is it important to understand challenges in a species' environment...
English - I urgently need to check the following statements concerning global ...
english - ok we are reading this book ella enchanted and we have focus questions...
Science - Why it's so important to have one set of chemical symbols in the ...
English - 1. Which are more important? 2. Which are most important? 3. Which is ...
early childhood education - an important use for telephone conversation at a ...
classroom instruction - Teachers do need to establish ground rules about ...
Math - Why is it important to understand rational exponents? |
The O Level Additional Mathematics syllabus assumes knowledge of O Level ...
terms and select and apply appropriate techniques of solution, including
manipulation ... Some questions may integrate ideas from more than one topic of
the ...
Each question is followed by a comment and a full solution. The comment will
contain hints .... Multipart questions of the A-level type are generally avoided; but
if they occur, there tends to be a 'sting in ...
A typical A-level question may take, say, ten minutes and consist of a single
guided step. ('Use the substitution x ... One of the errors in my solutions that I had
to correct involved the numbers in question ...
and their levels of difficulty. ... matics problems typically encountered in many
college-level mathematics courses and ... require the solution of linear equations
in one variable and other related topics.
O Level Syllabus ... level and for the mathematical requirements of a wide range
of professions. ... of solutions;. 3.3 ... Sl units will be used in questions involving
mass and measures; the use of the ...
A total of 20 questions are administered in the College-Level Mathematics Test (
CLM). CLM ... Q Solutions of Equations and Inequalities including the solution of
linear and quadratic equations and ...
Effective assessment of problem solving in math requires more than a look at the
answers students give. Teachers need to analyze ... in assessment of these
higher-level skills. Problem solving requires.
Cambridge O Level Mathematics Vol. 1. Cambridge O Level ... a two-year course
leading to the O Level examination from. University of ... to exercises and
examination questions to enable students to ... |
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.
Mathematicians in industry and commerce, and also those entering postgraduate study, are expected to possess a range of mathematical abilities from knowledge and implementation of mathematical and computational techniques to the development of mathematical skills. Within nearly all mathematics degree programmes in the UK the acquisition of subject-specific knowledge, essential IT skills, and the use of mathematical and statistical software, as well as subject-specific skills of logical thought and analysis and problem solving, are well embedded in the curriculum (Quality Assurance Agency for Higher Education, 2000). Typically, these are delivered through formal lectures supported by tutorials and/or seminars, problem classes and practical workshop sessions; while assessment is normally heavily weighted to formal examinations. Increasingly it is recognized that some variety of teaching and learning experience helps students to develop both subject-specific and transferable skills, and in many instances these can be accommodated through activities loosely grouped as 'mathematical modelling'. Associated assessments and feedback designed around project-based work, from more extensive coursework assignments through to substantial reports, can allow students to demonstrate their understanding and problem-solving abilities, and enhance both their mathematical and key skills. Often quoted attributes gained by graduates are the subject-specific, personal and transferable skills gained through a mathematics-rich degree. Increasingly, students are selecting their choice of degree to meet the flexible demands of a changing workplace and well-designed Mathematics, Statistics and Operational Research (MSOR) programmes have the potential to develop a profile of the knowledge, skills abilities and personal attributes integrated alongside the more traditional subject-specific education. |
See how mathematical techniques such as tables, graphs, measurements and equations help to find the missing part of a proportion.
Atlantean Dodgeball addresses number and operations standards, the algebra standard, and the process standard, as established by the National Council of Teachers of Mathematics (NCTM). It guides students in:
Understanding and using rati Author(s): No creator set
License information
Related content
No related items provided in this feed
One-Sided Limits - Free Math Video by Brightstorm A limit is the value that a function approaches as the input of that function approaches a certain value. In Calculus, sometimes functions behave differently depending on what side of the function that they are on. This video explains how a one-sided limit is the behavior on one only one side of the value where the function is undefined. (3:02) Author(s): No creator setPearl River, China (with window) Zoom down to land reclamation from the river delta. Dissolve between data collected in 1988, 1992, and 1995. Author(s): No creator set
Social Media + Job Search Conference Meet with social media experts who can help you develop your online presence to make connections, job search, demonstrate advocacy, expressions of your interest or establish your personal brand. Register in Gilmour Hall 110. $10 conference registration fee. Join the conversation #SMedia4Jobs To access the conference site visit Author(s): No creator set
License information
Related content
No related items provided in this feed
Why Give - Elena Fedyszyn Having volunteered during all four of her undergrad years with the Girl Scouts, Elena Fedyszyn '09 describes why she also now chooses to give monetarily every year to Johns Hopkins. Author(s): No creator set
English Conference: Medical Writing John Smieska, a Physician Assistant, explains the structure and importance of the SOAP note and SBAR formats, for medical communication and record keeping. Author(s): No creator set
Logarithm Rule - Problem 2 This video is a continuation of the logarithm rule and works through another example where this rule is used to find the derivative of the natural logarithm of a function. The logarithm rule is a special case of the chain rule. (2:13) Author(s): No creator set
Africa Speaks, America Answers In Bedford-Stuyvesant, Brooklyn, pianist Randy Weston and bassist Ahmed Abdul Malik celebrated with song the revolutions spreading across Africa. In Ghana and South Africa, drummer Guy Warren and vocalist Sathima Bea Benjamin fused local musical forms with the dizzying innovations of modern jazz. These four were among hundreds of musicians in the 1950s and '60s who forged connections between jazz and Africa that definitively reshaped both their music and the world.
In this video, as in his new Author(s): No creator set
License information
Related content
No related items provided in this feed
Programs of Distinction - Flannery O'Connor Studies Short biographical introduction to this famous Southern writer best known for eccentric, even grotesque characters and her wry, satiric style. O'Connor's Catholocism informs her writing on multiple levels. (1:28) Author(s): No creator set |
This book covers a wealth of material on special functions, notably knowledge which was developed by Richard Askey and his co-authors during the several decades of his contributions to this subject, but also material which connects special functions with combinatorial questions collected by George Andrews. These two researchers are well-known for their efforts to support and demand the use of hypergeometric functions in their respective fields, hence hypergeometric functions and q-hypergeometric functions (basic hypergeometric functions) play a prominent role in the book under review. The book covers 12 chapters and 6 appendices. Furthermore, it contains a rich collection of 444 (!) exercises that are distributed among the different chapters. Here are the details:
Chapter 1: The gamma and beta functions. In this chapter the usual material about the gamma and beta functions is covered. Moreover, results for the logarithmic derivative ψ(x)=Γ'(x)/Γ(x) of the gamma function and for the Hurwitz and Riemann zeta function are developed; in particular, several integral representations are given. The gamma function is characterized by the Bohr-Mollerup theorem, and finally the p-adic gamma function is introduced.
Chapter 2: The hypergeometric functions. The generalized hypergeometric function is introduced, and elementary examples are given. Euler's integral representation, and the usual summation theorems (Gauss, Chu-Vandermonde, Pfaff-Saalschütz, Dixon) come next. Then the hypergeometric differential equation is treated from the Riemannian point of view that analytic functions are determined to a large extent by their singularities. Next, Barnes type integrals, contiguous relations, and continued fractions of ratios of hypergeometric functions are covered. The Jacobi polynomials as specific hypergeometric polynomials are introduced. Finally, dilogarithms, binomial sums, and fractional integration by parts are treated.
Chapter 3: Hypergeometric Transformations and Identities. This chapter starts with quadratic transformations. Then elliptic integrals are considered as hypergeometric functions, and arithmetic-geometric mean sequences are introduced. Next, transformations for balanced series, Whipple's transformation and Dougall's formula are given. Integral analogues of hypergeometric sums lead to the Wilson polynomials. The Riemannian point of view is reconsidered in connection with quadratic transformations. Gosper's algorithm on indefinite hypergeometric summation is given, and the Wilf-Zeilberger method for proving hypergeometric identities is compared with Pfaff's method, and the question of how these methods are related to contiguous relations is analyzed.
Chapter 4: Bessel functions and Confluent hypergeometric functions. Here, the confluent hypergeometric function is introduced. Then a Barnes type integral is given. As special cases, the Whittaker and the Bessel functions are covered. Recurrence equations, integral representations, and asymptotic expansions are treated. A two-dimensional Fourier transform leads to a generating function of the Bessel functions. Addition theorems and integrals of Bessel functions come next. Finally zeros and monotonicity properties of Bessel functions are discussed.
Chapter 5: Orthogonal polynomials. The elementary properties of general orthogonal polynomials are derived. Next, Gauss quadrature is examined. Then zeros of orthogonal polynomials are discussed, and the connection of orthogonal polynomials with continued fractions is treated. After Parseval's formula, the moment-generating function is introduced.
Chapter 6: Special orthogonal polynomials. Under this heading comes a discussion of the classical hypergeometric type orthogonal polynomials. The Hermite, Laguerre and Jacobi polynomials and their properties are discussed in detail. Then linearization coefficients are considered, and combinatorial interpretations of the classical systems are given. The Wilson polynomials and their properties come next. Finally a q-generalization of the ultraspherical polynomials is deduced.
Chapter 7: Topics in orthogonal polynomials. Connection coefficients are introduced, and for the classical systems these coefficients are explicitly determined. Nonnegativity results for hypergeometric functions and positive polynomial sums come next. In particular, the Askey-Gasper inequality which was used by de Branges in his proof of the Bieberbach conjecture [L. de Branges, Acta Math. 154, 137-152 (1985; Zbl 0573.30014)] is deduced using results about connection coefficients. Theorems by Vietoris and Turán are covered. Finally, Apéry's irrationality proof of ζ(3) is given.
Chapter 8: The Selberg integral and its applications. Here, Selberg's and Aomoto's integrals and extensions of these formulas are given. A two-dimensional electrostatic problem studied by Stieltjes connects the zeros of the Jacobi polynomials with Selberg's integral in an interesting way. Siegel's inequality, which is a refinement of the arithmetic-geometric mean inequality, is studied next, and a connection to the Laguerre polynomials is considered. Applications of Selberg's integral to constant-term identities and nearly-poised 3F2 identities are given. The Hasse-Davenport relation and a finite-field analog of Selberg's integral finish this chapter.
Chapter 9: Spherical harmonics. Harmonic polynomials and the Laplace equation in three dimensions provide an introduction to the topic of this chapter. Then the harmonic polynomials of degree k and their orthogonality are studied. Their addition theorem yields an addition theorem for ultraspherical polynomials which was used by L. Weinstein [Int. Math. Res. Not. 5, 61-64 (1991; Zbl 0743.30021)] in his proof of the Bieberbach conjecture. It is shown that Fourier transforms of higher order are still expressible in terms of Bessel functions. Next, finite-dimensional representations of compact groups are studied. Finally, Koornwinder's product formula for Jacobi polynomials is given.
Chapter 10: Introduction to q-series. In this chapter, the theory of q-hypergeometric series (basic hypergeometric series) is motivated by considering non-commutative q-algebra, related with the rule yx=qxy. Using this approach, the definition of the q-binomial coefficients and their connection with the standard binomial coefficients are straightforward. The q-integral is defined, and the q-binomial theorem is proved by two different approaches both based on recurrence equations. The q-Gamma function, and Jacobi's triple product identity are next. Ramanujan's summation formula is used to give results about the representations of numbers as sums of squares. Elliptic and theta functions are covered, and q-beta integrals are used to find a q-analog of the Wilson polynomials. Finally, the basic hypergeometric series is studied. Basic hypergeometric identities, the q-ultraspherical polynomials and the Mellin transform finish this chapter.
Chapter 11: Partitions. Partitions are defined, and the connection of partition analysis with q-series is studied. Generating functions, and other results on partitions are obtained by this method. Next, graphical methods are discussed, and congruence properties of partitions are covered.
Appendices on infinite products, summability and fractional integration, Asymptotic expansions, Euler-Maclaurin summation formula, Lagrange inversion formula, and series solutions of differential equation follow, and a bibliography, an index, a subject index and a symbol index complete the book.
To begin with these last items: For a book of this size, the subject index is rather small (3 pages). Hence, obviously not every subject can be found here. Just to mention a few, one finds neither addition theorem, nor Bieberbach conjecture, nor irrationality of ζ(3), nor indicial equation (notation defined on p. 640 in Appendix F, and used on p. 74). Many other topics cannot be found in the subject index either. In my opinion, a book covering such a wealth of information needs a better index. Similarly, the bibliography (on purpose) contains only the articles that are explicitly mentioned in the text, and by no means covers the topic of the book encyclopedically. Another minor irritation is the fact that the notations [x] (e.g. on pp. 203, 314) and ⌊x⌋ (e.g. on pp. 279, 340) for the greatest integer in x are used synonymously, but only the latter is defined on p. 15.
On the other hand, the material is written in an excellent manner, and it gives the reader very interesting insights to special functions. On many occasions, theorems are proved by several alternative methods. This gives the reader a much better feeling for what is going on, indicating that 'Special functions' is not a topic which can be taught deductively. Furthermore, the book contains very few typos.
But a book of this size covers thousands of formulas, and by Murphy's law, a few of them should be incorrect. I tried to find such misprints, in particular in the sections 3.11 and 3.12 about summation methods, since there I could use my Maple software for purposes of detection [W. Koepf, Hypergeometric summation. An algorithm approach to summation and special function identities (1998; Zbl 0909.33001)]. Not surprisingly, this search was successful: Formula (3.11.10) is incorrect by a factor -n; both identities in the middle of p. 175 are incorrect restatements of the corresponding contiguous relations (3.11.12) and (3.11.15) on p. 173; furthermore in formula (3.12.1) the upper parameter z+n-1 should read z+n+1 (I would like to thank George Andrews for sending me the corrected formula).
In spite of these minor shortcomings, I recommend this book warmly as a rich source of information to everybody who is interested in 'Special Functions'. |
Students in Algebra I fully master linear equations and linear functions, especially the algebra-geometry interplay regarding slope and graphs. Students also work intensively to master quadratic functions, both from an algebraic and formal perspective as well as in the context of modeling. The work that students do with quadratic functions is connected with and reinforces their work in quadratic equations, polynomial arithmetic and seeing structure in expressions. From an applications perspective, quadratic functions provide opportunities for solving problems involving maxima and minima, an important aspect of modeling. Working intensively with linear and quadratic expressions, equations and functions in Algebra I enables students to focus and master this material.
At the same time, however, students in Algebra I encounter general principles and techniques that apply much more generally than in the linear or quadratic case — for example, learning that the graph of an equation in two variables often forms a curve, which could be a line (A-REI.10). Thus, although most of Algebra I focuses on linear and quadratic equations and functions, the course does include concepts that apply more generally and therefore need to be illustrated beyond the linear and quadratic case. Exponential functions may be discussed in this context but studied in depth later in Algebra II.
Within the domain of Statistics and Probability, Algebra I students work with data on a single count or measurement variable as well as data on two categorical and quantitative variables. Connecting their statistical work with their work in algebra and functions, they also interpret linear models.
To summarize, the critical areas in Algebra I include mastery of linear equations and inequalities, formalization and extension of function concepts (including function notation, domain and range, and exploration of many types of functions, including sequences), linear regression models, quadratic and exponential expressions (including rational exponents), and quadratic functions.
The Standards for Mathematical Practice apply throughout the Algebra I course and, when connected meaningfully with the content standards, allow for students to experience mathematics as a coherent, useful and logical subject. Details about the content and practice standards follow in this analysis. |
Algebra - Part 263
FREE
About the Book
This advanced QuickStudy guide is designed for students who are already familiar with Algebra 1. This 6-page guide is laminated and hole-punched for easy use. Covered topics include real number lines, graphing and lines, types of functions, sequences and series, conic sections, problems and solutions and much more! |
Discovering Geometry - (3rd edition
Summary: Michael Serra's Discovering Geometry will spark new excitement in your geometry classroom, involving your students and making them active participants in their own learning. This exciting text brings the subject to life with investigations, constructions, activities, and projects. Students explore geometric relationships with a wide variety of tools: from compasses to computers, from patty papers to graphing calculators.00 +$3.99 s/h
Acceptable
Goodwill Discount Books North Las Vegas, NV
Rough edges, some scratches on the covers and a few pages may be creased May have marks or highlighting Shows moderate shelf wearTextbook Barn Woodland Hills, CA
Hardcover Good 1559534591Acceptable
Textbook Barn Woodland Hills, CA
Hardcover Fair 1559534591 |
scape Problems and Solutions
Each problem/solution theme concludes with a step-by-step demonstration in a chosen medium to pull all the points covered in the theme together in ...Show synopsisEach problem/solution theme concludes with a step-by-step demonstration in a chosen medium to pull all the points covered in the theme together in practice |
Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text |
This convenient volume offers a popular selection of 100 practice problems — with hints and solutions — for students preparing for undergraduate-level math competitions. The challenging brainteasers will also appeal to anyone interested in problems concerning real numbers, differential eq... read more
Fifty Challenging Problems in Probability with Solutions by Frederick Mosteller Remarkable puzzlers, graded in difficulty, illustrate elementary and advanced aspects of probability. These problems were selected for originality, general interest, or because they demonstrate valuable techniques. Also includes detailed solutionsProduct Description:
This convenient volume offers a popular selection of 100 practice problems — with hints and solutions — for students preparing for undergraduate-level math competitions. The challenging brainteasers will also appeal to anyone interested in problems concerning real numbers, differential equations, integrals, polynomials, sets, and other mathematical topics. The hints are very helpful and the solutions are easy to follow. Questions drawn from geometry, group theory and linear algebra involve subjects ranging from multivariate integration to finite series to infinite sums and classical analysis. The only prerequisite is a high school-level background in mathematics. Problem-solvers at varying degrees of proficiency will find this treasury of top-notch numerical puzzles an invitation to hone their mathematical skills as well as a source of stimulating entertainment |
This course, designed especially for motivated high school students wishing to pursue interesting mathematical ideas, covers a wide range of current and significant non-calculus based topics in mathematics. Topics include:
Chaos: the study of dynamically changing systems
Combinatorics: the art of counting, using methods to eliminate the need to list items.
Game Theory: the study of strategic decision-making in presence of competition and uncertainty.
Linear Programming: a tool for optimizing return, given resource constraints.
Number Theory: the study of properties of the positive integers which form the basis for all arithmetic operations.
Topology: the study of geometric properties preserved while stretching and bending the plane.
Benefits of Taking This Course
Earn college credit which is transferable to any college or university in the country. |
Professional Commentary: In this problem, the PBS Mathline activity Getting Out of Line is modified to focus on linear, quadratic, and exponential functions in graphs, tables, and symbolic representations. This problem can serve as a modeling activity to review functions that students have previously studied....
Professional Commentary: The current default rate on home mortgages indicates what a complex topic amortization is. In this problem, students investigate amortization tables and see what effect the early payment of principal has on the total amount paid....
Professional Commentary: Discover how compounding changes how much money you earn on savings or how much you have to pay back on a loan. Find out how the length of a loan affects the interest that is charged, and discover that the relationship is not linear....
Professional Commentary: If you have been to the supermarket recently, you may have seen compact fluorescent light bulbs that can replace incandescent bulbs in ordinary household light sockets. The fluorescents are more expensive than incandescents but last longer and use less electricity....
Professional Commentary: Using the computational power of your calculator or computer, how might you convince yourself that the sum of the reciprocals of perfect squares, 1/1 + 1/4 + 1/9 + 1/16 + ... is equal to (pi)2/6?...
Professional Commentary: Students create a physical model of vector forces using ring stands, spring scales, string, and a weight. They apply the actual forces using the vectors and angles given in the problem....
Professional Commentary: Students investigate the trajectories of comets, which in almost all cases are elliptical. They study what they would need to know to determine the equation of a comet?s orbit or trajectory....
Professional Commentary: This problem relates the circular motion of a point on a Ferris wheel to its up-and-down motion relative to the ground. Students can measure the height of a particular point as the Ferris wheel rotates, plot the height versus time, and observe that the graph resembles that of a sine function....
Professional Commentary: Students compare trigonometric ratios for a unit and non-unit circle with the goal of observing that the ratios are independent of the radius. They thus see the benefit of using a radius of one unit....
Professional Commentary: Land has been donated to River City. Students must decide how to split the land use between development and recreation in a way that will minimize the cost to the city of the necessary improvements, while adhering to restrictions agreed on by the River City Council.... |
Boiled-down essentials of the top-selling Schaum's Outline seriesChaos exists in systems all around us. Even the simplest system can be subject to chaos, denying us accurate predictions of its behaviour, and sometimes giving rise to astonishing structures of large-scale order. This Very Short Introduction draws in philosophy, literature, and accessible maths to explain and illuminate Chaos Theory, showing the variety... more...
A one-volume, one-day algebra course.
Alpha Teach Yourself Algebra I in 24 Hours provides readers with a structured, self-paced, straight-forward tutorial on algebra. It's the perfect textbook companion for students struggling with algebra, a solid primer for those looking to get a head start on an upcoming class, and a welcome refresher for parents... more...
What's in this book? Open this book and you will... - Improve communication - Foster development - Establish goals - Encourage success Learn how to be a mentor: - Understanding mentoring - The mentoring process - Successful mentoring relationships - Skills for successful mentors and mentees - Common pitfalls... more... |
Course
2 Unit 1 - Matrix Models 1st Edition
Matrix Models
is the first unit in Course 2 of the Contemporary Mathematics in Context
program. Students beginning this course should have successfully completed
Course 1 of the program or an algebra 1 course. (See the descriptions
of Course 2 Units.) Note that there are
seven units and a capstone unit for this course. Units vary in length
but are typically completed in 3 to 6 weeks.
Unit Overview
Matrix Models
extends student ability to use matrices and matrix operations to represent
and solve problems from a variety of real-world settings while connecting
important mathematical ideas from algebra, geometry, statistics, probability,
and discrete mathematics.
Unit Objectives
To see the interconnectedness of mathematics through the use
of matrices and to explore topics in algebra, geometry, statistics,
probability, and discrete mathematics
To use matrices for organizing and displaying data in a variety
of real-world settings like brand switching, tracking pollution
through an ecosystem, and tournament rankings
To develop further the skill of mathematical modeling by building
matrix models and then operating on them to solve problems
To use matrices and inverse matrices to answer questions that
involve systems of linear equations
Sample Overview
The sample material
from Matrix Models is the second and third investigations of Lesson
1, "Building and Using Matrix Models." Prior to Investigation 2, students
will have recognized the usefulness of matrices to represent information.
In the two investigations included in this sample material, students analyze
the information available from the matrices using row sums, column sums,
and the mean of a row and combine matrices using addition, subtraction,
and scalar multiplication.
Instructional
Design
Throughout the curriculum,
interesting problem contexts serve as the foundation for instruction.
As lessons unfold around these problem situations, classroom instruction
tends to follow a common pattern as elaborated under Instructional
Design.
Unit 2, Modeling
Public Opinion, in Course 3, develops student understanding of how
public opinion can be measured using vote analysis methods, surveys, sampling
distributions, the relationship between a sample and a population, confidence
intervals, and margin of error. Also in Course 3, students study Discrete
Models of Change which extends their ability to represent, analyze,
and solve problems in situations involving sequential change and recursive
change.
Many of the mathematical
concepts developed in the discrete mathematics strand are revisited in
the other mathematical strands, thus enabling students to develop a robust,
connected understanding of mathematics. |
gattMath is a educational math (graphical) program that show some concepts behind Integral and Differential Calculus, like Riemann, Simpson, Darboux, Trapezoid, Monte-Carlo integration, derivative, antiderivative, tangent,..., and sure a plotter |
The teacher's guide includes...
Less
Relation algebras are algebras arising from the study of binary relations.They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This research text uses combinatorial games to study the fundamental notion of representations of relation algebras. Games allow an intuitive and appealing approach to the subject, and permit substantial advances to be made. The book contains many new results and proofs not published elsewhere. It should be invaluable to graduate students and researchers interested in relation algebras and games.After an introduction describing the authors' perspective on the material, the text proper has six parts. The lengthy first part is devoted to background material, including the formal definitions...
Less is one of many Mathematics Books & Activities available through Office Depot. Made by Scholastic.
Free Worldwide Delivery : Basic Math and Pre-Algebra For Dummies Education Bundle : Paperback : John Wiley and Sons Ltd : 9780470537008 : 0470537000 : 22 Jun 2009 : Get the skills you need to solve problems and equations and be ready for algebra class. Whether you're a student preparing to take algebra or a parent who wants to brush up on basic math, this fun, friendly guide has the tools you need to get in gear.
Buy Mystery Math: A First Book of Algebra by David A Adler,Edward MillerRetail $80.85 Algebra ½ covers all topics normally taught in prealgebra, as well as additional topics from geometry and discrete mathematics (used in engineering and computer sciences). With Algebra ½ , students can deepen their understanding of prealgebraic topics. Algebra ½ includes: instruction and enrichment on such topics as compressions, approximating roots, polynomials, advanced graphing, basic trigonometry, and more. Homeschool Kit does not include the Solution Manual.
Math Triumphs is an intensive intervention resource for students who are two or more years below grade level. The series accompanies Glencoe Algebra 1, Geometry, and Algebra 2 and provides step-by-step intervention, vocabulary support, and data-driven decision making to help students succeed in high school mathematics.
Buy Basic Math and Pre-Algebra For Dummies by Mark Zegarelli and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!
Buy Basic Math & Pre-Algebra Super Review by The Editors of REA and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!
Provide students with a college-prep Algebra II course that will allow them to easily progress onto even more difficult mathematical challenges. Saxon Algebra 2, 4th Edition prepares students for calculus through explicit embedded geometry instruction. Trigonometry concepts, statistics, and applications for other subjects such as physics and chemistry are also included. Incremental lessons include a Warm Up activity; New Concepts section that introduces new concepts through examples with sidebar hints and notes; and Lesson Practice questions with lesson reference numbers underneath the question number. Online connections are given throughout for additional help. Real-world applications and continual practice & review provide the time needed to master each concept, helping students to...
Less
Buy Do the Math: Secrets, Lies, and Algebra by Wendy Lichtman and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones! index...
Less
VISU ALGEBRA BLOCKS Math Teaching Tool Description: Visually demonstrate four basic algebra relationships with this great set of foam blocks! Think about these four basic algebra relationships: (a + b) = a + 2ab + b (a + b) = a + 3a b + 3ab + b (a - b) = a - 2ab + b (a - b) = a - 3a b + 3ab - b This set of foam blocks uses area and volume to represent terms that are the product of two and three quantities. The edge lengths of the blocks are labeled a and b to help kids and students unders
MacMillan/McGraw- Hill School Division 9780078882067 Math Triumphs, Book 3 Grade 5: Geometry, Measurement, and Algebra Description Math Triumphs is intended for use as a pull out intervention class (RtI level 3) for students who are struggling in mathematics concepts two or more grade levels below their current grade. It is designed for use in after school, before school, summer school, intercession, tutoring, or pull- out/resource rooms. Math Triumphs is the first intervention program designed a Readiness is one of many Mathematics Books & Activities available through Office Depot. Made by Scholastic.
ISBN-10: 0716786672 | ISBN-13: 9780716786672 | Edition: First Edition Holt's Linear Algebra with Applications blends computational and conceptual topics throughout. Early treatment of conceptual topics in the context of Euclidean space gives students more time, and a familiar setting, in which to absorb them. This organization also makes it possible to treat eigenvalues and eigenvectors earlier than in most texts. Abstract vector spaces are introduced later, once students have developed a solid conceptual foundation. Concepts and topics are frequently accompanied by applications to provide context and motivation. Because many students learn by example, Linear Algebra with Applications provides a large number of representative examples, over and above those used to introduce...
Less
$18.99
Kobo eBooksAlgebra Readiness Made Easy: Grade 2: An Essential Part of Every Math Curriculum eBook
Free Shipping
/algebra-readiness-made/Cpd8jBnEfJLBQbMZEnF7aQ==/info
Kobo eBooks
(
In stock
)
Store not rated
Free Shipping
Buy Algebra Readiness Made Easy: Grade 2: An Essential Part of Every Math Curriculum by Greenes, CaroleProvide students with a college-prep math course that will give them the foundation they need to successfully move into higher levels of math. Saxon Algebra 1, 4th Edition covers all of the traditional first-year algebra topics while helping students build higher-order thinking skills, real-world application skills, reasoning, and an understanding of interconnecting math strands. Saxon Algebra 1 focuses on algebraic thinking through multiple representations, including verbal, numeric, symbolic, and graphical, while graphing calculator labs model mathematical situations. Incremental lessons include a Warm Up activity; New Concepts section that introduces new concepts through examples with sidebar hints and notes; and Lesson Practice questions with lesson reference numbers underneath the...
Less...
Less
Buy The Math Dude's Quick and Dirty Guide to Algebra by Jason Marshall and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!
Buy 50 Fill-in Math Word Problems: Algebra: Engaging Story Problems for Students to Read, Fill-in, Solve, and Sharpen Their Math Skills by Krech, Bob and Read this Book on Kobo's Free Apps. Discover Kobo's Vast Collection of Ebooks Today - Over 3 Million Titles, Including 2 Million Free Ones!
The modern theory of algebras of binary relations, reformulated by Tarski as an abstract, algebraic, equational theory of relation algebras, has considerable mathematical significance, with applications in various fields: e.g., in computer science--- databases, specification theory, AI---and in anthropology, economics, physics, and philosophical logic.This comprehensive treatment of the theory of relation algebras and the calculus of relations is the first devoted to a systematic development of the subject.
- Introduce your junior high student to the world of advanced math with the Horizons Pre-Algebra Student Book from Alpha Omega Publications! Containing 160 colorful lessons with perforated pages for easy removal, this workbook teaches your child volume and surface area of solids, four operations with monomials and polynomials, representations of data, trigonometric ratios, and more. A tests and resources book included. - Solidify your child's pre-algebra skills with the Horizons Pre-Algebra Tests and Resources Book from Alpha Omega Publications! This handy resource improves concept comprehension of lessons with easy-to-use, tear-out materials that include hands-on activities, 80 review worksheets, 16 tests, and four exams. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent |
View PUMAS Example
Teaching Radicals in Less than Five Minutes
Many students approach college level math courses with anxieties approaching phobic levels. Math instructors continue to search for innovative teaching methods which make math concepts easier to understand, and at the same time, lessen student fears. Various techniques, such as mnemonics, acronyms and other minds/hands-on techniques, have been used in attempts to increase student understanding, encoding, retrieval and usage of information. This article presents a conceptual teaching tool which consists of attaching new ideas or techniques to a previously learned concept or behavior. |
, Updated Media Edition
Tussy and Gustafson's fundamental goal is to have students read, write, and talk about mathematics through building a conceptual foundation in the ...Show synopsisTussy and Gustafson's fundamental goal is to have students read, write, and talk about mathematics through building a conceptual foundation in the language of mathematics. Their text blends instructional approaches that include vocabulary, practice, and well-defined pedagogy, along with an emphasis on reasoning, modeling, communication, and technology skills. With an emphasis on the "language of algebra," they foster students' ability to translate English into mathematical expressions and equations. Tussy and Gustafson make learning easy for students with their five-step problem-solving approach: analyze the problem, form an equation, solve the equation, state the result, and check the solution. In addition, the text's widely acclaimed study sets at the end of every section are tailored to improve students' ability to read, write, and communicate mathematical ideas. The Third Edition of INTERMEDIATE ALGEBRA also features a robust suite of online course management, testing, and tutorial resources for instructors and students. This includes iLrn Testing and Tutorial, vMentor live online tutoring, the Interactive Video Skillbuilder CD-ROM with MathCue, a Book Companion Web Site featuring online graphing calculator resources, and The Learning Equation (TLE), powered by iLrn. TLE provides a complete courseware package, featuring a diagnostic tool that gives instructors the capability to create individualized study plans. With TLE, a cohesive, focused study plan can be put together to help each student succeed in math495188759-5-1 Hardcover. May include moderately worn cover, writing,...Good. Hardcover. May include moderately worn cover, writing, markings or slight discoloration. SKU: 9780495188759 |
Calculus Differentiation Teacher Resources
Find Calculus Differentiation educational ideas and activities
Title
Resource Type
Views
Grade
Rating
Forgot how to multiply matrices? Well, this app can help. It is like a gigantic, well-organized reference card for all things math. Customize your personal reference material by adding your own notes and build up a personalized list of favorites.
In this circuits worksheet, students answer 25 questions about passive integrator circuits and passive differentiator circuits given schematics showing voltage. Students use calculus to solve the problems.
In this electrical worksheet, students draw a schematic design circuit board to grasp the understanding amplification in linear circuitry before answering a series of 35 open-ended questions pertaining to a variety of linear circuitry. This worksheet is printable and there are on-line answers to the questions. An understanding of calculus is needed to complete these questions.
Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The calculus controversy paper is not included but one can find a number of good resources on the Internet regarding the development of calculus and the role of Newton and Leibnez.
In this calculus worksheet, students solve three problems regarding the differentiation of inverse functions. Students are also asked to show that a function is one to one and to evaluate functions at a given value.
What does Usain Bolt and calculus have in common? Using Usain Bolt as an example of distance traveled over a period of time, Sal shows why you need differential calculus to answer the question of how fast something is traveling at a specific instance in time. He also touches on a bit of the history of calculus. This video would make a good introduction to a calculus class or as a start to a larger discussion about the uses of calculus today.
Sal starts with an example of finding dy/dx of y = x2 and builds to showing the solution to the more complicated implicit differentiation problem of finding the derivative of y in terms of x of y = x ^ x ^ x .
This video covers the differential notation dy/dx and generalizes the rule for finding the derivative of any polynomial. It also extends the notion of the derivatives covered in the Khan Academy videos, �Calculus Derivatives 2� and �Calculus Derivatives 2.5 (HD).� Note: Additional practice using the power rule for differentiating polynomials (including some with negative exponents) is available to the listener, using our knowledge of limits, defining the limit as _x approaches zero to get the slope of the tangent line to the curve. Along with the video, there is an interesting practice problem that models the connection between the slopes of the tangent lines and the derivative of a function. Note: This video has similar content as the Khan Academy video of the same name with �(new HD version),� however, the graphs on the HD version are clearer.
Sal continues where he left off with the last video, �Derivatives 1,� by looking at the equation y = x2 and examining the slope of the secant line at a specific point, and again defining the limit as _x approaches zero to get the slope of the tangent line (derivative to the curve) at a specific point. He then generalizes this technique to find the general formula for the slope at any point. Note: This video has similar content to the Khan Academy videos �Derivatives 2� and �Derivatives 2.5� with the �(new HD version)� label, however, the graphs on the HD versions are clearer.
Sal continues where he left off with the last video, �Derivatives 1,� by looking at the equation y = x2 and examining the slope of the secant line at a specific point. He continues with defining the limit as _x approaches zero to get the slope of the tangent line (derivative to the curve) at a specific point. In the next Khan Academy video, �Derivatives 2.5,� he will generalize this technique to find the general formula for the slope at any point.
By defining the formal definition of a derivative, f�(x), Sal is able to find the general form of the derivate function for the example f(x) = x2. He continues to stress the importance of an intuitive understanding of derivative functions using our knowledge of limits, defining the limit as _x approaches zero to get the slope of the tangent line to the curve. Along with the video, there is an interesting practice module that models the connection between the slopes of the tangent lines and the derivative of a function.
This video is the 4th in a series of videos that explains derivatives. First, Sal shows another example of differentiating a polynomial and then shows two examples using the chain rule. Sal continues the chain rule in the next video.
This video continues with examples of differentiating functions using the chain rule including examples that use negative exponents and more complicated nested parenthesis. Note: Additional practice on using the chain rule is available. |
1. Apply the principles of trigonometry to the solution of equations and verification
of identities.
2. Sketch the graphs of the trigonometric functions.
3. Identify the basic properties of vectors.
4. Use matrix properties to solve systems of linear equations.
Math 2240 Survey of Calculus
Upon completing this course students should be able to:
1. Find limits of functions and determine continuity of functions.
2. Find derivatives of algebraic, logarithmic, and exponential functions, and use
derivatives to solve applied problems.
3. Find integrals of some algebraic and exponential functions, and use integrals to
solve applied problems.
Math 2253Honors Math 2253 Honors4. Find integrals of some logarithmic and exponential functions, and use integrals
to solve applied problems.
5. Demonstrate clear and effective oral and written communication skills as they pertain
to course concepts.
Math 2254 Calculus II
Upon completing this course students should be able to:
1. Find derivatives and integrals of transcendental functions 2. Apply techniques to evaluate integrals 3. Use tests to determine series convergence 4. Determine Taylor series for common functions 5. Describe curves in parametric form and polar coordinates
3. State, perform, and understand the theory of, standard numerical solution methods
for ordinary differential equations, including the derivation of, and limitations
of, error bounds for some of these methods.
2. Obtain power series solutions for certain classes of linear ordinary differential
equations.
3. Recognize Sturm-Liouville equations, be aware of the existence and uniqueness properties
of boundary value problems, and demonstrate the orthogonality property of solutions
of Sturm-Liouville equations.
4. Classify second order linear partial differential equations as parabolic, elliptic,
or hyperbolic, and obtain solutions to certain equations by the method of separation
or Laplace transforms.
Math 4407 Vector Analysis
Upon completing this course students should be able to:
1. Define, and understand the geometry of, vector differential operators and line
and surface integrals. |
Student Solutions Manual for Parks/Musser/Trimpe/Maurer/Maurer's A Mathematical View of Our World
Summary
A MATHEMATICAL VIEW OF OUR WORLD helps students understand and harness the power of mathematics in their present studies and future careers. Designed for a liberal arts mathematics course that has a strong focus on applications, this student-friendly textbook helps students see the beauty and power of mathematics as it is applied to the world around them. Recognizing that quantitative literacy is essential in an increasing number of professional fields as well as in the daily decision-making and communication of informed citizens, the book develops students' mathematical self-confidence and prepares them to use mathematics in the future. In writing the book, the authors endeavored to be faithful to the recommendations of such professional mathematics associations as the MAA, AMATYC, and NCTM. Overall, students will recognize the connections, patterns, and significance of the mathematics they study, and see that mathematics has a meaningful place in their lives. |
Beginning Pre-Calculus for Game Developers
9781598632910
ISBN:
1598632914
Edition: 1 Pub Date: 2006 Publisher: Course Technology
Summary: Beginning Pre-Calculus for Game Developers provides entertaining, hands-on explanations of topics central to calculus as related to game development. It explains the mathematics and programming involved in developing nine computer programming applications furnished with the book's CD-ROM. Begin by working your way through first semester calculus topics and then use your new math skills to create programs that apply e...ach topic. Beginning Pre-Calculus presents math topics in a method that is direct, easy-to-understand, and pertinent to all studies related to calculus math.
Flynt, John P. is the author of Beginning Pre-Calculus for Game Developers, published 2006 under ISBN 9781598632910 and 1598632914. Five hundred fifty one Beginning Pre-Calculus for Game Developers textbooks are available for sale on ValoreBooks.com, one hundred fourteen used from the cheapest price of $11.20, or buy new starting at $12.68 |
Mathematica Basics
Jon McLoone
This screencast helps you to get started using Mathematica by introducing some of the most basic concepts, including entering input, understanding the anatomy of functions, working with data and matrix operations, and finding functions. |
0321575695
9780321575692
Introductory and Intermediate Algebra: The Lial series has helped thousands of students succeed in developmental mathematics through its approachable writing style, supportive pedagogy, varied exercise sets, and complete supplements package. With this new edition, the authors continue to provide students and instructors with the best package for learning and teaching support–a book written with student success as its top priority, now with an emphasis on study skills growth and an expanded instructor supplements package. Prealgebra Review; The Real Number System; Linear Equations, Inequalities, and Applications; Graphs of Linear Equations and Inequalities; Functions; Systems of Equations and Inequalities; Exponents and Polynomials; Factoring and Applications; Rational Expressions and Functions; Equations, Inequalities, and Systems Revisited; Roots, Radicals, and Root Functions; Quadratic Equations, Inequalities, and Functions; Exponential and Logarithmic Functions; Nonlinear Functions, Conic Sections, and Nonlinear Systems; Transition from Introductory to Intermediate Algebra (Review of Exponents, Polynomials, and Factoring); Strategies for Problem Solving For all readers interested in beginning and intermediate algebra.
Back to top
Rent Introductory and Intermediate Algebra 4th edition today, or search our site for Margaret L. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. |
CliffsQuickReview course guides cover the essentials of your toughest classes. You're sure to get a firm grip on core concepts and key material and be ready for the test with this guide at your side.
Whether you're new to functions, analytic geometry, and matrices or just brushing up on those topics, CliffsQuickReview Precalculus can help. This guide introduces each topic, defines key terms, and walks you through each sample problem step-by-step. In no time, you'll be ready to tackle other concepts in this book such as
Arithmetic and algebraic skills
Functions and their graphs
Polynomials, including binomial expansion
Right and oblique angle trigonometry
Equations and graphs of conic sections
Matrices and their application to systems of equations
Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Pre-Calculus Super Review includes sets, numbers, operations and properties, coordinate geometry, fundamental algebraic topics, solving equations and inequalities, functions, trigonometry, exponents and logarithms, conic sections, matrices, and determinants. Take the Super Review quizzes to see how much you've learned - and where you need more study. Makes an excellent study aid and textbook companion. Great for self-study!
500 Pre-Calculus Questions Sharpen your skills and prepare for your precalculus exam with a wealth of essential facts in a quick-and-easy Q&A format!
Get the question-and-answer practice you need with McGraw-Hill's 500 College Precalculus Questions. Organized for easy reference and intensive practice, the questions cover all essential precalculus topics and include detailed answer explanations.
The 500 practice questions are similar to course exam questions so you will know what to expect on test day. Each question includes a fully detailed answer that puts the subject in context. This additional practice helps you build your knowledge, strengthen test-taking skills, and build confidence. From ethical theory to epistemology, this book covers the key topics in precalculus.
Prepare for exam day with:
500 essential precalculus questions and answers organized by subject
Detailed answers that provide important context for studying
Content that follows the current college 101 course curriculum
Item:007178953
Price:$16.00
Quantity:
ALGEBRA PART 1 Quick Study Guide For a subject that is a challenge at all levels of education, this chart covers principles for basic algebra, intermediate algebra and college algebra courses.
Calculus Equations & Answers ( Quickstudy: Academic ) For every student who has ever found the answer to a particular calculus equation elusive or a certain theorem impossible to remember, QuickStudy comes to the rescue! This 3-panel (6-page) comprehensive guide offers clear and concise examples, detailed explanations and colorful graphsall guaranteed to make calculus a breeze! Easy-to-use icons help students go right to the equations and problems they need to learn, and call out helpful tips to use and common pitfalls to avoid. Item:142320856
Well, the good news is that you can
Calculus For Dummies is intended for three groups of readers:
Students taking their first calculus course – If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.
Students who need to brush up on their calculus to prepare for other studies – If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, Calculus For Dummies will give you a thorough, no-nonsense refresher course.
Adults of all ages who'd like a good introduction to the subject – Non-student readers will find the book's exposition clear and accessible. Calculus For Dummies takes calculus out of the ivory tower and brings it down to earth. |
This package contains basic mathematical operations,
such as summation and multiplication, and basic mathematical
functions, such as sqrt and sin, as
input/output blocks. All blocks of this library can be either
connected with continuous blocks or with sampled-data blocks. |
Thinkfinity Podcasts
Title: Art Algorithms
Description:
In
Standard(s): [MA2010] ALC (9-12) 9: Analyze aesthetics of physical models for line symmetry, rotational symmetry, or the golden ratio. (Alabama) [MA2010] DM1 (9-12) 7: Solve problems through investigation and application of existence and nonexistence of Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. (Alabama) [MA2010] DM1 (9-12) 8: Apply algorithms, including Kruskal's and Prim's, relating to minimum weight spanning trees, networks, flows, and Steiner trees. (Alabama) [MA2010] DM1 (9-12) 9: Determine a minimum project time using algorithms to schedule tasks in order, including critical path analysis, the list-processing algorithm, and student-created algorithms. (Alabama) [MA2010] MI1 (9-12) 9: Analyze works of visual art and architecture for mathematical relationships. (Alabama)
Subject: Arts, Mathematics, Science Title: Art Algorithms Description: In |
Discrete Mathematics With Application - 4th edition
Summary: Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such conce...show morepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses175215.10 +$3.99 s/h
VeryGood
Penntext Downingtown, PA
Excellent Condition. No |
40 years of teaching experience, the author presents the basic concepts of mathematical modeling of fluids and solids. A useful resource for every teacher and student of the mechanics of continua, fluid mechanics and mechanics of deformable solids. The author's unique approach, using the concept of intermediate asymptotics, has been tried and tested over a period of 40 years teaching the subject in Russia, Europe and America. Over 40 years of teaching experience are distille... MOREd into this text. The guiding principle is the wide use of the concept of intermediate asymptotics, which enables the natural introduction of the modeling of real bodies by continua. Beginning with a detailed explanation of the continuum approximation for the mathematical modeling of the motion and equilibrium of real bodies, the author continues with a general survey of the necessary methods and tools for analyzing models. Next, specific idealized approximations are presented, including ideal incompressible fluids, elastic bodies and Newtonian viscous fluids. The author not only presents general concepts but also devotes chapters to examining significant problems, including turbulence, wave-propagation, defects and cracks, fatigue and fracture. Each of these applications reveals essential information about the particular approximation. The author's tried and tested approach reveals insights that will be valued by every teacher and student of mechanics. |
graphs - Grade 10
Introduction to Functions and Graphs
Functions are mathematical building blocks for designing machines, predicting natural disasters, curing diseases, understanding world economies and for keeping aeroplanes in the air. Functions can take input from many variables, but always give the same answer, unique to that function. It is the fact that you always get the same answer from a set of inputs that makes functions special.
A major advantage of functions is that they allow us to visualise equations in terms of a graph. A graph is an accurate drawing of a function and is much easier to read than lists of numbers. In this chapter we will learn how to understand and create real valued functions, how to read graphs and how to draw them.
Despite their use in the problems facing humanity, functions also appear on a day-to-day level, so they are worth learning about. A function is always dependent on one or more variables, like time, distance or a more abstract quantity.
Functions and Graphs in the Real-World
Some typical examples of functions you may already have met
include:-
how much money you have, as a function of time. You never have more than one amount of money at any time because you can always add everything to give one number. By understanding how your money changes over time, you can plan to spend your money sensibly. Businesses find it very useful to plot the graph of their money over time so that they can see when they are spending too much. Such observations are not always obvious from looking at the numbers alone.
the temperature is a very complicated function because it has so many inputs, including; the time of day, the season, the amount of clouds in the sky, the strength of the wind, where you are and many more. But the important thing is that there is only one temperature when you measure it in a specific place. By understanding how the temperature is effected by these things, you can plan
for the day.
where you are is a function of time, because you cannot be in two places at once! If you were to plot the graphs of where two people are as a function of time, if the lines cross it means that the two people meet each other at that time. This idea is used in logistics, an area of mathematics that tries to plan where people and items are for businesses.
your weight is a function of how much you eat and how much exercise you do, but everybody has a different function so that is why people are all different sizes.
Recap
The following should be familiar.
Variables and Constants
In Review of past work, we were introduced to variables and constants. To recap, a variable can take any value in some set of numbers, so long as the equation is consistent. Most often, a variable will be written as a letter.
A constant has a fixed value. The number 1 is a constant. Sometimes letters are used to represent constants, as they are easier to work with.
Investigation : Variables and Constants
In the following expressions,
identify the variables and the constants:
2x2=12x2=1
3x+4y=73x+4y=7
y=-5xy=-5x
y=7x-2y=7x-2
Relations and Functions
In earlier grades, you saw that variables can be related to each other. For example, Alan is two years older than Nathan. Therefore the relationship between the ages of Alan and Nathan can be written as A=N+2A=N+2, where AA is Alan's age and NN is Nathan's age.
In general, a relation is an equation which relates two variables. For example, y=5xy=5x and y2+x2=5y2+x2=5 are relations. In both examples xx and yy are variables and 5 is a constant, but for a given value of xx the value of yy will be very different in each relation.
Besides writing relations as equations, they can also be represented as words, tables and graphs. Instead of writing y=5xy=5x, we could also say "yy is always five times as big as xx". We could also give the following table:
Table 1
xx
y=5xy=5x
2
10
6
30
8
40
13
65
15
75
Investigation : Relations and Functions
Complete the following table
for the given functions:
Table 2
xx
y=xy=x
y=2xy=2x
y=x+2y=x+2
1
2
3
50
100
The Cartesian Plane
When working with real valued functions, our major tool is drawing graphs. In the first place, if we have two real variables, xx and yy, then we can assign values to them simultaneously. That is, we can say "let xx be 5 and yy be 3". Just as we write "let x=5x=5" for "let xx be 5", we have the shorthand notation "let (x,y)=(5,3)(x,y)=(5,3)" for "let xx be 5 and yy be 3". We usually think of the real numbers as an infinitely long line, and picking a number as putting a dot on that line. If we want to pick two numbers at the same time, we can do something similar, but now we must use two dimensions. What we do is use two lines, one for xx and one for yy, and rotate the one for yy, as in Figure 1. We call this the Cartesian plane.
Figure 1: The Cartesian plane is made up of an x-x-axis (horizontal) and a y-y-axis (vertical).
Drawing Graphs
In order to draw the graph of a function, we need to calculate a few points. Then we plot the points on the Cartesian Plane and join the points with a smooth line.
Assume that we were investigating the properties of the function f(x)=2xf(x)=2x. We could then consider all the points (x;y)(x;y) such that y=f(x)y=f(x), i.e. y=2xy=2x. For example, (1;2),(2,5;5),(1;2),(2,5;5), and (3;6)(3;6) would all be such points, whereas (3;5)(3;5) would not since 5≠2×35≠2×3. If we put a dot at each of those points, and then at every similar one for all possible values of xx, we would obtain the graph shown in Figure 2
Figure 2: Graph of f(x)=2xf(x)=2x
The form of this graph is very pleasing – it is a simple straight line through the middle of the plane. The technique of "plotting", which we have followed here, is the key element in understanding functions.
Investigation : Drawing Graphs and the Cartesian Plane
Plot the
following points and draw a smooth line through them.
(-6; -8),(-2; 0), (2; 8), (6; 16)
Notation used for Functions
Thus far you would have seen that we can use y=2xy=2x to represent a function. This notation however gets confusing when you are working with more than one function. A more general form of writing a function is to write the function as f(x)f(x), where ff
is the function name and xx is the independent variable. For example, f(x)=2xf(x)=2x and g(t)=2t+1g(t)=2t+1 are two functions.
Characteristics of Functions - All Grades
There are many characteristics of graphs that help describe the graph of any function. These properties will be described in this chapter and are:
dependent and independent variables
domain and range
intercepts with axes
turning points
asymptotes
lines of symmetry
intervals on which the function increases/decreases
continuous nature of the function
Some of these words may be unfamiliar to you, but each will be clearly described. Examples of these properties are shown in Figure 3.
Figure 3: (a) Example graphs showing the characteristics of a function. (b) Example graph showing asymptotes of a function. The asymptotes are shown as dashed lines.
Dependent and Independent Variables
Thus far, all the graphs you have drawn have needed two values, an xx-value and a yy-value. The yy-value is usually determined from some relation based on a given or chosen xx-value. These values are given special names in mathematics. The given or chosen xx-value is known as the independent variable, because its value can be chosen freely. The calculated yy-value is known as the dependent variable, because its value depends on the chosen xx-value.
Domain and Range
The domain of a relation is the set of all the xx values for which there exists at least one yy value according to that relation. The range is the set of all the yy values, which can be obtained using at least one xx value.
If the relation is of height to people, then the domain is all living people, while the range would be about 0,1 to 3 metres — no living person can have a height of 0m, and while strictly it's not impossible to be taller than 3 metres, no one alive is. An important aspect of this range is that it does not contain all the numbers between 0,1 and 3, but at most six billion of them (as many as there are people).
As another example, suppose xx and yy are real valued variables, and we have the relation y=2xy=2x. Then for any value of xx, there is a value of yy, so the domain of this relation is the whole set of real numbers. However, we know that no matter what value of xx we choose, 2x2x can never be less than or equal to 0. Hence the range of this function is all the real numbers strictly greater than zero.
These are two ways of writing the domain and range of a function, set notation and interval notation. Both notations are used in mathematics, so you should be familiar with each.
Set Notation
A set of certain xx values has the following form:
x: conditions , more conditions x: conditions , more conditions
(5)
We read this notation as "the set of all xx values where all the conditions are satisfied". For example, the set of all positive real numbers can be written as {x:x∈R,x>0}{x:x∈R,x>0} which reads as "the set of all xx values where xx is a real number and is greater than zero".
Interval Notation
Here we write an interval in the form 'lower bracket, lower number, comma, upper number, upper bracket'. We can use two types of brackets, square ones [;][;] or round ones (;)(;). A square bracket means including the number at the end of the interval whereas a round bracket means excluding the number at the end of the interval. It is important to note that this notation can only be used for all real numbers in an interval. It cannot be used to describe integers in an interval or rational numbers in an interval.
So if xx is a real number greater than 2 and less than or equal to 8, then xx is any number in the interval
(2;8](2;8]
(6)
It is obvious that 2 is the lower number and 8 the upper number. The round bracket means 'excluding 2', since xx is greater than 2, and the square bracket means 'including 8' as xx is less than or equal to 8.
Intercepts with the Axes
The intercept is the point at which a graph intersects an axis. The xx-intercepts are the points at which the graph cuts the xx-axis and the yy-intercepts are the points at which the graph cuts the yy-axis.
In Figure 3(a), the A is the yy-intercept and B, C and F are xx-intercepts.
You will usually need to calculate the intercepts. The two most important things to remember is that at the xx-intercept, y=0y=0 and at the yy-intercept, x=0x=0.
For example, calculate the intercepts of y=3x+5y=3x+5. For the yy-intercept, x=0x=0. Therefore the yy-intercept is yint=3(0)+5=5yint=3(0)+5=5. For the xx-intercept, y=0y=0. Therefore the xx-intercept is found from 0=3xint+50=3xint+5, giving xint=-53xint=-53.
Turning Points
Turning points only occur for graphs of functions whose highest power is greater than 1. For example, graphs of the following functions will have turning points.
There are two types of turning points: a minimal turning point and a maximal turning point. A minimal turning point is a point on the graph where the graph stops decreasing in value and starts increasing in value and a maximal turning point is a point on the graph where the graph stops increasing in value and starts decreasing. These are shown in Figure 4.
Figure 4: (a) Maximal turning point. (b) Minimal turning point.
In Figure 3(a), E is a maximal turning point and D is a minimal turning point.
Asymptotes
An asymptote is a straight or curved line, which the graph of a function will approach, but never touch.
In Figure 3(b), the yy-axis and line hh are both asymptotes as the graph approaches both these lines, but never touches them.
Lines of Symmetry
Graphs look the same on either side of lines of symmetry. These lines may include the xx- and yy- axes. For example, in Figure 5 is symmetric about the yy-axis. This is described as the axis of symmetry. Not every graph will have a line of symmetry.
Figure 5: Demonstration of axis of symmetry. The yy-axis is an axis of symmetry, because the graph looks the same on both sides of the yy-axis.
Intervals on which the Function Increases/Decreases
In the discussion of turning points, we saw that the graph of a function can start or stop increasing or decreasing at a turning point. If the graph in Figure 3(a) is examined, we find that the values of the graph increase and decrease over different intervals. We see that the graph increases (i.e. that the yy-values increase) from -∞∞ to point E, then it decreases (i.e. the yy-values decrease) from point E to point D and then it increases from point D to +∞∞.
Discrete or Continuous Nature of the Graph
A graph is said to be continuous if there are no breaks in the graph. For example, the graph in Figure 3(a) can be described as a continuous graph, while the graph in Figure 3(b) has a break around the asymptotes which means that it is not continuous.
In Figure 3(b), it is clear that the graph does have a break in it around the asymptote.
Graphs of Functions
x + q
Functions of the form y=ax+qy=ax+q
Functions with a general form of y=ax+qy=ax+q are called straight line functions. In the equation, y=ax+qy=ax+q, aa and qq are constants and have different effects on the graph of the function. The general shape of the graph of functions of this form is shown in Figure 8 for the function f(x)=2x+3f(x)=2x+3.
Figure 8: Graph of f(x)=2x+3f(x)=2x+3
Investigation : Functions of the Form y=ax+qy=ax+q
On the same set of axes, plot the following graphs:
a(x)=x-2a(x)=x-2
b(x)=x-1b(x)=x-1
c(x)=xc(x)=x
d(x)=x+1d(x)=x+1
e(x)=x+2e(x)=x+2
Use your results to deduce the effect of different values of qq on the resulting graph.
On the same set of axes, plot the following graphs:
f(x)=-2·xf(x)=-2·x
g(x)=-1·xg(x)=-1·x
h(x)=0·xh(x)=0·x
j(x)=1·xj(x)=1·x
k(x)=2·xk(x)=2·x
Use your results to deduce the effect of different values of aa on the resulting graph.
You may have that the value of aa affects the slope of the graph. As aa increases, the slope of the graph increases. If a>0a>0 then the graph increases from left to right (slopes upwards). If a<0a<0 then the graph increases from right to left (slopes downwards). For this reason, aa is referred to as the slope or gradient of a straight-line function.
You should have also found that the value of qq affects where the graph passes through the yy-axis. For this reason, qq is known as the y-intercept.
Sketch the following relations on the same set of axes, clearly indicating the intercepts with the axes as well as the co-ordinates of the point of interception of the graph:
x+2y-5=0x+2y-5=0 and 3x-y-1=03x-y-1=0 Click here for the solution
Functions of the Form y=ax2+qy=ax2+q
The general shape and position of the graph of the function of the form f(x)=ax2+qf(x)=ax2+q, called a parabola, is shown in Figure 16. These are parabolic functions.
Figure 16: Graph of f(x)=x2-1f(x)=x2-1.
Investigation : Functions of the Form y=ax2+qy=ax2+q
On the same set of axes, plot the following graphs:
a(x)=-2·x2+1a(x)=-2·x2+1
b(x)=-1·x2+1b(x)=-1·x2+1
c(x)=0·x2+1c(x)=0·x2+1
d(x)=1·x2+1d(x)=1·x2+1
e(x)=2·x2+1e(x)=2·x2+1
Use your results to deduce the effect of aa.
On the same set of axes, plot the following graphs:
f(x)=x2-2f(x)=x2-2
g(x)=x2-1g(x)=x2-1
h(x)=x2+0h(x)=x2+0
j(x)=x2+1j(x)=x2+1
k(x)=x2+2k(x)=x2+2
Use your results to deduce the effect of qq.
Complete the following table of values for the functions aa to kk to help with drawing the required graphs in this activity:
Table 8
xx
-2-2
-1-1
00
11
22
a(x)a(x)
b(x)b(x)
c(x)c(x)
d(x)d(x)
e(x)e(x)
f(x)f(x)
g(x)g(x)
h(x)h(x)
j(x)j(x)
k(x)k(x)
This simulation allows you to visualise the effect of changing a and q. Note that in this simulation q = c. Also an extra term bx has been added in. You can leave bx as 0, or you can also see what effect this has on the graph.
Figure 17
Phet simulation for graphing
From your graphs, you should have found that aa affects whether the graph makes a smile or a frown. If a<0a<0, the graph makes a frown and if a>0a>0 then the graph makes a smile. This is shown in Figure 18.
Figure 18: Distinctive shape of graphs of a parabola if a>0a>0 and a<0a<0.
You should have also found that the value of qq affects whether the turning point is to the left of the yy-axis (q>0q>0) or to the right of the yy-axis (q<0q<0).
Table 9: Table summarising general shapes and positions of functions of the form y=ax2+qy=ax2+q.
a>0a>0
a<0a<0
q>0q>0
Figure 19
Figure 20
q<0q<0
Figure 21
Figure 22
Domain and Range
For f(x)=ax2+qf(x)=ax2+q, the domain is {x:x∈R}{x:x∈R} because there is no value of x∈Rx∈R for which f(x)f(x) is undefined.
The range of f(x)=ax2+qf(x)=ax2+q depends on whether the value for aa is positive or negative. We will consider these two cases separately.
If a>0a>0 then we have:
x2≥0( The square of an expression is always positive )ax2≥0( Multiplication by a positive number maintains the nature of the inequality )ax2+q≥qf(x)≥qx2≥0( The square of an expression is always positive )ax2≥0( Multiplication by a positive number maintains the nature of the inequality )ax2+q≥qf(x)≥q
(14)
This tells us that for all values of xx, f(x)f(x) is always greater than qq. Therefore if a>0a>0,)}.
Similarly, it can be shown that if a<0a<0 that This is left as an exercise.
For example, the domain of g(x)=x2+2g(x)=x2+2 is {x:x∈R}{x:x∈R} because there is no value of x∈Rx∈R for which g(x)g(x) is undefined. The range of g(x)g(x) can be calculated as follows:
x2≥0x2+2≥2g(x)≥2x2≥0x2+2≥2g(x)≥2
(15)
Therefore the range is {g(x):g(x)∈[2,∞)}{g(x):g(x)∈[2,∞)}.
Intercepts
For functions of the form, y=ax2+qy=ax2+q, the details of calculating the intercepts with the xx and yy axis is given.
The yy-intercept is calculated as follows:
y=ax2+qyint=a(0)2+q=qy=ax2+qyint=a(0)2+q=q
(16)
For example, the yy-intercept of g(x)=x2+2g(x)=x2+2 is given by setting x=0x=0 to get:
However, Equation 18 is only valid if -qa≥0-qa≥0 which means that either q≤0q≤0 or a<0a<0. This is consistent with what we expect, since if q>0q>0 and a>0a>0 then -qa-qa is negative and in this case the graph lies above the xx-axis and therefore does not intersect the xx-axis. If however, q>0q>0 and a<0a<0, then -qa-qa is positive and the graph is hat shaped and should have two xx-intercepts. Similarly, if q<0q<0 and a>0a>0 then -qa-qa is also positive, and the graph should intersect with the xx-axis.
If q=0q=0 then we have one intercept at x=0x=0.
For example, the xx-intercepts of g(x)=x2+2g(x)=x2+2 is given by setting y=0y=0 to get:
g(x)=x2+20=xint2+2-2=xint2g(x)=x2+20=xint2+2-2=xint2
(19)
which is not real. Therefore, the graph of g(x)=x2+2g(x)=x2+2 does not have any xx-intercepts.
Turning Points
The turning point of the function of the form f(x)=ax2+qf(x)=ax2+q is given by examining the range of the function. We know that if a>0a>0 then)} and if a<0a<0 then
So, if a>0a>0, then the lowest value that f(x)f(x) can take on is qq. Solving for the value of xx at which f(x)=qf(x)=q gives:
q=axtp2+q0=axtp20=xtp2xtp=0q=axtp2+q0=axtp20=xtp2xtp=0
(20)
∴∴x=0x=0 at f(x)=qf(x)=q. The co-ordinates of the (minimal) turning point is therefore (0,q)(0,q).
Similarly, if a<0a<0, then the highest value that f(x)f(x) can take on is qq and the co-ordinates of the (maximal) turning point is (0,q)(0,q).
Axes of Symmetry
There is one axis of symmetry for the function of the form f(x)=ax2+qf(x)=ax2+q that passes through the turning point. Since the turning point lies on the yy-axis, the axis of symmetry is the yy-axis.
Sketching Graphs of the Form f(x)=ax2+qf(x)=ax2+q
In order to sketch graphs of the form, f(x)=ax2+qf(x)=ax2+q, we need to determine five characteristics:
sign of aa
domain and range
turning point
yy-intercept
xx-intercept
For example, sketch the graph of g(x)=-12x2-3g(x)=-12x2-3. Mark the intercepts, turning point and axis of symmetry.
Firstly, we determine that a<0a<0. This means that the graph will have a maximal turning point.
The domain of the graph is {x:x∈R}{x:x∈R} because f(x)f(x) is defined for all x∈Rx∈R. The range of the graph is determined as follows:
x2≥0-12x2≤0-12x2-3≤-3∴f(x)≤-3x2≥0-12x2≤0-12x2-3≤-3∴f(x)≤-3
(21)
Therefore the range of the graph is {f(x):f(x)∈(-∞,-3]}{f(x):f(x)∈(-∞,-3]}.
Using the fact that the maximum value that f(x)f(x) achieves is -3, then the yy-coordinate of the turning point is -3. The xx-coordinate is determined as follows:
which is not real. Therefore, there are no xx-intercepts which means that the function does not cross or even touch the xx-axis at any point.
We also know that the axis of symmetry is the yy-axis.
Finally, we draw the graph. Note that in the diagram only the y-intercept is marked. The graph has a maximal turning point (i.e. makes a frown) as determined from the sign of a, there are no x-intercepts and the turning point is that same as the y-intercept. The domain is all real numbers and the range is {f(x):f(x)∈(-∞,-3]}{f(x):f(x)∈(-∞,-3]}.
Figure 23: Graph of the function f(x)=-12x2-3f(x)=-12x2-3
The following video shows one method of graphing parabolas. Note that in this video the term vertex is used in place of turning point. The vertex and the turning point are the same thing.
Asymptotes
There are two asymptotes for functions of the form y=ax+qy=ax+q. Just a reminder, an asymptote is a straight or curved line, which the graph of a function will approach, but never touch. They are determined by examining the domain and range.
We saw that the function was undefined at x=0x=0 and for y=qy=q. Therefore the asymptotes are x=0x=0 and y=qy=q.
For example, the domain of g(x)=2x+2g(x)=2x+2 is {x:x∈R,x≠0}{x:x∈R,x≠0} because g(x)g(x) is undefined at x=0x=0otes are at x=0x=0 and y=2y=2.
Sketching Graphs of the Form f(x)=ax+qf(x)=ax+q
In order to sketch graphs of functions of the form, f(x)=ax+qf(x)=ax+q, we need to determine four characteristics:
domain and range
asymptotes
yy-intercept
xx-intercept
For example, sketch the graph of g(x)=2x+2g(x)=2x+2. Mark the intercepts and asymptotes.
We have determined the domain to be {x:x∈R,x≠0}{x:x∈R,x≠0} and the range to be Therefore the asymptotes are at x=0x=0 and y=2y=2.
There is no yy-intercept and the xx-intercept is xint=-1xint=-1.
Figure 31: Graph of g(x)=2x+2g(x)=2x+2.
Graphs
Using graph (grid) paper, draw the graph of xy=-6xy=-6.
Does the point (-2; 3) lie on the graph ? Give a reason for your answer.
Why is the point (-2; -3) not on the graph ?
If the xx-value of a point on the drawn graph is 0,25, what is the corresponding yy-value ?
What happens to the yy-values as the xx-values become very large ?
With the line y=-xy=-x as line of symmetry, what is the point symmetrical to (-2; 3) ?
which has no real solution. Therefore, the graph of g(x)=3·2x+2g(x)=3·2x+2 does not have any xx-intercepts.
Asymptotes
There is one asymptote for functions of the form y=ab(x)+qy=ab(x)+q. The asymptote can be determined by examining the range.
We saw that the function was undefined at y=qy=q. Therefore the asymptote is y=qy=q.
For example, the domain of g(x)=3·2x+2g(x)=3·2x+2 is {x:x∈R}{x:x∈R} because g(x)g(x) is defined for all xxote is at y=2y=2.
Sketching Graphs of the Form f(x)=ab(x)+qf(x)=ab(x)+q
In order to sketch graphs of functions of the form, f(x)=ab(x)+qf(x)=ab(x)+q, we need to calculate determine four characteristics:
domain and range
yy-intercept
xx-intercept
For example, sketch the graph of g(x)=3·2x+2g(x)=3·2x+2. Mark the intercepts.
We have determined the domain to be {x:x∈R}{x:x∈R} and the range to be {g(x):g(x)∈[2,∞)}{g(x):g(x)∈[2,∞)}.
The yy-intercept is yint=5yint=5 and there are no xx-intercepts.
Figure 37: Graph of g(x)=3·2x+2g(x)=3·2x+2.
Exponential Functions and Graphs
Draw the graphs of y=2xy=2x and y=(12)xy=(12)x on the same set of axes.
Is the xx-axis and asymptote or and axis of symmetry to both graphs ? Explain your answer.
Which graph is represented by the equation y=2-xy=2-x ? Explain your answer.
Solve the equation 2x=(12)x2x=(12)x graphically and check that your answer is correct by using substitution.
Predict how the graph y=2.2xy=2.2x will compare to y=2xy=2x and then draw the graph of y=2.2xy=2.2x on the same set of axes.
After a ball is dropped, the rebound height of each bounce decreases. The equation y=5·(0,8)xy=5·(0,8)x shows the relationship between xx, the number of bounces, and yy, the height of the bounce, for a certain ball. What is the approximate height of the fifth bounce of this ball to the nearest tenth of a unit ? Click here for the solution
Mark had 15 coins in five Rand and two Rand pieces. He had 3 more R2-coins than R5-coins. He wrote a system of equations to represent this situation, letting xx represent the number of five rand coins and yy represent the number of two rand coins. Then he solved the system by graphing |
INTEGRATED PATHWAY: MATHEMATICS III
999It is in Mathematics III that students pull together and apply the accumulation of learning that they have from their previous courses, with content grouped into four critical areas,
organized into units. They apply methods from probability and statistics to draw inferences and conclusions from data. Students expand their repertoire of functions to include
polynomial, rational, and radical functions.3 They expand their study of right triangle trigonometry to include general triangles. And, finally, students bring together all of their
experience with functions and geometry to create models and solve contextual problems. The Mathematical Practice Standards apply throughout each course and, together with the
content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
3Inthis course rational functions are limited to those whose numerators are of degree at most 1 and denominators of degree at most 2; radical functions are limited to square roots or
cube roots of at most quadratic polynomials.
★ Standards indicated by a star symbol (★) involve making mathematics models which address Mathematical Content Standards and Standards of Mathematical Practice. Modeling is
best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling
standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it
should be understood to apply to all standards in that group.
+ Standards indicated with an addition symbol (+) are included to increase coherence but are not necessarily expected to be addressed on high stakes assessments. These standards
specify additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics
All standards without a (+) symbol should be in the common mathematics curriculum for all college and career ready students.
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and the Standards for
Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time,
resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in
mathematics. A detailed explanation of the Standards for Mathematical Practice follows the units.
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and
1 1: INFERENCES AND CONCLUSIONS FROM DATA
In this unit, students see how the visual displays and summary statistics they learned in earlier grades relate to different types of data and to probability distributions. They identify
different ways of collecting data—including sample surveys, experiments, and simulations—and the role that randomness and careful design play in the conclusions that can be drawn.
CLUSTER CONTENT STANDARD
Summarize, represent, and
interpret data on a single count
or measurement variable.
While students may have heard
of the normal distribution, it is
unlikely that they will have prior
S.ID.4 Use the mean and standard deviation of a data set to fit it to a
experience using it to make
normal distribution and to estimate population percentages. Recognize
specific estimates. Build on
that there are data sets for which such a procedure is not appropriate.
students' understanding of data
Use calculators, spreadsheets, and tables to estimate areas under the
distributions to help them see
normal curve.
how the normal distribution uses
area to make estimates of
frequencies (which can be
expressed as probabilities).
Emphasize that only some data
are well described by a normal
distribution.
S.IC.1 Understand that statistics allows inferences to be made
Understand and evaluate about population parameters based on a random sample from that
random processes underlying population.
statistical experiments.
S.IC.2 Decide if a specified model is consistent with results from a
For S.IC.2, include comparing given data-generating process, e.g., using simulation.
theoretical and empirical results
to evaluate the effectiveness of a For example, a model says a spinning coin falls heads up with
treatment. probability 0.5. Would a result of 5 tails in a row cause you to question
the model?
Make inferences and justify
conclusions from sample
surveys, experiments, and S.IC.3 Recognize the purposes of and differences among sample
observational studies. surveys, experiments, and observational studies; explain how
randomization relates to each.
In earlier grades, students are
introduced to different ways of
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and
2collecting data and use graphical
displays and summary statistics
to make comparisons., These S.IC.4 Use data from a sample survey to estimate a population mean
ideas are revisited with a focus on or proportion; develop a margin of error through the use of simulation
how the way in which data is models for random sampling.
collected determines the scope
and nature of the conclusions that
can be drawn from that data. The
concept of statistical significance
is developed informally through
S.IC.5 Use data from a randomized experiment to compare two
simulation as meaning a result treatments; use simulations to decide if differences between
that is unlikely to have occurred
parameters are significant.
solely as a result of random
selection in sampling or random
assignment in an experiment.
For S.IC.4 and 5, focus on the
variability of results from
experiments—that is, focus on S.IC.6 Evaluate reports based on data.
statistics as a way of dealing with,
not eliminating, inherent
randomness.
Use probability to evaluate
outcomes of decisions. S.MD.6 (+) Use probabilities to make fair decisions (e.g., drawing by
lots, using a random number generator).
Extend to more complex
probability models. Include
situations such as those involving S.MD.7 (+) Analyze decisions and strategies using probability concepts
quality control or diagnostic tests (e.g., product testing, medical testing, pulling a hockey goalie at the
that yields both false positive and end of a game).
false negative results Content and
3 2: POLYNOMIALS, RATIONAL, AND RADICAL RELATIONSHIPS
This unit develops the structural similarities between the system of polynomials and the system of integers. Students draw on analogies between polynomial arithmetic and base-ten
computation, focusing on properties of operations, particularly the distributive property. Students connect multiplication of polynomials with multiplication of multidigit integers, and
division of polynomials with long division of integers. Students identify zeros of polynomials and make connections between zeros of polynomials and solutions of polynomial
equations. The unit culminates with the fundamental theorem of algebra. Rational numbers extend the arithmetic of integers by allowing division by all numbers except 0. Similarly,
rational expressions extend the arithmetic of polynomials by allowing division by all polynomials except the zero polynomial. A central theme of this unit is that the arithmetic of rational
expressions is governed by the same rules as the arithmetic of rational numbers.
CLUSTER CONTENT STANDARD
Use complex numbers in
polynomial identities and N.CN.8 (+) Extend polynomial identities to the complex numbers.
equations.
For example, rewrite x2 + 4 as (x + 2i)(x – 2i).
Build on work with quadratics
equations in Mathematics II. Limit N.CN.9 (+) Know the Fundamental Theorem of Algebra; show that it is
to polynomials with real true for quadratic polynomials.
coefficients.
A.SSE.1 Interpret expressions that represent a quantity in terms of its
context.★
a. Interpret parts of an expression, such as terms, factors, and
coefficients.
Interpret the structure of b. Interpret complicated expressions by viewing one or more of their
expressions. parts as a single entity.
For example, interpret P(1+r)n as the product of P and a factor
Extend to polynomial and rational not depending on P.
expressions. A.SSE.2 Use the structure of an expression to identify ways to rewrite
it.
For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a
difference of squares that can be factored as (x2 – y2)(x2 + y2).
Write expressions in equivalent
forms to solve problems.
A.SSE.4 Derive the formula for the sum of a geometric series (when
the common ratio is not 1), and use the formula to solve problems.
Consider extending A.SSE.4 to
infinite geometric series in
For example, calculate mortgage payments. ★
curricular implementations of this
course description.
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and
4Perform arithmetic operations
on polynomials. A.APR.1 Understand that polynomials form a system analogous to
the integers, namely, they are closed under the operations of
Extend beyond the quadratic addition, subtraction, and multiplication; add, subtract, and
polynomials found in Mathematics multiply polynomials.
II.
A.APR.2 Know and apply the Remainder Theorem: For a polynomial
p(x) and a number a, the remainder on division by x – a is p(a), so p(a)
Understand the relationship
= 0 if and only if (x – a) is a factor of p(x).
between zeros and factors of
A.APR.3 Identify zeros of polynomials when suitable factorizations are
polynomials.
available, and use the zeros to construct a rough graph of the function
defined by the polynomial.
Use polynomial identities to
solve problems. A.APR.4 Prove polynomial identities and use them to describe
numerical relationships.
This cluster has many possibilities
for optional enrichment, such as For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be
relating the example in A.APR.4 used to generate Pythagorean triples.
to the solution of the system
u2+v2=1, v = t(u+1), relating the
Pascal triangle property of A.APR.5 (+) Know and apply the Binomial Theorem for the expansion of
binomial coefficients to (x+y)n+1 = (x + y)n in powers of x and y for a positive integer n, where x and y are
(x+y)(x+y)n, deriving explicit any numbers, with coefficients determined for example by Pascal's
formulas for the coefficients, or Triangle.
proving the binomial theorem by
induction.
A.APR.6 Rewrite simple rational expressions in different forms; write
a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are
Rewrite rational expressions polynomials with the degree of r(x) less than the degree of b(x), using
inspection, long division, or, for the more complicated examples, a
The limitations on rational computer algebra system.
functions apply to the rational
expressions in A.APR.6. A.APR.7 A.APR.7 (+) Understand that rational expressions form a system
analogous to the rational numbers, closed under addition,
requires the genera division
algorithm for polynomials. subtraction, multiplication, and division by a nonzero rational
expression; add, subtract, multiply, and divide rational
expressions.
Understand solving equations
as a process of reasoning and
explain the reasoning. A.REI.2 Solve simple rational and radical equations in one variable,
and give examples showing how extraneous solutions may arise.
Extend to simple rational and
radical equations.
Represent and solve equations A.REI.11 Explain why the x-coordinates of the points where the graphs
and inequalities graphically. of the equations y = f(x) and y = g(x) intersect are the solutions of the
equation f(x) = g(x); find the solutions approximately, e.g., using
Include combinations of linear, technology to graph the functions, make tables of values, or find
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and
5polynomial, rational, radical, successive approximations. Include cases where f(x) and/or g(x) are
absolute value, and exponential linear, polynomial, rational, absolute value, exponential, and
functions. logarithmic functions.★
Analyze functions using
F.IF.7 Graph functions expressed symbolically and show key features
different representations.
of the graph, by hand in simple cases and using technology for more
complicated cases.★
Relate F.IF.7c to the relationship
c. Graph polynomial functions, identifying zeros when suitable
between zeros of quadratic
factorizations are available, and showing end behavior.
functions and their factored forms6 the Standards for Mathematical Practice 3: TRIGONOMETRY OF GENERAL TRIANGLES AND TRIGONOMETRIC FUNCTIONS
Students develop the Laws of Sines and Cosines in order to find missing measures of general (not necessarily right) triangles. They are able to distinguish whether three given
measures (angles or sides) define 0, 1, 2, or infinitely many triangles. This discussion of general triangles open up the idea of trigonometry applied beyond the right triangle—
that is, at least to obtuse angles. Students build on this idea to develop the notion of radian measure for angles and extend the domain of the trigonometric functions to all real
numbers. They apply this knowledge to model simple periodic phenomena.
CLUSTER CONTENT STANDARD
Apply trigonometry to general G.SRT.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle
triangles. by drawing an auxiliary line from a vertex perpendicular to the opposite
side.
With respect to the general case G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to
of the Laws of Sines and solve problems.
Cosines, the definitions of sine G.SRT.11 (+) Understand and apply the Law of Sines and the Law
and cosine must be extended to of Cosines to find unknown measurements in right and non-right
obtuse angles. triangles (e.g., surveying problems, resultant forces).
F.TF.1 Understand radian measure of an angle as the length of the
arc on the unit circle subtended by the angle.
Extend the domain of
trigonometric functions using F.TF.2 Explain how the unit circle in the coordinate plane enables the
the unit circle. extension of trigonometric functions to all real numbers, interpreted as
radian measures of angles traversed counterclockwise around the unit
circle.
Model periodic phenomena F.TF.5 Choose trigonometric functions to model periodic phenomena
with trigonometric functions. with specified amplitude, frequency, and midline.7 4: MATHEMATICAL MODELING
In this unit students synthesize and generalize what they have learned about a variety of function families. They extend their work with exponential functions to include solving
exponential equations with logarithms. They explore the effects of transformations on graphs of diverse functions, including functions arising in an application, in order to abstract the
general principle that transformations on a graph always have the same effect regardless of the type of the underlying functions. They identify appropriate types of functions to model a
situation, they adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a
good fit. The description of modeling as "the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make
decisions" is at the heart of this unit. The narrative discussion and diagram of the modeling cycle should be considered when knowledge of functions, statistics, and geometry is
applied in a modeling context.
CLUSTER CONTENT STANDARD
Create equations that describe A.CED.1 Create equations and inequalities in one variable and use
numbers or relationships. them to solve problems.
For A.CED.1, use all available Include equations arising from linear and quadratic functions, and
types of functions to create such simple rational and exponential functions.
equations, including root
functions, but constrain to simple A.CED.2 Create equations in two or more variables to represent
cases. While functions used in relationships between quantities; graph equations on coordinate axes
A.CED.2, 3, and 4 will often be with labels and scales.
linear, exponential, or quadratic
the types of problems should
draw from more complex A.CED.3 Represent constraints by equations or inequalities, and by
situations than those addressed systems of equations and/or inequalities, and interpret solutions as
in Mathematics I. For example, viable or non-viable options in a modeling context.
finding the equation of a line
through a given point For example, represent inequalities describing nutritional and cost
perpendicular to another line constraints on combinations of different foods.
allows one to find the distance
from a point to a line. Note that A.CED.4 Rearrange formulas to highlight a quantity of interest, using
the example given for A.CED.4 the same reasoning as in solving equations.
applies to earlier instances of this
standard, not to the current For example, rearrange Ohm's law V = IR to highlight resistance R.
course.
F.IF.4 For a function that models a relationship between two quantities,
Interpret functions that arise in
interpret key features of graphs and tables in terms of the quantities,
applications in terms of a
and sketch graphs showing key features given a verbal description of
context.
the relationship.
Emphasize the selection of a
Key features include: intercepts; intervals where the function is
model function based on behavior
increasing, decreasing, positive, or negative; relative maximums and
of data and context.
minimums; symmetries; end behavior; and periodicity.★
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and
8F.IF.5 Relate the domain of a function to its graph and, where
applicable, to the quantitative relationship it describes.
For example, if the function h(n) gives the number of person-hours it
takes to assemble n engines in a factory, then the positive integers
would be an appropriate domain for the function.★
F.IF.6 Calculate and interpret the average rate of change of a function
(presented symbolically or as a table) over a specified interval.
Estimate the rate of change from a graph.★
F.IF.7 Graph functions expressed symbolically and show key features
of the graph, by hand in simple cases and using technology for more
complicated cases.★
b. Graph square root, cube root, and piecewise-defined functions,
Analyze functions using including step functions and absolute value functions.
different representations. e. Graph exponential and logarithmic functions, showing intercepts
and end behavior, and trigonometric functions, showing period,
Focus on applications and how midline, and amplitude.
key features relate to F.IF.8 Write a function defined by an expression in different but
characteristics of a situation, equivalent forms to reveal and explain different properties of the
making selection of a particular function.
type of function model F.IF.9 Compare properties of two functions each represented in a
appropriate. different way (algebraically, graphically, numerically in tables, or by
verbal descriptions).
For example, given a graph of one quadratic function and an algebraic
expression for another, say which has the larger maximum.
Build a function that models a
relationship between two F.BF.1 Write a function that describes a relationship between two
quantities. quantities.*
b. Combine standard function types using arithmetic operations.
Develop models for more For example, build a function that models the temperature of a
complex or sophisticated cooling body by adding a constant function to a decaying
situations than in previous exponential, and relate these functions to the model.
courses.
Build new functions from
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k
existing functions.
f(x), f(kx), and f(x + k) for specific values of k (both positive and
negative); find the value of k given the graphs. Experiment with cases
Use transformations of functions
and illustrate an explanation of the effects on the graph using
to find more optimum models as
technology.
students consider increasingly
more complex situations.
Include recognizing even and odd functions from their graphs and
algebraic expressions for them.
For F.BF.3, note the effect of
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and
9multiple transformations on a
single function and the common
effect of each transformation
across function types F.BF.4 Find inverse functions.
Include functions defined only by a. Solve an equation of the form f(x) = c for a simple function f that
a graph. has an inverse and write an expression for the inverse.
Extend F.BF.4a to simple rational, For example, f(x) = 2 x3 or f(x) = (x+1)/(x-1) for x ≠ 1.
simple radical, and simple
exponential functions; connect
F.BF.4a to F.LE.4.
Construct and compare linear,
quadratic, and exponential
models and solve problems.
Consider extending this unit to
F.LE.4 For exponential models, express as a logarithm the solution to
include the relationship between
a bct = d where a, c, and d are numbers and the base b is 2, 10, or e;
properties of logarithms and
evaluate the logarithm using technology.
properties of exponents, such as
the connection between the
properties of exponents and the
basic logarithm property that log
xy = log x + log y.
Visualize relationships between G.GMD.4 Identify the shapes of two-dimensional cross-sections of
two dimensional and three- three dimensional objects, and identify three-dimensional objects
dimensional objects. generated by rotations of two-dimensional objects.
G.MG.1 Use geometric shapes, their measures, and their properties to
describe objects (e.g., modeling a tree trunk or a human torso as a
cylinder).★
G.MG.2 Apply concepts of density based on area and volume in
Apply geometric concepts in modeling situations (e.g., persons per square mile, BTUs per cubic
modeling situations. foot).★
G.MG.3 Apply geometric methods to solve design problems (e.g.,
designing an object or structure to satisfy physical constraints or
minimize cost; working with typographic grid systems based on
ratios).10MATHEMATICS | STANDARDS FOR MATHEMATICAL PRACTICE
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on
important "processes and proficiencies" with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and
proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up:
adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out
procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a
belief in diligence and one's own efficacy).
1 MAKE SENSE OF PROBLEMS AND PERSEVERE IN SOLVING THEM.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints,
relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They
consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and
change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing
calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw
diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help
conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make
sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
2 REASON ABSTRACTLY AND QUANTITATIVELY.
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving
quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of
their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for
the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of
quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
3 CONSTRUCT VIABLE ARGUMENTS AND CRITIQUE THE REASONING OF OTHERS.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build
a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use
counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible
arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments,
distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete
referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades.
Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask
useful questions to clarify or improve the arguments.
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and
114 MODEL WITH MATHEMATICS.
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple
as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By
high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students
who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able
to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze
those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense,
possibly improving the model if it has not served its purpose.
5 USE APPROPRIATE TOOLS STRATEGICALLY.
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a
protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools
appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For
example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically
using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions,
explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources,
such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
6 ATTEND TO PRECISION.
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning
of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the
correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In
the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of
definitions.
7 LOOK FOR AND MAKE USE OF STRUCTURE.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven
and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in
preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an
existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can
see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive
number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and
128 LOOK FOR AND EXPRESS REGULARITY IN REPEATED REASONING.
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by
11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly
check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel
when
mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
CONNECTING THE STANDARDS FOR MATHEMATICAL PRACTICE TO THE STANDARDS FOR MATHEMATICAL CONTENT
The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter
as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development
should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction. The Standards for Mathematical Content are a balanced
combination of procedure and understanding. Expectations that begin with the word "understand" are often especially good opportunities to connect the practices to the content.
Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems,
represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics
accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from
engaging in the mathematical practices. In this respect, those content standards which set an expectation of understanding are potential "points of intersection" between the
Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in
the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment,
professional development, and student achievement in mathematics.
Content standards which set an expectation of understanding (in bold) are potential "points of intersection" between the Standards for Mathematical Content and
13 |
Peer Review
Ratings
Overall Rating:
This site contains reference material and sample problems in Calculus. Topics covered include sequences, series, limits, continuity, differentiation, integration, and Fourier series. Many problems have answers and detailed solutions. S.O.S. Mathematics/Calculus is a part of an independent, commercial site that offers straightforward technical assistance primarily to high school and college students.
Learning Goals:
To serve as a supplement for a standard course in calculus and provide some additional instruction.
Target Student Population:
Calculus students.
Prerequisite Knowledge or Skills:
College Algebra.
Type of Material:
Reference and tutorial.
Recommended Uses:
This site can be used as a supplement to a standard Calculus course or as an online referrence guide.
Technical Requirements:
It requires a "Java-enabled" browser.
Evaluation and Observation
Content Quality
Rating:
Strengths:
The site focuses on traditional Calculus content covering most topics in a typical Calculus I, II, and III course sequence. It is devoted to general explanations and examples as well as exercises with solutions. A major strength of this site's content lies in its many sample problems and examples. These "examples" are actually practice exercises that students can attempt on their own before clicking on a button that takes them to a detailed solution.
A sequence of topics makes it easy to use this interactive textbook in a "linear", not hyper-referenced way.
Concerns:
Some pages do not load completely thus creating omissions. Here are two:
Also, in the section on Indeterminate Forms, more care should be taken when doing arithmetic with the infinity symbol Students will come to think infinity is a number.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This online text provides major help in learning the concepts of Calculus and, in particular, in solving problems.
The hyper-referenced definitions and theorems are extremely helpful if the site is used as a reference material.
The material is presented in worksheet format and requires students to actively participate in the learning process.
Concerns:
At its current state the site is unlikely to be used as a textbook for a course in Calculus but certainly makes an excellent tutorial supplement. Some sample problems are lacking answers and/or solutions but hopefully this will be completed in the near future.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This learning resource is easily navigable. The topics are well-organized and all the key concepts are properly emphasized. Commercial advertising is somewhat distracting in places, but the layout is otherwise clean and simple, with good displays of mathematical formulas that load acceptably fast |
MATH 222-001 Calculus 2,
TWF at 10:20, Hurst 210.
Textbook: Your choice!
We will use
Piazza
for on-line discussions and polls,
and
WeBWorK
for most of our homework.
If you're not on campus, you need to set up a VPN connection to the university
in order to use this latter system.
Sorry.
Here are some instructions for that. |
College Algebra : Graphs and Models -Text Only - 4th edition
Summary: The approach of this text is more interactive than most precalculus texts and the goal of the author team is to enhance the learning process through the use of technology and to provide as much support and help for students as possible. In Connecting the Concepts, comprehension is streamlined and retention is maximized when the student views a concept in visual, rather than paragraph, form. Zeros, Solutions, and X-Intercepts Theme Carried Throughout helps students vi...show moresualize and connect the following three concepts when they are solving problems: the real zeros of the function, the solutions of the associated equation, and the x-coordinates of the x-intercept of the graph of the function. Each chapter begins with a relevant application highlighting how concepts presented in the chapter can be put to use in the real world. These applications are accompanied by numerical tables, equations, and grapher windows to show students the many different ways in which problems can be examined. End-of-Chapter material includes a summary and review of properties and formulas along with a complete set of review exercises. Review exercises also include synthesis, critical thinking, and writing exercises. The answers to all of the review exercises appear in the back of the text and have text section references to further aid students. For anyone interested in learning algebra |
Algebra 1
9780078738227
ISBN:
0078738229
Pub Date: 2007 Publisher: McGraw-Hill Higher Education
Summary: THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT! "Glencoe Algebra 1" is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments.
McGraw-Hill Staff is the author of Algebra 1, published 2007 under ISBN 9780078738227 and 0078738229. One thousand ...eighty two Algebra 1 textbooks are available for sale on ValoreBooks.com, eight hundred eighty one used from the cheapest price of $7.00, or buy new starting at $123.46.[read more]
Ships From:Wentzville, MOShipping:Standard, ExpeditedComments:DUE TO PUBLISHING DEFECT CORNERS OF COVERS AND PAGES ARE CUT OFF DOES NOT AFFECT TEXT. Student Ed... [more]. [less38227-4-0-3 Orders ship the same or next business day. Expedited shipping within U.S. [more]
May include moderately worn cover, writing, markings or slight discoloration. SKU:9780078738227 s [more o [moreWE HAVE NUMEROUS COPIES. HARDCOVER some pages wrinkled from water damage but no staining and dos not affect usability, Moderate wear to cover,edges, and corners, covers begin [more]
WE HAVE NUMEROUS COPIES. HARDCOVER some pages wrinkled from water damage but no staining and dos not affect usability, Moderate wear to cover,edges, and corners, covers beginning to separate from pages exposing a small amount of binding but page binding is still good - Student name/s inside front cover -school stamp inside front cover pages appear free of markings/writing |
Math tool for high school math, middle school math teaching and studying. Function graphing and analyzing, sequence of number, analytic geometry and solid geometry. Math tool for high school math, middle school math teaching and studying. Function graphing and analyzing, sequence of number, analytic geometry and solid geometry.
Portfolio Calculator PCal allows you to calculate and record financial measures such as Value at Risk, Volatility, loss/gain and investment value changes of a portfolio composition consisting of 5 U.S. or E.U. stocks.
SystemSwift Boost your computer, game and internet speed the easy way, make games faster |
Student and tutor module reviews
Discovering mathematics
Student reviews
Very good course. No matter how good you think you are at maths, this course shows how you can still improve your written skills.
I took this course as a filler, but it opened my eyes to the bad habits which I had picked up. As an introductory course to maths, it is brilliant. Would well recommend.
Course starting: February 2013
Review posted: November 2013
I would highly recomend this course to any forty something "mature" students like myself. I really had a strong aversion to Mathematics at high school, I think this can be fairly attributed to poor teachers who probably did not fully understand the subject themselves. This course however was extremely well structured in my opinion for beginers or people like myself who use a lot of general Mathematical principles in their everyday job but have picked up bad techniques from fellow workers along the way. The tutor was always available to answer questions via email.
Course starting: October 2012
Review posted: November 2013
This was a wonderful experience and a dream come true doing this course. I left school with no knowledge of mathematics or examinations so this course was an eye opener. I have always wanted to understand mathematics, and I found it fascinating. I did find it hard at times but that may be because I was also doing a language course at the same time. I surprised myself in getting reasonable results for my TMAs and EMA.
Also I am hearing impaired and had to rely on online tutorials because of the area I live in, which was hard because of not being able to understand 100% of what went on with the tutorials but my tutor and others were very good and helped a lot.
I would like to thank the OU for making this happen for me. One day who knows I may carry on with mathematics but at the moment I'm going towards language courses which is also a challenge for me and once again something I always wanted to learn.
Course starting: October 2012
Review posted: September 2013
I enjoyed this course very much and the learning of algebra was fascinating. I would have preferred just one big textbook rather than all the books as I kept having to find them all the time for referring back. The TMAs are not easy and take a lot of studying but all in all it is a worthy course for anyone who wants to understand maths. It has helped me also to engage with the children with their homework especially algebra!
Course starting: February 2012
Review posted: August 2013
Lovely course. Material was easy to understand and TMA easy to do. I had great support from tutor as well. It is a revision if you had math few years ago and do not feel confident in the subject. I feel that I should have done MS121 rather then mu123 as I found it too easy for me.
Course starting: February 2012
Review posted: July 2013
The perfect course for anyone who was told they were useless at maths at school! The course books were fun and lively (not two adjectives I would previously have thought appropriate to maths books)and my tutor was excellent. I also really enjoyed using the online resources such as dataplotter and graphplotter, which certainly beat drawing graphs by hand.
This course certainly boosted my confidence - if I can complete (and pass) a maths course, anything is possible! My only slight criticism was that the EMA came rather hard on the heels of the last TMA, so that my EMA was rather more rushed than I would have liked. All in all, a thoroughly enjoyable introduction to OU Maths - highly recommended.
Karen Thomas
Course starting: October 2012
Review posted: July 2013
The course is very enjoyable and very helpful to refresh high school math. However, if you are looking for a challenge and you were good at math in high school, then MU123 is probably not a good choice for you.
The course material is very well written and enjoyable, and our tutor was very professional and prepared. Overall, I am satisfied with the course.
Course starting: February 2012
Review posted: July 2013
An easy one. A pleasure to study it. The course is for beginners and the material is easy to read and understand. If you have studied math before you should skip it but if you have not then do it as it is good preparation for MST121. I would definitely recommend it.
Emil Eftimov
Course starting: October 2011
Review posted: April 2013
Far too easy for me. I wish I started straight on MST121 (Using Mathematics). If you've studied GCSE maths or something at a similar level then this should be easy enough for you. If you haven't then it shouldn't tax your brain cells too much. But everything is clearly explained and there's plenty of worked examples which show you how the problems are solved.
It's an easy 30 credits towards your degree though; ideal if you've other modules/courses that are taking up most of your time.
Course starting: October 2011
Review posted: August 2012
A very rewarding course! I hadn't studied mathematics since last taking this subject(at GCSE in 1996)and I was pleased to find that any gaps in my knowledge were more than covered in the available course Books A-D. There are also two additional books, supplementing the units including a glossary, summaries of maths concepts and calculator exercises. It is worth cross-checking with these as you progress through the units as they help to reinforce your learning.
The tutorials were held approximately once a month with interspersed Elluminate-Live online tutorials, which were also very useful. I have to say, my tutor was absolutely excellent and replied to any of my queries within a couple of hours and the tutorials always addressed any concerns students had.
Completing this course and achieving 95 percent was largely due to the professional way in which the literature was presented; it was very comprehensive, varied and enjoyable. Although some students disliked the iCMAs (interactive computer marked assignments) I gained a lot from them as you have ample opportunity to test yourself via online (end of unit)Practice Quizzes, which are also interactive - they test your recently learned knowledge and you gain instant feedback once you have completed the end of unit quiz.
Many of the earlier concepts, which are often not covered in basic maths qualifications, such as surds made this course much more interesting and algebra(the part I most feared), was by the end my strongest area-thanks largely to the way it was taught in the materials.
Finally, for any prospective MU123 students; have faith in the course materials and cover as much of the subject content as possible, the effort is worth it!
Hilary Jane Kitching
Course starting: February 2011
Review posted: August 2012
This was my first introduction to studying with the Open University and I thoroughly enjoyed it. I came into it having not done any maths for 20+ years.
It starts with a very gentle approach and constantly builds upon what you have learned previously. The learning curve does tend to get a little sharper towards the latter end of the units but it is definitely manageable. I managed very high marks throughout.
The course materials were excellent, as was my tutor. I would highly recommend this module to anyone.
Craig Cope
Course starting: October 2011
Review posted: August 2012
I was a little nervous before starting this course as I have avoided maths like the plague in the past, but needed it for career purposes. But I worried for nothing because the maths is so well explained throughout.
Initially the maths was very basic, a bit like brushing up on old school skills and gradually built up along with my confidence in my ability. Very soon I was solving problems I would not have even attempted in the past and I find that I still use the skills learned in this course in everyday situations.
The course books are excellent, taking you through each area of maths step by step, giving plenty of examples and opportunities to practice throughout, linking the topics to real life situations. I was also very fortunate to have an excellent tutor.
Course starting: October 2010
Review posted: August 2012
Really enjoyed this module. My tutor was fantastic, and the materials were well put together, and explained things well. The practice quizes which accompanied each unit were invaluable, as you could do them as many times as you wanted and they really helped me get my head around things from time to time.
There is a learning curve, but because of the excellence of the materials it is almost unnoticeable till you get to the end and look back and see how far you have come!
One of the most pleasurable OU modules I have ever done. Would recommend to anyone.
Louise Grassie
Course starting: October 2011
Review posted: July 2012
MU123 is a very good course to prepare for further study in mathematics or do it just as a refresher. The material is taught using real world examples and is easily applied everywhere around you.
I really liked the statistics part and started collecting data everywhere to work with.
The TMA were very manageable, I also took the opportunity to learn some LaTeX doing them (which is not required by the course at all). You can also do everything by hand and there is no need to use word processor or anything. TMAs are handwritten or printed and send by post, whereas CMA are done online in a web browser.
In fact, everything is available online in form of websites to produce graphs for example. There is no need to install any additional software.
The tutor was great! I really enjoyed doing the course.
Marcus Becker
Course starting: October 2010
Review posted: June 2012
Great Module. Eases you into the course so well. A fantastic tutor. What can I say about this course other than it worked well.
I got a bit lazy around the middle of the course but with some encouragement from the tutor I was back on track and was able to easily pass.
The books and information provided were spot on.
I loved Maths in school but this really reminded me of how difficult it can be. But don't be alarmed, the coursework will lead you right into it so you can't go wrong if you read it.
I would definitely recommend this module to ANYONE. It was my first module with OU and a great introduction Thanks
Patrick Byrne
Course starting: February 2011
Review posted: May 2012Enter a module code to find a review
To send us reviews on modules you have
studied with us, please click the sign in button below. |
Linear Algebra with Applications, CourseSmart eTextbook, 4th Edition
Description
Offering the most geometric presentation available, Linear Algebra with Applications, Fourth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the many techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Extensive problem sets keep students involved in the material, while genuine applications for a broad range of sciences prepares them for the methods and models of contemporary scientists. In addition, the wealth and variety of exercise sets enable instructors to design a course to best suit the goals and needs of their students. This revision reflects careful review and appropriate changes to the wording of each idea, while preserving the content structure of the previous edition.
CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book. |
124124.66
FREE
About the Book
This edition features the exact same content as the traditional book in a convenient, three-hole- punched, loose-leaf version. Books a la Carte also offer a great value--this format costs significantly less than a new textbook. More than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teachers since its first edition, and it remains the gold standard today. This book not only helps students learn the material by promoting active learning and developing skills and concepts- To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit This package contains:
Books a la Carte for A Problem Solving Approach to Mathematics for Elementary School Teachers, Eleventh Edition |
To learn and understand mathematics, students must engage in the process of doing mathematics. Emphasizing active learning, Abstract Algebra: An Inquiry-Based Approach not only teaches abstract algebra but also provides a deeper understanding of what mathematics is, how it is done, and how
… |
$98 last five years have seen an immense growth in the use of symbolic computing and mathematical software packages such as Maple. The first three chapters of this book provide a user-friendly introduction to computer-assisted algebra with Maple. The rest of the book then develops these techniques and demonstrates the use of this technology for deriving approximate solutions to differential equations (linear and nonlinear) and integrals. In each case, the mathematical concepts are comprehensively introduced, with an emphasis on understanding how solutions behave and why various approximations can be used. Where appropriate, the text integrates the use of Maple to extend the utility of traditional approximation techniques. Advanced Mathematical Methods with Maple is the ideal companion text for advanced undergraduate and graduate students of mathematics and the physical sciences. It incorporates over 1000 exercises with different levels of difficulty, for which solutions are provided on the Internet.
A user-friendly introduction to using Maple for computer-assisted algebra
Richly illustrated with examples from applied mathematics and physics
Includes over 1000 exercises, for which solutions are provided at |
National 2.5% also qualify for the AIME.
The Mathematical Association of America wants to increase interest in mathematics and to develop problem solving through a friendly and fun competition. The purpose of the AMC 8 is to demonstrate the broad range of topics available for the junior high school mathematics curriculum. The AMC 12 covers the high school mathematics curriculum, excluding calculus. The AMC 10 covers subject matter normally associated with grades 9 and 10. Site includes past AMC Archives.
Math Contests contains the actual math contests given to students participating in Math League Contests, Grades 4, 5, and 6, School Years 1979-1980 through 2010-2011, and Grades 7, 8, and Algebra Course 1, School Years 1996-1997 through 2010-2011. The contests are designed to build student interest and confidence in mathematics.
The USAMO provides a means of identifying and encouraging the most creative secondary mathematics students in the country. It serves to indicate the talent of those who may become leaders in the mathematical sciences of the next generation. The USAMO is part of a worldwide system of national mathematics competitions. Sponsored by MAA American Mathematics Competitions. |
The purpose of the GPS Geometry Support Class is to address the needs of students who have traditionally struggled in math. This will be done by providing the additional time and attention they need in order to help them be successful in their regular grade-level mathematics course. GPS Geometry Support is an elective class taught concurrently with the students regular math class.
The purpose of the GPS Algebra Support Class is to address the needs of students who have traditionally struggled in math. This will be done by providing the additional time and attention they need in order to help them be successful in their regular grade-level mathematics course. GPS Algebra Support is an elective class taught concurrently with the students regular math class.
This is the first in a sequence of mathematics courses designed to ensure that all students are ready for work and college. It includes radical, polynomial and rational expressions, basic functions and their graphs, step and piecewise functions, solving simple equations, quadratic equations and inequalities, quadratic functions, complex numbers, sample statistics, and curve fitting.
This is the first in a sequence of mathematics courses designed to prepare students to take Advanced Placement Calculus. It includes radical, polynomial and rational expressions; functions and their graphs; quadratic and radical equations; fundamentals of proof; properties of polygons, circles and spheres; coordinate geometry; sample statistics and curve fitting.
EOCT Required: Yes
]]>MaryCatherine PhyfeFri, 14 Mar 2008 14:09:31 GMT Courses/DispForm.aspx?ID=5CCGPS Analytic Geometry Courses/DispForm.aspx?ID=2
Major Topics Covered: This is the second in a sequence of mathematics courses designed to prepare students for work and college. It includes complex numbers; quadratic, piecewise, and exponential functions; right triangles, and right triangular trigonometry; properties of circles; and statistical inference. |
Type of assessment:
Exam duration:
Aid:
Evaluation:
Not applicable together with:
General course objectives:
To provide the student with thorough knowledge and practical skills in the parts of mathematics necessary in modern engineering. To give the students the ability to read scientific papers that use mathematics.
Learning objectives:
A student who has met the objectives of the course will be able to:
Apply the algebraic and geometric representation of the complex numbers and the complex exponential function
Apply the complex exponential function.
Do calculations with complex numbers both by hand and using a computer.
Use polynomials with complex coefficients
Do calculations with polynomials, both by hand and using a computer.
Solve simple differential equation of first and second order
Use Taylor polynomials for the approximation of functions in up to two variables. |
Customer Reviews for McGraw-Hill Key To Decimals, Book #4
Key to Decimals begins with basic concepts and operations on decimals, allowing it be used for simple review, a non-threatening introduction, or as a supplement for struggling students. It covers real-world uses of decimals in pricing, sports, metrics, calculators and science. Written with secondary students in mind, their success-oriented, self-paced, self-guided approach builds confidence and independence. Book Four covers rounding off decimals, estimating, graphing averages, the metric system and scientific notation. 45 pages, paperback. Notes and answer key sold separately (stock # 33087).
Customer Reviews for Key To Decimals, Book #4
This product has not yet been reviewed. Click here to continue to the product details page. |
Just for you, we curate a growing list of independent booksellers, giving you even MORE choices when shopping for your textbooks.Keep in mind: Marketplace orders do NOT qualify for free shipping. More about the Marketplace
Brand new. We distribute directly for the publisher. The fundamental idea of geometry is that of symmetry. With that principle as the starting point, Barker and Howe begin an insightful and rewarding...show more study of Euclidean geometry.The primary focus of the book is on transformations of the plane. The transformational point of view provides both a path for deeper understanding of traditional synthetic geometry and tools for providing proofs that spring from a consistent point of view. As a result, proofs become more comprehensible, as techniques can be used and reused in similar settings.The approach to the material is very concrete, with complete explanations of all the important ideas, including foundational background. The discussions of the nine-point circle and wallpaper groups are particular examples of how the strength of the transformational point of view and the care of the authors' exposition combine to give a remarkable presentation of topics in geometry.This text is for a one-semester undergraduate course on geometry. It is richly illustrated and contains hundreds of exercises |
Mathematics
Mathematics
The Mathematics Department offers a broad, in-depth curriculum for exploring all aspects of mathematics – including quantities, changes, abstraction, structure and space – through small, engaging classroom settings. Within the department there is a great sense of discovery and collaboration as students and faculty are active in research, journal publication, conference presentations, mathematics competitions and many have received distinguished awards and recognition.
Research
is an integral part of the program and is incorporated into coursework as well as ongoing, unique research solutions outside of the classroom. In addition to collaborative research projects with faculty, students are highly active in the Math Club where they have the opportunity to discuss mathematics, solve problems and participate in social activities. A dedicated tutoring facility, great professor accessibility and the encouragement of open discussions in the classroom all contribute to a nurturing and supportive learning environment that lends a deep exploration of mathematics. Graduates are poised to excel in graduate programs and have become highly successful alumni who are skilled educators, actuaries, engineers, financial mathematicians and more.
Marion V. Smith, 93, passed on Friday, Sept. 13, 2013, at the Shepherd of the Valley Healthcare Center. A native of St. Paul Minn., she had retired as professor emerita from Moorhead State University, where she taught mathematics from 1945 to1982. As a hobbyist photographer she enjoyed summer vacations touring the world's exotic locals, which [...]
Sayel Ali, Justin James, and Wally Sizer, Mathematics, attended the North Central Section meeting of the Mathematical Association of America in Brookings, S.D., Oct. 18 and 19. The section includes Minnesota, North Dakota, Saskatchewan, Manitoba, and part of South Dakota. Sizer presented the paper, Formation of the North Central Section, describing the early years of [...]
1 of 3 Minnesota universities, only Tri-College University The Society of Actuaries has categorized the Actuarial Program in the Department of Mathematics as an Advanced Undergraduate Program. MSUM is the one of the three universities in Minnesota that has such advanced program, and only one in the Tri-College area. Visit the Society of Actuaries website [...] |
AP Calculus
Through intensive research and development, Agile Mind Calculus was created for teachers, administrators, and schools seeking to offer this central college-level course to a broad cross-section of students.
Calculus AB follows the well-respected AP® syllabus and emphasizes algebraic, numerical, and graphical representations throughout. Students will be prepared for success on the AP Calculus exam and in college, with thorough grounding in:
Functions, inverse functions, and limits of functions
Differentiation
Integration
The fundamental theorem
More than one hundred real-world applications
Talk with us about working together to close the achievement gaps in math and science. For all students.
AP-style multiple-choice practice exams, written by past members of the College Board AP Calculus Test Development Committee to mirror the content and structure of the two-part multiple choice portion of the AP Calculus AB exam
Real-time reporting of progress that allows students to take responsibility for their own learning
Robust Supports for Teachers
In addition to Internet-delivered services, educators and administrators also receive face-to-face seminars, mentoring, and high-quality support materials to help them manage their demanding workloads, enhance their expertise, and dramatically improve outcomes for their students.
Online and face-to-face professional development seminars and mentoring directly tied to practice
Day-by-day lesson support with advice and classroom strategies, equipping teachers to enact each day of instruction to achieve success for all students
Collaboration with Leading Educational Research Center
Our mathematics and academic youth programs are developed in collaboration with the Charles A. Dana Center at the University of Texas at Austin. Working with leading educators throughout the country, we have developed mathematics programs for middle school, Algebra I, Geometry, Algebra II, Precalculus, Calculus, and AP Statistics. These programs build on the Dana Center's trusted work with more than 100,000 teachers over the past decade and on the core belief that all students can succeed in mathematics if given the opportunity. |
In this unit students will build on the work they have already done with linear relationships.While they will see and work with other function families, the emphasis will be on linear and exponential families.They will compare and contrast the properties of linear and exponential functions. They will spend time working to understand functions as an important mathematical structure by examining function characteristics, notation, representations, and operations of specific function families.Students will practice building functions that describe the relationship between two quantities from a context.They will look at multiple ways to apply functions to solve problems and represent situations.They will also work with sets of order pairs that do not represent functions.
Next Generation Content Standards and Objectives:
Objectives Directly Taught or Learned Through Inquiry/Discovery
Evidence of Student Mastery of Content
M.1HS.LER.1 understand
M.1HS.LER.2 explain
M.1HS.LER.3 graph
Determine a feasible region of solution (Lesson 13)
M.1HS.LER.4 understand
M.1HS.LER.7 for
M.1HS.LER.8 relate
M.1HS.LER.9 calculate
M.1HS.LER.11 compare.
M.1HS.LER.12 write a function that describes a relationship between two quantities.
Determine an explicit expression, a recursive process, or steps for calculation from a context.
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
M.1HS.LER.13 write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. (Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.)
M.1HS.LER.14 identify
M.1HS.LER.16 construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship or two input-output pairs (include reading these from a table).
M.1HS.LER.17 observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (Limit to comparisons between exponential and linear models.)
Lesson 14:Copies of the following for each student:Attachments for Part 1 (Attachment 1A, Attachment 1B, Attachment 1C), index cards, and centimeter cubes available for each student who wants to use them (optional).
Each lesson contains the possibility for both formative and summative assessment.The lessons have been written with a concern for providing teachers with the flexibility to make decisions that will best meet their students' needs.See evidence of student mastery.For the unit assessment students are asked to find two functions that are important to a specified topic and discuss its use and representations in both a paper and presentation.
Major Products:
Lesson 6Presentation (Group)
Lesson 10Presentation (Group)
Lesson 15Newspaper Article (Individual)
UnitFunction Presentation and Paper (Individual)
Unit Reflection:
Teachers need to consider the level of understanding students have achieved relative to the cluster topics.Can students represent and solve equations and inequalities graphically?Do students understand the concept of function and the use of function notation?Can students interpret functions that arise in the context of an application?Can students analyze functions using different representations?Can students build a function that models a relationship between two quantities?Can students build new functions from existing functions?Can student construct and compare linear and exponential models and solve related problems?Can students interpret expressions for functions in terms of the situation they model?
Tagged Next Generation Content Standards and Objectives
NxG ID
NxG Objectives
M.1HS.LER.1
understand(CCSS.Math.Content.HSA-REI.D.10)
M.1HS.LER.2
explain(CCSS.Math.Content.HSA-REI.D.11)
M.1HS.LER.3
graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. (CCSS.Math.Content.HSA-REI.D.12)
M.1HS.LER.4
understand (CCSS.Math.Content.HSF-IF.A.1)
M.1HS.LER.5
use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context. (CCSS.Math.Content.HSF-IF.A.1)
for(CCSS.Math.Content.HSF-IF.B.4)
M.1HS.LER.8
relate(CCSS.Math.Content.HSF-IF.B.5)
M.1HS.LER.9
calculate(CCSS.Math.Content.HSF-IF.B.6)
M.1HS.LER.10
graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
graph linear and quadratic functions and show intercepts, maxima, and minima.
compare.(CCSS.Math.Content.HSF-IF.C.9)
M.1HS.LER.12
write a function that describes a relationship between two quantities.
Determine an explicit expression, a recursive process, or steps for calculation from a context.
Combine standard function types using arithmetic operations.
For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.(CCSS.Math.Content.HSF-BF.A.1)
M.1HS.LER.13
write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. (Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.)(CCSS.Math.Content.HSF-BF.A.2)
M.1HS.LER.14
ident.(CCSS.Math.Content.HSF-BF.B.3)
M.1HS.LER.15
distinguish between situations that can be modeled with linear functions and with exponential functions.
recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. (CCSS.Math.Content.HSF-LE.A.1)
M.1HS.LER.16
construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship or two input-output pairs (include reading these from a table). (CCSS.Math.Content.HSF-LE.A.2)
M.1HS.LER.17
observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. (Limit to comparisons between exponential and linear models.)(CCSS.Math.Content.HSF-LE.A.3)
M.1HS.LER.18
interpret the parameters in a linear or exponential function in terms of a context. (CCSS.Math.Content.HSF-LE.B.5) |
$ 14.79 14.79
Word problems are the most difficult part of any math course –- and the most important to both the SATs and other standardized tests. This book teaches proven methods for analyzing and solving any type of...
$ 12.99
Algebra: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using Algebra. Written by a leading expert, this book will help you if you are studying for an important exam or essay,...
$ 119.29
General concepts and methods that occur throughout mathematics - and now also in theoretical computer science - are the subject of this book. It is a thorough introduction to Categories, emphasizing the geometric...
$ 128.49
Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who...
$ 294.99
Graphics Gems V is the newest volume in The Graphics Gems Series. It is intended to provide the graphics community with a set of practical tools for implementing new ideas and techniques, and to offer working...
$ 68.79
The book is devoted to the perturbation analysis of matrix equations. The importance of perturbation analysis is that it gives a way to estimate the influence of measurement and/or parametric errors in mathematical...
$ 196.79
Aimed at starting researchers in the field, Realizability gives a rigorous, yet reasonable introduction to the basic concepts of a field which has passed several successive phases of abstraction. Material from...
$ 114.99
Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these...
$ 210.79
The problems of constructing covering codes and of estimating their parameters are the main concern of this book. It provides a unified account of the most recent theory of covering codes and shows how a number... |
Sheryl Allison
Homepage
Our curriculum aligns with the new Kansas College and Creer Ready Standards. We foster development in algebraic thinking through exploration, discovery, and instructional activities in the four strands of mathematics – number and computation, algebra, geometry, and probability and statistics.
Textbook
Our textbook is Big Ideas Math. Online access to the textbook can be found at This series offers many online resources for parents and students. The website provides copies of all activities, extra practice, remediation, practice tests/quizzes, online games, web lessons and many other valuable resources.
Assignments
You can find a listing of all assignments by viewing the SHMS Google Apps calendar, or by looking at Skyward.
Extra Help
I am available to provide additional help from 7:30 - 7:50 A.M. before school, or after school on most days from 3:25 - 3:45. Please contact me anytime if you have a questions or concern about your student.
Second Quarter Curriculum
Second quarter we will be doing lots of graphing! We will be graphing linear equations and systems of linear equations, learning about slope and slope-intercept form. We will also write linear equations and systems using slope and a point, and two points.
"The essence of mathematics is not to make simple things complicated, but to make complicated things simple." ~S. Gudder |
This subsite of Mathematics Tutorials and Problems (with applets) is divided into Interactive Tutorials, Calculus Problems,...
see more
This subsite of Mathematics Tutorials and Problems (with applets) is divided into Interactive Tutorials, Calculus Problems, and Calculus Questions, Answers and Solutions. Here the user will find applets with guided exercises and many examples and worked out problems applicable to the first year of Calculus.
This site is devoted to learning mathematics through practice. Many dozens of practice problems are provided in Precalculus,...
see more
This site is devoted to learning mathematics through practice. Many dozens of practice problems are provided in Precalculus, Calculus I - III, Linear Algebra, Number Theory, and Abstract Algebra. The last two subject areas -- referred to as "books" on the site -- are under construction. To each topic within a book (for example, Epsilon and Delta within Calculus I) there is a "module" of approximately 20 to 30 problems. Each module also includes a help page of background material. The modules are interactive to some extent and often provide suggestions when wrong answers are entered.
site consists of examples, exercises, games, and other learning activities associated with the textbook, Discrete...
see more
This site consists of examples, exercises, games, and other learning activities associated with the textbook, Discrete Mathematics: Mathematical Reasoning and Proof with Puzzles, Patterns and Games by Doug Ensley and Winston Crawley. Requires Adobe Flash player.
This is a graduate level reference work with 8,000 entries illuminating nearly 50,000 mathematical notions. If you are...
see more
This is a graduate level reference work with 8,000 entries illuminating nearly 50,000 mathematical notions. If you are looking for the definition of a term, this site most likely has it.Each entry is actually a small survey article on the subject in question, written by an expert. Articles list further references, so that deeper study after a quick refresher is possibleThis is a website that is designed for use in extending more able pupils in maths. It includes investigations, interactive...
see more
This is a website that is designed for use in extending more able pupils in maths. It includes investigations, interactive resources as well as printable resources. This resource can be used to extend children at difeerent stages. I found it to be really useful, not only are there resources for children there is also information to improve your own subject knowledge. |
Solutions To Complex Analysis Ahlfors
An Introduction to Complex Analysis and Geometry John P. D. when viewed from the perspective of complex analysis. My own of elementary complex analysis and geometry. a solution in Z unless b is an even number.
4. CHAPTER 1. THE HOLOMORPHIC FUNCTIONS operations: both the inner. Z = (t0x, t0y,1 ? t0) with t0 being the solution of t2. papers were not widely known - even Cauchy who has obtained numerous fundamental results in complex analysis considered early in his career the complex numbers simply as symbols
analysis to advanced undergraduate and graduate Principle.- Sequences and Series of Numbers.-. Sequences and Series of Functions. ISBN 978-88-470- 1940-9 bounds to the solutions of the above equations. The last chapter, which includes many examples,. exercises 7 The 6th edition includes a systematic
How is real analysis and complex analysis different? 1. 2. Applications of complex analysis. 3. What is complex analysis? If forced to give a one-sentence description, many math-. applications of complex analysis in physics and engineering.
deep appreciation of complex analysis and how this perspectrve of complex analysrs The book begins at an elementary solutions at regular singular pornts Bessel functrons, of linear functional analysis as related to fundamental aspects
Encribd is NOT affiliated with the author of any documents mentioned in this site. All sponsored products, company names, brand names, trademarks and logos found on this document are the property of its respective owners. |
The Nuffield Foundation provides this activity which can be used to review students' knowledge of the derivatives of quadratic and cubic functions and their graphs. The slideshow provides an introduction by considering a quadratic example and a cubic example.
There are 12 sets of cards, each set containing a polynomial function, its graph, the corresponding derivative function and the graph of the derivative function.
Possible matching activities
• use all four cards from each set (but perhaps not all the sets, depending on the time you have available). Shuffle each type of card, then ask students to match each function with its graph, the derivative function, and the graph of the derivative function.
• for a more difficult activity use just the graphs and match the graphs of polynomials and their derivatives, students will need to think carefully about the relationship between the features of the graph of a function and its derivative |
Summary: KEY BENEFIT: TheBittinger Concepts and Applications Seriesextends proven pedagogy to a new generation of students, with updates throughout to help today's students learn. Bittinger transitions students from skills-based math to the concepts-oriented math required for college courses, and supports students with quality applications and exercises to help them apply and retain their knowledge. New features such as Translating for Success and Visualizing the Graph unlock the way students...show more think, making math accessible to them. KEY TOPICS: MARKET: |
Computer explorations with a computer algebra system (CAS) can be used to illuminate ideas in analytic geometry and calculus. Given five points in a plane, a unique conic section will pass through them, but the details of finding it are overwhelming to do by hand. The computer algebra system Mathematica is used to assist with these computations which are suitable for an undergraduate computer laboratory exercise. |
The Programme in Mathematical Simulation provides an introduction to the exciting interactions between Mathematics, Technology and Education. This programme has its roots in the Mathematics and the Modern World programme that MSF faculty ran from 1995 to 2001 with funding fom the Department of Science & Technology. It takes forward one of the primary aims of the MSF: promoting exciting mathematics-based activities that will take the student beyond the confines of the curriculum. We seek to promote this among all students with an interest in mathematical thought, whatever their background or specialization.
Highlights:
Part of the programme consists of foundational classes in basic applied mathematics (Advanced Calculus, Linear Algebra, Probability) and programming (C++, Matlab, Flash). The remainder consists of Projects carried out by student teams.
Internships will be awarded, to those students who fulfill the qualifying criteria, in companies such as Tata Interactive Services (Mumbai) and HeyMath! (Chennai).
TIS is a global leader in the design and development of e- learning tools and products. Set up in 1990, TIS has created learning methodologies and systems that work all over the world. The TIS work force includes software engineers, instructional designers, content developers, visual designers, and animators.
HeyMath! helps students in Grades 5-12 build a strong foundation in Mathematics and become independent learners. Their innovative use of technology has been recommended by the Millennium Mathematics Project of the University of Cambridge.
Students will undertake projects in teams mentored by MSF faculty. The projects will blend Mathematics, Technology and Education in various ways.
Past projects have included Image Compression, Search Engines, Data Encryption, Error-Correcting Codes, Stock Price Modeling, etc. The range of possible projects, as well as the different skills required within each project, will enable you to do something that is interesting and unusual – whatever your background or talent set may be.
The programme is self-contained and does not require any prerequisite beyond high school mathematics. No prior knowledge of computer programming is necessary.
Thus, besides showing you some exciting (and unexpected) applications of Mathematics, the Programme in Mathematical Simulation also helps you learn how to work in groups, develops your communication skills, and provides exposure to the corporate world. |
If it has been a while since you took a math course, or you aren't really sure if you know the material to take a course, the review sheets on this page should help you to decide.
Students who have been away from mathematics for awhile have often forgotten some of the material. Yet most college mathematics courses rely heavily on students recalling material from previous courses. Our experience has led us to believe that using the results of an assessment test which the students take "cold" for placement is not very effective. What we really need to measure is how quickly the student will recall material which they have previously learned. These prerequisite review sheets were developed to aid in this process. We strongly encourage you to work your way through the one appropriate to your course before the course starts and preferably before you take the assessment test.
If you find that you need help on these problems, you can get help from a friend or a tutor, look at an algebra book yourself, or use some algebra review software on a computer. Please get as much help as you need to recall how to do the problems.
Caution:
Please keep in mind that working these few problems does not substitute for actually taking the prerequisite course(s). In a one-semester course, you should spend about 150 hours of work, working between 300 and 700 problems, and be tested on 50 to 150 problems. Learning how to do one set of prerequisite review problems will not replace all the material that you would have learned in a course. So, do not be tempted to use these to replace actually taking the appropriate courses.
Here are links for each of the courses for which we have such review sheets on the Web. As additional materials are developed or made available for the Web, they will be added. We hope that you find these useful. |
0534529054
9780534529055
Mathematics:Since its initial publication, MATHEMATICS: A GOOD BEGINNING has set the standard for math methods books. More than just a textbook, this is a complete instructional program that serves a multitude of curriculum needs. The book has been praised for its depth and clarity, its imaginative activities, and its attentiveness to the philosophy and recommendations of the National Council of Teachers of Mathematics (NCTM). This edition is solidly grounded in the latest research on how children learn mathematics and how teachers develop attitudes, beliefs, and knowledge that promote successful teaching.
Back to top
Rent Mathematics 6th edition today, or search our site for Andria P. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Wadsworth Publishing. |
Advanced Mathematics 1
Advanced Mathematics 1
This free online training explores complex numbers and equations, polynomial equations, conics, advanced trigonometry, differentiation, antiderivatives, and vectors in 2- and 3-space. This course is both an ideal study-aid for students to improve their skills in their spare time or for anyone interested in exploring the world of mathematics.
Improve your algebra, calculus and trigonometry skills
Learning Outcome
Upon completion of this course you will understand nominal, discrete and continuous data in frequency tables. You will know the product rule and you will be able to easily perform calculations of differentiation. You will gain a good knowledge of antiderivatives including Hyperbolic functions, partial fractions, linear substitution, odd and even powers. You will understand the relationship between graphs and their antiderivatives. You will be able to calculate complex numbers using addition, subtraction, multiplication and division. You will be familiar with DeMoivre's Theorom, polar form multiplication and division. This course will teach you how to calculate conics, degrees, radians, inverse circular functions, polynomial equations and much more. |
Horizons Algebra 1 - Tests and Resource Book
Evaluate your homeschooler's comprehension of algebraic concepts with the Horizons Algebra I Tests & Resources Book from Alpha Omega Publications! Designed for your convenience, this book assesses the information your child has learned to lay a solid foundation for upper-level math. Each page is perforated for easy removal and includes bi-weekly tests, quarterly exams, and 80 review worksheets that can be used for additional practice or as extra quizzes.
In addition, a detailed guide in the Horizons Algebra I Tests & Resources Book makes homeschooling easier with page listings that coordinate when and where to use each worksheet, test, and exam in the Alpha Omega curriculum. Plus, hands-on algebra square manipulatives assist visual and kinesthetic learners in retaining lesson concepts and mastering algebra more quickly. |
PAPERBACK New 1418000752 Premium Books are Brand New books direct from the publisher sometimes at a discount. These books are NOT available for expedited shipping and may take ...up to 14 business days to receive.Read moreShow Less
1418000752Math is at the heart of pharmaceutical care. A sound knowledge of math concepts is critical to the success of the Pharmacy Technician. Pharmaceutical Calculations for The Pharmacy Technician focuses on dosage calculations and basic math skills: from simple addition and subtraction to formulas used in dosage calculations to business math concepts. Accuracy in calculations will guide the Pharmacy Technician in the prevention of medication errors. From Doody's Book Review: "This." Reviewed by Lindsay I. Varga, Temple University School of Pharmacy. Weighted Numerical Score: 100
Editorial Reviews
From The Critics
Reviewer: Lindsay I. Varga, B.S. (Temple University School of Pharmacy) Description: This workbook is for pharmacy technician students wishing to improve their knowledge in basic math skills, systems of measurement, dosage calculations, and interpreting a medication order. This book approaches these subjects by giving real-life examples that can be seen every day in the pharmacy field. Purpose: The author's purpose is to empower pharmacy technicians through an understanding of the fundamental skills of calculating drug dosages and converting within the metric, apothecary, and household systems. The book also attempts to provide good understanding of medical terms and the different dosage forms used in the pharmacy. It is absolutely necessary to be proficient in these subjects in order to ensure a safe healthcare environment. Too many lives have been lost due to medication errors that could have been avoided with a little education. This book achieves its goals and then some. The practical, real-life approach to the subject makes learning and applying the new knowledge seamless. Not only is this book important because it is an excellent learning tool, but it is also innovative because it acknowledges the fact that a pharmacy technician is a specialized occupation that requires precision, accuracy, and a wide range of education. Audience: The book is written primarily for pharmacy technician students. However, many other health professions can benefit from it. Anyone working with prescription medications should read and work through this book. The author is an expert in the field and has had experience with students since he created the associate degree program for pharmacy technicians in 2000 at Florida Metropolitan University. Features: The book starts by giving a thorough overview of basic math and conversions between different systems of measurement. These important fundamentals could easily become boring, but the author applies them to the daily proceedings in a pharmacy setting and makes them fascinating. The book then goes on to describe different dosage forms, how to calculate doses, and specific considerations when dealing with pediatric and geriatric patients. The strongest feature of the book is its practice problems. There are example problems throughout the tutorial, and then there are a set of problems for the reader to try on their own at the end of each chapter. These problems take on many different perspectives of the subject, which further reinforces the information for the reader. The book also incorporates real pictures of medication labels and shows where to find the information you need on the label. Assessment: This.
From the Publisher
"The material is very up-to-date and would really help my students prepare for the math on the national exam. It is superior to many texts on the market in terms of industry standards."Bobbi Steelman, CPT, BSEd, MAEd , Pharmacy Technician Program Director, Daymar Colleges Group Bowling Green, KY
"This book is excellent! In all chapters there are plenty of practice problems which is essential. The math fundamentals are presented well."Douglas Scribner, MEd, CPhT, Director of Pharmacy Technology, Central New Mexico Community College Albuquerque, New Mexico
Related Subjects
Meet the Author
Jahangir Moini is Professor of Allied Health Programs at Everest University in Melbourne, Florida where he established the Medical Assisting Program and Associate Degree Program for Pharmacy Technicians, as well as other programs. He is also a past Director of both the Allied Health Programs and the Associate Degree Program. Previously, Dr. Moini worked with the Brevard County Health Department as an epidemiologist and health educator consultant, offering continuing education courses and updating nurses on new developments related to pharmacology, medication errors, immunizations, and other important topics. Over the past two decades, Dr. Moini a variety of health books internationally. He holds a Medical Doctor Degree, a Master's Degree in Public Health, and is a Certified Pharmacy Technician Use |
Calculus Workbook For Dummies (eBook)Short DescriptionLong description
From differentiation to integration - solve problems with ease
100s of Problems!
Step-by-step answer sets clearly identify where you went wrong (or right) with a problem
The inside scoop on calculus shortcuts and strategies
Know where to begin and how to solve the most common problems
Use calculus in practical applications with confidence
Product details
Not compatible with:
Kindle, Digibook, Verso, RK Book, Pocketbook 306
Download size:
6793 KB
Digital Rights:
51DCAD87-FB05-4697-8241-F19214268950-50
Maximum Downloads:
3
Printable:
Not Allowed
Author:
Mark Ryan
Imprint:
For Dummies
Publisher:
John Wiley & Sons Ltd
ISBN:
9780471762751
Series Title:
Dummies |
Business Math Brief, CourseSmart eTextbook, 10th Edition
Description
For courses in business mathematics, personal finance, or small business management.
Business Math Brief, Tenth Edition unlocks the world of math by showing how it is used in the business world. Written in a conversational style, the book covers essential topics such as banking, interest, insurance, taxes, depreciation, and inventory. It carefully explains common business practices such as markup, markdown, and cash discounts–showing students how these tools work in small business or personal finance. Authors encourage self-starters from the beginning, with the review of basic math, annotated examples, stop and check exercises, skill builders and application exercises. This edition includes updated problem sets, new trends and laws, and the one-of-a-kind MyMathLab website. |
OCR Mathematics for GCSE Specification B - Foundation Initial and Foundation Bronze Student's Book has been published to support students and teachers of the OCR course. The resource has been written and edited by experienced examiners and authors, combining their teaching and examining expertise to deliver relevant and meaningful coverage of the course. Each student's book provides complete coverage of relevant Specification B units at Foundation and Higher respectively. The structure and content of the resources allow teachers to prepare students for the final exams in an incremental way as well as across the entire tier. The great advantage of using the Hodder series is that pupils can be benchmarked at the end of each stage through use of the new progress papers available in print and online. These progress papers fully support the linear exams (calculator and non-calculator) that test attainment across the entire tier. The content also supports delivery of the revised Assessment Objectives including Problem Solving.
- Endorsed by OCR for use with Mathematics GCSE Specification B - Full coverage of the topics required by the tiers of the course - Appropriate questions and revision activities - Dedicated student books, teacher's resources, homework books, and online digital assessment and resources. |
...
Show More introduction of graphing lines in a rectangular coordinate system and functions in Chapter 3. This organization provides readers/students with increased exposure to basic graphing and function concepts, an integral part of later mathematics courses, as they study polynomial, rational, and radical expressions in Chapters 4-6. Chapters 8-10 provide comprehensive coverage of additional graphing and function |
You said it right there. It is a hoop/hurdle that satisfies the degree requirement. Of no use otherwise. It also eliminates a large percentage of students that can't relate to such absurd number/letter drills. Algebra does more damage than good as many highly talented and intelligent individuals lose out on higher education because of the algebra hurdle. It's called "The Wall" by administrators at my college because more students drop out due to the algebra requirement.
I'm glad you enjoyed it, but your ability to be a free thinker was not enhanced at all by the math. And I disagree that algebra is the language of science and research. Conveying ideas with unlimited imagination is how we progress in science and research. All scientists and mathematicians use machines to do the computations. So, subjecting all young students to the abuse of endless math drills serves no purpose whatsoever other than to steal time from more valuable learning, or to discourage students from enjoying their learning, or continue learning throughout life.
NCLB has squeezed the life and vitality out of our schools, and the obsessive attention to math and grammar is at the heart of our schools' failure. We can do so much better. Study number letter games on your own time if you love it so much. Do |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.