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Principles of TopTopology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. Customary topics of point-set topology include metric spaces, general topological spaces, continuity, topological equivalence, basis, subbasis, connectedness, compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces. In addition, the text introduces geometric, differential, and algebraic topology. Each chapter includes historical notes to put important developments into their historical framework. Exercises of varying degrees of difficulty form an essential part of the text.
Fred H. Croom is Professor of Mathematics at The University of the South, Sewanee, Tennessee. | 677.169 | 1 |
More college students use Amos Gilat's MATLAB: An Introduction with Applications than any other MATLAB textbook. This concise book is known for its just-in-time learning approach that gives students information when they need it.
MATLAB: An Introduction with Applications 4th Edition walks readers through the ins and outs of this powerful software for technical computing. The first chapter describes basic features of the program and shows how to use it in simple arithmetic operations with scalars. | 677.169 | 1 |
Math Bridge
Three items are added to Geometry section.
Length (Pythagorean theorem)
Area (Triangle, rectangle and circle)
Geometry with Algebra (Triangle figured by three linear functions)
Description
In this Math App, there are no words to explain except at index. So let me introduce the concept of Math Bridge in English. You can try free sample version on web.
This App is not Math itself, but Math-related supplemental program. Math can only exist when you are doing it as if your thinking exists when you think.
1. Calculation
In this App, there are three levels and one challenge mode in following calculations.
i) Addition:
ii) Subtraction:
iii) Multiplication:
iv) Division:
After every five questions, quick review is set to check right and wrong. All four challenge modes for calculations have a five seconds timer to answer the question. They are difficult but concentration can enable us to get right answers.
5 Differentiation
In calculus, a branch of mathematics, the derivatives is a measure to know how a function changes as its input changes. (from wikipedia)
In this App, you can find points of extreme by a quadratic derivative in trinomials.
6 Integration
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. (from wikipedia)
In this App, you can learn the calculation of an area between quadratic function and linear function. At first, the cross-points of two functions are calculated by factoring and calculate the area by integration. Please touch screen to take steps.
An Orbit of thrown object as quadratic curve can be a bridge connected between the real world and math. Math is a tool as well as a world. The difference of the real world and a world is ambiguous, because we can't see the real world without a world, which is our own world. Math has a history over 3000 years as well as language, both of which are very powerful to explore the real world. Life may be a problem much more complex than math, but logic is useful for both of them. To handle logic or theory requires much energy in brain so that doing math is a good training for thinking about the world and life with your own logic. These can be reasons why we learn math. How about you?
Have fun!
ver 1.1
"Quadratic formula" and "Trinomial" are added in Equation.
In Quadratic formula, you can see the course from a general quadratic equation to the quadratic formula by 7 steps. The logic of four arithmetic operations and notion of equal is the basic skill.
In trinomial, you can solve cubic equations by factoring. Please note that plus and minus notations are needed to be cared for as well as calculating fraction. When f(a) = 0 in f(x)=0, it means that the "a" can be factored.
In this article we've tried to bring together games from a wide spectrum to give you the best chance possible of finding something within a genre you like: reaction, strategy, adventure, brainteaser...
Rebuild 2
Reclaim a city from the zombie hordes while managing supplies, housing and morale. Featuring new buildings, plotlines, characters, customizable survivors with skills and equipment, new & improved art and all new hidden endings to discover.
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iCars: On-Demand Chauffeur
iCars is a chauffeured "car" service ordered "in the moment" for one to 12 passengers – in and around San Francisco and to and from SFO (San Francisco International Airport).
iCars is your premier On-Demand Black Car service for luxury transportation made easy, when and where you need it! iCars is a unique application that allows you to immediatel…
Symmetry*
Symmetry* is simple yet sophisticated brain challenging puzzle game.
Each stage, only 1/4 of the symmetry pattern is revealed and it is your job to finish up the rest!
Sounds simple? Well, let's see.
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Tlaloc's Temple
Developper message : I didn't thought i'll got so many users from this very special niche game.
Thank you everybody who tried it and shared this adventure with me ! I stay on touch for your feedback to tell me what to change and improve !
Trapped in the temple of the Aztec's god of water, sadistics and cunning traps awaits you in the… | 677.169 | 1 |
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Description: The Bedside Book of Geometry is a fascinating, interactive guide to the history and uses of geometry. It contains clear and concise explanations of different geometric concepts, as well as profiles of key thinkers and their discoveries. A unique feature of the book is its simple, step-by-step exercises. Some of these have everyday applications, others are theoretical puzzles, but all are designed to challenge the reader and test their newly acquired knowledge. The perfect companion for beginners and experts alike, The Bedside Book of Geometry does not assume prior knowledge of the subject beyond basic numeracy skills. Its aim is to convey the basic elements of geometry to everyone, no matter what their level of mathematical | 677.169 | 1 |
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.
Hermann Weyl was among the greatest mathematicians of the twentieth century. He made fundamental contributions to most branches of mathematics, but he is best remembered as one of the major developers of group theory, a powerful formal method for analyzing abstract and physical systems in which symmetry is present. In "The Classical Groups," his most important book, Weyl provided a detailed introduction to the development of group theory, and he did it in a way that motivated and entertained his readers. Departing from most theoretical mathematics books of the time, he introduced historical events and people as well as theorems and proofs. One learned | 677.169 | 1 |
How to Solve Word Problems in Calculus by Eugene Don
Book Description
Word problems? NO problem!! Be prepared when you get to the word-problem section of your test! With this easy-to-use pocket guide, solving word problems in calculus becomes almost fun. This anxiety-quelling guide helps you get ready for those daunting word problems, one step at a time. With fully explained examples, it shows you how easy it can be to translate word problems into solvable calculus problems - and get the answers right! You get complete directions for solving problems commonly found in high-school and college text books. There's no word problem too tough for "How To Solve Word Problems in Calculus"! The sanity-saving features include: step-by-step approach to word problems; complete explanations of every step; fully explained answers; dozens of sample problems; problems of every type; and, skill-checking practice drill. If you don't have a lot of time but want to excel in class, this book helps you: brush up before tests; solve problems quickly; understand the material; and, master word problems without spending hours with lengthy textbooks. This is the book that solves word-problem problems!
Buy How to Solve Word Problems in Calculus book by Eugene Don from Australia's Online Bookstore, Boomerang Books.
Schaum's Outlines present all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your | 677.169 | 1 |
Summary and Info
For adult educators and researchers who want to get to the root cause of the difficulties adults can have learning math. With participation in A-level and higher education math courses in real decline, more adults are going to be facing difficulties in math. The book points out ways of reconceptualizing current debates in math education, to take into account psychological and sociological perspectives. The findings have practical applications in education and training, clarifying problems such as making learning relevant to life, and countering "math anxiety. It also highlights areas for further research in mathematical and numerate thinking and emotion, particularly among adults.
More About the Author
Jeff Evans (born 1960) is a British writer and journalist. He is the author the Good Bottled Beer Guide, and was the editor of the Good Beer Guide from 1991 to 1998. He has also written about television. | 677.169 | 1 |
Resource Added!
Type:
Description:
Comparing linear vs exponential growth and classifying all parts of a function.
Subjects:
Mathematics > General
Education > General
Education Levels:
Grade 9
Grade 10
Grade 11
Grade 12 2 Appropriate Pedagogy: 0
Reviewer Comments:
The professional baseball contract activity provides two scenarios involving salary options; one with linear growth and the other exponential growth. The student is tasked with deciding which contract is better for the given range. Students will need previous experience related to linear and exponential relationships. The activity provides for a variety of problem types; however, answer keys are not provided. This may be best used to review linear and exponential relationships.
Not Rated Yet.
Comparing linear vs exponential growth and classifying all parts of a function. | 677.169 | 1 |
Find a Macungie StatisticsAnalytical reading and writing can be a lot of fun, actually. Ultimately, my paradigm as a teacher will always be to make myself progressively unnecessary.An introduction to algebra includes topics such as linear equations, ratios, quadratic equations, special factorizations, complex numbers, gr... | 677.169 | 1 |
Linear Algebra with Applications (8th Edition)
Author:Steve Leon
ISBN 13:9780136009290
ISBN 10:136009298
Edition:8
Publisher:Pearson
Publication Date:2009-09-05
Format:Hardcover
Pages:552
List Price:$201.40
 
 
This thorough and accessible text–from one of the leading figures in the use of technology in linear algebra–gives readers a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer readers examples of how mathematics is used in the real world. This book stresses the important roles geometry and visualization play in understanding linear algebra. | 677.169 | 1 |
ISBN 9788126547432
ISBN-10
812654743X
Binding
Paperback
Number of Pages
932 Pages
Language
(English)
Subject
JEE
The Book Has Been Designed To Help The Students Overcome The Hurdles While Preparing For Jee In Terms Of Concepts And Problem Solving. The Book Offers A Unique Combination Of Authoritative Content And Stimulating Problems. This Book Includes Additional Topics And Sample Problems For Complete Coverage Of Jee Syllabus. It Also Includes Substantial Reasoning Type, Multiple Choice Questions And Unsolved Numerical Problems At The End Of Each Chapter With Answer Key. The Previous 7 Year Solved Jee Questions Are Included As Appendix In The Book. | 677.169 | 1 |
ISBN 9788177098471
ISBN-10
8177098470
Binding
Paperback
Number of Pages
217 Pages
Language
(English)
Subject
Educational: English language: readers & reading schemes
Mathematics Multiple Choice Question Bank by A. Das Gupta is designed to help students who are preparing to attempt entrance examinations for the IIT. The book includes various multiple choice questions in the subject of Mathematics and thus gives the reader an effective preparation and practice for the examination. Also included in the chapters are solutions and hints to make problem solving easy. The student will also find in the book, solved questions from the IIT JEE examinations as well as a sample question paper that can give them an effective practice for the test. | 677.169 | 1 |
MA 405 Test 3 Study Guide - MA 405 Test 3 - Study Guide...
MA 405 April 12, 2009 Test 3 - Study Guide The topics for Test 3 are covered in Sections 6.1 - 6.3, 5.1 - 5.5 in the textbook. Learning objectives: • define and compute eigenvalues, eigenvectors, eigenspaces; • recognize diagonalizable matrices; be able to write a diagonalizable matrix as A = PDP-1 , for some invertible matrix P and diagonal matrix D ; use it to compute powers of A . • apply the dot product, and use its properties; relationship between the dot product and matrix mul-tiplication; • identify orthogonal subspaces; define the orthogonal complement of a vector space; • define the four fundamental subspaces associated with a matrix; identify the relationship between them; compute the basis for each; use their properties; • calculate the least-squares solution of an inconsistent linear system; compute the residual and the projection of a vector onto a subspace on R n ; calculate the equation of a line/parabola that best fits a given set of data; • inner product spaces; definitions and properties; be able to check that an operation is an inner product; • identify orthogonal/orthonormal sets of vectors in an inner product space; • calculate the coordinates of a vector with respect to an orthogonal/orthonormal basis; • identify orthogonal matrices and use their properties; 1
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Practice Questions 1. Consider the matrix A = 2 3 0 4 3 0 0 0 6 . (a) Find the eigenvalues of A . (b) Find bases for the eigenspaces corresponding to each eigenvalue of A . (c) Check that A is diagonalizable. Find the invertible matrix P that diagonalizes A and the diagonal matrix D which is similar to A, that is, P-1 AP = D . (d) Use part (d) to calculate
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Real Numbers
Learn to perform operations with integers (positive and negative numbers).This course covers algebraic topics including integers and real numbers, number lines, the order of operations, square roots, absolute value, and inequalities. The course curriculum aligns to content that is common to most high school algebra 1 courses as well as college level developmental mathematics. Content is taught through interactive video lectures that include guided practice problems and the associated live action solutions. The curriculum is organized into 2 chapters (sections), containing a total of 19 video lectures that are approximately 10 minutes in length each. The course culminates with end of chapter assessments to check for skills mastery. Answer Keys are included for all assessments. The instructor for this course is a certified math instructor with over 10 years of middle school, high school, and college level teaching experience.
This course is one part of our comprehensive Beginning Algebra course.
What are the requirements?
A scientific calculator would be helpful, but not required.
What am I going to get from this course?
Differentiate between the different sets of real numbers
Use a number line to identify the value of real numbers
Understand the concepts of absolute value, exponents, and square roots
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Instructor Biography
I have been using projects, games, cooperative learning, and interactive activities to teach mathematics at the middle school, high school, and college levels for the last 8 years.
I run a highly interactive classroom that promotes student participation and critical thinking. In a typical class period (my class periods are 100 minutes long), I generally limit my speaking time to two-20 minute sessions. These sessions are broken up by class projects, assignments, and explorative activities that engage the students with the material (often in small group settings).
-State of Florida Star teacher award
-2 x teacher of the month (HS)
-Rookie Teacher of the year (HS)
-High School Student Learning Gains 83%-89% each year
-Foundation Grant 2008, 2009, 2011, 2012
-Lockheed Martin Academy Grant 2006-2008
Florida International University (BBA Finance)
University of Central Florida (MA Math Education)
The Florida State University (Institutional Research Graduate Certificate) | 677.169 | 1 |
Description:
This algebra lesson from Illuminations lets students gain experience solving problems using systems of equations. The example problem provided has one solution, but multiple variations may be used to derive the answer. A student activity sheet is included. The lesson is intended for grades 9-12 and should require 1 class period to complete. | 677.169 | 1 |
ISBN 9788186734254
ISBN-10
8186734252
Binding
Paperback
Edition
2nd
Number of Pages
178 Pages
Language
(English)
Subject
Crime & criminology
Master Math: Algebra makes the transition from pre-algebra smooth and stress-free. This math reference guide makes learning and understanding algebraic equations, inequalities, polynomials and linear equations as simple as ?two plus two.? Well, may be more like ?five squared.?
Topics covered include:
Solving systems of linear equations
Translating problems into algebraic equations
Solving simple algebraic equations
Understanding Coordinate systems and graphing equations
Adding polynomials
Learning will never be easier-simple step-by-step procedures and solutions, concrete examples and applications, concise definitions of terms and a detailed description of techniques. You will soon be pusing your calculator aside.
About the Author
Debra Anne Ross has a double BA in Chemistry and Biology from the University of California, Santa Cruz, and an MS in Chemical Engineering from Stanford University.
Table of Contents
Introduction
I Translating Problems into Algebraic Equations
Introduction to algebra
Translating English into algebraic equations
Algebra terminology
Simple word problems
II Simplifying Algebraic Equations
Commutative, associative and distributive properties of addition and multiplication
Using associative and distributive properties
Combining like terms in algebraic equations
Simplifying algebraic equations by removing parenthese and combining like terms
The general order to perform operations in algebra
III Solving Simple Algebraic Equations
Sovling algebraic equaions that have one unknown variable
Solving simple algebraic equations containing fractions
Solving simple algebraic equations containing radicals
IV Algebraic Inequalities
Solving algebraic inequalities with one unknown variable
V Polynomials
Definitions
Addition of polynomials
Substraction of polynomials
Multiplication of polynomials
Division of polynomials
Factoring polynomials with a common monomial factor
Factoring polynomial expressions with the form ax2+bx+c
VI Algebraic Fractions with Polynomial Expressions
Factoring and reducing algebraic fractions
Multiplication of algebraic fractions
Division of algebraic fractions
Addition and substraction of algebraic fractions
VII Solving Quadratic Polynomial Equations with One Unknown Variable
Defining and solving quadratic (polynomial) equations
Using factoring to solve quadratic equations with one unknown variable
Using the quadratic formula to solve quadratic equations with one known variable
Using the square root method to solve quadratic equations with one unknown variable
Using the method of completing the square to solve quadratic equations with one unknown variable
VIII Solving Systems of Linear Equations with Two or Three Unknown Variables
Solving systems of linear equations with two or more unknown variables
Using the elimination method to solve systems of linear equations with two unknown variables
Solving systems of three linear equations with three unknown variables
Using the elimination method to solve systems of three linear equations with three unknown variables
Using the substitution method to solve systems of three linear equations with three unknown variables
Using the matrix method to solve systems of three linear equations with three unknown variables
IX Working with Coordinate Systems and Graphing Equations
Introduction and definitions
Graphing linear equations
Slope of a line
Graphs of the equations for the parabola
Graphing quadratic equations
Using graphing to solve quadratic equations
Using graphing to solve two linear equations with two unknown variables
Examples of other equations forms that graph to shapes on a coordinate system
Index
Appendix Tables of Contents of First and Thrid Books in the Master Math Series | 677.169 | 1 |
Monica Neagoy
Monica Neagoy
is author of Planting the Seeds of Algebra, PreK-2: Explorations for the Early Grades and the creator of three innovative mathematics video series on algebra for teachers and students. Monica Neagoy, PhD, has built her career in mathematics but her experience has also included university teaching, specialist training, professional development, live television courses, video creation and hosting, and serving as an international consultant and popular keynote speaker. She has also taught at Georgetown University in the mathematics department, served as program director at the National Science Foundation, and consulted with many US school districts, national, and international organizations. She has had a parallel career in theater as actor, choreographer and stage director, particularly with the professional LE NEON Theater in the Washington, D.C. area | 677.169 | 1 |
Offering a uniquely modern, balanced approach, Tussy/Gustafson/Koenig's BASIC MATHEMATICS FOR COLLEGE STUDENTS, Fourth Edition, integrates the best of traditional drill and practice with the best elements of the reform movement. To many developmental math students, mathematics is like a foreign language.
This book aims at restructuring some fundamentals in measure and integration theory. It centers around the ubiquitous task to produce appropriate contents and measures from more primitive data like elementary contents… | 677.169 | 1 |
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Be sure that you have an application to open this file type before downloading and/or purchasing. How to unzip files.
4 MB | N/A pages On the other hand, I DO INCLUDE a "READ ME FIRST" text file giving what has worked well for me.
The Pre-Algebra A course that I teach to at-risk secondary students has been significantly honed over 8 years. This is the first unit of a 2-semester course that has proven to be valuable over this timeframe.
This unit concerns the 3 properties of numbers and has several practice problems as well as conceptual problems and practical uses of the 3 properties. I GREATLY ENCOURAGE MENTAL MATH TECHNIQUES STARTING WITH THIS-THE FIRST-UNIT (simplest) problems that basically provides you with a preview of each of the skills.
NINE skill areas included: 7 3rd grade skills and 2 6th grade skills. The skills themselves are simply subsets of CC Standards. The very last skill is one aimed at understanding the somewhat mythical problem faced by Gauss when he, himself, was in elementary school!
Admittedly, you need to come up with unique and interesting ways to approach this material. It is CRUCIAL to the students' grasp of mathematics--trust me. I, myself, have experimented with all kinds of approaches.
THREE worksheets are provided: one with 10 problems per skill; one with 20 per skill; and one with 30 per skill. You decide which is best for you.
SIX quizzes (all with 20 problems each) are provided: TWO at a level 2 (not too hard); TWO at a level 3 (harder); TWO that are a mix of level 2 and 3 problems (I personally use these a lot). | 677.169 | 1 |
This volume is intended to help graduate-level students of Continuum Mechanics become more proficient in its applications through the solution of analytical problems. Published as two separate books — Part I on Theory and Problems
Computer algebra systems have revolutionized the use of computers within mathematics research, and are currently extending that revolution to the undergraduate mathematics curriculum. But the power of such systems goes beyond simple algebraic or numerical manipulation. In this practical resource Roman Maeder shows how computer-aided mathematics has reached a level where it can support effectively many of the computations in science and engineering. | 677.169 | 1 |
About
Overview
Maple is a powerful software tool for mathematical computations and visualization. The goal of this manual is to introduce Maple to students who are taking first year calculus. As such, Maple is a tool to solve problems that are too difficult to solve by hand. In addition, students will improve their understanding of the concepts of calculus. The order of the material is organized by computational topic and should be suitable for most texts on Single Variable calculus.
Features and Benefits
This manual was originally written in the spring of 1995 with Maple V Release 3 and was independent of any particular textbook. Subsequent editions were modified to match various editions of the Calculus textbooks by James Stewart. The current edition is again independent of any particular textbook. In each edition, the files were originally written as Maple worksheets and then exported as LaTeX files in order to ensure that no errors (hopefully) were made in transcribing Maple output into the text.
The projects are generally ordered according to calculus topic required. | 677.169 | 1 |
Find a HawthorneIt is important in any level of math to have the skills to complete each section in their math book. I | 677.169 | 1 |
Predictive Analytics For Dummies, 2e willhelp the you understand the core of predictive analytics and get started putting it to use with readily available tools to collect and analyze data.You will learn how to incorporate algorithms through discovering data models, identifying s ...
This new book from the author of 'The Music of the Primes' combines a personal insight into the mind of a working mathematician with the story of one of the biggest adventures in mathematics: the search for symmetry.
The new Mathematics General syllabus describes two pathways that start in Year 11. Even though both pathways share a common Preliminary course, students taking each pathway have specific learning needs, so we have published two levels of text for both Years 11 and 12.
This volume features selected and peer-reviewed articles from the Pan-American Advanced Studies Institute (PASI). The chapters are written by international specialists who participated in the conference. Topics include developments based on breakthroughs in the mathematical under ...
Designed to introduce students in middle/upper primary to the mathematical concept of algebra, this book helps them to place it in everyday life. It provides activities and problems, which give students the confidence to reach beyond their current experience. It also includes a s ... | 677.169 | 1 |
Barron's Sat Subject Test Math Level manual opens with a diagnostic test that includes explained answers to help students pinpoint their math strengths and weaknesses. In chapters that follow, detailed topic reviews cover polynomial, trigonometric, exponential, logarithmic, and rational functions; coordinate and three-dimensional geometry; numbers and operations; data analysis, statistics, and probability; and graphing calculators, their operations and applications. Six full-length model test with answers, explanations, and self-evaluation charts conclude this manual. | 677.169 | 1 |
Featuring more than 200 illustrations, this practical, comprehensive resource presents complex operations and formulas in an easy-to-understand way and demonstrates how to incorporate helpful software tools into your daily | 677.169 | 1 |
Synopses & Reviews
Publisher Comments
Student tested and approved! If you suffer from math anxiety, thensign up for private tutoring with Bob Miller! Do sets, theorems, andequations leave your head spinning? If so, you are like hundreds ofthousands of other students who face math--especially, algebra--withfear. Luckily, there is a cure: Bob Miller's Clueless series! Like theteacher you always wished you had (but never thought existed), BobMiller brings a combination of knowledge, empathy, and fun to theoften-troubling subject of algebra. He breaks down the learningprocess in an easy, nontechnical way and builds it up again using hisown unique methods. "Basically, the Clueless books are my notes.Exactly the way I teach: friendly, clear...with some humor and plentyof emotion!!" Meant to bridge the gulf between the student, thetextbook, and the teacher, Algebra for the Clueless is packed with allthe information you need to conquer algebra. This extensive guidegives you: anxiety-reducing features on every page; easy-to-graspmethods that make algebra understandable; bite-sized math portionsthat fit short study sessions (and short attention spans); fullexplanations of basic principles to make hard problems easy; quicktips for solving difficult problems; . "I am always delighted when astudent tells me that he or she hated math...but taking a class withme has made math understandable...even enjoyable." Now it's your turn.Sharpen your #2 pencils, and let Bob Miller show you how to never beclueless again!
Synopsis
'A is for Algebra-and that\'s the grade you\'ll pull when you use Bob Miller\'s simple guide to the math course every college-bound kid must take
With eight books and more than 30 years of hard-core classroom experience, Bob Miller is the frustrated student\'s best friend. He breaks down the complexities of every problem into easy-to-understand pieces that any math-phobe can understand-and this fully updated second edition of Bob Miller\'s Algebra for the Clueless covers everything a you need to know to excel in Algebra I and II.'
Table of Contents
TO THE STUDENT
Chapter 1: Natural Numbers and Introductory Terms
Chapter 2: Integers Plus More
Chapter 3: First-Degree Equations
Chapter 4: Problems with Words: Why So Many Students Have Problems on the SAT | 677.169 | 1 |
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Unformatted text preview: lorida International University Florida International University Fall 2008 What are numerical methods? Numerical methods are used to solve mathematically posed problems (usually in the form of equations) that nnot be solved by analytical (exact by hand) cannot be solved by analytical ( exact , by hand ) methods. We could also refer to this course as numerical analysis But, this is not a course in math, at least not in the traditional sense hy do we need numerical Why do we need numerical methods; why are they relevant? Numerical methods are used every day in science, engineering, medicine, health, and businessthey are used to solve mathematical models of interacting chemical species, the llision f ars ultifunctional aterials ridges uffeted y collision of stars, multifunctional materials, bridges buffeted by high winds, groundwater pollution, a beating heart, spreading epidemics, and tomorrow's stock prices. Numerical methods are indispensable because the real world's behavior is almost always li t d d t d d t i l iffi lt too complicated t o understand, and certainly too difficult to predict accurately, by observation alone. In extreme cases, certain real world phenomena that need to be studied, such as nuclear explosions or ingestion of carcinogens by babies, do not permit systematic observation or even experimentation. Combined with intuition, experience, and data, the abstraction and generality of mathematics allow us to create models that can e nalyzed mputed ith d isualized be analyzed, computed with, and visualized. Historical Perspective...
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MCQs in Advanced Engineering Math Part I
Compiled MCQs in Advanced Engineering Math Part 1 of the series as one topic in Engineering Mathematics in the ECE Board Exam.
This is the Multiple Choice Questions Part 1 of the Series in Advanced Engineering Math topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.
Multiple Choice Questions Topic Outline
MCQs in Complex Numbers | MCQs in Mathematical Operation of Complex Numbers | MCQs in Matrices | MCQs in Sum of Two Matrices | MCQs in Difference of Two Matrices | MCQs in Product of Two Matrices | MCQs in Division of Matrices | Transpose Matrix | MCQs in Cofactor of an entry of a Matrix | Mcqs in Cofactor Matrix | MCQs in Inverse Matrix | MCQs in Determinants | MCQs in Properties of Determinants | MCQs in Laplace Transform | MCQs in Laplace transform of elementary functions
Online Questions and Answers in Advanced Engineering Math Series
Following is the list of multiple choice questions in this brand new series: | 677.169 | 1 |
Study and Solutions Guide for Algebra and Trigonometry, 6th
Here is an example of how to apply a trigonometric ratio. Registration in this course includes an electronic textbook. Let me mention two excellent books in order of my preference. Moosebutter's song "Uncle Earl's Hairpiece", which mostly contains lyrics about various bad things that have happened to the singer, contains the lyric: "My poor brain was pureed when I tried to do math..." How to dividing polynomials for dummies, ti 83+ emulator download, powers of fractions, Newton - Raphson for quadratic equations in three variables, how to teach mixed operation involving 1 and 2 bracketsfor year 4, least to greatest math fraction and decimal sheet.
Pages: 680
Publisher: Houghton Mifflin; 6th edition (January 27, 2003)
ISBN: 0618317848
A treatise on trigonometry. By Profs. Oliver, Wait and Jones.
Elements of Geometry, and Plane and Spherical Trigonometry. with Numerous Practical Problems
You can buy a personal copy of our site on CD, or browse our recommended book list. Math::Trig defines many trigonometric functions not defined by the core Perl which defines only the sin() and cos(). The constant pi is also defined as are a few convenience functions for angle conversions, and great circle formulas for spherical movement. The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cot are aliases) The arcus (also known as the inverse) functions of the sine, cosine, and tangent The arcus cofunctions of the sine, cosine, and tangent (acosec/acsc and acotan/acot are aliases) Algebra and Trigonometry. Custom Edition for California State University, Los Angeles. The 10th Century Persian mathematician Muhammad Al-Karaji worked to extend algebra still further, freeing it from its geometrical heritage, and introduced the theory of algebraic calculus. Al-Karaji was the first to use the method of proof by mathematical induction to prove his results, by proving that the first statement in an infinite sequence of statements is true, and then proving that, if any one statement in the sequence is true, then so is the next one The food of the Elevation and Depression 2: Mathematics is your food. Once set, the application presents questions that are generated randomly using the above criteria. As guidance, if the user is a kindergartener and wants to practice basic division facts, you might choose to start with one digit and may set your divisor limit to the same number say 4 to practice dividing by 4 (see the screenshot below) Logarithmic and trigonometric tables and mathematical formulas, (The University of Chicago. Mathematical series. The school of education. Texts and manuals). The University of Arizona Published in 2000, 99 pages Published in 1993, 501 pages Published in 2009, 362 pages Published in 1906, 75 pages Lucia Caporaso, et al. Cambridge University Press Published in 2012, 438 pages A "phasor" is a complex-number representation of an electrical quantity, such as voltage, current, or impedance. The ingredient of complex must be present in any definition of a phasor Findamentals Of Trigonometry. Note if you had tried to press the CE key to clear the incorrect + sign you are likely to have got rid of the 41 as well. It is always a good idea to precede any calculation by pressing the ON/C or all clear key and to remember to finish a calculation or part calculation by pressing the = key Trigonometry: With The Theory And Use Of Logarithms (1914).
He served as a Senior Policy Adviser at the USDOE from 2007-2009. Common Core replaces the traditional foundations of Euclidean geometry with an experimental approach. 2. Common Core excludes certain Algebra II and Geometry content that is a prerequisite at almost every four-year college. 3. Common Core fails to teach prime factorization. Consequently, CCS does not include teaching about least common denominators or greatest common factors. 4 Plane and Spherical Trigonometry and Four-Place Tables of Logarithms. Mathematics Describing the Real World: Precalculus and Trigonometry is your unrivaled introduction to this crucial subject, taught by award-winning Professor Bruce Edwards of the University of Florida Solutions Manual to Odd-numbered Exercises for Raymond A. Barnett's Analytic Trigonometry with Applications Fifth Edition. S-V. 1995. 0387943803 The reason that there are so many expositions of relativity with little more than algebra is that special relativity can be covered with little more than algebra. It is however rather subtle and deserves a lot of attention. (A literature professor would explain that the special relativity is a nuanced paradigm reflecting in essence Einstein's misogyny.) As to general relativity it can not be understood with little more than algebra By Ron Larson - Algebra and Trigonometry: 5th (fifth) Edition.
If 'X' = 1, then the vertical leg 'A' is the opposite side, and 'B' is the adjacent side. If 'X' = 2, then 'A' is adjacent and 'B' is opposite. Set A, B to the required leg lengths, then click the 'Update' button to refresh the diagram and calculations TRIGONOMETRY (College Level Examination Series) (Passbooks) (COLLEGE LEVEL EXAMINATION SERIES (CLEP)). An intensive program designed to assist in preparing students for college-preparatory mathematics. These academies provide interactive classes and activities that emphasize collaboration, creative thinking, and logical reasoning Ie Trigonometry 7e. An openness to more recent research findings, especially in the case of Indian and Chinese mathematics, is sadly missing" [81] The historian of mathematics, Florian Cajori, suggested that he and others "suspect that Diophantus got his first glimpse of algebraic knowledge from India." [82] However, he also wrote that "it is certain that portions of Hindu mathematics are of Greek origin". [83] More recently, as discussed in the above section, the infinite series of calculus for trigonometric functions (rediscovered by Gregory, Taylor, and Maclaurin in the late 17th century) were described (with proofs) in India, by mathematicians of the Kerala school, remarkably some two centuries earlier Plane trigonometry with tables, (Addison-Wesley mathematics series). The second difficulty has been to decide what preliminary mathematics should be included in the volume so that it may be intelligible to those students whose previous mathematical equipment is slight. The general aim of the volumes in the series is that, as far as possible, they shall be self-contained Trigonometry (with Digital Video Companion). Trigonometry - Shows visuals of basic functions. Trigonometry Lessons - A variety of lessons and quizzes by Joe Mercer. Trigonometry for Solving Problems - This lesson offers a pair of puzzles to enforce the skills of identifying equivalent trigonometric expressions. Additional worksheets enhance students' abilities to appreciate and use trigonometry as a tool in problem solving Understanding Trigonometry. | 677.169 | 1 |
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Algebra I Prerequisites It is of great importance that the student performs a serious introspective analysis concerning the weaknesses one may have in Algebra I and make amends as soon as possible! Algebra I & II will be your foundation for the rest of your High School and College Math, and it is not enough to "know", you must be proficient in all of the main points mentioned in next table.
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Cell Phones Cell Phones need to be turned off and placed inside the backpacks Failure to do this will result in cell phone to be taken away and returned at the end of classes upon receipt of students paper with 25 lines saying "Cell phones are not permitted in classroom" [ Never use pen in class ]
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Date Day P To CoverPeriods 1, 2 & 5 Q/THW 8/18 Mon 1 – Angles and Radian Measures 5.2 Right Angle Trigonometry HW Ex: /8 8/19 Tue 2 – 8/20 Wed 3 – - Announce a test on 5.1 for Wednesday Announce T 5.1 for Wednesday HW Ex: /6 8/21 Thu 4 – /22 Fri 5 – Review: Degrees vs. Radians – Have the class practice on Handouts 5.1a, b, c Introduce: Mr. Pit's Triangles and their applications – Angular & Linear Speed and Have the class practice on Handouts 5.1d in class – Announce a test on 5.1 for Tuesday Announce T 5.1 for Tuesday Q-1Trigonometry Honors Pacing Guide & Planning for Wk-1 [August 18-22] | 677.169 | 1 |
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Mathematics is a crucial part of everyone's life. One cannot do away by not studying mathematics. However, despite its importance, it is still considered the subject which is feared most in schools. Thus, it calls for immediate attention to look for causes which makes mathematics one of the most feared subject. One of the cause is learning difficulties in mathematics. Since, secondary level education is a stepping platform, thus learning difficulties at secondary level is an important topic of study. Learning difficulties not only reveal level and extent of student's knowledge about a concept, it also gives a framework to teachers to reflect upon their practices and act in consequence. Thus, this book makes an attempt to study learning difficulties in mathematics at secondary level and its plausible causes. I hope this book is equally helpful to parents, teachers and teacher educators. | 677.169 | 1 |
Precalculus
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Read More Pearson representative for more information. MyMath With this new edition, Mike Sullivan has developed MyMathLab features to help better prepare students and get them thinking more visually and conceptually. Features like Getting Ready exercises, Video Assessment exercises Enhanced Graphing Functionality and Skills for Success modules benefit student learning. Also, by implementing the New! Guided Lecture notes that focus students on the important concepts and help structure studying, students will have the most effective tools to succeed.
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Fair. Hardcover. Instructor Edition: Same as student edition but has free copy markings. SKU: 9780321979292-5Fine. Hardcover. Instructor Edition: Same as student edition but has free copy markings. SKU: 9780321979292-2Very good. Hardcover. Instructor Edition: Same as student edition but has free copy markings. SKU: 9780321979292Good. Hardcover. Instructor Edition: Same as student edition but has free copy markings. SKU: 9780321979292New. Hardcover. Instructor Edition: Same as student edition but has free copy markings. SKU: 9780321979292-1Fair. 0321979079Good in good dust jacket. 1168 p. Audience: College/higher education. Good condition-no marks or highlights-There is some tape on the cover as the book was previously used as an instructor edition., .-.-.
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Precalculus
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A Truly Dreadful Book
This is a truly dreadful book and I can't see how it would be helpful in terms of either algebra, trigonometry, or calculus! If you want to relearn calculus, and need to start from scratch, purchase Barbara Lee Bleau's "Forgotten Calculus" -- you won't be disappointed | 677.169 | 1 |
Characteristics of Graphs Practice
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0.17 MB | 4 pages
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This is a set of four graphs I created for my students to practice skills such as: domain, range, end behavior, asymptotes, relative & absolute maxiums & minimums, intercepts, intervals of increase & decrease. I found this to be a skill set my kids needed to practice regularly. By the fourth graph, I also threw in some average rate of change problems as well.
These sheets could be used as homework, quizzes (what I do--take best two out of four), practice sheets at a station, however you please | 677.169 | 1 |
math-1 - 1. Simplify each of the following expressions as...
Practice Problems on Required Mathematical Skills This problem set is designed to help you identify areas in which your mathematical skills might be weak. It is not designed to test every last skill you might need in this course. Nevertheless, it will give you an idea of the level of mathematics required in this course.
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Graph2Go Graph2Go is a special-purpose graphing calculator that operates for given sets of function expressions
sodBrain MathEasy SodBrain MathEasy is a brain-trainer that allows you to accelerate your brain by solving basic mathematical and logical problems | 677.169 | 1 |
Academics
Algebra 1 & 2
Algebra 1
This course provides the foundation for secondary mathematics study. Topics covered include algebraic expressions including polynomials and rational expressions, solving linear and quadratic equations, inequalities and systems of equations, and radicals and exponents. Emphasis is placed on problem solving and graphing.
Prerequisites: Pre-Algebra is recommended; this course may not be developmentally appropriate for students who have not yet reached the 8th grade.
Algebra 2
Algebra 2 is a college preparatory course which builds on the foundation of Algebra 1. Topics covered include: the Real and Complex Number Systems, solving equations and inequalities, and functions including linear, quadratic, exponential, logarithmic, and rational. Analytic geometry, sequences and series, statistics and probability, and matrices and determinants are also covered.
Algebra Refresher
This is a summer Algebra 1 refresher course intended for students who need to improve or refresh their Algebra 1 skills before entering Geometry or Algebra 2 in the fall. The course will generally follow the concepts taught in Algebra 1, but will involve material developed by the teacher for this specific application. Students who struggled with Algebra 1 last year and want to solidify their foundation or those who are a year removed from Algebra 1 and want to refresh their skills before the fall are both welcome. | 677.169 | 1 |
Graphs - Graphing and Data Tab Book
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This is a tab book that includes tally tables, frequency charts, data collection, all of the graphs, and a glossary. This is a great project for introducing a graphing unit or complete the booklet in sections as you teach each graph. The book gives an example and explanation of each graph. On the second and/or third page it challenges students to answer graphing questions, collect data, generate their own graph, or analyze information. When the booklet is complete it becomes a great reference piece. It is great for review or test prep in the spring! There are twenty-one pages in the booklet. I have included three sets; one color set, one gray scale set, and one black and white set. Print whichever fits your needs. The glossary is a great resource for understanding all of the graphing terminology as well as practice with reference | 677.169 | 1 |
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Mathematical Knowledge has become such an essential reqiurement to cope with the modern life trends and the work demands. Employers need workers who can readily adapt to the technological world and be more productive. Teachers, who teach mathematics have to ensure that their learners are well equiped with mathematical knowledge that they teach them. This book contains information that mathematics teachers need in order to be effective teachers. It is a must read for all mathematics teachers. | 677.169 | 1 |
Math Study Guide III
4.11 - 1251 ratings - Source
This tri-fold laminated reference guide is a valuable tool for both students who are studying level 7th grade math as well as for thier teachers related to curriculum.This tri-fold laminated reference guide is a valuable tool for both students who are studying level 7th grade math as well as for thier teachers related to curriculum.
Title
:
Math Study Guide III
Author
:
Bar Charts, Joe Casbarro, Helene Hanson
Publisher
:
Dude Publishing - 2010-01-01
ISBN-13
:
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241lab - Lab Suggestions for Calculus I, Math 241/251...
Lab Suggestions for Calculus I, Math 241/251 Getting Started. Introduce the students to the basics of DfW. Open the program, explain what you see, big white work page, line where you enter expression, pull down menus, tool bar, and special character pads. Next you can start doing things. Entering expressions and operations: 1. 3 + 5, enter, then simplify. 2. 1 / 3, enter, then show the difference between simplify and approximate. 3. Simplify (-1) 1 / 3 and solve x 3 =-1. 4. Enter x 3-a 3 x-a , illustrate the need of parentheses to get exactly this expres-sion. Notice, when you simplify the program performs a long division. 5. Square roots can be entered using the special character pad, or using the function sqrt .E v e n√x - √ax - a and x 1/3 - a 1 /3x - a are simplified by long division. 6. Mention the mathematical constants π , the Euler number e ,andthe factor ◦ = π/ 180 for converting degrees into radians on the pad for special characters. 7. Enter the equationx3 - 5x2 -x + 5 = 0, and find its solutions al- gebraically using the command solve . You can solve other equations numerically. 8. DfW knows a lot of functions. Just type sin x ,tan x ,andy ouhav e the function to work with. The inverse functions are denoted by, e.g., asin x . You can find a long list of functions by going to the help index under Functions, Derive Functions. 9. You can use the substitute command to replace a variable by anything of your choosing. So, if you substitute a number, then you can evaluate a function at a point. 10. The program will implement some identities when you simplify, e.g., sin 2 x+cos 2
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Basic graphing: 1. Open a graphing window by clicking on the button with the sine curve on the tool bar. Click on Window, and tile vertically. Then you will have your algebra window and a graphing window. 2. In the algebra window, highlight a function which you like to graph, click on the button with the sine curve at the top of the graphing window. You will see the graph of the function. 3. Use the zoom buttons for zooming in and out, one direction at a time, or both. 4. You can make a specific point the center of the graphing window, click on the point, then the appropriate button on the tool bar. 5. Toggle between the regular and the tracing mode (F3 key or appropriate button on the tool bar), and explore tracing. 6. For a given function, you might use the tracing mode to find the coor-dinates of a point, the zeros, or extrema. 7. You can graph function, and you can graph the solutions of an equation in two unknowns. Try the hyperbola x 2-y 2 = 1, or other equations of your choice. 8. You can graph in the cartesian plan (default), or you can use polar
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Get A* in GCSE Maths (Quadratic equations and graph)
make you solve maths problem easily with direction a exam oriented course, which mean it will focus on the type of questions within GCSE syllabus. You will feel maths is easy and build your confidence to face the examinations.
We will focus on the topic of quadratic graph and equations, here we will learn different methods to solve the quadratic equations, we will also show you how to use your calculator correctly and some mistakes that you should beware of. More importantly, we will show you the technique to solve the equations with steps and know the how the quadratic graph look like fast.
Transformation of graph may make you feel frustrated, especially with sine curve and cosine curve. Just to remember some main point will make your life easy.
What are the requirements?
Have ambitious to get A* in edexcel maths
What am I going to get from this course?
learn to think with direction in order to solve the maths problem easily
write steps in special orders to reduce the careless mistakes
how to know the quadratic graph look like before you draw.
How to solve the quadratic equations fast but with steps
How to transform the graph easily without any hesitation
What is the target audience?
This course is meant to anyone who want to seek a high score in gcse maths. This course is specified on the quadratic graph and equation, if you have problems on this topics, this is a good course for you | 677.169 | 1 |
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PRE Lesson 1.1-Tools of Algebra Objectives: To review the set of Real Numbers To review the properties of Algebra To understand interval and set notation.
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SETS & ELEMENTS A set is a collection of objects. - the objects are called the elements of theset. If S is a set, the notation of means that a is an element of S.
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means that b is not an element of S. Ex1. If Z represents the set of integers, then but
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NOTATION OF SETS The set A that consists of positive integers less than 7 Braces { } Set-builder notation – "A is the set of all x such that x is an integer and " Interval notation – Is a way to write the domain and the range. (0,7) | 677.169 | 1 |
Precalc Problems Explained
By Chris Thiel
To listen to an audio podcast, mouse over the title and click Play. Open iTunes to download and subscribe to podcasts.
Description
A video podcast that show how to solve algebra, trigonometry and other skills needed to enroll in Calculus
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Description
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Price
1
CleanVideoAngles and Radians
Find out how to convert fractions of a degree with Degrees, minutes and seconds, and enter the wonderful world of the radian. I have a some examples of how to convert from degrees to radians and back again, as well as angular and linear speed using radia
Video at Archive.org Video at YouTube Solving for an unknown in the exponent requires logarithms! 19 Problems are explained that involve graphing and the properties of exponents and logarithms, as well using your graphing calculator
Here we have basic angles in radians, and graphing the trig functions of these angles. These functions, with their ability to transform waves with different periods and amplitudes, can be used to mathematically express all sorts of waves we find in real
The old dice game "Farkle" is explained and probabilities are discussed. Special "Thank You"'s go to Br Jack, Br Chris, and all my Christian Brother buddies at Camp La Salle! See for a written summary of the rules | 677.169 | 1 |
variable on both sides
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0.21 MB | 17 pages
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This powerpoint is used to provide students with the foudational understanding of Algebra1. Its is Do Now Direct Instruction Guided Practice format. There a three opportunity to write about Algebra and display their conceptual understanding. Student in this are pushed to truly understand the concept so that they hold this learning for the challenges to come | 677.169 | 1 |
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43210 In addition to level 3, students make connections to other content areas and/or contextual situations outside of math. Students will construct, compare, and interpret linear and exponential function models and solve problems in context with each model. - Compare properties of 2 functions in different ways (algebraically, graphically, numerically in tables, verbal descriptions) - Describe whether a contextual situation has a linear pattern of change or an exponential pattern of change. Write an equation to model it. - Prove that linear functions change at the same rate over time. - Prove that exponential functions change by equal factors over time. - Describe growth or decay situations. - Use properties of exponents to simplify expressions. Students will construct, compare, and interpret linear function models and solve problems in context with the model. - Describe a situation where one quantity changes at a constant rate per unit interval as compared to another. Students will have partial success at a 2 or 3, with help. Even with help, the student is not successful at the learning goal. Focus 8 Learning Goal – (HS.N-RN.A.1 & 2, HS.A-SSE.B.3, HS.A-CED.A.2, HS.F-IF.B.4, HS.F- IF.C.8 & 9, and HS.F-LE.A.1) = Students will construct, compare and interpret linear and exponential function models and solve problems in context with each model.
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Simple interest: I=prt I = interest p = principal: amount you start with r = rate of interest t= time in years
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If you invest $3,000 at 5% for one year, how much will you make for the year? I = prt = 3000 0.05 1 = 150 You made $150 for the year. | 677.169 | 1 |
courses in College Algebra, Algebra and Trigonometry, Trigonometry, and Precalculus. A proven motivator for students of diverse mathematical backgrounds, this text explores mathematics within the context of real-life, using understandable, realistic applications consistent with the abilities of any student. Graphing techniques are emphasized, including a thorough discussion of polynomial, rational, exponential, and logarithmic functions and conics. The use of a graphing calculator is optional. | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
Tuesday, 6 October 2015
NDA Syllabus
NDA Syllabus 2016 :Candidates
who are preparing for UPSC NDA / NA Entrance Exam they must have to know the
complete NDA Syllabus for the
right preparation. Here on this page of we are providing you complete
information about of the UPSC NDA/NA Entrance Exam Syllabus. Contenders
must have a look below and start their preparation according to the syllabus.
UPSC
NDA/NA Entrance Exam Syllabus
In
NDA Written Exam there are two objective type question papers.
The first paper is of mathematics (300 Marks)
The second one is of general ability contains English-200
marks and GK- 400 Marks.
NDA Syllabus
In
the mathematics portion exam paper contains the following sections. The student
must practice carefully for all the sections:
Sections
Concepts
Algebra
Concept of a set,operations on sets,Venn diagrams. De Morgan laws,
Cartesian product relation,equivalence relation,Representation of real numbers on a line,Complex numbers – basic properties,modulus argument,Cube roots of unity,Binary system of numbers,Conversion of a number in decimal system to binary system and vice-versa.,Arithmetic,Geometric and Harmonic progressions,Quadratic equations with real coefficients,Solution of linear inequations of two variables by graphs,Permutation and Combination,Binomial theorem and its application,Logarithms and their applications.
Matrices and Determinants
Types of matrices,Operations on matrices,Determinant of a matrix
Basic properties of determinants,Adjoint and inverse of a square matrix,Applications – Solution of a system of linear equations in two or three unknowns by Cramer's rule and by Matrix Method.
Trigonometry
Angles and their measures in degrees and in radians,Trigonometrical ratios,Trigonometric identities Sum and difference formulae,Multiple and Sub-multiple angles,Inverse trigonometric functions,Applications – Height and distance ,Properties of triangles.
Analytical Geometry of two and three dimensions
Rectangular Cartesian Coordinate system,Distance formula,Equation of a line in various forms,Angle between two lines,Distance of a point from a line,Equation of a circle in standard and in general form,Standard forms of parabola,Ellipse and hyperbola,Eccentricity and axis of a conic
Differential Calculus
Concept of a real valued function – domain,range and graph of a function,Composite functions,Derivative of function at a point,Derivatives of sum,Product and quotient of functions,Derivative of a function with respect of another function,Derivative of a composite function,Second order derivatives,Increasing and decreasing functions,Application of derivatives in problems of maxima and minima.
Integral Calculus and Differential Equations
Integration as inverse of differentiation,Integration by substitution and by parts,Standard integrals involving algebraic expressions,Trigonometric,Exponential and hyperbolic functions,General and particular solution of a differential equation
Vector Algebra
Vectors in two and three dimensions,Magnitude and direction of a vector,Unit and null vectors addition of vectors,Scalar multiplication of vector
Physical Properties and States of Matter,Mass,Weight,Volume,Density,Specific,Gravity
Principle of Archimedes,Pressure Barometer.
Motion of objects,Velocity and Acceleration,Newton's Laws of Motion,Force and Momentum,Parallelogram of Forces,Stability and Equilibrium of bodies,Gravitation,elementary ideas of work,Power and Energy.,Effects of Heat,Measurement of temperature and heat,change of State and Latent Heat,Modes of transference of Heat.,Sound waves and their properties,Simple musical instruments.,Rectilinear propagation of Light,Reflection and refraction.,Spherical mirrors and Lenses.,Human Eye.,Natural and Artificial Magnets,Properties of a Magnet,Earth as a Magnet.,Static and Current Electricity,conductors and Non-conductors,Ohm's Law Simple Electrical,Circuits,Heating,Lighting and Magnetic effects of Current,Measurement of Electrical Power,Primary and Secondary Cells,Use of X-Rays.
Physical and Chemical changes.,Elements Mixtures and Compounds Symbols Formulae,Simple Chemical Equations Law of Chemical Combination (excluding problems).,Properties of Air and Water.,Preparation and Properties of Hydrogen Oxygen Nitrogen and Carbondioxide Oxidation and Reduction,Acids bases and salts.,Carbon – different forms.,Fertilizers Natural and Artificial,Material used in the preparation of substances like soap Glass Ink Paper Cement Paints Safety Matches and Gun-Powder.,Elementary ideas about the Structure of Atom Atomic Equivalent and Molecular Weights Valency.
History Freedom Movement
Broad survey of Indian History with emphasis on Culture and Civilisation.,Freedom Movement in India.
Elementary study of Indian Constitution and Administration.,Elementary knowledge of Five Year Plans of India.,Panchayati Raj Co-operatives and Community Development.,Bhoodan Sarvodaya National Integration and Welfare State Basic Teachings of Mahatma Gandhi.,Forces shaping the modern world,Renaissance Exploration and Discovery
War of American Independence,French Revolution,Industrial Revolution and Russian Revolution.,Impact of Science and Technology on Society.,Concept of one World United Nations Panchsheel Democracy.,Socialism and Communism.,Role of India in the present world.
Geography
Earth its shape and size.,Latitudes and Longitudes ,Concept of time.,International Date Line.
Movements of Earth and their effects.,Origin of Earth.,Rocks and their classification,Weathering
Mechanical and Chemical Earthquakes and volcanoes.,Ocean Currents and Tides,Atmosphere and its composition;Temperature and Atmospheric Pressure Planetary Winds cyclones and Anti-cyclones,Humidity,Condensation and Precipitation,Types of Climate.,Major Natural regions of the World.,Regional Geography of India,Climate Natural vegetation.,Mineral and Power resources,Location and distribution of agricultural and industrial activities.,Important Sea ports and main sea land and air routes of India.,Main items of Imports and Exports of India.
Knowledge of Important events that have happened in India in the recent years.,Current important world events.,Prominent personalities – both Indian and International including those connected with cultural activities and sports.
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may check any other career related information through visiting our web portal
privatejobshub.in like latest job openings, admissions, admit card, entrance
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package contains the following components: -0321652797: Using and Understanding Mathematics: A Quantitative Reasoning Approach -0201716305: MathXL (12-month access) | 677.169 | 1 |
Assuming only calculus and linear algebra, Professor Taylor introduces readers to measure theory and probability, discrete martingales, and weak convergence. This is a technically complete, self-contained and rigorous approach that helps the reader to develop basic skills in analysis and probability.
This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. | 677.169 | 1 |
Visualizing Sequences and Series
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1.05 MB | 12 pages
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This bundle contains 3 files: the primary file is a applet named "Series" that requires JAVA 8. "Series" in a dynamic and interactive way to introduce students to sequences and series, especially with respect to the convergence and divergence of the series. The applet promotes an inquiry-based learning approach, allowing students to create and explore series of their own creation. Also included in the bundle is a single page "User Guide to the 'Series' Applet." The final document contains a set of problems to get the students started exploring series, with a slight focus on geometric and p-series | 677.169 | 1 |
Holt McDougal Larson Algebra 2, Teacher's Edition
Cool Math.com Math Dictionary, games, math instruction practice, etc. Add the values in the next place, one at a time, to the previous sum, and keep track of the new sum each time. In 1912, First Year Algebra by Webster Wells and Walter W. Each issue also includes articles on real-world uses of math and how math is used in various careers. Teachers might take an existing question and turn it into an open question. I am writing them letters," Jamia, a rising seventh-grader, said of her goodbyes to administrators, teachers and friends.
Moran et al. (2006) indicated that multiple intelligences theory proposes viewing intelligence in terms of nine cognitive capacities, rather than a single general intelligence Real-Life Math for Algebra, Grade 9-12. There are other bits of information you also should give: The names of the texts for the course, your office hours, and any supplemental texts or materials you will use. Now that you have spent about twenty minutes on the nuts and bolts of the course, it is time to turn your attention to content Holt McDougal Larson Algebra 2, Teacher's Edition online. Algebraic topology, including the fundamental group, covering spaces, homology and cohomology. Homotopy or applications to manifolds as time permits. Prerequisites: Math 100A-B-C and Math 140A-B-C. Introduction to varied topics in topology Mathsworks for the CSF Teacher's Book Teacher's book. Provide a meaningful context for the concept/skill or problem solving strategy (e.g. word or story problem suited to the age and interests of your students. Invite parents/family members of your students or members of the community who work in an area that can be meaningfully applied to the concept/skill or strategy and ask them to show how they use the concept/skill/strategy in their work English Composition Book 2 (Bk. 2). The program takes seriously the need for students to develop a balance of conceptual understanding, procedural fluency, and the ability to use mathematics in real-world contexts. Its instructional approach is based on a small but powerful repertoire of teacher moves, adapted to different learning goals download Holt McDougal Larson Algebra 2, Teacher's Edition pdf. Is th Using the classroom environment and the demographics created in Week Two, the instructional strategies that align with the CCSS in the blog created in Week Three, the unit plan created in Week Four, and the summative assessment created in Week Five, you will create the framework for a TPACK lesson plan Physics. In contrast to a classroom whose main activities are listening to the teacher and filling out worksheets, such a learning environment is distinguished by students "sitting in groups, discussing ideas, doing experiments, making diagrams, using concrete objects to test their conjectures, following blind alleys, and now and then experiencing the satisfaction of discovering something they did not know before."[17] Several features of such classrooms should sound quite familiar by now epub.
Play a game where you and your students try to "catch" each other making a mistake or leaving out a step in the process. Select the appropriate level of understanding to model the concept/skill or problem solving strategy (concrete, representational, abstract). Ensure that your students have the prerequisite skills to perform the skill or use the problem solving strategy Every-Day-of-the-School-Year Math Problems (Grades 3-6). The Common Core Standards, which have been adopted by most states since 2011, adopt such a mediating position for curricula, requiring students to achieve both procedural fluency and conceptual understanding. The Common Core does not endorse any particular teaching method, but does suggest students solve word problems using a variety of representations. Most of these organizations are critical of reform mathematics and have given poor reviews to textbooks such as Investigations in Numbers, Data, and Space, Mathland and Core-Plus Mathematics Project because they do not follow traditional methods Multi-Sensory Math Sequencing (Readingby6). Among the concerns are the lack of references to students with disabilities in the [NCTM] Standards document, lack of research related to the [NCTM] Standards, and overall vagueness of the document Essential Mathematics VELS Edition Year 8 Homework Book. During the next class, the instructor uses a projector to show the class selected answers as a way to guide the lessons each class period Using Counters to Show Subtraction - Teacher Edition. We are at a time when our curriculum and our instruction speaks in the language of inquiry, constructivism, and active learning while many of our assessment methods listen only to the rapid recall of isolated facts. Mathematics teachers experience a schizophrenic situation when they attempt to utilize instructional resources that reflect the NCTM Standards and, at the same time, prepare students for the multiple-choice tests that make up many state assessment systems Math Games, Grade 8. The tutorials are outstanding in explaining concepts that students often struggle with." "Our son was failing algebra, and we had almost given up hope. Your software program made all the difference. Now math is his favorite subject!" "The MathTutor series is the best educational investment we have ever made Games in the Teaching of Mathematics (Cambridge Primary Mathematics).
Mathematics instruction, like other forms of educational teaching, has undergone significant changes in the early part of the 21st century. These changes have affected education levels from preschool to college and subjects as far ranging as art and physics. Though there has been a shift away from traditional education methods such as exposition to more student-led approaches such as constructivist learning, there is still an important place for the expository form of teaching in math education Eureka Math, A Story of Functions: Algebra I, Module 5: A Synthesis of Modeling with Equations and Functions. Math Methodology Instruction Essay: Page 1 114th Congress of the United States. (2015). Retrieved from Breaux, E. (2009). How the best teachers avoid the 20 most common teaching mistakes. Retrieved from Charles A Fourth Grade Math Book 1 Parent Edition - Homeschool Curriculum (Fourth Grade Homeschool Curriculum). Again, we start off the math model by using realistic objects. Once the child is similar with subtracting, we can proceed to using a more abstract representation. In this step, we replace the objects with blocks. In the final step, replace the individual blocks with larger blocks. This sets the foundation of all future problems where a child can just use the bigger blocks to present items that can be added or subtracted Groundworks, Reasoning About Measurement: Grade 3. For all students, the Standards place a greater emphasis on areas that traditionally have been emphasized for the gifted. All students are now expected to complete a core curriculum that has shifted its emphasis away from computation and routine problem practice toward reasoning, real-world problem solving, communication, and connections. "The Standards propose that all students be guaranteed equal access to the same curricular topics; it does not suggest that all students should explore the content to the same depth or at the same level of formalism" (NCTM, 1989, p. 131) Basketball Angles: Understanding Angles. Teachers, therefore, should do the following: Sound teaching usually begins with questions and phenomena that are interesting and familiar to students, not with abstractions or phenomena outside their range of perception, understanding, or knowledge. Students need to get acquainted with the things around them—including devices, organisms, materials, shapes, and numbers—and to observe them, collect them, handle them, describe them, become puzzled by them, ask questions about them, argue about them, and then to try to find answers to their questions Teaching Secondary Mathematics: Techniques and Enrichment Units (7th Edition). This article describes several teaching method options. Keep reading for more information on teaching methods. There are so many possible teaching methods that a single article can only skim the surface. So that's what we'll do here: an overview of some of the many possibilities for instructing students. One of the ways of clarifying, applying, or organizing knowledge is by means of an organizer Essential Skills: Math Grd 3 (Essential Skills (Teacher Created Resources)). Outstanding in this regard was the work of the Greeks, exemplified by Archimedes' solutions to numerous problems of quadrature, and the works of the Chinese mathematicians Liu Hui and Zu Chongzhi McDougal Littell Middle School Math California: Transparency Book Chapter 1 Course 1. | 677.169 | 1 |
Find a Kennesaw Algebra 2This algebra deals mostly with linear functions. Algebra 2 is a more advanced, more complex version of algebra 1. Here we get more involved with non-linear functions as well as imaginary and complex numbers | 677.169 | 1 |
Faculty
The mathematics faculty do research and write papers on algebra, combinatorics, dynamical systems, geometric knot theory, graph theory, logic, mathematical crystallography, mathematical biology, number theory, singularity theory, statistics and quantum logic. Within those fields, the research goes from the very abstract to the quite applied. Faculty also write textbooks, mount exhibits and build sculptures. There are a number of opportunities for students to participate in research projects for undergraduates and work as a grader or teaching assistant. | 677.169 | 1 |
Composition of Functions Coloring Activity
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Provide your Algebra 2 students with practice over finding the composition of functions including addition, subtraction, multiplication by a constant, multiplication, division and one function composed of another. Composition is written both as f(g(x)) and (f o g)(x).
This one-sided page provides 5 functions to work with and 12 questions for practice. Once the student finds the answer, they use a coloring key to color a tessellation design. Why not color something mathematical?! Key | 677.169 | 1 |
In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one | 677.169 | 1 |
excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introdu | 677.169 | 1 |
Resource Added!
Type:
Description:
CCSS Mathematics as aligned to Unit One as taught by Gateway STEM High School.
Subjects:
Mathematics > General
Mathematics > Algebra
Education Levels:
Grade 9
Grade 10
Keywords:
algebra 1CCSS Mathematics
Number and Quantity Strand
·N-Q-1:Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
·N-Q-3:Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
·A-SSE-1:Interpret expressions that represent a quantity in terms of its context.
·A-SSE-2:Use the structure of an expression to identify ways to rewrite it.
·A-CED-1:Create equations and inequalities in one variable and use them to solve problems.
·A-CED-2:Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
·A-CED-3:Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
·A-CED-4:Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
·A-REI-1:Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution.Construct a viable argument to justify a solution method.
·A-REI-3:Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
·F-IF-1:Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x.The graph of f is the graph of the equation y=f(x).
·F-LE-2: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). | 677.169 | 1 |
Step by Step Calculus 1 : Learn from scratch
Learn about Functions, Limits, Derivatives, Curve Sketching and more at your own paceCalculus one is the introductory course of Calculus as it covers all the essentials; From knowing what a function is to finding limits, taking derivatives, and sketching a given curve. This course is vital for any student wishing to pursue a degree in Science or Engineering.
For each topic that is covered in this course, I will start by giving a general introduction of concepts then I will move on to solve actual problems, because practice is definitely the best way to learn. I will conclude the course by introducing you to MATLAB which is a powerful tool, that allows you to graph curves, take derivatives and much more using few lines of code.
This course will be constantly updated and new material will be posted every now and then. And if you seek help I will be more than happy to answer your questions on the course page.
What are the requirements?
Have a general understanding of Algebra
What am I going to get from this course?
Manipulate Functions
Know how to find a limit
Know how to take derivatives
Know how to sketch a curve
Basic knoweldge using Matlab for curve sketching.
What is the target audience?
This course is meant for High school and/or College Students, or anyone interested in learning calculus really.
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Instructor Biography
Hello there my name is Bryant and I am 24 years old. I have a Bachelor of Science in Physics. Through out my college years I had the opportunity to be a tutor for about 2 years and what I learned from this experience is that the majority of students tend to be visual learners. This is why I have taken the opportunity to develop this online course trying my best through videos to teach calculus 1. My major has also helped me to know where to start teaching. | 677.169 | 1 |
Functions Foldable
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This foldable teaches students what is a function. It starts with an input/output function machine that defines the term function, then moves to a real world example (a vending machine) of a function vs. a "malfunction", then it discusses how to identify a function from a table and graph. This foldable also contains mapping diagrams.
Included is an animated PowerPoint that can be played in class to help the students fill out the foldable and a printable template with the image included. It is a great combo of having students take their own notes, but with a time-saving template | 677.169 | 1 |
MathAid Algebra II is a new Java-based package for e-learning and home schooling. It guides the user through all steps of the learning process, from theoretical concepts, examples, problem-solving lessons, and drills for customized tests including solutions and evaluation. The emphasis is on interactivity and "living" formulas; the unique graphics and animations bring life to the formulas and make learning and exploring math real fun. Topics covered include rectangular coordinate systems, functions and graphs, linear equations and inequalities, systems, polynomial and rational functions, exponents and radicals, complex numbers, quadratic functions, conic sections, exponential and logarithmic functions, sequences, and series. The demo version contains selected lessons from the full version and is fully functional, and all features are included.
Requirements:
Java (both SunJRE and MSJVM are supported)
Limitations:
Selected lessons only
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Other Windows Software of Developer «MathAid»:
SAT. Math Practice Highly interactive tutorials and self-test system for individual e-learning, home schooling, college and high school computer learning centers, and distance learning. The product emphasizes on building problem-solving skills. Tutorials include the reviewsSimple Complex Numbers Calculator This is a small program that can perform basic calculations with complex numbers. This includes adding, subtracting, multiplication, and division. The program can also convert a complex number from algebraic to trigonometric form and draw it on a complex c
Pi Generator The program generates Pi to a desired level of precision. It allows the user to save the data in a text file or to copy the data from the console window onto other programs. The user is also able to use a fast mode where the calculation is much faster butDynamics Explorer Dynamics Explorer is a dynamical systems research tool. It is a tool designed to let users explore dynamical systems, particularly focused on enabling mathematicians to improve the efficiency and quality of their research in the field of complex dynamics.
rSim A standalone Windows program that interactively simulates how the 95% confidence interval and statistical significance (probability) of the correlation coefficient vary as a function of sample size. Change r and N and watch the probability and confidence i | 677.169 | 1 |
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Practice makes perfect! Get perfect with a thousand and one practice problems! 1,001 Geometry Practice Problems For Dummies gives you 1,001 opportunities to practice solving problems that deal with core geometry topics, such as points, lines, ...
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1,001 practice opportunities to score higher in statistics 1,001 Statistics Practice Problems For Dummies takes you beyond the instruction and guidance offered in Statistics For Dummies to give you a more hands-on understanding of statistics. ...
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Relax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. This book is designed to showcase the beauty of mathematics - including images inspired by mathematical ...
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Leo Corry tells the story behind the idea of number, from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the ...
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The updated new edition of the classic and comprehensive guide to the history of mathematics For more than forty years, A History of Mathematics has been the reference of choice for those looking to learn about the fascinating history of ...
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Mathematics is a human endeavour of long standing and is deeply ingrained in Western philosophy and thinking. This illustrated book presents the science of mathematics in an innovative and engaging way. Its aim is to make maths more accessible ...
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A Panorama of Statistics: Perspectives, Puzzles and Paradoxes in Statistics Eric Sowey, School of Economics, The University of New South Wales, Sydney, Australia Peter Petocz, Department of Statistics, Macquarie University, Sydney, Australia ...
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Audio Book
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A funny and enlightening romp through the world of numbers with one of Australias best-loved broadcasters.By popular demand, Australias funniest and most famous mathematician is back with a brilliant new book. Adam Spencers World of Numbers ...
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Advanced Engineering Mathematics, 10th Edition is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self-contained subject matter parts for maximum flexibility. The new edition continues with the ...
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This market-leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self contained subject matter parts for maximum flexibility. The new edition continues with the tradition of providing ...
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Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of
ISBN: 9781848216167
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With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra I Essentials For Dummies provides ...
ISBN: 9780470618349
Binding: Paperback
$13.95
Your complete guide to acing Algebra II Do quadratic equations make you queasy? Does the mere thought of logarithms make you feel lethargic? You're not alone! Algebra can induce anxiety in the best of us, especially for the masses that have ... | 677.169 | 1 |
Inequalities with set builder and interval notations
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#1-6 Given graphs, write in set builder and interval notations, #7-12 given inequality, provide graph and write in set builder and interval notations, and #13-18, given interval, provide graph and set builder | 677.169 | 1 |
ISBN 9781905740543
ISBN-10
1905740549
Binding
Hardback
Edition
3rd
Number of Pages
190 Pages
Language
(English)
Subject
Medical genetics
This book is intended to suit mathematics courses for post-graduate students. It has been written by an author with 25 years experience of lectures on differential geometry, and is therefore designed to help the reader overcome the difficulties in understanding the underlying concepts of the subject. The book will also be useful for introducing the methodology of differential geometry to research students in associated disciplines; physics, engineering, biosciences and economics. The book is divided into 5 chapters - curvilinear co-ordinates, geometry of space curves, intrinsic geometry of a surface, fundamental formulae of a surface, curves on a surface - and each chapter contains numerous examples which are either worked out or given as an exercise in order to facilitate understanding. Finally the book concludes with a brief history of differential geometry. This book is an excellent text for post-graduate maths courses, and will also be of interest to all mathematicians. Contents: 1. CURVILINEAR COORDINATES 1.1 Curvilinear Coordinate System in E3 1.2 Elementary Arc Length 1.3 Length of a Vector 1.4 Angle betweenTwo Non-null Vectors 1.5 Reciprocal Base System 1.6 On the Meaning of Covariant Derivatives 1.7 Intrinsic Differentiation 1.8 Parallel Vector Fields 2. GEOMETRY OF SPACE CURVES 2.1 Serret-Frenet Formulae 2.2 Equation of a Straight Line in Curvilinear Coordinate system 2.3 Some Results on Curvature and Torsion. How to Find out Curvature and Torsion of Space Curves 2.4 Helix 3. INTRINSIC GEOMETRY OF A SURFACE 3.1 Curvilinear Coordinates of a Surface 3.2 The Element of Length and the Metric Tensor 3.3 The First Fundamental Form 3.4 Directions on a Surface. Angle between Two Directions 3.5 Geodesic and its Equations 3.6 Parallelism with respect to a Surface 3.7 Intrinsic and Covariant Differentiation of Surface Tensors 3.8 The Riemann-Christoffel Tensor. The Gaussian Curvature of a Surface
Also available: | 677.169 | 1 |
Most Recent Documents for Young Women's Preparatory Academy
Introduction to Limits
Section 1.2
What is a
limit?
A Geometric Example
Look at a polygon inscribed in a circle
As the number of sides of the polygon
increases, the polygon is getting closer to
becoming a circle.
If we refer to the polygon as an n-gon,
w
Continuity and One-Sided Limits
Lesson 2.4
2
3
4
Intuitive Look at Continuity
A function without
breaks or
jumps
The graph can be
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5
Continuity at a Point
A function can be discontinuous at a point
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2.4
Most of the techniques of calculus require that functions
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in one motion without picking up your pencil.
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as the value of
The derivative as the slope of the
tangent line
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f(a) - f(x)
a
What is calculus?
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10.1 Introduction to Limits
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calculus
Ecology:
the study of the interactions of living things
with each other and their physical
environment
Ecological Organization:
1. Population: all the members of a species
inhabiting a given location
2. Community: all the interacting
populations in a giv | 677.169 | 1 |
Physics Task Cards Introduction to Vectors
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Since Physics involves working with vectors, learning algebra vectors represents an important step in the ability of students to solve problems. These tasks cards will help students master the ability to Drawing Vectors Tip-To-Tail, Adding Vectors at Right Angles, and Resolving Vector into X and Y Components.
Included are Task Cards, Student Worksheet to Record Answers, and Teacher Answer Keys | 677.169 | 1 |
Discrete Mathematics Using Latin Squares
4.11 - 1251 ratings - Source
An intuitive and accessible approach to discrete mathematics using Latin squares In the past two decades, researchers have discovered a range of uses for Latin squares that go beyond standard mathematics. People working in the fields of science, engineering, statistics, and even computer science all stand to benefit from a working knowledge of Latin squares. Discrete Mathematics Using Latin Squares is the only upper-level college textbook/professional reference that fully engages the subject and its many important applications. Mixing theoretical basics, such as the construction of orthogonal Latin squares, with numerous practical examples, proofs, and exercises, this text/reference offers an extensive and well-rounded treatment of the topic. Its flexible design encourages readers to group chapters according to their interests, whether they be purely mathematical or mostly applied. Other features include: An entirely new approach to discrete mathematics, from basic properties and generalizations to unusual applications 16 self-contained chapters that can be grouped for custom use Coverage of various uses of Latin squares, from computer systems to tennis and golf tournament design An extensive range of exercises, from routine problems to proofs of theorems Extended coverage of basic algebra in an appendix filled with corresponding material for further investigation. Written by two leading authorities who have published extensively in the field, Discrete Mathematics Using Latin Squares is an easy-to-use academic and professional reference.MDS codes are optimal in that there does not exist a code of length s and
minimum distance s a€" 1 that contains more ... define the function dma€ža€ž(n, k; q) to
be the largest minimum distance among all [n, k] linear codes over the field Fq.
One wayanbsp;...
Title
:
Discrete Mathematics Using Latin Squares
Author
:
Charles F. Laywine, Gary L. Mullen
Publisher
:
John Wiley & Sons - 1998-09-17
ISBN-13
:
Continue
You Must CONTINUE and create a free account to access unlimited downloads & streaming | 677.169 | 1 |
The sample questions below give a brief introduction to the materials used to assess the mathematical ability of twelfth-grade students. All questions are based on the NAEP mathematics framework, which defines the test design and content. The framework was developed through an extensive national consensus process and adopted by the National Assessment Governing Board. Visit the Governing Board's website to browse the full text of the mathematics framework. In addition to the overall percentage of students who answered the question correctly, the percentage of students at each achievement level who answered correctly is presented. To learn more about achievement levels, read specific descriptions of the Basic, Proficient, and Advanced achievement levels in mathematics.
Several other tools are available to help students, parents, and teachers look more closely at NAEP questions. View the item maps that provide concrete examples of what students at various achievement levels likely know and can do. Visit the NAEP Questions Tool to see over 1,800 released items in all NAEP subject areas.
The following multiple-choice question comes from the measurement and geometry content area. The question required students to determine an angle formed by a cross street between two parallel streets.
The following is a short constructed-response question from the algebra content area. The question asked students to determine the composition f ° g of a quadratic function f and a linear function g. Responses were rated as "Correct," "Partial," or "Incorrect." The sample student response below was rated "Correct." | 677.169 | 1 |
Shapes, relationships in one, two and three dimensions are covered. Algebra is continually reviewed and used throughout the course. Prealgebra is a very important subject since it is the foundation for a new language, the language of algebra | 677.169 | 1 |
Summary and Info
This textbook is written for senior undergraduate and graduate students as well as engineers who will develop or use code in the simulation of fluid flows or other physical phenomena. The objective of the book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of physical phenomena. It is based on the finite-difference method and simple enough problems that allow also the analytic solutions to be worked out. ODEs as well as hyperbolic, parabolic and elliptic types are treated. The reader also will find a chapter on the techniques of linearization of nonlinear problems. The final chapter applies the material to the equations of gas dynamics. The book builds on simple model equations and, pedagogically, on a host of problems given together with their solutions. | 677.169 | 1 |
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Collections:
This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2009-03-29.
Component Ratings:
Technical Completeness: 3 Content Accuracy: 3 Appropriate Pedagogy: 3
Reviewer Comments:
This resource is a collections of 4 Flash-based Algebra I lessons: Real numbers and expressions; Simplifying expressions; Solving equations; More on solving equations. The lessons are presented in a straight-forward pattern that is easy to follow. The students are also presented with interactive practice problems. It would be beneficial if students could receive additional instruction when making a mistake in a problem, instead of moving on to the next topic.
This curriculum emphasizes a multi-representational approach to algebra, with concepts, results, and problems being expressed graphically, analytically, and verbally. It develops algebraic fluency by providing students with the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. In addition, the course develops proficiency with operations involving monomial and polynomial expressions. The main unifying themes of the course include understanding, writing, solving, and graphing linear equations, systems of linear equations and inequalities, quadratic equations, and rational equations. Upon completion of this course you will: | 677.169 | 1 |
Presented is a comparison of the Texas Education Agency Essential Objectives for Mathematics and the instructional concepts of the Conceptually Oriented Mathematics Program (COMP). COMP is a management program of 25 levels of mathematics instruction in 10 broad concept areas. Listed are relevant steps, levels, and strands of COMP for each of the 24 Essential Objectives. (MK) | 677.169 | 1 |
Solving Multi-Step Inequalities Partner Match-Up {Algebra 1]
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Students will solve 11 problems and compare answers with their partner to determine the answer to the riddle. (What is the best time to go to the dentist?) Students will get matching inequality symbols and numerical answers (variables may be different) on each set to help them determine what letter goes in what numbered box.
The skills required are:
*Solving Inequalities with variables on one side
*Solving Inequalities with variables on both sides
*Solving Multi-Step Inequalities (distributing more than once | 677.169 | 1 |
Showing 1 to 2 of 2
To enhance your math skills. This was a required course for me, but I find math very useful in real life situations. Learning how to integrate and derive functions occurred in my science courses as well. Most programmers or engineers are required to take this course.
Course highlights:
derive and integrate functions
Hours per week:
9-11 hours
Advice for students:
make sure you spend time reviewing your material
Course Term:Fall 2015
Professor:Smith
Course Required?Yes
Course Tags:Math-heavyMany Small AssignmentsParticipation Counts
Sep 03, 2016
| Would highly recommend.
Not too easy. Not too difficult.
Course Overview:
It is a great course to begin with if you are interested in a major that includes any form of engineering. A lot of the basics of this course helps translates to the applications of engineering. For example, bridge designing involves several concepts of geometry and algebra.
Course highlights:
The highlights where the learning the derivatives of functions. This is the basis of the course. Without this it is difficult to succeed later in the course or other courses in mathematics or engineering.
Hours per week:
3-5 hours
Advice for students:
The material is comprehensive. In order to completely understand the second step, you must first learn have a strong foundation of the first step. This may take a few tries to master. | 677.169 | 1 |
Precalculus
Test 1
Sections 4.1 and 4.3
Name _
SHOW ALL WORK!
I. Multiple Choice
_ 1. Determine the quadrant in which the terminal side of an
angle of 215 lies.
(A) I (B) II (C) III (D) IV
(E) The terminal side lies on one of the axes
_ 2. Convert 25 to r
Pre-Calculus Review
5.1 5.3 Trigonometric Functions
(A calculator is only allowed on #19 24)
Name _
Date _ Period _
1.] Sketch the angle whose measure is 200 (in standard position).
_ 2.] What is the domain of the sine function?
_ 3.] What is the period o
Precalculus: 9.1,9.3 Quiz Review
Name_
1. How many different license plates can be made if each consists of 3 letters followed by 2 digits followed by
1 letter if the last letter can not be a vowel (consider y a vowel for this scenario)?
2. There are 8 dr
Pre-Calculus Quiz: Parabolas
1.) Write an equation in standard form for the conic to the right.
2.) Rewrite the equation below in standard form.
x2 4x 8y 20 0
3.) a.) Graph the parabola with a focus of (3 , 5) and a directrix
of y = 7. Label the vertex, f
Showing 1 to 2 of 2
Him as a teacher, he understands so much on his own, i think he needs to teach a harder class or to only seniors. He wasn't a bad teacher but he rarely knew how to teach, and show other ways to do certain things. Because he's been so good at math for so long, those of u who don't understand have difficulty passing because we just don't understand how to do what he wants and he grades based on process not just if we knew how to get the answer.
Course highlights:
highlights of this course was that he was always there to help. he did what he thought he could, but he came to class early and he stayed late also, as well as being able to keep in contact with.
Hours per week:
12+ hours
Advice for students:
Considering this course... be ready to give 2-3 hours of homework time to just this class, its hard if you don't understand, and not everyone knows how to do it right.. memorize all the basics before you came to class that first day of school. if you don't need the credit maybe try algebra 3 or even stats and prob. Do not take tis class lightly just because it is an intro class.
Course Term:Fall 2014
Professor:Mr. Takahashi
Course Tags:Math-heavyBackground Knowledge ExpectedGo to Office Hours
Jul 15, 2016
| Would highly recommend.
This class was tough.
Course Overview:
Trigonometry and Precalculus is a good introduction to harder math levels. It gives you an idea on whether or not you would like to continue to a career that is very heavy on math or not. I also believe that Trigonometry and Precalculus tied up the connection between algebra and geometry well.
Course highlights:
The highlights were the trigonometry identities and I learned that the harder maths are the maths prior to it with a harder application.
Hours per week:
9-11 hours
Advice for students:
Do homework. Do not procrastinate. Ask your teacher or peers for help when you do not understand the lesson because it is tough. | 677.169 | 1 |
Rational Functions
A series of free College Algebra Video Lessons from UMKC - The University of Missouri-Kansas City.
College Algebra - Lecture 27 -
Rational Functions.
In this lecture, we learn about Asymptotes and finding Asymptotes of rational functions.
General Rational Functions [14 min.]
What Is An Asymptote? [17 min.]
Finding Asymptotes of Rational Functions [35 min.]
Graphing Rational Functions [19 min.] | 677.169 | 1 |
Love this Arithmetic and Geometric Sequence, Sum, Nth Term, Cheat Sheet/Foldable! This is a comprehensive guide to the Arithmetic and Geometric Series. Summation notation is included along with common difference, common ratio, nth term, sum of a finite sequence and sum of an infinite sequence. | 677.169 | 1 |
Endorsed by Cambridge International Examinations, this new series offers all the resources you will need to completely cover the Cambridge IGCSE Mathematics (0580) syllabus. A Coursebook, two Practice Books and a Teacher's Resource provide thorough explanation and ample practice opportunity to help students to understand their IGCSE maths course and support teachers in guiding them. Suitable for all classrooms, whether core and extended students are learning together or separately, these resources will help students to achieve their potential in maths.
Cambridge Paperback. Condizione libro: New. Not Signed;. book. Codice libro della libreria ria9781107609884_rkm
Descrizione libro Cambridge7609884 | 677.169 | 1 |
calculus easy or difficult addition and subtraction is the basic of all mathematical operation, the differentiation and integration is the basic of calculus. If you understand these two topics well, calculus will become a primary school game for you, otherwise it will be a nightmare. So, better to take reference from good books, hope you love this topic . All the best :) | 677.169 | 1 |
Using Functions to Model Relationships Worksheet
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.33 MB | 2 pages
PRODUCT DESCRIPTION
The graph of this function represents all ordered pair combinations of two kinds of candy that can be bought with $50.00. This application works for both 8th grade and algebra-1. If you are using it for an algebra-1 class, you could use the function notation such as f(x) instead of what I have here. 8th graders are not required to use function notation in Common Core. I have included a detailed | 677.169 | 1 |
The horizontal and vertical lines in a matrix are called rows and columns , respectively. The numbers in the matrix are called its entries or its elements . To specify a matrix's size, a matrix with m rows and n columns is called an m -by- n matrix or m × n matrix, while m and n are called its dimensions . The above is a 4-by-3 matrix. </li></ul>
4.
TYPES OF MATRICES <ul><li>Upper triangular matrix If a square matrix in which all the elements that are below the main diagonal are zeros. the matrix must be square. </li></ul><ul><li>Lower triangular matrix If a matrix in which all the elements that are above the main diagonal are zeros. the matrix must be square. </li></ul>
5.
TYPES OF MATRICES <ul><li>Determinant of a matrix. The determinant of a matrix A (n, n) is a scalar or polynomial, which is to obtain all possible products of a matrix according to a set of constraints, being denoted as [A]. The numerical value is also known as the matrix module. </li></ul><ul><li>EXAMPLE: </li></ul>
6.
TYPES OF MATRICES <ul><li>Band matrix: </li></ul><ul><li>In mathematics, particularly in the theory of matrices, a matrix is banded sparse matrix whose nonzero elements are confined or limited to a diagonal band: understanding the main diagonal and zero or more diagonal sides. Formally, an n * n matrix A = a (i, j) is a banded matrix if all elements of the matrix are zero outside the diagonal band whose rank is determined by the constants K1 and K2: Ai, j = 0 if j <i - K1 j> i + K2, K1, K2 ≥ 0. </li></ul>
7.
TYPES OF MATRICES <ul><li>Transpose Matrix If we have a matrix (A) any order mxn, then its transpose is another array (A) of order nxm where they exchange the rows and columns of the matrix (A). The transpose of a matrix is denoted by the symbol "T" and is, therefore, that the transpose of the matrix A is represented by AT. Clearly, if A is an array of size mxn, At its transpose will nxm size as the number of columns becomes row and vice versa.If the matrix A is square, its transpose is the same size. </li></ul><ul><li>EXAMPLE: </li></ul>
9.
BASIC OPERATIONS <ul><li>SUM OR ADITION: </li></ul><ul><li>Given the matrices m-by-n, A and B, their sum A + B is the matrix m-by-n calculated by adding the corresponding elements (ie (A + B) [i, j] = A [i, j] + B [i, j]). That is, adding each of the homologous elements of the matrices to add. For example: </li></ul>
11.
BASIC OPERATIONS <ul><li>The product of two matrices can be defined only if the number of columns in the left matrix is the same as the number of rows in the matrix right. If A is an m × n matrix B is a matrix n × p, then their matrix product AB is m × p matrix (m rows, p columns) given by: </li></ul><ul><li>for each pair i and j. </li></ul><ul><li>For example: </li></ul> | 677.169 | 1 |
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None.
The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. | 677.169 | 1 |
Editors: Bartel, A., Clemens, M., Günther, M., ter Maten, E.J.W. (Eds.) Covers topics in scientific computing in electrical engineering from both academia and industry, as well as mathematics and electrical engineering perspective Shows state of the art in SCEE Includes advanced topics of MOR and UQ in methodology
In this volume, the author covers the mathematical methods appropriate to both linear-systems theory and signal processing. The text deals with a number of topics usually found in introductory linear-systems courses, such as complex numbers and Laplace transforms, and addresses additional topics such as complex variable theory and Fourier series and transforms. | 677.169 | 1 |
MATH Documents
Showing 1 to 30 of 41
AP BC Calc P.2 Properties of Functions
Ferguson Notes
After carefully reviewing the definition of a function, we should have a clearer understanding of what it is, from a rather
practical standpoint, and what it represents. In this second section, we will
AP BC Calc P.2 Properties of Functions
Notes
Ferguson
After carefully reviewing the definition of a function, we should have a clearer understanding of what it is, from
a rather practical standpoint, and what it represents. In this second section, we will
AP BC Calc P.1 Functions & Important Vocabulary
Ferguson Notes
Welcome to the first section of the introductory chapter! In this chapter, we will explore the preliminary skills and
critical thinking that is needed for a calculus class. In all honesty, cal
AP BC Calc P.1 Functions & Important Vocabulary
Ferguson Notes
Welcome to the first section of the introductory chapter! In this chapter, we will explore the preliminary skills
and critical thinking that is needed for a calculus class. In all honesty, cal
AP BC Calc 4.5 Approximating Solutions to Non -separable Differential Equations
(Eulers Method/Slope Fields)
Ferguson Notes
Suppose that we were looking at differential equations that were non-separable and could not be solved using a specific
formula. Fo
AP BC Calc 4.5 Approximating Solutions to Non-separable Differential Equations
Ferguson Notes
(Eulers Method/Slope Fields)
Suppose that we were looking at differential equations that were non-separable and could not be solved using a
specific formula. For
AP BC Calc 4.4 Separable Differential Equations
Ferguson Notes
Now that we know what an actual differential equation is, it seems that some of them could be hard to solve. For
instance what if we had a differential equation that was simply a sum of an x a
AP BC Calc 4.4 Separable Differential Equations
Ferguson Notes
Now that we know what an actual differential equation is, it seems that some of them could be hard to solve.
For instance what if we had a differential equation that was simply a sum of an x a
AP BC Calc 4.3 What is a Differential Equation?
Ferguson Notes
Weve somewhat seen differential equations before. When we found a derivative of a function, that was technically a
differential equation. Differential Equations have many practical uses for ex
AP BC Calc 4.3 What is a Differential Equation?
Ferguson Notes
Weve somewhat seen differential equations before. When we found a derivative of a function, that was
technically a differential equation. Differential Equations have many practical uses for ex
AP BC Calc 4.2 Integration By Partial Fractions
Ferguson Notes
In 4.1, we learned how to integrate a lot of different things but we didnt really learn how to integrate advanced
rational functions. That is, its not always true that we can do some substitut
AP BC Calc 4.2 Integration By Partial Fractions
Ferguson Notes
In 4.1, we learned how to integrate a lot of different things but we didnt really learn how to integrate
advanced rational functions. That is, its not always true that we can do some substitut 4.1 Basic Antidifferentiation
Ferguson Notes
Antidifferentiation is just what it sounds like: the opposite of differentiation. Its going the other way. What
this means is that imagine that we have a function that is the derivative of another fu Substitution
Rule was a response to differentiation by
Substitution Rule was a response to differentiation by you can
go about using: the first two are somew
you can go about using: the first two are somew 3.3 Optimization
Ferguson Notes
The goal of optimization is to find a maximum or minimum value in an application problem. For instance, a CEO of a
company may want to minimize costs while simultaneously maximizing revenues. A surgeon may want t
AP BC Calc 3.3 Optimization
Ferguson Notes
The goal of optimization is to find a maximum or minimum value in an application problem. For instance, a
CEO of a company may want to minimize costs while simultaneously maximizing revenues. A surgeon may
want t F ( x) f g ( x) .
For instanc .
For instance, what if we we
AP BC Calc 2.2 The Product and Quotient Rules
Ferguson Notes
Lets review what we can do with functions, from an algebraic standpoint. Let f ( x) and g ( x) be the functions
that were considering. For these two functions, We can:
1) Find the sum:
f ( x) g
AP BC Calc 2.2 The Product and Quotient Rules
Ferguson Notes
Lets review what we can do with functions, from an algebraic standpoint. Let and be the functions that were
considering. For these two functions, We can:
1) Find the sum:
2) Find the difference
AP BC Calc 2.1 The Power Rule and Linearity
Ferguson Notes
During the last couple of sections of chapter 1, we learned about the derivative: its definition, its methodology, and its
applications. Additionally, we covered when the derivative exists and how | 677.169 | 1 |
...for future work to our students. The topics on which seminars are being conducted at present by the department include Coxeter groups, Chevalley groups... Learn about: Applied Mathematics, Basic Mathematics...
...for future work to our students. The topics on which seminars are being conducted at present by the department include Coxeter groups, Chevalley groups... Learn about: Basic Mathematics, Applied Mathematics...
... of high-school algebra. The content of the tutorial is built, in a self-contained fashion, starting with basic notions of real numbers and elementary set theory. Ideas of vectors and vector operations are developed next, in an intuitive way, by appealing, simultaneously to their algebraic and geometric... Learn about: Mathematical structures, Vector Spaces, vector algebra...
...-provoking Certificate in Introduction to Algebra Online Course integrates algebra with many other areas of study, including history, biology, geography, business, government, and more. By the time you finish this course, you will understand how algebra is relevant to almost every aspect of your daily... Learn about: Basic IT training, Basic IT, Skills and Training... | 677.169 | 1 |
Linear and Exponential Functions Complete Bundled Unit
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing. How to unzip files.
1.06 MB
PRODUCT DESCRIPTION
This listing is a bundle offering my listings titled Linear and Exponential Functions Lessons 1-10. If you were to purchase all the lessons individually, it would cost $50, bundled together you save $10.
Topics included in this unit are:
Identifying a sequence as arithmetic, geometric or neither.
Discrete and continuous relationships.
Calculating the slope of a line that passes through a set of points.
Determining which situation has the greatest rate of change.
Finding the recursive and explicit equations for a given table of values.
Graphing linear equations in slope-intercept form.
Determining which situation has the greatest rate of change.
Finding the recursive and explicit equations for a given table of values.
Graphing linear equations in slope-intercept form.
Identify an exponential and linear function given a graph and decide which has the greatest rate of change.
Given one of the following: a table, story, graph or an explicit/recursive equation, come up with the rest.
Given a geometric sequence in context, come up with the recursive and explicit equations.
Determining which function (linear and exponential) has the greater rate of change given graphs or tables of values. Giving intervals where each function has a greater rate of change.
Given the first and last term of a geometric sequence, determining the rate of change, the explicit and recursive equations and the missing terms.
Finding a geometric and arithmetic representation for the same sequence (given the first and last terms).
Writing the explicit and recursive equations for a geometric and arithmetic sequence.
Given the graph of two functions (linear and exponential) determine which has the greater rate of change over different intervals.
Comparing and contrasting a linear function and an exponential function.
Finding a solution to a system of linear equations graphically.
Writing a linear equation given slope and y-intercept.
Using point-slope form of a linear equation to write an equation for a line given a point and slope (or having to calculate slope given two points).
Given a verbal description of a sequence and a rate of change, come up with the recursive and explicit equations that match the description and a graphical representation.
Given a multi step linear equation, isolating y.
Using the simple interest formula to calculate the value of different variables.
Solving multi-step linear equations.
Completing a table of values given a linear equation and a set of x-values.
Using the simple interest formula.
Using the compound interest formula.
Evaluating multi-variable equations given values for the variables.
Describing discrete and continuous relationships.
Finding a geometric and arithmetic representation for a table of values (given the first and last values). Giving the recursive and explicit functions for each.
Comparing intervals where functions have a greater rate of change given a graph.
Identifying sequences as arithmetic, geometric or neither and writing recursive and explicit equations for each.
Comparing and contrasting a linear and exponential function given the equation.
Solving a multi-step linear equation for the y-variable.
Writing a linear equation given different types of information (two points, a point and slope, a recursive equation, etc)
Calculating different variables in the compound and simple interest formulas | 677.169 | 1 |
Complex Numbers Calculator Using the complex numbers calculator the answers to algebra problems covering this topic is only as far as your mobile phoneQuad2Go Quad2Go is a handy tool for learning about quadrilaterals by generating examples, observing, and experimenting with examples with a view toward forming generalized conjectures
matrixmobile linear equations This app helps you solving systems of linear equations up to 9 unknown, working with matrices (inverse, transpose, multiply)
Maths Training Math Training is a fun way to practice your basic arithmetic. Choose from four signs of math!
BrainBooster Train your brain with this simple maths and time it to beat your own record | 677.169 | 1 |
The Input Box
The input box is located just beneath the scientific pad.
There are different ways to insert a problem;
The scientific pad, Latex or via copy-paste. All of the above eventually lead to your problem
being displayed within the input box. This helps to check if it was inputted and understood correctly.
After the problem was inserted, you can hit "enter", or click "go".
Using the Keybaord + Keyboard Shortcuts
For many cases, you will not need anything but the keyboard.
Trigonometric functions, basic arithmetic operations, letters and numbers can be written regularly.
Multiplication, Superscripts and Subscript are three commonly used signs that are not explicitly
present on the keyboard. They can be inserted, though, using simple keyboard-shortcuts:
Multiplication is inserted with the "*" character ("shift"+"8").
Superscript can be inserted with the "^" character ("shift"+"6")
Subscript can be inserted with the "_" character ("shift"+"-")
All of the other mathematical elements can be inserted with the keyboard as well, with a language
called Latex. Latex is a widely used form of writing mathematical scientific expressions.
To learn how to write a specific expression, present on the pad, with Latex,
just hover over it and a window will appear with the Latex form.
The Scientific Pad
The Scientific pad enables to insert elements that are not in the keyboard, without having to know Latex.
The pad has two states. The first is the default, or compact state. The pad is in the compact state when you first enter the solutions page.
This pad covers the great majority of common symbols that are not present on your keyboard.
Click the sign you want to insert and it will immediately pop up in the text box.
If there is a symbol, or a short expression, that isn't in the default pad, chances are that it can be found in the full pad.
In order to open the full pad, press the full pad link on the top-left of the basic pad.
The full pad is...well... fuller.
On the top tabs you can see the different groups of signs that Symbolab supports.
Each tab contains symbols representing that particular group.
Another important aspect of the full pad is that the first row doesn't change between groups.
The reason being is that these symbols are prevalent in all groups.
Let us go over the different tabs:
The basic pad has a few extra symbols, like absolute value, and a few basic trigonometry signs.
These, together with the compact pad, cover whatever you need for Algebra and Calculus.
The rest of the pad is for either symbols used in advanced math or for common expressions that contain basic
symbols numerous times (A triple integral, for instance).
Lower Case Greek Letters
Upper Case Greek Letters
Trigonometric and Hyperbolic Functions
Comparison Operators:
Advanced Accents:
Complex Calculus Expressions
Differential Equations:
Physical Constants:
Chemistry: Coming soon...
Calculator:
Latex
Some of you may know Latex. If that is the case, you can make great use of it in Symbolab.
The input box supports nearly all of the Latex symbols.
In order to insert a Latex expression, just write it into the input box.
Don't forget the '\' character preceding each Latex expression. When you are done, hit the space bar, or any non-letter key on the keyboard.
You can also copy chunks of Latex from a document and paste it into the input box (more on that in the copy-past section)
If you want to learn how to insert a sign from the pad using Latex, hover over it for a second.
Caution: Since we want to show any part of the Latex input the instance we understand it,
you should look at the input box after each symbol is entered.
Copy Paste
Sometimes the problem you want to solve is already written somewhere else.
In that case you can copy and paste it into the text box.
Symbolab supports Latex completely. It also supports less formal forms that are used in various forums.
In the later case, though, especially when the text
isn't written very meticulously, you sometimes need to modify it after pasting.
Using Templates
For some problems, you need more than just entering expressions.
You have to specify what it is you want to do with the expressions.
If you want to do a certain operation on the expression,
state it in the beginning of the textbox. For example, if you want to compute the slope of a function, start the input with the word "Slope"
If you also want the operations to be done at a certain point, or value, add ", at" and specify the wanted value.
Regardless, there is no need to remember or start experimenting if you're not sure.
You can find the appropriate topic in the topic menu,
located on the left side of the screen, and the template will automatically be added in the text box.
Moreover, when reaching a topic from the menu, you can use the examples to get a better understanding of both the extent of coverage,
and the input forms being supported. Bellow you can see an example of entering a derivative at a point problem.
Inserting Conditions and Multiple Expressions
In order to insert a system of equations, insert a comma (',') between each expression.
Adding conditions, or additional data into a problem varies between topics:
To specify a value, or a point, for which an operation is done, add ", at" and the point.
When adding initial conditions, it is enough to add them at the end of the main expression with a comma separating each part.
There are a few ways to specify the wanted range of a trigonometric equation. Generally speaking, all the scientifically acceptable methods
for stating a range are supported by Symbolab, as long as a comma separates the main expression and the wanted range.
For example, in order to state that the range of x should be between 0, and 2\pi, inclusive, you can use the following forms: | 677.169 | 1 |
If you can find one case for which a statement is not true,
called a counterexample, then the statement is a false statement.
Deductive reasoning is distinguished from inductive reasoning in that it is the process of
reaching a conclusion by applying gen
Showing 1 to 3 of 3
I have never been good in math and that was the first aspect our professor stated. She asked who hated math and who has never been good at it; more than half the class raised thier hands as reassured us we would do fine. She was so funny and used visual aid to help us understand challenenging material. The information didnt seem as bad when you have a teacher like her!
Course highlights:
I learned quite a bit about probabilty and everything related to it. Using real life events and dolls to get her point across. We played games and laughed so much. The environment is just overall very welcoming. It made you want to come to class to learn. The quizzes were very easy and the exams were even better!
Hours per week:
3-5 hours
Advice for students:
Simpy come to class and everything you need to know and ways to understand it will be given to you. She is the best math teacher I have ever had!
Ms. Bieske is a wonderful teacher who really cares about her students. If you don't understand something she will go over it until you do. Instead of taking up class time she does tutoring in the library as well. I personally am not the best at math but I aced this course! It's fairly easy and with Ms. Bieske's help, you'll breeze through it.
Course highlights:
If you do well on all your home works and quizzes you get to play candy land at the end of the semester for a grade.
Hours per week:
3-5 hours
Advice for students:
Make sure you take good notes. Although this material is mostly easy, there are some confusing parts. If you took good notes in class, just glancing over them while doing the homework will assure an understanding.
Course Term:Spring 2016
Professor:Bieske
Course Required?Yes
Course Tags:Great Intro to the SubjectMany Small AssignmentsGreat Discussions
Jan 24, 2016
| Would recommend.
Not too easy. Not too difficult.
Course Overview:
if you do not need a complicated math course then this is a good class to take, plus the teacher is really nice. If you are really good at math but want a really challenging class this is not you class.
Course highlights:
The professor makes the lessons really relatable to the class so it is easier to learn the material. You learn really simple math, there is very little algebra, no geometry and it goes up until basic statistics
Hours per week:
9-11 hours
Advice for students:
Always got to the smartlab hours your required and do the homework, I mean actually do it and you should be fine. If you do not understand something in class do not be intimidated because it is a lecture hall she will take all questions , but if It was just asked she might tell the class to answer.
Course Term:Fall 2015
Professor:Bieske
Course Required?Yes
Course Tags:Great Intro to the SubjectAlways Do the ReadingMany Small Assignments | 677.169 | 1 |
Math 1110 Homework 1 Name: Due 9/1 or 9/2 in class GRADES Text exercises / 20 Pres probs / 20 Staple / 1 Please print out these pages. Answer the "presentation problems" in the spaces provided. Include full explanations and write your answers in complete, mathematically and grammatically correct sentences. Your answers will be assessed for style and accuracy; you will be given written feedback on these problems. Please write your answers to the "text exercises" on separate paper and staple it to these pages. You should include computational details. These problems will be assessed for completeness. Always write neatly and legibly. Text exercises. Please do the following problems from the book. § 1.1 # 4, 8, 10, 11, 24, 28, 32, 34, 40, 54, 66, 72 § 1.2 #4, 6, 8, 11abc, 24, 26, 42, 47, 48, 59 § 1.3 #6, 7, 18, 43, 50, 55 The following problems are recommended if you would like to practice with your graphing cal-culator, or play with one online (here, for example) . You should not turn these in. § 1.4 #2. 3. 20, 26, 33
This preview
has intentionally blurred sections.
Sign up to view the full version. | 677.169 | 1 |
Testimonials
What educators are saying...
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Agile Mind is essential in today's learning environment. For me, it has been a journey that I would not trade for myself or my students. I am very thankful!"
Josie Mallery, Calculus Teacher, Klein High School, Klein, Texas
"Just a quick update as to how Agile Mind did in the Math pullout program at McCollum HS. We used it for approximately 35 kids. The pullout program is for 11th graders who are not currently enrolled in a math class at the high school, and are in particular danger of not doing well on the TAKS Math test. The overwhelming response of the kids was favorable, with a couple of kids actually asking for ANOTHER session during the day to keep working on it!
Your program is a hit here! I think its use as an individualized tool to help students stay sharp for TAKS and to bolster up their math weaknesses is right on target. Thanks so much for your help and prompt assistance." | 677.169 | 1 |
c)Find the projection of one vector to another vector , find the sine or cosine of angle between the vectors, unit vector in the direction of vector,
Groups
a)Proving a particular set forms an abelian group like Show that a*b=a+b-ab forms an abelian group, Show that G={5^n, (integral multiples of 5) } forms an abelian group etc refer topic wise questions in mathematics in this website.
Elements of Number theory :
a)Finding GCD of two numbers and representing them as a linear combination of x and y and showing x and y is not unique
b)Find the number and sum of divisors
c)Finding the last digit or unit digit, solving linear congruence.
TRIGONOMETRY
INVERSE TRIGONOMETRIC FUNCTIONS:
a)problems on use of formula tan^-1 x + tan^1 y= tan^1(x+y/1-xy) etc
GENEREAL SOLUTION OF TRIGONOMETRIC EQUATION
a)GS of trignometric equation of the form acosx+bsinx=c
b)GS by using FORMULA OF CONVERTING sum of trigonometric functions into product or product into sum
COMPLEX NUMBERS
a)State and prove Demoivre's theorem
b)problems on this, see topic wise questions in this website.
CIRCLES
a)all derivations: equation of tangent, condition of orthogonality, finding length of tangent, condition for the line y=mx+c to be tangent to to circle x^2+y^2 =a^2
b)problems on orthoganal circles, and finding equation of circle by finding g, f and c using conditions in the given problem.
Definition of ellipse , hyperbola, parabola as a locus and Derivation of parabola, ellipse , hyperbola in standard form in conic section (Important) or all derivations in conic section like condition for the line y =mx+c to be tangent to parabola, ellipse, hyperbola including problem etc 6 marks
Problems on differentiation from first principles: 3 marks
Complex numbers: problems on demovires theorem
and its proof : 6 marks
Vectors: Application of vectors or problems 4 marks
Problems on Derivative as a rate measure , angle of intersection between two curves, maximal and minima (application of derivative problems) : 6 marks
Finding Area under a curve 5 marks
Proving some important properties of Definite integral and problem on this 6 marks
"I knew answer for all questions but I did not get sufficient time to answer". These are the words students usually utter once they come out of the exam hall! Some students even say " I knew every thing but i had written only for 80-90 marks" . Some students may write only for 50-60marks, even if they are prepared very well. Why this happens ? how this happens ? can it be avoided?
YES!
These can be avoided (100%) just by proper time management and by selecting the proper questions
Scoring in exam depends not only on your preparation but also on your mind set, time management, proper selection of questions and precise answering.
Now here are some advice to students
DURING THE EXAM DAY:
Arrive at the exam center 30 minutes early. Find your register number, the allotted room .Compose yourself. Consciously relax and take a few deep breaths. Think of your reward after the EXAM is completed. Be confident! Think positively
1. Remember ,,, P.U. Department has given an opportunity to select proper questions with out wasting your 180 minutes, by providing extra 15 min for reading the question paper. In this 15 min of time go through the question paper and gauze or identify the easy questions which can be solved in lesser time . .while doing this don't write or mark anything on the question paper except your register number.
2. Start looking at the question paper from question no 1. DECIDE the question IN WHICH U R CONFIDENT OF ANSWERING AND also decide about the questions which you cannot answer. Solve the problems for which you know the answers partially at the end.
3. Here I have given average time for attending each question but you may follow other known methods also. But the questions in which you are confident should be solved in less time ( say for attending 5 mark question u may need 5-6 min but it should be solved with in 4 min) so, remaining time can be utilized to try some lengthy or known questions
PART A: (1 MARK): MAX TIME: 15-20MINUTES(TEN QUESTIONS)
PART B: (2 MARK): MAX TIME: 40 MINUTES(ANY TEN QUESTIONS)
PART C: (5 MARK): MAX TIME: 56 MINUTES( EIGHT QUESTIONS)
PART D: (10 MARK): MAX TIME: 26 MINUTES(ANY TWO)
PART E: (10 MARK): MAX TIME: 18 MINUTES (ANY ONE)
TOTAL: MAX TIME: 160 MINUTES OUT OF 180 MINUTES
So you have 20 -30 minutes left if you complete problems in the above method. After finishing answering of all required known questions, go through it rapidly. then in the remaining time you can attend extra questions either in part B or in Part C (where you have doubts) or other wise you can revise and recheck the answered one, once again.
There are many students who will able to complete all prescribed questions within two hour.
7. It always better to attend questions on proof( provided you know well), in sub groups, circles, conics , complex number, vectors,) and It is better to avoid questions which is having figure in circles and conics to save time . Remember your sketch should be clear. You will get ZERO if u don't write the correct figure especially in derivations in conic section and circles.
For example: In part D if u have questions on a) derivation in conic section b)problem on application of differentiation c) problem on complex numbers , It is better to choose 'b' and 'c' instead ' a'
8.If they asked the questions of type differentiate cosecx, secx, tan^-1x, cot^-1 x, and other inverse trigonometric functions (IN MY VIEW , ACTUALLY QUESTIONS on DIFFERENTIATING INVERSE FUNCTIONS FROM FIRST PRINCIPLES SHOULD NOT BE ASKED AS PER RECENT SYLLABUS, STILL SOME ARE ASKING ABOUT SUCH QUESTIONS FOR JUST 3 MARKS ,) In that case it is better to leave differentiate from First principle , attempt some other question( from choice,if u know) as it time is consuming, if don't know any other then u have to attend it.
9. Now take up the questions u know how to do but it take little time to think and solve ,attempt those questions now and if u don't get the exact solutions just think for 1 min and leave that question and attend other question. don't waste your valuable time in solving single unknown problem
10. Don't change your plan at any cost that to in exam hall, which may lead you to confusion
11.If possible , Day before the exam take 2-3 question paper ( take 2march, 1July supplementary exam)and allot 15 min of time and select the questions as stated above (no need to solve the paper just to practice).
12.On the exam day after u wake up imagine u r self as a good math teacher and say with confidence that , in exam i will solve the questions that i have studied.
"I'm a 2nd puc student studying in bangalore. Can you tell me the important definitions required to learn? Because I have observed in many question papers and found out that we can lose one marks many a times, which should not happen while we are aiming for 100. It will be a great help to all the students here!!"
For proving the questions on Groups many students commits mistakes on the following questions.2.If Q-1 is the set of all rational numbers except -1 and * is a binary operation defined on Q-1 by a*b= a+b+ab, Prove that Q-1 is an abelian group.
For verifying closure law for the above the problems, many students simply do in the following way Wrong approach:
Closure law: a*b=a+b-ab is again a rational number and hence closure law is true.
However Here student did not verified a*b is a rational number except 1. Hence it is very necessary to show that a*b is a rational numbr other than 1 . Other wise 1Mark will be reduced in the valuation. In april 2002, the 1 Mark is reduced for the students who did not verified the closure law correctly. The correct approach is as follows:
For question number 1:
Let a, b Q1 such that a #1, b#1 a+b-ab is also a rational number and it cannot be equal to 1
Because If a+b-ab=1, then a+b-ab-1=0
then (a-1)(b-1)=0
thereofore a=1 or b=1 which is not true as a#1 and b#1. a*b belongs to Q1
therefore Q1 is closed w.r.t * (GIVING REASONS IS IMP)
Similarly for verfying closure for 2 question
Closure law: or Q-1 a*b=a+b-ab is again a rational number and hence closure law is true.
Let a, b Q-1such that a # -1 b#-1 a+b+ab is also a rational number and it cannot be equal to -1
Because If a+b+ab=-1, then a+b+ab+1=0
therefore (a+1)(b+1)=0
Hence a= -1 or b= -1 which is not true as a# -1 and b# -1. a*b belongs to Q-1
Q-1 is closed w.r.t * (GIVING REASONS IS IMP) | 677.169 | 1 |
Haberman
MTH 95
Section IV: Radical Expressions, Equations, and Functions
Module 2: Rational Numbers as Exponents
In Introductory Algebra (MTH 60/65 at PCC) and in Section I, Module 1: Review you should
have studied how to work with exponents that are int
Haberman / Kling
MTH 95
Section V: Quadratic Equations and Functions
Module 2: The Quadratic Formula
You should remember from your course on introductory algebra that you can use the quadratic
formula to solve quadratic equations.
The Quadratic Formula:
I
Haberman / Kling
MTH 95
Section II: Functions, Inequalities, and the Absolute Value
Module 1: Introduction to Functions
A function is a special type of binary relation. So before we discuss what a function is, we
need to define binary relation.
DEFINITION
Haberman
MTH 95
Section IV: Radical Expressions, Equations, and Functions
Module 1: Intro. to Radical Expressions and Functions
The term radical is a fancy mathematical term for the things like square roots and cube roots
that you may have studied in prev
Haberman
MTH 95
Section IV: Radical Expressions, Equations, and Functions
Module 7: The Complex Numbers
So far in your mathematics careers you have (probably) only used real numbers (denoted by
R ). This set has worked pretty well for us. The only time wh
Haberman
MTH 95
Section IV: Radical Expressions, Equations, and Functions
Module 6: Solving Radical Equations
x = 5 for x.
EXAMPLE: Solve the equation
SOLUTION: To solve this equation, we need to find a number x whose square root is 5. This
one we can do
Haberman
MTH 95
Section I: Review
Module 2: Sets and Numbers
DEFINITION: A set is a collection of objects specified in a manner that enables one to
determine if a given object is or is not in the set.
In other words, a set is a well-defined collection of
MTH 95
Haberman
Section IV: Radical Expressions, Equations, and Functions
Module 4: Dividing Radical Expressions
Recall the property of exponents that states that
am
bm
m
a
= . We can use this property to
b
obtain an analogous property for radicals:
a
Math 95 with Jeremy Shaw was by far my favorite class upon returning to school for some prerequisites. His methods were clear and concise.
In addition to Professor Shaw's methods, the students in the class were quick to participate and collaborate. We were able to learn a lot from each other with the groundwork that was established by Professor Shaw
Course highlights:
This class was an excellent wrap up to an intensive few classes with focus on algebra. The material that was covered was an excellent preparation for Math 111.
The true highlights, however, included some interesting discoveries. I partnered up with a woman who was also doing well in the class, but would think through the martial in a completely different way. The discovery that math was not as rigid as it is often presented was a fascinating one.
Hours per week:
9-11 hours
Advice for students:
Any students taking Math 95 should dedicate themselves to attending class regularly and taking detailed notes. If the material does not make sense, bring up the points that have you stuck before you fall too far behind.
Math is not everyone's favorite, but it can be enjoyable in an informative and collaborative environment. Go in with an open mind! | 677.169 | 1 |
The second edition of this highly successful textbook has been completely revised and now includes a new chapter on vectors. Mathematics is the basis of all science and engineering degrees, and a source of difficulty for some students. Jenny Olive helps resolve this problem by presenting the core mathematics needed by students starting science or engineering courses in user-friendly comprehensible terms. | 677.169 | 1 |
Audience
College General Ed
High School
Topics
Scatter Plots, Slope, X and Y-Intercepts, Line of Regression
Requirements
linear equations, functions, graphing
Learning Objectives
Students will develop the ability to collect data and record data in a table; represent, analyze, and generalize patterns with tables, graphs, words, and symbolic rules; model problems using various representations such as graphs, tables, and equations; and make connection among the three.
To represent situations with symbolic algebra to solve problems.
Type of Task
Individual
Student-centered
Supplemental activity
Team
Unsupervised | 677.169 | 1 |
Lindqvist, Peter Provides concise though comprehensive overview on the topic This book will appeal to a wide readership, from graduate students to researchers Enriches understanding on the topic
Differential Equations is a difficult subject for most students because each type of equation has many solution methods that the student must understand how to perform. In addition, each solution method usually is very involved with many different steps that require the student to have a solid foundation in Calculus.
Solving higher order differential equations is challenging for most students simply because the solution methods usually run several pages in length even for the easier problems. The student must identify the type of equation to solve and apply the appropriate solution method, which can lead to valuable lost time on an exam if the wrong solution method is chosen at the outset.
Tsunamis and hurricanes have had a devastating impact on the population living near the coast during the year 2005. The calculation of the power and intensity of tsunamis and hurricanes are of great importance not only for engineers and meteorologists but also for governments and insurance companies. This book presents new research on the mathematical description of tsunamis and hurricanes. A combination of old and new approaches allows to derive a nonlinear partial differential equation of fifth order describing the steepening up and the propagation of tsunamis. The description includes dissipative terms and does not contain singularities or two valued functions. The equivalence principle of solutions of nonlinear large gas dynamics waves and of solutions of water wave equations will be used. An extension of the continuity equation by a source term due to evaporation rates of salt seawater will help to understand hurricanes. Detailed formula, tables and results of the calculations are given. | 677.169 | 1 |
Description of the book "Advancing Maths for AQA: Statistics 2 (S2)":
Thorough revision for the AQA exams These brand new revision guides contain all the help, guidance and support students need in the run-up to the 2005 exams, ensuring they achieve the grades they deserve. The familiar format helps to trigger students' memories, making revision easier. Key point summaries at the start of each chapter focus students' minds on what they need to know for the exam. Worked examples with examiners' hints ensure students are following the best practice and approach for answering questions successfully. Practice questions, including a test-yourself section that references the main textbooks, encourage independent revision. Written by PDF a Senior Examining Team to make sure students get the most beneficial advice on tackling their exams. Revision exercises and an exam-style paper give essential preparation for the AQA exams.
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Roger Williamson
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Calculus AB: 1st Time (MATH.1263)
About the Workshop
This course will consider topics typically included in the first year of a college-level calculus course. It will cover elementary functions, limits, and differential and integral calculus. Time will be set aside for discussion related to how to best set up a high school AP® Calculus course. Methods, teaching materials and facility with the graphing calculator will be emphasized. Students will be actively engaged in problem solving, lesson design and discussion of the AP® program.
We will also focus on the changes to the AP® Calculus syllabus that will be implemented in the 2016-2017 school year and tested in May 2017.
Register for the 2017 Calculus AB: 1st Time workshop online.
-Register now with a credit card.
About the Instructor
Rose Gundacker taught AP® Calculus, both AB and BC, for over 20 years at Rosemount High school. She retired in 2008 and has been teaching part-time at local colleges, most recently at the University of St. Thomas in St. Paul. She has been an AP® reader since 1998 and has served as a reader, table leader, question team member, and question leader. She has been a consultant with the College Board* since 2000, teaching summer workshops at Carleton, Augsburg, Loyola University, and the University of Iowa. She also teaches one-day workshops in the Midwest region for the College Board*.
Summer Academic Programs
The Summer Writing Program emphasizes a writing process approach, teaching you how to compose academic papers similar to those you will write in college. The program is designed for college-bound students with strong reading and writing abilities.
The Carleton Summer Science Institute will help students learn to think and write like a scientist by doing science. CSSI students, faculty, and Carleton undergraduate research assistants will engage in classroom and hands-on research related to faculty and student interests.
The Summer Quantitative Reasoning Institute is designed to give high school sophomores and juniors a substantial college-level experience in how social scientists think about the world, measure important variables of study, prepare research, and present their findings. Students will examine theories in three core disciplines - Economics, International Relations and Psychology.
Students will learn how to systematically approach problems like a computer scientist as they engage in classroom learning, hands-on lab activities, and collaborative guided research directed by Carleton faculty and mentored by undergraduate research assistants. The program will culminate with a Research Symposium where students will demonstrate the results of their collaborative guided research project.
The world is a complicated place—a tangle of languages and cultures and market forces. We've devised the Summer Language and Global Issues Institute to show how these entities are intertwined. While giving students an experience of language immersion in French or Spanish, we also provide an introduction to a global topic (this year: immigration) that reveals how language, culture, religion, history, economics and politics converge to influence the flow of populations.
The Summer Humanities Institute is a three week program in which students develop and present interdisciplinary, guided research projects in History (including art historical topics) or literature and theater, and acquire tools and techniques of research, interpretation, and presentation essential to achieve the goal of humanistic research: to understand with depth and complexity the nature of human thought, action, and expression. | 677.169 | 1 |
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
0.32 MB | 11 pages
PRODUCT DESCRIPTION
These guided notes are designed to help students understand the objective, explore the standard, and apply the concepts. This is designed to be used along with teacher led discussions, instruction, and facilitation. An answer key is included. Thank you for using Mac's Guide to Discovering Algebra | 677.169 | 1 |
No terms or rules were declared by Con in the first round. Thus it is unclear (to me) whether an argument should be fully presented. Since Con did not begin with a fully argument, I will simply take this opportunity to define terms and state my position more precisely, leaving the main argument for Rounds 2 and 3. Apologies if the content of this post extends beyond the expectations for the first round of this debate.
Calculus can be defined as the mathematical study of limits [1], and/or the mathematical study of change [2].
A limit is a concept in mathematics which is used to describe the behaviour of a function or a system as its inputs approach a particular set of values. Limits are of particular interest where the behaviour of the function or system is not obvious (often when the inputs are zero, negative infinity, or positive infinity).
My position is that the basics of calculus can, and should, be taught in the 4th grade. My argument will consist mainly of two basic points: (1) children of that age are capable of understanding the basic concepts of calculus, and (2) an understanding of the basic concepts of calculus is beneficial for children of that age.
To premise the argument, I would like to differentiate between a few levels of understanding in calculus.
(1)A basic understanding of the concepts of calculus involve a conceptual understanding of limits, working with infinity, rates of change and changing rates of change, and accumulation (integration) of quantity.
(2)A further level of understanding in calculus is the learned ability to compute derivatives and integrals.
(3)A deeper level of understanding in calculus implies the ability to generate and manipulate mathematical expressions to make derivatives and integrals easier to compute, but also to describe different aspects of real world problems.
(4)A deep understanding of calculus implies the ability to derive theorems and produce mathematical proofs relating to the concepts and principles of calculus.
A basic understanding is sufficient to allow one to appreciate the significance of calculus in the world to a valuable degree, and to gain a deeper understanding of reality. Therefore, I will be arguing for teaching the basic concepts of calculus to 4th grade students. I will also give examples of how the concepts of calculus can be taught to a student who has only a 4th grade level of mathematical ability and why even this rudimentary level of understanding is beneficial for their conceptual understanding of the world, their development, and their future success.
I look forward to an interesting debate and hope for the best from both sides!
The concepts of calculus can easily be explained with visual examples that a 4th grader can understand.
Infinity implies a quantity that is large to an unlimited degree, while infinitesimal is a quantity that is small to an unlimited degree. Here is a simple illustration: if you start drawing a straight line and just go on forever, the length of the line is infinite. Or, if you keep dividing a line in half, you will get smaller and smaller lines but you can always divide it in half forever.
Limits: Draw a triangle. Then a square. Continue to add one side to the polygon. By adding sides, the shape becomes closer and closer to a circle. Indeed, the limit of a polygon as the number of sides approaches infinity is a circle. Similarly, if you collapse one side of a triangle, you get two lines on top of each other (2 sides). Collapsing one of the lines gives you a line again (1 side). And if you collapse that line, you get a dot (0 sides). So the limit of a polygon as the number of sides approaches 0, is a dot. This is the essence of limits.
Differentiation tells you how much a quantity is changing at a specific point. Understanding this only requires knowledge of basic division, which all 4th graders have. Take a right-angle triangle and color it in. Ask how much the height of the triangle changed from the start to the end. This is of course the height of the triangle divided by the length. Now erase some of the color from the beginning and the end, and ask the same question. Keep erasing to get smaller and smaller slices of the triangle and repeat the calculation. The limit as the colored slice gets infinitely thin is the derivative at the point along the length where the triangle is still colored.
Integration: Integration is basically the generalized concept of area or volume for any shape. Draw an irregular shape and explain how you can roughly estimate the area by drawing thing rectangles side by side with the tops touching the curve and adding up the areas. Now make the rectangles thinner and show that the estimated area is slightly more precise (color the part of the rectangle that is inside the shape blue, and the parts outside the shape red, and as you make the rectangles thinner, you can see the amount of red decreasing). The integral is what you get when you take the limit of the total area of all the rectangles as their widths become infinitesimally small (which also means the number of rectangles approaches infinity).
These together are the essentials of understanding calculus. With this, equations become more intuitive. But equations are only descriptions and not calculus itself, in much the same way that the word 'dog' is not actually a dog. Therefore, conceptually and visually understanding the above examples is actually understanding calculus, just like a toddler understands what a dog is before they can read and write 'dog'.
I will explain why these concepts are important for 4th graders in the final round.
It doesn't seem right to present the final portion of my argument. I will instead summarize very briefly and state some reasons understanding calculus can be beneficial for children.
Calculus is the foundation of all modern scientific understanding, even in fields which are not typically associated with mathematics, such as biology and medicine. Underlying the principles and methods used in all fields of science, whether directly or indirectly, is calculus. For example, see the Noyers Whiter equation for calculating dosage rates ( or see hypothesis testing in statistics, which is used in most scientific studies and clinical trials to establish whether acquired data supports or fails to support a particular hypothesis. As someone with a mathematics degree specializing in statistics, I can say that almost all of probability and statistics is based upon calculus.
Calculus itself is not the symbols and calculations most people associate with it. Calculus, in reality, is the set of concepts, ideas, and principles which give meaning to those symbols and allow us to develop methods for those calculations. Therefore I have argued that this level of understanding calculus should be the focus of education. I have also argued that a basic level of each of the essential concepts of calculus (infinity, limits, derivatives, integrals) is within reach of children at the 4th grade level and I have provided basic sketches of how these concepts can be taught to children.
However, the question of this debate is 'why' teach calculus to children, not whether or not it is possible. I will presume that establishing benefits from learning calculus for children in the 4th grade which outweigh the effort involved in learning the concepts involved is sufficient to answer the question.
As I said at the beginning of this post, I will not put in the effort to establish the validity of these benefits when my opponent has not taken the time or effort to argue his side. I will simply list these benefits and invite any reader to take up this debate with me if they disagree.
Benefits:
1) Improved ability to understand scientific concepts, including such things as velocity and acceleration in physics, which are currently taught in high school without calculus, even though calculus is required for learning the actual concepts.
2) Improved understanding of the natural world around them (all sorts of phenomena involving rates of change and accumulation).
3) Understanding infinity and limits in a concrete sense have great potential to expand the mind and develop the brain for higher level concepts.
4) Greater appreciation of math and science.
I will conclude by thanking Con for setting up this debate. It is a topic in which I am very interested, and I strongly advocate teaching calculus to children of this age. I personally intend to teach my children calculus starting from the first grade.
I was really looking forward to a debate. Sadly, it isn't really a debate at this point. But I want to finish my argument because one major reason for doing this debate was to formalize my thoughts on this topic. Hopefully anyone reading the debate will find it useful on some level. Maybe Con will find some value in my posts as well.
To Con, I sincerely hope you will try to make the best argument you can on your next post =)
By the way, could anyone inform me if it inappropriate for me to comment on this forum while the debate is still active, as long as I don't further my arguments?
Reasons for voting decision: Conduct - Pro. This is due to Con's forfeit in R3 which is rarely acceptable behavior in any debate setting. S&G - Pro. Con failed to use proper grammar throughout the debate. Arguements - Pro. Con failed to provide rebuttals to most of Pro's arguments. This allowed Pro to continue debating unchallenged and in doing so, fully affirmed the resolution. Sources - Pro. Con failed to utilize sources or cite anything throughout the debate, whereas Pro did. Due to this, Pro is awarded source points. This is a solid 7-point win for Pro. | 677.169 | 1 |
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