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Consumer Math Elective Course Length 2 semesters Available in Ignitia Switched-On Schoolhouse LIFEPAC This practical math elective trains students in mathematical applications used in everyday situations. Consumer math includes real-world examples and an emphasis on critical thinking skills to solve problems. Topics in the first semester of this course from our online academy include an overview of basic math skills, personal finance skills, statistics and home recordkeeping, taxes, insurance, and banking services. Building financial literacy, this course from our online academy's second semester includes topics such as credit cards and loan interest, purchasing items, discounts and markups, travel and transportation costs, vacation spending, retirement planning, and job related services. Encouraging solid financial habits, consumer math is essential for success in adulthood no matter students' desired career paths. Each unit of the course contains quizzes and a test to evaluate progress and student mastery. Additional Details Ready to Get Started with Our Online Academy? Alpha Omega Academy has year-long open enrollment, so you can start this course at any time! Visit the tuition page of our online academy to learn more about pricing or click the button below to get started with enrollment today. Have questions first? Call us at 800.682.7396. I am a junior and I have been with the Alpha Omega programs since kindergarten (with Horizons Math, etc.)! When I got into high school, my parents put me into the academy online. Alpha Omega Academy is an accredited secondary school. They also have a chapter from the National Honor Society. If you are looking for great teachers, a flexible schedule, easy to understand yet advanced material, and a ...moregreater learning for your child, then AOA is it! I do most of my schoolwork on my own, and it has taught me wonderful time management skills and great study skills and has given me a greater sense of responsibility when it comes to my education. These traits have come in quite handy at work and at "play."Julia S. – United States
Presentation Transcript NUMERICAL METHODS : NUMERICAL METHODS/ANALYSIS : NUMERICAL METHODS/ANALYSIS IT IS THE DEVELOPMENT & STUDY OF PROCEDURES FOR SOLVING PROBLEMS WITH A COMPUTING INSTRUMENT OR COMPUTER. ALGORITHM : ALGORITHM IT IS USED FOR A SYSTEMATIC PROCEDURE THAT SOLVES A PROBLEM OR A NUMBER OF PROBLEMS. ITS EFFICIENCY MAY BE MEASURED BY THE NUMBER OF STEPS IN THE ALGORITHM, THE COMPUTER TIME, AND THE AMOUNT OF MEMORY (OF THE COMPUTING INSTRUMENT) THAT IS REQUIRED. NOTE AND UNDERSTAND : NOTE AND UNDERSTAND THE MAJOR ADVANTAGE OF NUMERICAL ANALYSIS IS THAT A NUMERICAL VALUE CAN BE OBTAINED EVEN WHEN THE PROBLEM HAS NO "ANALYTICAL" SOLUTION. THE MATHEMATICAL OPERATIONS REQUIRED (GENERALLY) ARE ESSENTIALLY ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION PLUS MAKING COMPARISONS. NOTE AND UNDERSTAND : NOTE AND UNDERSTAND IT IS IMPORTANT TO REALIZE THAT A NUMERICAL ANALYSIS SOLUTION IS ALWAYS NUMERICAL. ANALYTICAL METHODS, ON THE OTHER HAND, USUALLY GIVE A RESULT IN TERMS OF MATHEMATICAL FUNCTIONS THAT CAN THEN BE EVALUATED FOR SPECIFIC INSTANCES. NOTE AND UNDERSTAND : NOTE AND UNDERSTAND NUMERICAL ANALYSIS IS AN APPROXIMATION, BUT RESULTS CAN BE MADE AS ACCURATELY AS DESIRED. TO ACHIEVE HIGH ACCURACY, NUMEROUS SEPARATE OPERATIONS MUST BE CARRIED OUT, BUT CURRENT COMPUTERS DO THEM SO RAPIDLY WITHOUT EVER MAKING MISTAKES. SOME OPERATIONS THAT NUMERICAL ANALYSIS CAN DO : SOME OPERATIONS THAT NUMERICAL ANALYSIS CAN DO SOLVE FOR THE ROOTS OF A NON-LINEAR EQUATION. SOLVE FOR LARGE SYSTEMS OF EQUATIONS. GET THE SOLUTIONS OF A SET OF NON-LINEAR EQUATIONS. INTERPOLATE TO FIND THE INTERMEDIATE VALUES WITHIN A TABLE OF DATA. SOME OPERATIONS THAT NUMERICAL ANALYSIS CAN DO : SOME OPERATIONS THAT NUMERICAL ANALYSIS CAN DO FIND EFFICIENT & EFFECTIVE APPROXIMATIONS OF FUNCTIONS. APPROXIMATE DERIVATIVES OF ANY ORDER FOR FUNCTIONS EVEN WHEN THE FUNCTION IS KNOWN ONLY AS A TABLE OF VALUES. INTEGRATE ANY FUNCTION EVEN WHEN IT IS KNOWN ONLY AS A TABLE OF VALUES. SOME OPERATIONS THAT NUMERICAL ANALYSIS CAN DO : SOME OPERATIONS THAT NUMERICAL ANALYSIS CAN DO SOLVE ORDINARY DIFFERENTIAL EQUATIONS WHEN GIVEN INITIAL VALUES OR CONDITIONS FOR THE VARIABLES. THESE CAN BE OF ANY ORDER &/OR COMPLEXITY. SOLVE BOUNDARY-VALUE PROBLEMS & DETERMINE EIGENVALUES & EIGENVECTORS. SOME OPERATIONS THAT NUMERICAL ANALYSIS CAN DO : SOME OPERATIONS THAT NUMERICAL ANALYSIS CAN DO OBTAIN NUMERICAL SOLUTIONS OF ALL TYPES OF PARTIAL DIFFERENTIAL EQUATIONS. FIT CURVES TO DATA BY A VARIETY OF METHODS STATE THE PROBLEM CLEARLY, INCLUDING ANY SIMPLIFYING ASSUMPTIONS. DEVELOP A MATHEMATICAL STATEMENT OF THE PROBLEM IN A FORM THAT CAN BE SOLVED FOR A NUMERICAL ANSWER THIS PROCESS MAY INVOLVE, AS IN THE PRESENT CASE, THE USE OF CALCULUS. IN OTHER SITUATIONS, OTHER MATHEMATICAL PROCEDURES MAY BE EMPLOYED. WHEN THIS STATEMENT IS A DIFFERENTIAL EQUATION, APPROPRIATE INITIAL CONDITIONS AND/OR BOUNDARY CONDITIONS MUST BE SPECIFIED SOLVE THE EQUATIONS THAT RESULT FROM STEP #2. SOMETIMES THE METHOD WILL BE ALGEBRAIC, BUT FREQUENTLY MORE ADVANCED METHODS WILL BE NEEDED. THE RESULT OF THIS STEP IS A NUMERICAL ANSWER OR SET OF ANSWERS INTERPRET THE NUMERICAL RESULT TO ARRIVE AT A DECISION. THIS WILL REQUIRE EXPERIENCE & AN UNDERSTANDING OF THE SITUATION IN WHICH THE PROBLEM IS EMBEDDED. THEORETICAL MATTERS : THEORETICAL MATTERS ANY USER OF MATHEMATICAL PROCEDURES SHOULD ALWAYS BE CONCERNED WITH ITS THEORETICAL UNDERPINNINGS BECAUSE THESE EXPLAIN THE LIMITATIONS OF THE PROCEDURES TO PRODUCE THE RELIABLE RESULTS. WHEN THEORY IS TO BE DISCUSSED, TWO QUESTIONS ARISE: : WHEN THEORY IS TO BE DISCUSSED, TWO QUESTIONS ARISE: WHERE DO WE START? WHAT BACKGROUND IS ASSUMED? DOES EVERY DEFINITION &/OR POSTULATE HAVE TO BE STATED OR CITED BEFORE PERTINENT THEOREMS ARE DEVELOPED? WHEN THEORY IS TO BE DISCUSSED, TWO QUESTIONS ARISE: : WHEN THEORY IS TO BE DISCUSSED, TWO QUESTIONS ARISE: 2. HOW ARE THE THEOREMS PRESENTED? IS IT BETTER TO USE THE RATHER CONDENSED NOTATIONS OF MATHEMATICIANS & THEIR SPECIAL SYMBOLS, OR TO USE LANGUAGE & STYLE THAT IS MORE ACCESSIBLE TO THE AVERAGE PERSON UNDER WHAT CONDITIONS DOES THE METHOD APPLY? FOR WHAT KINDS OF FUNCTIONS DO THE METHOD WORK AND HOW CAN WE KNOW THAT THE CONDITIONS ARE SATISFIED 2. DOES THE METHOD CONVERGE? DO THE SUCCESSIVE APPROXIMATIONS REACH THE TRUE ANSWER TO A GIVEN ACCURACY WHAT BOUNDS CAN BE PLACED ON THE ERROR OF EACH ESTIMATE? CAN WE KNOW IN ADVANCE THE MAXIMUM SIZE OF THE ERROR AFTER A CERTAIN HOW RAPIDLY DO THE ERRORS OF THE SUCCESSIVE ESTIMATES DECREASE? DO ERRORS DECREASE PROPORTIONALLY TO THE IS THE ACCURACY IMPROVED MORE RAPIDLY (EXPONENTIALLY) RATHER THAN LINEARLY? (MOST DESIRABLE SITUATION) HOW ACCURATELY DO WE KNOW THE ERROR?
13.1 Additional Graphs of Functions 13.2 The Circle and the Ellipse 13.3 The Hyperbola and Functions Defined by Radicals 13.4 Nonlinear Systems of Equations 13.5 Second-Degree Inequalities and Systems of Inequalities
A fully featured scientific calculator with convert fractions, calculate areas of circles, perform trigonometry and type out fancy equations. Looks like real calculator. Scientific calculators are used widely in any situation where quick access to certain mathematical functions is needed, especially those such as trigonometric functions that were once traditionally looked up in tables.Science helper for MS WordŽ is a fundamental tool for the aspiring science teacher, student or researcher. This program will allow the user to make a professional and functional document with ease of point and click usage. Easily add 1200 Scientific Graphs & Charts to your word docsCreateIn each square put numbers until the total for the row is equal to the value next to the row. Make sure you get the right values in each column and in the diagonal direction too! To see what it looks like, look below. Educational math software for school or personal. Math Genius is a powerful and original software. Those who are concerned about their child's math skills should find Math Genius a very good way to get started. It is for children ages from 4 to 8. The Game lets your child easily learn the Multiplication Table. Usually, the Game captures the child's attention for 5-15 minutes. As you play Math Genius every3-5 days, you will see the progress in your child's knowledgeCurvFit (tm) is a curve fitting program 4 Windows 95/98. Lorentzian, Sine, Exponential and Power series are available models to match your data. A Lorentzian series is highly recommended for real data especially for multiple peaked/valleys data. CurvFit is an example of Calculus level programming... ie. minutes to solve, days or years to understand solution and what it implies (e.g. wrong model, sampling rate error). See comments in EX-*.?The Bluebit LU, Cholesky, QR, SVD. Both real and complex matrices are supported.
MAT117 Week 9 Discussion 1 Week 9 DQ 1 1) From the concepts you have learned in this course, provide a real-world application of something that you think has been the most valuable to you? Why has it been valuable? 2) How do you think you will use the information you learned in this course in the future? 3) Which concepts will be most important to you? Explain why. 4) Which do you anticipate will be the least important? Explain why. RESPONSE 1 1) From the concepts you have learned in this course, provide a real-world application of something that you think has been the most valuable to you? Why has it been valuable? From the concepts that I have learned in this course, algebra in this class has showed me that it can be a useful tool that can be used in various amount of ways. First of off to start out with that math can be used to determine things like distance, measurement, and percentage. The use of equations has helped better my knowledge solving quadtraic, polynomial and radical equations. The concept in how it has provided a real-world application to myself is how I will be able to use rational expressions to solve like baking and cooking and also calculating my past and taxes. The my math lab helped me a lot with equations because it gave examples that explained how to solve each problem making it easier for me while taking my tests because I was already was doing them and had notes to help me out. Also the use of mymath lab helped break the equations in steps making it less complex and easier to understand. I suggest that students taking this course are well organized and very good with keeping up with due dates and studying.... View Full Document MOST POPULAR MATERIALS FROM MAT 117 Week 9 DQ 2 1) What one concept learned in this course was the easiest for you to grasp? Why do you think it was easy for you? 2) Which was the hardest? What would have made that hard-to-learn concept easier to learn? RESPONSE 1 The easiest concept for me Week 1 DQ 1 1. What four steps should be used in evaluating expressions? 2. Can these steps be skipped or rearranged? Explain your answers. 3. Provide an expression for your classmates to evaluate. RESPONSE 1 In Algebraic expression letters are used to st Week 1 DQ 2 1. Do you always use the property of distribution when multiplying monomials and polynomials? Explain why or why not. 2. In what situations would distribution become important? 3. Provide an example using the distributive property for your claWeek 8 DQ 3 Which of the four operations on functions do you think is the easiest to perform? What is the most difficult? Explain why for the easiest and most difficult. RESPONSE 1 Of the four basic operations on functions the one I would choose is additi Week 3 DQ 1 Answer the following in no less than 150 words. 1. 2. 3. 4. How do you factor the difference of two squares? How do you factor the perfect square trinomial? How do you factor the sum and difference of two cubes? Which of these three makes the MOST POPULAR MATERIALS FROM University of PhoenixAPA Reference and Citation Worksheet 1 GEN/200 Version 2 University of Phoenix Material APA Reference and Citation Worksheet Write a sentence to illustrate each of the following. Refer to the appropriate Center for Writing Excellence resources. Sentence 1
MATH 1332: College Mathematics (3-0-3) Modern algebra and geometry. Topics may include sets, logic, number systems, number theory, functions, equivalence, congruence, measurement, other geometric concepts, and the introduction to probability and statistics. Prerequisite: DMTH 0200 or equivalent as determined by THEA/THEA alternative test. MATH 1342: Statistics (3-0-3) Presentation and interpretation of data, probability, sampling, correlation and regression, analysis of variance, and the use of statistical software. Prerequisite: DMTH 0200, or equivalent as determined by THEA/THEA alternative test.
Saxon Math Placement Test Click on a Saxon math placement test from the list shown above to open the test. These are PDF files that you can save to your local computer or print. Each test comes complete with everything needed including all test questions and answers. In the early grades from kindergarten to third grade, Saxon math directly corresponds to grade levels. However, higher levels of Saxon math from Math 54 and up do not necessarily correspond directly to any grade levels. The levels indicated below are provided only to show the grade levels when most students typically take each Saxon Math level. It is strongly recommended to have your student take the Saxon math placement test to determine which level is best for them. Typically students take the higher level Saxon courses as follows: Saxon Math 54 in the 4th grade Saxon Math 65 in the 5th grade Saxon Math 76 in the 6th grade Saxon Math 87 in the 7th grade (see note below) Saxon Algebra 1/2 in 7th or 8th grade Saxon Algebra 1 in the 8th or 9th grade Saxon Algebra 2 in 9th or 10th grade Saxon Geometry in 10th or 11th grade Saxon Advanced Math in 11th or 12th grade Saxon Calculus in 12 grade or college Note: Saxon Math 87 contains a lot of review of previous levels. As a result, some students who demonstrate a good grasp of the lessons from Math 54 to Math 76 are able to skip most or all of Math 87. Towards the end of Math 87, pre-algebra concepts are introduced so it is not all review. Students should take the Saxon math placement test to determine what level is best for them.
More About This Book Inside the Book: All the Practice & Strategies You Need · 200+ practice questions with detailed answers and explanations · Step-by-step strategies to master every type of math question on the GRE, including tricky Quantitative Comparison, All-That-Apply, and Numeric Entry questions · Helpful review of the math basics, algebra, and geometry you'll need on the Math section of the GRE · Glossary of common terms to brush up on your math vocabulary · Summary of important triggers to maximize your test-taking
Personal tools Click on the image above to have a high-resolution version of the poster Info Modern Mathematics International Summer School for Students 2014 This summer school is an introduction to mathematical research topics for international students at the age of transition between high school and university. Presentations and mini-courses will be given by international university mathematicians. The summer school combines the best features from several successful international activities for talented students, such as: The first three international summer schools in our series, held since 2011 in Bremen (Germany) at Jacobs University and in Lyon (France) at École Normale Supérieure All of these activities have created great excitement among the participants and the speakers alike. In particular, in the past editions, the participants were thrilled about the great mathematicians that came as speakers. They were easy accessible, and on their side, speakers were impressed by the young mathematical excitement they met during the school. We hope that our school will help foster connections among the international participants as well as develop the attractiveness of the European Research Area at international level, and we hope that it will encourage international students to study in Europe and in particular in the host countries. We are very happy that some of the most prominent and exciting international research mathematicians have agreed to joining the Scientific Committee and coming to Lyon as lecturers. The scientific age of the contestants should be so that they are in their last years of high school, or in their first two years of university. Of course this means different things, in terms of preparation, for different countries. In particular, participants should have working knowledge in basic calculus, and they should not yet have specialized into any particular area of mathematics. We are committed to admitting talented students with diverse backgrounds. We hope that many young women will apply and will be admitted.
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).
*Abstract Algebra: Intro - 3rd edition Summary: ABSTRACT ALGEBRA: AN INTRODUCTION is intended for a first undergraduate course in modern abstract algebra. The flexible design of the text makes it suitable for courses of various lengths and different levels of mathematical sophistication, ranging from a traditional abstract algebra course to one with a more applied flavor. The emphasis is on clarity of exposition. The thematic development and organizational overview is what sets this book apart. The chapters are organized around th...show moreree themes: arithmetic, congruence, and abstract structures. Each Them is developed first for the integers, then for polynomials, and finally for rings and groups. This enables students to see where many abstract concepts come from, why they are important, and how they relate to one another. ...show less Hardcover Fair 1111569622
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).
Alameda Algebra 1 tutored all of the above concepts and their applications to high school and college students. Microsoft Excel is spreadsheet software whose parts create a powerful tool for presenting financial information. Program parts make gathering and presenting of information easier, and allow for advanced spreadsheet functions
A classic single-volume textbook, popular for its direct and straightforward approach. Understanding Pure Mathematics starts by filling the gap between GCSE and A Level and builds on this base for candidates taking either single-subject of double-subject A Level.
Understanding Calculus II: Problems, Solutions, and Tips Professor Bruce H. Edwards Solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas with the skills you learn in Understanding Calculus II: Problems, Solutions, and Tips. This second course in the calculus sequence introduces you to exciting new techniques and applications of one of the most powerful mathematical tools ever invented. Professor Bruce H. Edwards of the University of Florida enriches these 36 lectures with crystal-clear explanations, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce key concepts. Inscribed over the entrance of Plato's Academy were the words, "Let no one ignorant of geometry enter my doors." To ancient scholars, geometry was the gateway to knowledge. Its core skills of logic and reasoning are essential to success in school, work, and many other aspects of life. Yet sometimes students, even if they have done well in other math courses, can find geometry a challenge. Now, in the 36 innovative lectures of Geometry: An Interactive Journey to Mastery, Professor James Tanton of The Mathematical Association of America shows students a different and more creative approach to geometry than that usually taught in high schools. Like building a house brick by brick, students learn to use logical reasoning to uncover fundamental principles of geometry, and then use them in fascinating applications. Understanding Calculus: Problems, Solutions, and Tips Professor Bruce H. Edwards Immerse yourself in the unrivaled experience of learning—and grasping—calculus with Understanding Calculus: Problems, Solutions, and Tips. These 36 lectures cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college. Award-winning Professor Bruce H. Edwards guides you through hundreds of examples and problems, each of which is designed to explain and reinforce the major concepts of this vital mathematical field. Algebra I Professor James A. Sellers Algebra I is an entirely new course designed to meet the concerns of both students and their parents. These 36 accessible lectures make the concepts of first-year algebra—including variables, order of operations, and functions—easy to grasp. For anyone wanting to learn algebra from the beginning, or for anyone needing a thorough review, Professor James A. Sellers will prove to be an inspirational and ideal tutor. Open yourself up to the world of opportunity that algebra offers by making the best possible start on mastering this all-important subject. Algebra II Professor James A. Sellers Make sense of Algebra II in the company of master educator and award-winning Professor James A. Sellers. Algebra II gives you all the tools you need to thrive in a core skill of mathematics. In 36 engaging half-hour lectures, Professor Sellers walks you through hundreds of problems, showing every step in their solution and highlighting the most common missteps made by students. Designed for learners of all ages, this course will prove that algebra can be an exciting intellectual adventure and not nearly as difficult as many students fear In Professor James A. Sellers' engaging course, Mastering the Fundamentals of Mathematics, you learn all the key math topics you need to know. In 24 lectures packed with helpful examples, practice problems, and guided walkthroughs, you'll finally grasp the all-important fundamentals of math in a way that truly sticks. Mathematics Describing the Real World: Precalculus and Trigonometry Professor Bruce H. Edwards Finally make sense of the mysteries of precalculus and trigonometry in the company of master educator and award-winning Professor Bruce Edwards. In the 36 intensively illustrated lectures of Mathematics Describing the Real World: Precalculus and Trigonometry, he takes you through all the major topics of a typical precalculus course taught in high school or college. You'll gain new insights into functions, complex numbers, matrices, and much more. The course also comes complete with a workbook featuring a wealth of additional explanations and problems. Chemistry, 2nd Edition Professor Frank CardullaHow to Become a SuperStar Student, 2nd Edition ProfessorHigh School Level—Geometry Professor James Noggle Professor Noggle's lectures on geometry are exceptionally clear and well organized. He has an evident love for the topic, and a real gift for conveying the elegance and precision of geometric concepts and demonstrations. You will learn how geometrical concepts link new theorems and ideas to previous ones. This helps you see geometry as a unified body of knowledge whose concepts build upon one another. Save Up To $185 Prove It: The Art of Mathematical Argument Professor Bruce H. Edwards Mathematical proof is the gold standard of knowledge. Once a mathematical statement has been proved with a rigorous argument, it counts as true throughout the universe and for all time. Imagine, then, the thrill of being able to prove something in mathematics. But you don't have to imagine the exhilaration of constructing a proof—you can do it! Prove It: The Art of Mathematical Argument initiates you into this thrilling discipline in 24 lectures by Professor Bruce H. Edwards of the University of Florida. This course is suitable for everyone from high school students to the more math-savvy. Get an essential primer on the core subjects of geometry and algebra in this fundamental course set that opens the door to higher math. In Professor James Tanton's Geometry: An Interactive Journey to Mastery, students learn how to draw inferences from established ideas to build a line of reasoning, rather than start with the result and work backward. And in Professor James Sellers' Algebra I, students learn or review all the key topics normally covered in a first-year algebra course. Master the core subject of geometry and then see its integral relationship to trigonometry in this course set taught by two innovative and exceptionally clear mathematicians. First, in Professor James Tanton's Geometry: An Interactive Journey to Mastery, students learn all the key concepts of high-school geometry and explore real-world applications. Then, in Professor Bruce Edwards's Mathematics Describing the Real World: Precalculus and Trigonometry, students study advanced algebra, trigonometry, exponents, logarithms, and much more to prepare for calculus and higher mathematics.
Cliffs Quick Review for Geometry - 01 edition Summary: When it comes to pinpointing the stuff you really need to know, nobody does it better than CliffsNotes. This fast, effective tutorial helps you master core geometry concepts -- from perimeter, area, and similarity to parallel lines, geometric solids, and coordinate geometry -- and get the best possible grade. At CliffsNotes, we're dedicated to helping you do your best, no matter how challenging the subject. Our authors are veteran teachers and talented wri...show moreters who know how to cut to the chase -- and zero in on the essential information you need to succeed. ...show less Ed Kohn, MS is an outstanding educator and author with over 33 years experience teaching mathematics. Currently, he is the testing coordinator and math department chairman at Sherman Oaks Center for Enriched Studies.0764563807
Mathematics and Statistics for the Life Sciences Assuming no previous knowledge of statistics or mathematical skills, we aim to bring students to the point where they may confidently apply basic mathematical and statistical technicques to their own data and understand such applications. A History of Mathematics from Euclid to Weiss We cover some of the key developments, moments, and personalities in the creation of mathematics over the last two thousand years. We start with a look at Greek mathematicians, following on with Pascal, Descates, Newton and Gauss.
More About This Book Overview ARE YOU READY TO TEACH IN GEORGIA? THEN USE THE MOST COMPREHENSIVE GUIDE ON THE MARKET TODAY. GACE Mathematics Assessment (022, 023) The Most Complete Subject Review Everything you need to know for the GACE Mathematics Assessment (022, 023) exams, prepared by a leading specialist in teacher education. Comprehensive review chapters cover all the subjects and skills tested on the exams. Examples in each chapter reinforce knowledge as you study. The Best Practice Exams Available 2 practice exams (each contains both 022 and 023 subtests) based on the official GACE Mathematics Assessment – balanced to include every topic and type of question you can expect on the actual GACE Mathematics Assessment exams GACE Mathematics content and practical advice have helped millions succeed on their exams. With our step-by-step plan, you can score high on the GACE and get certified to teach in Georgia! Federal Guidelines for NCLB Compliance You can expect that candidates with NCLB-compliant credentials will enjoy preferential status in hiring. In Georgia, this means you need to pass the GACE. Maximize your exam performance and master the GACE with the unrivaled certification expertise that only REA can offer. Get the World's Most Advanced GACE Software REA's GACE Mathematics Assessment GACE! Product Details Meet the Author About the Author Dr. Greg Chamblee has taught mathematics on both the high school and university levels. He is currently a full professor at Georgia Southern University in the Department of Middle Grades and Secondary Education. He specializes in the area of middle grades and secondary mathematics education. His research emphasis is on the impact of technology on the teaching and learning process. Dr. Chamblee completed his doctorate at the University of North Carolina at Chapel Hill. Read an Excerpt About This Book and TestWare® REA's GACE (022, 023) Mathematics Assessment Test is a comprehensive guide designed to assist you in preparing to take this GACE test. To help you to succeed in this important step toward your teaching career in Georgia schools, this test guide features: • An accurate and complete overview of the GACE (022, 023) Mathematics Assessment Test • The information you need to know about the exam • A targeted review of each subarea • Tips and strategies for successfully completing standardized tests • Diagnostic tools to identify areas of strength and weakness • Two full-length, true-to-format practice tests based on the most recently administered GACE (022, 023) Mathematics Assessment Test • Detailed explanations for each answer on the practice tests. These allow you to identify correct answers and understand not only why they are correct but also why the other answer choices are incorrect. When creating this test prep, the authors and editors considered the most recent test administrations and professional standards. They also researched information from the Georgia Professional Standards Commission, professional journals, textbooks, and educators. The result is the best GACE test preparation materials based on the latest information available. About Test Selection The GACE tests are offered during morning and afternoon test sessions. However, this test is only given in the afternoon. Test sessions are four hours in length. About the GACE 022, 023 Mathematics Assessment Test • The purpose of the GACE (022, 023) Mathematics Assessment Test is to assess the knowledge and skills of prospective Georgia mathematics teachers. How Is the GACE 022, 023 Mathematics Assessment Test Scored? Your total test score will be a scaled score. A scaled score combines your correct answers to the scorable questions on the selected-response section of the test with the scores you received on the constructed-response questions. The scale runs from 100 to 300, with 220 being the passing score. When Will I Receive My Score Report, and What Will It Look Like? Reporting of Scores. Your scores are reported directly to the Georgia Standards Commission and are automatically added to your certification application file. Unofficial test scores are posted on the Internet at 5:00 p.m. Eastern Time on the score report dates listed on Can I Retake the Test? If you wish to retake a test, you may do so at a subsequent test administration. Please consult the GACE Website for information about test registration. The GACE website also includes information regarding test retakes and score reports. Who administers the test? The Georgia Professional Standards Commission (GaPSC) has contracted with the Evaluation Systems group of Pearson to assist in the development and administration of the Georgia Assessments for the Certification of Educators (GACE). When and where is the test given? How long will it take? The GACE is administered seven times a year at five locations across the state, as detailed on the GACE website. The 022, 023 Mathematics Assessment test is available during the morning sessions on all test days except during May and June. To receive information on upcoming test dates and locations, you may contact the test administrator at: When Should I Start Studying? It is never too early to start studying for the GACE 022, 023 Mathematics Assessment. The earlier you begin, the more time you will have to sharpen your skills. Do not procrastinate. Cramming is not an effective way to study because it does not allow you the time you need to think about the content, review the content required in the objectives, and take the practice tests. What Do the Review Sections Cover? The targeted review in this book is designed to help you sharpen the skills you need to approach the GACE 022, 023 Mathematics Assessment, as well as provide strategies for attacking the questions. Each teaching area included in the GACE 022, 023 Mathematics Assessment is examined in a separate chapter. The skills required for all areas are extensively discussed to optimize your understanding of what the examination covers. Your schooling has taught you most of the information you need to answer the questions on the test. The education classes you took should have provided you with the know-how to make important decisions about situations you will face as a teacher. The review sections in this book are designed to help you fit the information you have acquired into the objectives specified on the GACE. Going over your class notes and textbooks together with the reviews provided here will give you an excellent springboard for passing the examination. Studying for the GACE 022, 023 Mathematics Assessment Choose the time and place for studying that works best for you. Some people set aside a certain number of hours every morning to study, while others prefer to study at night before going to sleep. Other people study off and on during the day—for instance, while waiting for a bus or during a lunch break. Only you can determine when and where your study time will be most effective. Be consistent and use your time efficiently. Work out a study routine and stick to it. When you take the practice tests, simulate the conditions of the actual test as closely as possible. Turn off your television and radio, and sit down at a table in a quiet room, free from distraction. On completing a practice test, score it and thoroughly review the explanations to the questions you answered incorrectly; however, do not review too much at any one time. Concentrate on one problem area at a time by reviewing the question and explanation, and by studying the review in this guide until you are confident that you have mastered the material. Keep track of your scores so you can gauge your progress and discover general weaknesses in particular sections. Give extra attention to the reviews that cover your areas of difficulty, so you can build your skills in those areas. Many have found the use of study or note cards very helpful for this review. Test-Taking Tips Although you may not be familiar with tests like the GACE, this book will acquaint you with this type of exam and help alleviate your test-taking anxieties. By following the seven suggestions listed here, you can become more relaxed about taking the GACE, as well as other tests. Tip 1. Become comfortable with the format of the GACE. When you are practicing, stay calm and pace yourself. After simulating the test only once, you will boost your chances of doing well, and you will be able to sit down for the actual GACE with much more confidence. Tip 2. Read all the possible answers. Just because you think you have found the correct response, do not automatically assume that it is the best answer. Read through each choice to be sure that you are not making a mistake by jumping to conclusions. Tip 3. Use the process of elimination. Go through each answer to a question and eliminate as many of the answer choices as possible. If you can eliminate two answer choices, you have given yourself a better chance of getting the item correct, because only two choices are left from which to make your guess. Do not leave an answer blank. It is better to guess than not to answer a question on the GACE test because there is no additional penalty for wrong answers. Tip 4. Place a question mark in your answer booklet next to the answers you guessed, and then recheck them later if you have time. Tip 5. Work quickly and steadily. You will have four hours to complete the test, so the amount of time you spend will depend upon whether you take both subtests in one test session. Taking the practice tests in this book or on the CD will help you learn to budget your precious time. Tip 6. Learn the directions and format of the test. This will not only save time but also will help you avoid anxiety (and the mistakes caused by being anxious). Tip 7. When taking the multiple-choice portion of the test, be sure that the answer oval you fill in corresponds to the number of the question in the test booklet. The multiple-choice test is graded by machine, and marking one wrong answer can throw off your answer key and your score. Be extremely careful. Before the Test On the morning of the test, be sure to dress comfortably so you are not distracted by being too hot or too cold while taking the test. Plan to arrive at the test center early. This will allow you to collect your thoughts and relax before the test and will also spare you the anguish that comes with being late. You should check your GACE Registration Bulletin to find out what time to arrive at the center. What to Bring Before you leave for the test center, make sure that you have your admission ticket. Your admission ticket lists your test selection, test site, test date, and reporting time. See the Test Selection You must also bring two pieces of personal identification. One must be a current, government-issued identification, in the name in which you registered, bearing your photograph and signature, and one additional piece of identification (with or without a photograph). If the name on your identification differs from the name in which you are registered, you must bring official verification of the change (e.g., marriage certificate, court order). You must bring several sharpened No. 2 pencils with erasers, because none will be provided at the test center. If you like, you can wear a watch to the test center. However, you cannot wear one that makes noise, because it might disturb the other test takers. Dictionaries, textbooks, notebooks, calculators, cell phones, beepers, PDAs, scratch paper, listening and recording devices, briefcases, or packages are not permitted. Drinking, smoking, and eating during the test are prohibited. You may not bring any visitors, including relatives, children, and friends.You may bring a water bottle into the testing room, as long as it is clear without a label but with a tight lid. During testing, you will have to store your bottle under your seat. Security Measures As part of the identity verification process, your thumbprint will be taken at the test site. Thumbprints will be used only for the purpose of identity verification. If you do not provide a thumbprint, you will not be permitted to take the test and you will not receive a refund or a credit for the fee paid. Enhanced security measures, including additional security screenings, may be required by test site facilities. If an additional screening is conducted, only screened persons will be admitted to the test site. If you do not proceed through the security screening, you will not be allowed to test and you will not receive a refund or credit of any kind. Late Arrival Policy If you are late for a test session, you may not be admitted. If you are permitted to enter, you will not be given any additional time for the test session. You will be required to sign a statement acknowledging this. If you arrive late and are not admitted, you will be considered absent and will not receive a refund or credit of any kind. You will need to register and pay again to test at a future administration. Table of Contents CHAPTER 1 - INTRODUCTION About This Book and TestWare About Test Selection About the GACE 022, 023 Mathematics Assessment Test Overview Chart How to Use This Book and TestWare Studying for the GACE 022, 023 Mathematics Assessment Study Schedule Test-Taking Tips The Day of the Test CHAPTER 2 - NUMBER CONCEPTS AND OPERATIONS Real Number System and Its Components Real Number Properties of Equality Real Number Operations and Their Properties Absolute Value Number Theory Real Number and Integer Exponents Rational Exponents and Roots Complex Numbers Vectors Chapter 2 Quiz CHAPTER 3 - ALGEBRA Algebraic Terms Addition of Polynomials Subtraction of Polynomials Multiplication of a Polynomial by a Monomial Multiplication of Two Binomials Multiplication of Two Polynomials Division of a Monomial by a Monomial Division of a Polynomial by a Polynomial Binomial Theorem Direct and Inverse Variation Relations and Functions Linear Equations Determining the Equation of a Line Given a Table Determining the Equation of a Line Given a Graph Quadratic Functions Function Transformations Quadratic Equations Systems of Linear Equations Inequalities Linear Programming Matrices Sequences Chapter 3 QuizTeacher92 Posted November 20, 2010 Highly recommended! The format of this study guide was very easy to understand. I teach middle school mathematics. I passed the high school certification tests 022 and 023 on the first try with the help of this book! The software was not that useful. It could not give you an accurate score because of the constructed response questions you will have to answer on the real test. The content reviews were wonderful. This book is a great choice. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
statistics I can help you pass the class, take the test, or get into the college. ...Algebra 2 is a high school mathematics class often required for graduation. Algebra 2 expands upon the principles students learned in Algebra 1, including rules of operations and relations. The topics studied in Algebra 2 include equations and inequalities, quadratic
Advanced Engineering Mathematics with MATLAB - 2nd edition Summary: Advanced Engineering Mathematics using MATLAB® underlying philosophy of the book is: "The purpose of computing is insight, not numbers." The book features co...show moremplete MATLAB integration throughout, abundant examples that show real practical applications, and end-of-chapter problems that reinforce techniques
1111989761 9781111989767 Student Solutions Manual for McKeague/Turner's Trigonometry, 7th:Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.
Beginning Algebra John Tobey and Jeff Slater are experienced developmental math authors and active classroom teachers. They have carefully crafted their texts to ...Show synopsisJohn Tobey and Jeff Slater are experienced developmental math authors and active classroom teachers. They have carefully crafted their texts to support students in this course by staying with them every step of the way. Tobey and Slater...With you every step of the way. This 6th edtion of Beginning Algebra is appropriate for a 1-sem course in appropriate for a 1-sem course in Introductory, Beginning or Elementary Algebra where a solid foundation in algebraic skills and reasoning is being built for those students who have little or no previous experience with the topice. The utlimate goal of this text is to effectively prepare students to transition to Intermediate Algebra. One of the hallmark characteristics of Beginning Algebra 6e that makes the text easy to learn from is the building-block organization. Each section is written to stand on its own, and each homework set is completely self-testing. Beginning Algebra 6e is a worktext, meaning the design is open and friendly with wide margins so can you can encourage your students to take notes and work exercises right on the text page.Also with worktexts, images/visuals are used more frequently to convey the math concept so there are fewer words and less text for the student to read.Hide synopsis Description:Good. Minimal shelf wear, 8th edition Item may show signs of...Good. Minimal shelf wear, 8th69527Description:Fine. Paperback. Instructor Edition: Same as student edition...Fine. Paperback. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 9780321759061
Ms. Anne King/Integrated Algebra Contact Information Classroom Rules & Procedures Be prepared for class (textbook, notebook, pen/pencil, calculator, and assignment) - math is not a spectator sport Be respectful Common Core Algebra Year 1 – Grade 9 Students will study Common Core Algebra. We will cover all chapters in the book. Students will take their Common Core Algebra regents in June. Upon successful completion of the class and the regents, students will move onto Geometry. Grading Criteria Algebra - Year 1 of 2 – GRADE 9 Students will complete 1/2 of the course of Common Core Algebra. Upon successful completetion they will move onto Year 2 of Common Core Algebra. At the end of Year 2, they will take their Regent exam Year 2 of 2 – Grade 10 + Students will continue to study Common Core Algebra. The first ten weeks will be a review of the first year of Algebra. We will finish all of the chapters not completed in the first year. The students will have a regents in Common Core Algebra in June
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How To Graph Points & Lines (Algebra Graphs 101) Editorial Reviews Product Description Do you feel like your Algebra class is already over your head? Has it been a while since you've taken a math class but you want to get back in the game? Does your teacher draw points, lines, and curves on the graph so fast you don't even know where to start? I've been there, and trust me, it can be intimidating. Putting information on the graph doesn't have to be as hard as you think. Maybe your teacher is going too fast or the textbook doesn't make sense. In most cases, they each only have enough time to go over a few example problems before they move on to a new section. In the worst case, the teacher and the textbook just skip over the basic parts of the graph and assume you know it. You are not alone. This book will actually break down the different parts of the graph so you understand the graph itself before you have to plot anything on it. This book takes everything step by step, so you don't get (or stay) confused. This book will teach you: - The four key parts to any coordinate plane. - How to read each axis. - What are points, and where do they go? - The ONE way to graph ANY function. - Introduction to Graphing Lines. - Standard Form - Slope Intercept Form - Point Slope Form - How to actually graph a line using each of those 3 methods - Vertical and Horizontal Lines Demystified Still not convinced this book will teach you how to graph points and lines of any kind? Get FREE Video Training As A Bonus That's right, I have been a math tutor for years, and have recorded some tutorials just for you. I have tutored hundreds of hours of algebra material and have put the most useful graphing information in this book and in video training. The videos cover every example in the book and more. How this works is there's a secret website URL in the last section of the book where you can go and tell me where to email your free training videos. That's right, for less than what it would cost to get a private tutor for 15 minutes you will have a book AND video training on graphing points and lines. Don't let graphs keep you from understanding Algebra, you can learn it fast!
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edic mathematics Made Easy Description About the Book : A Simplified Approach For Beginners Can you multiply 231072 by 110649 and get the answer in just a single line? Can you find the cube root of 262144 or 704969 in two seconds? Can you predict the birth-date of a person without him telling you? Can you predict how much money a person has without him telling you? Can you check the final answer without solving the question? Or, in a special case, get the final answer without looking at the question? Can you solve squares, square roots, cube-roots and other problems mentally?All this and a lot more is possible with the techniques of Vedic Mathematics described in this book. The techniques are useful for students, professionals and businessmen. The techniques of Vedic Mathematics have helped millions of students all over the world get rid of their fear of numbers and improve their scores in quantitative subjects. Primary and secondary school students have found the Vedic mathematics approach very exciting. Those giving competitive exams like MBA, MCA, CET, UPSC, GRE, GMAT etc. have asserted that Vedic Mathematics has helped them crack the entrance tests of these exams. Similar Items by Category Discussion : Vedic mathematics Made Easy
Can low achieving mathematics students succeed in the study of linear inequalities and linear programming through real world problem based instruction? This study sought to answer this question by comparing two groups of low achieving mathematicsThe purpose of this study was to examine the effects of using Multiple Representations Charts in the classroom. This thesis was focused on the comparison of students' abilities to solve word problems using Multiple Representations Charts as anFor over thirty-five years average mathematics scores of students in the United States have been below the international average, indicating problems with performance when compared with students from other countries. The United States National... A review of the literature on the gambling behavior of college and university undergraduates explores the prevalence of gambling and also the prevalence of what is variously referred to as problem, pathological, disordered, or compulsive gambling... In recent years, there has been a focus on standards based tests results. The mathematics portions of these tests contain vast amounts of reading, which may affect how accurately they measure the mathematics achievement of the students beingThis research focuses on the role of pictures in elementary mathematics, specifically algebra. The participants in the study were elementary algebra students in Math 099 at Central Connecticut State University, chosen for this study based on their... This project focused on designing an individualized plan of instruction in mathematics. The participants in this project were adult incarcerated males between 18 and 52 years of age. These men were enrolled in an Adult Basic Education program students have been underperforming on international standardized tests for over thirty years. These concerns have been documented in publications (i.e. A Nation at Risk). The United States federal government has also written ―No Child
Precalculus - With 2 CDS - 4th edition Summary: Bob Blitzer's background in mathematics and behavioral sciences, along with his commitment to teaching, inspired him to develop a precalculus series that gets students engaged and keeps them engaged. Presenting the full scope of mathematics is just the first step. Blitzer draws students in with applications that use math to solve real-life problems.20 +$3.99 s/h Acceptable CampusBookRentals Ogden, UT Upper Saddle River, NJ 2009 Other 4th ed. Fair. $16.39 +$3.99 s/h Good SellBackYourBook Aurora, IL 0321559843 Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!! $201559845-5-0 $20.9727.97 +$3.99 s/h Good Nivea Books Lynnwood, WA Hardcover Good 0321559843 Used copy, without any marks or highlights. 2 of 2 CDs included. Has extensive shelf wear on covers. Might have several pages with tears This is Student US Edition. Same d...show moreay shipping with free tracking number. Expedited shipping available. A+ Customer Service! ...show less $29.03 +$3.99 s/h Acceptable newrecycleabook centerville, OH 0321559843 -used book - book appears to be recovered - has some used book stickers - free tracking number with every order. book may have some writing or highlighting, or used book stickers on front ...show moreor back ...show less $31.38 +$3.99 s/h Acceptable txtbroker Murfreesboro, TN Worn, but functional 4th Edition. Used - Acceptable. Used books do not include online codes or other supplements unless noted. Choose EXPEDITED shipping for faster delivery! r $33.99 +$3.99 s/h Acceptable walker_bookstore tempe, AZ 0321559843 WE HAVE NUMEROUS COPIES -HARDCOVER moderate/heavy wear to cover,edges, and corners - has cardboard showing on
InteGreat! allows the user to visually explore the idea of integration through approximating the integral value with partitions. The activity integrates a function and displays the value of the defini... More: lessons, discussions, ratings, reviews,... Graphical illustration of the Riemann sums of a function defined by its graph. The tool allows selecting the point inside the subintervals in several ways which helps show the dependence of the approx... More: lessons, discussions, ratings, reviews,... Experiment with left, right, and midpoint Riemann sums for functions you enter, as well as inscribed rectangles, circumscribed rectangles, and the trapezoid rule. Includes extensive directions for cu... More: lessons, discussions, ratings, reviews,... Sketchpad Activities for Introducing Calculus Topics is a series of five activities designed to introduce students to the basic concepts of calculus. Use these activities near the end of Precalculus c... More: lessons, discussions, ratings, reviews,... This activity builds on the previous activity, One Type of Integral, by suggesting two more efficient ways of estimating the area under a curve (definite integral) than counting squares: adding the ar... More: lessons, discussions, ratings, reviews,... This is a Java graphing applet that can be used online or downloaded. The purpose it to construct dynamic graphs with parameters controlled by user defined sliders that can be saved as web pages or em
Graduate Diploma of Mathematics Graduate Certificate in Mathematics What is this course about? CSU's Graduate Diploma of Mathematics provides mathematical training for people who do not have a university background in mathematics. Graduates in other disciplines who need to know and use mathematics in order to progress in their careers will also find the course meets their needs. CSU's Graduate Diploma of Mathematics includes topics in algebra and calculus that every advanced user of mathematics needs to know. It will supplement the knowledge and skills base of the graduate who has found that their previous mathematical training is now limiting. It can provide a flexible, tailored program of study to meet the varied needs of graduates in fields such as secondary education, research and extension work. Workplace learning Those students undertaking the teaching stream will need to complete a Curriculum Methods subject, where they will prepare assessments that are directly relevant to mathematics teaching. Students must also complete a Professional Experience subject, where they must demonstrate their competence by completing a 25-day mathematics teaching professional experience in a secondary school. Students with current mathematics teaching experience may apply for an exemption from the Professional Experience component of the course. Professional recognition A secondary teacher who has completed the teaching stream of this course will have met the minimum eligibility requirements for accreditation to teach mathematics as a second discipline in a NSW secondary school. Flexible study options Subjects are taught using a range of blended learning techniques. These include distance education study materials, video-captured lectures, online meetings, subject forums and additional online subject resources. The flexible learning environment allows students to study this online course from anywhere in the world. In the mathematics subjects, students are introduced to a mathematical computer software program, Maple, and are encouraged to apply this when solving more advanced problems. As with all CSU's courses, the Graduate Diploma of Mathematics and Graduate Certificate in Mathematics are designed and delivered with study flexibility in mind. Our students choose between full-time and part-time study options to fit in with work and lifestyle commitments. You could choose to study just one subject in an academic session or, with approval, fast-track degree completion by undertaking two or more subjects per session. This course is offered across a two-session academic year with sessions commencing in February and July each year. The Graduate Diploma of Mathematics has a minimum full-time duration of four sessions, however actual duration is dependent on subject availability and the session of commencement. Course structure The Graduate Certificate in Mathematics consists of four subjects including two core subjects and two restricted electives (from a choice of 10). The Graduate Diploma in Mathematics consists of eight subjects including two core subjects, with either a teaching stream or a quantitative stream. Graduation requirements The Graduate Diploma and the Graduate Certificate make up an articulated set of courses, and credit is awarded in the Graduate Diploma for subjects completed in the Graduate Certificate. Students may elect to exit the Graduate Diploma after completion of four specified subjects and graduate with the Graduate Certificate in Mathematics. To graduate with the Graduate Certificate in Mathematics, students must satisfactorily complete 32 points (four subjects). To graduate with the Graduate Diploma of Mathematics, students must satisfactorily complete 64 points (eight subjects). Academic expectations For each 8 point subject at CSU, students should normally expect to spend between 140-160 hours engaged in the specified learning and assessment activities (such as attending lectures or residential schools, assigned readings, tutorial assistance, individual or group research/study, forum activity, workplace learning, assignments or examinations). The student workload for some subjects may vary from these norms as a result of approved course design. Students will be assessed on the basis of completed assignments, examinations, workplace learning, or other methods as outlined in specific subject outlines. Where applicable, students are responsible for travel and accommodation costs involved in workplace learning experiences, or attending residential schools (distance education students). Expectations relating to academic, workplace learning, time and cost requirements for specific subjects are provided in the subject abstracts and in course materials.
... Show More are followed by Matched Problems that reinforce the concepts being taught. New to these editions, Technology Connections illustrate how concepts that were previously explained in an algebraic context may also be solved using a graphing calculator. Students are always shown the underlying algebraic methods first so that they do not become calculator-dependent. In addition, each text in the series contains an abundance of exercises - including numerous calculator-based and reasoning and writing exercises - and a wide variety of real-world applications illustrating how math is useful
Mathématiques: Cours - Exercices - Informatique Written for undergraduate courses in mathematics, this book is composed of three parts: geometry, linear algebra, and probability. The book presents a series of definitions and theorems used to understand mathematical reasoning. Exercises are then presented to reinforce the topics presented. MATLAB is used throughout the book to solve numerous application examples.
Moran/Davis/Murphy's text implements a modern approach to teaching precalculus by heavily emphasizing contexts in which mathematics can be used to solve real-world problems, and through active involvement of the student in the learning process. Students are asked to answer questions and discover ideas throughout the body of the text, and to explore mathematical concepts in group lab projects. It employs a lively, fun writing style to communicate concepts to students in a way that can be easily understood. Graphing utilities are thoroughly integrated into the text, and their use is required. Users and reviewers have given this text high acclaim for its fresh applications, projects, and wonderful use of the discovery approach.
North Central College Professor of Mathematics Richard Wilders and Professor of Music Larry Van Oyen publish article on art and transformations in math class. Lawrence Van Oyen (photo, right), professor of music, and Richard Wilders (left), Marie and Bernice Gantzert Professor in the Liberal Arts and Sciences and professor of mathematics, had their co-authored article, "Turning Students into Symmetry Detectives," published in the September issue of Mathematics Teaching in the Middle School, a publication of the National Council of Teachers of Mathematics. The article discusses how the mathematical concept of symmetry can be used to analyze certain kinds of art. C.J. started at North Central planning to double-major in chemistry and physics. He earned a Dr. Robert H. Good Scholarship for physics majors, one of many scholarships available to North Central students. As a freshman, he found he was "terrible in the chem lab" but loved problem-solving in physics. So he changed his second major from chemistry to applied mathematics. His sophomore year, C.J. took two classes with less than seven students and liked that professors devote personal attention to students, no matter the class size. "You can talk to the professors any time, even if you don't have that professor for a current class. They work with you to make sure you have what you need for the course." C.J. enjoyed working as a lab assistant during the College's Summer Undergraduate Research Colloquium and looks forward to conducting additional research with a professorDec. 9, 2010—North Central College will host a testing site for the American Mathematics Contest 10 and 12 (AMC 10 and AMC 12) on Feb. 23. These contests are the premier high school examinations in mathematics. Murawska presents workshop to math teachers Michelle investigated all that North Central's math department had to offer before she declared her major. "Having a close relationship with my professors helped me find just what I was looking for," she recalls. "Professor (Linda) Gao told me about the applied math major and I realized that's what I needed for working in a business setting." Michelle appreciates the major's focus on solving real-life problems and looks forward to studying econometrics, which uses statistical methods and empirical data to test economic models. "Applied math is perfect for me," she says. "Plus I can still consider graduate school in statistics or economics down the road," she says.
Express computations and sets of equations compactly in matrix format. And more ... Topics are introduced in short, easy-to-understand modules. Each lesson covers a single topic, and most lessons include one or more review questions to reinforce learning. How to Use This Tutorial Individual lessons are accessible directly through links in the table of contents, on the left side of the page. If you are already familiar with matrix algebra, you can choose any lesson at random and work effectively. However, if you are new to the topic, you should work through lessons in the order in which they appear; because each lesson builds on previous lessons. Additional Helpful Resources As you progress through this matrix algebra tutorial, take advantage of the following helpful resources. Sample problems. Most of the lessons include sample problems. The sample problems reinforce key concepts and help you test your knowledge. On-line help. The Stat Trek Glossary takes the mystery out of technical jargon. If any term or concept is unclear, visit the Glossary for additional explanation. Note: The Glossary can be accessed through the Help tab that appears in the header at the top of every Stat Trek web page.
How many you're required to take depends entirely on the institution and departments involved. How many you ought to take depends on the sort of applied mathematics and physics you want to do. A standard introductory course of the sort that you're now taking ought to be required of anyone going into any field of applied mathematics, but if your interests lean heavily towards physics, you might not need much more than that. Then again, you might: I know a theoretical chemist whose work involved a lot of combinatorics. Did you find this question interesting? Try our newsletter You should encounter thermodynamics and statistical mechanics at some point, so you ought to understand combinatorics. I would recommend an introductory discrete mathematics course that covers combinatorics. I took modern physics which served as an introduction to special relativity, quantum theory, thermodynamics, and statistical mechanics. Most people struggled with quantum mechanics because they had never seen PDEs before. Moreover, many students dropped statistical mechanics because they could not understand how to turn a word problem into a combinatorics problem.
Spectrum Math: Grade 5 Test with success using the Spectrum Math workbook! This book helps students in grade 5 apply essential math skills to everyday life.Test with success using the Spectrum Math workbook! This book helps students in grade 5read book. Has shelf wear to the cover, edges and...Like New. Unread book. Has shelf wear to the cover, edges and corners, may have cracked spine. Has slightly dusty edges from shelf wear. Has light pressure marks or/and tiny scuff marks and some light scratches on the cover. May have small or big creases on the cover. May have back cover and 7 last pages left upper corner tear-off. Otherways pages are clean, tight and free from any marks. Our proven Spectrum Math grade 5 workbook features 184 pages of drills and practice in math fundamentals. Recently updated to current national math and testing standards. Description:Very Good. Unread book. Has tear on back cover upper edge....Very Good. Unread book. Has tear on back cover upper edge. Cracked spine. Has a right lower corner tear on front cover and first page. Has slight shelf wear. Or has a piece of bottom right corner of front cover torn off. Has creases on front cover or/and has long vertical creases on front and back cover. May have 2" cut-trough from the front cover to the page 53 and few tears on spine, but this doesn't effect book
Differential Equations 9780495012658 ISBN: 0495012653 Edition: 3 Pub Date: 2005 Publisher: Thomson Learning Summary: Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of readily available technology, the authors eliminate most of the specialized techniques for deriving formulas for solutions found in traditional texts and replace them with topi...cs that focus on the formulation of differential equations and the interpretations of their solutions. Students will generally attack a given equation from three different points of view to obtain an understanding of the solutions: qualitative, numeric, and analytic. Since many of the most important differential equations are nonlinear, students learn that numerical and qualitative techniques are more effective than analytic techniques in this setting. Overall, students discover how to identify and work effectively with the mathematics in everyday life, and they learn how to express the fundamental principles that govern many phenomena in the language of differential equations. Devaney, Robert L. is the author of Differential Equations, published 2005 under ISBN 9780495012658 and 0495012653. One hundred twenty Differential Equations textbooks are available for sale on ValoreBooks.com, and nineteen used from the cheapest price of $8edited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions.[less]
Devoted to offering fun, yet challenging, lessons and activities in high school/college level mathematics and computer programming to students and teachers. Includes Teacher Resources for Algebra, Geometry, Algebra 2, and Statistics; Finding Your Way Around the TI-83+/TI-84+ Graphing Calculator; Using the TI-89 Titanium and the Voyage 200; Geometer's Sketchpad: Already Made Files and Materials for GSP 4.0; Beginning Programming in Java; Introduction to Programming in C++; Using PowerPoint for Interactive Math Games and Activities; and Workshop Information.
This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement. Most helpful customer reviews Easy reading, excellent text on the topic. I'm coming from a Geomatics (CompSci/Geog) based background and in my 4th year of University. Every chapter starts with an overview of the problem with real world examples, simple solutions to this that are not optimized nor consider degenerate cases, and then goes into a 'how can we make this better' style of discussion with excellent justifications along the way. There is an expectation that you are familiar with basic algorithm design, performance analysis, and data structures. Pro: (1) Each chapter begins with a practical example. For example, the chapter computing intersections of lines starts with a discussion of a map-making application that goes into enough detail to see how the algorithms they present would be useful. This is a considerable step up from the common practice in algorithms literature of motivation by way of vaguely mentioning some related field (i.e. "These string matching algorithms are useful in computational biology"). This book does a much better job of motivating the material it presents, but if you're primarily interested in the abstract problem, these sections can be skipped. (2) Each chapter is relatively self-contained. Feel free to skip ahead to subjects that interest you. (3) Surprisingly readable. Unlike most technical material, one can read an entire chapter in a single sitting without missing much. Generally, each chapter will develop a single algorithm for a single kind of problem. (4) It's very up to date. This second edition is less than two years old, it includes some new results in the field. Con: (1) Algorithms are only given in pseudocode. The emphasis is on describing algorithms and data structures clearly and completely. If you're looking for a "cookbook" with code to copy and paste into an application, perhaps O'Rourke's "Computational Geometry in C" would be a better choice. (2) There are many important advanced results that are not discussed in the main text. An obvious example is the first chapter, which describes a well-known convex hull algorithm that takes O(n log n) time but algorithms that are faster for most inputs are mentioned only in the "Notes and Comments" at the end of the chapter. Someone interested in lots of gory details would be well-served to combine this book with Boissonnat and Yvinec's more detailed and mathematical "Algorithmic Geometry". Algorithm books are often quite hard to understand, but this is not the case with this book. The information is very compact so it is a slow read but due to the high quality of the text this is only an advantage. You are never left wondering what the authors might have meant with a certain statement. The book focuses solely on theory, so it presents no real source code (only pseudo-code) which I think is good thing since that would otherwise have polluted the clarity of the explanations. Many of the topics it covers has been a help to me as a programmer. Can be recommended for anyone interested in computation geometry - but it requires some computer science maturity so I don't recommend it unless you have a bachelor's degree in C.S. or something similar. Jacob Marner, M.Sc. This book serves as a survey of computational geometry algorithms. The explanations are very readable. The authors have taken special care to prove algorithm correctness and time complexity bounds. Although I have yet to actually implement one of the algorithms in the book directly, I was exposed to a number of general techniques which I have used, such as randomized techniques to eliminate pathological worst-case performance problems, and various space partitioning techniques. The algorithms are all presented in pseudocode, unfortunately, which is the reason for only 4 out of 5 stars. Also, some important details are omitted which make a few of their algorithms practically useless (although they are interesting theoritically). For example, there is an algorithm for pathfinding and collision avoidance for a translating (but not ROTATING!) robot. If you're lookin for a computational geometry bible, this isn't it. But there are certainly some gems in this book and it is a very interesting read. The book is well written and easy to understand. An ideal book for someone planning to apply computation geometry for real-life problems. This is not a definitive book for computational geometry, but does give you good examples and ideas. Could do with more references to figures. There is scope for expansion of this book to include more detailed case studies and more pseudo code examples Compared to other texts on Computational Geometry, like the Preparata / Shamos collection -- this book is simple to read; it's very well written. I cannot understate the clarity of the book; if you try comparing this to other graduate texts on Computational Geometry -- this one blows them away. I think it covers a broad range of topics and covers them well. It is a wealth of algorithms.
practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam. {"currencyCode":"USD","itemData":[{"priceBreaksMAP":null,"buyingPrice":84.83,"ASIN":"0387961712","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":102.91,"ASIN":"0387982191","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":80.4,"ASIN":"0471789011","isPreorder":0}],"shippingId":"0387961712::XFvSFNP3MaUmD0xVKEuGENmHpRfvruJnQh0vOZd70j4g2H6EjwnMmCJnh0s24nTTxfoxJxJhg5Stne4Qm1poP0J%2Bf7PC8Hf5j9LomNRc%2Bwk%3D,0387982191::9tY7KrudmCnP5J347Yal2pUExKLCBKra%2FHz3ELbZp4MDutsC866WCmtFXbRwwihcFFoXen0ukbuEyZP9Lk5UnXi86%2BXuKV6onbviRbpdfBk%3D,0471789011::9EUNbdZGpAWbsv5dSr6AA4x%2BX29NJqPxUGlQmUgbrqRKzGq2M2TMmKGRdvKEQwgnw%2Bmu2AlbfbtpNMw8xc5v2HA2AwlIxatGIU8aYdLBRU5C3egcKQw is a very welcome addition. The main message of the book is that the only way to learn to solve problems is to solve problems! I found this book very helpful. I am quite sure the book will be in constant use and I have no hesitation in recommending it." (The Mathematical Gazette) Most Helpful Customer Reviews I would like to suggest that the audience for this book is somewhat broader than just the "all-star" math students. I will indeed use this book to help students preparing to take the Putnam exam this fall - it is the best book I have seen for this purpose. But in just the first two chapters, Larson presents strategies such as working backwards, modifying the problem, mathematical induction, and the pigeonhole principle, in a way which all math majors can benefit from. A graduating senior reported that once he started participating in math contests, his performance in ALL of his math classes improved. Problem solving unifies mathematical understanding. This student took the Putnam last fall (which, if you've got this far without knowing, is a six-hour national undergraduate mathematics competition taken by 3000 students in the US and Canada each year, approximately half of whom score zero) just to see what he could do, to gauge his improvement in mathematics. There isn't much more of a compliment a student could give me, intentional or otherwise. That can't all be attributed to this book, but it is that good. The presentation is unique; the organization - by strategy, rather than by year or whatever you see in other problem books - is illuminating by itself, and has improved my pedagogy; and he just makes hard problems look easy. Any student past the level of Linear Algebra who is up for a challenge will benefit from this book. An excellent resource for anyone interested in mathematical problem solving at the undergraduate level. Comes with many interesting problems taken from various mathematics contests. Additionally, the writing is clear and user-friendly. The only thing lacking is a companion workbook/solution guide. If you know anyone taking the AIME, USAMO, IMO, or Putnam exam, do them a favor and buy them this book! It's well worth it! This book would be especially helpful for someone planning to compete in the Putnam Exam. Lots of example covering many topics in upper undergraduate maths and of course the classic "folklore" techniques, strategies, and tools of problem solving(e.g., pigeonhole, invariants, coloring proofs, etc.). This is more of an advanced book as compared to others aimed at Olympiad contestants. Nonetheless, it is an invaluable source for anyone interested in non-routine mathematics. Finally, a book that develops problem solving techniques in a structured way for the Putnam. However, the techniques can be generally applicable to solve problems in many different areas. The power of using "first principles" to solve problems that at first sight seem almost impossible is brought out clearly. (Example, show that any sequence of consecutive integers is divisible by n!. Where does even start to solve such problems? The book shows you how.) You can read the book from the beginning to end, but a better way is to read it at random. Read the first chapter, though. It does a marvellous job of enumerating the different types of techniques. Enjoy this book. You'll be amazed at how simple ideas can lead to difficult problems. I have been teaching for the Math Olympiad for seven years and this book is one of my favorite resources. It covers a lot of great techniques for problem solving, specially the first chapter. The first chapter is a great introduction to problem solving. The chapters covers several techniques which the author calls heuristics, which are the basics. This chapter is kind of like learning the basic moves of a new dance. To do learn any other aspects of the dance, you need to master the basics and this book really honed in on the basics. Mastering the first chapter is, in my opinion, a crucial step in preparing for mathematical competitions, like the Mathematical Olympiad or the Putnam.
What is Mathematica? Mathematica is widely used in engineering, mathematics, finance, physics, chemistry, biology, and a wide range of other fields. It provides a wide variety of tools for analysis, simulation and visualization. Getting Mathematica... Mathematica is currently installed in several labs across campus. Check with the administrators (listed below) for details.
Chapter8: Area ... specifically to reviewing and practicing a key algebra topic. These "Using Your Algebra Skills" lessons may be assigned by the teacher, ... Discovering Geometryhas been designed with an investigative approach to engage Key Curriculum Press Response to Indiana Review of DiscoveringGeometry In DiscoveringGeometry, Chapter 2 is an example of where students first progress from inductive to deductive reasoning through the use of paragraph proof, Key Curriculum Press DiscoveringGeometry, ... Often the issue is that the writer is too vague in their answer, ... through the work they complete in the chapter on volume. Students complete investigations to determine shortcuts ...
Introductory Algebra Real-life applications"-- unparalleled in terms of quantity, quality, degree of integration, nontrivial use of real data, variety of fields, and ...Show synopsisReal-life applications"-- unparalleled in terms of quantity, quality, degree of integration, nontrivial use of real data, variety of fields, and level of interest, and many based on real data from a variety of fields-- highlight the relevance of math to various careers. Prealgebra Review, Real Numbers, Equations, Inequalities, and Problem Solving, Exponents and Polynomials, Factoring Polynomials, Rational Expressions, Graphing Equations and Inequalities, Systems of Equations, Roots and Radicals, Quadratic Equations. Includes approximately 550 worked examples, and 4000 exercises. For a variety of business, science, math, and technology careers17319201731920Paperback. Instructor Edition: Same as student edition with...Paperback. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 9780321731920Very good. Annotated Instructor's Edition. The pages are clean...Very good. Annotated Instructor's Edition. The pages are clean and unmarked. Minor peeling on corners of cover. Attractive book with some signs of use. All items guaranteed, and a portion of each sale supports social programs in Los Angeles. Ships from CA26384 Introductory Algebra I ordered the Introductory Algebra book for class. The book that I received was a teacher's edition. I ended up having to purchase a separate book to use in class. The book arrived one day before my 1st class started. I had to rush out to find a book before my 2nd
The problems you encounter in algebra 1 are more challenging than those you encounter in arithmetic. However, you often use the same techniques you used in arithmetic to solve algebra 1 problems! So really, algebra 1 is a lot like the kinds of things you have already worked with - it just "looks" different.
Modern Geometry / With CD - 02 edition Summary: Modern Geometry was written to provide undergraduate and graduate level mathematics education students with an introduction to both Euclidean and non-Euclidean geometries, appropriate to their needs as future junior and senior high school mathematics teachers. Modern Geometryprovides a systematic survey of Euclidean, hyperbolic, transformation, fractal, and projective geometries. This approach is consistent with the recommendations of the National Council of Teachers...show more of Mathematics (NCTM), the International Society for Technology in Education (ISTE), and other professional organizations active in the preparation and continuing professional development of K-12 mathematics teachers. ...show less The Concept of Parallelism. Points, Lines, and Curves in Poincare's Disc Model. Polygons in Hyperbolic Space. Congruence in Hyperbolic Space. 4. TRANSFORMATION GEOMETRY. An Analytic Model of the Euclidean Plane. Representing Linear Transformations in 2-space with Matrices. The Direct Isometries: Translations and Rotations. Indirect Isometries: Reflections. Composition and Analysis of Transformations. Other Linear Transformations. 5. FRACTAL GEOMETRY. Introduction to Self-similarity. Fractal Dimension. Iterated Function Systems. From Order to Chaos. The Mandelbrot Set. 2001-09-04 Hardcover Very Good EXCELLENT EX/LIBRARY HB COPY WITH CLEAN, CRISP PAGES AND TIGHT BINDING. INCLUDES CD-ROM. PICTORIAL COVER, NO DUST JACKET AS ISSUED. BOOK SHOWS LIGHT EDGE/CORNER WEAR ...show moreAND FAINT COVER RUBBINGS. CD-ROM HAS A SMALL AMOUNT OF LIGHT SURFACE SCRATCHES THAT DO NOT AFFECT THE QUALITY. SOME LIBRARY MARKINGS. ALL OF OUR ITEMS ARE GUARANTEED. WE SHIP DAILY WITH TRACKING. ...show less $126
Fundamental Math
More About This Textbook Overview Linear Algebra: An Introduction Using Maple is designed to provide a positive and fruitful experience during a first encounter with linear algebra. Mathematical ideas are presented as a story, built on the solution of linear systems. Gaussian elimination and the singular value decomposition serve as motivating themes. Maple provides students with frequent opportunities to engage in modest forms of research, enabling individuals or groups to work on meaningful projects. The author's narrative presentation is enriched by the interactive use of Maple. Programming and computational complexity are kept to a minimum. Szabo uses Maple's symbolic and numerical calculation capabilities to distinguish between exact and approximate solutions of mathematical problems. Linear Algebra: An Introduction Using Maple provides a uniquely concrete foundation for the fundamental issue of linear algebra: solving linear systems. "It does a great job of teaching the student how real people solve real linear algebra problems (by computer), frees up time for conceptual issues, and allows real experimentation by the student so they can feel comfortable with the concepts." -Todd Arbogast, University of Texas, Austin "The book reads easily....What I liked most is that he weaves in from the beginning basic concepts like determinants and eigenvalues, not waiting for a formal introduction of them, and thus being able to discuss early on a variety of interesting examples...In this way, the whole presentation of the book forms a unity, as opposed to the presentation of disconnected chapters." -Karen Reinhold, State University of New York at Albany. "This is an excellent modern text...I really like this book and I will use it enthusiastically." -Eric Carlen, Georgia Institute of Technology Related Subjects Table of Contents Linear Algebra: An Introduction Using Maple uses a matrix-based presentation and covers the standard topics any mathematician will need to understand linear algebra while using Maple. Development of analytical and computational skills is emphasized, and worked examples provide step-by-step methods for solving basic problems using Maple. The subject's rich pertinence to problem solving across disciplines is illustrated with applications in engineering, the natural sciences, computer animation, and
High School Math Made Simple" tackles the math concepts that form the foundations of secondary and higher education in this third edition. The book includes chapters on essential math skills (pre-algebra), algebra 1, geometry, algebra 2, trigonometry, pre-calculus, calculus and statistics. High School Math Made Simple is full of examples and exercises. The book was written using the principles and standards for school mathematics published by the National Council of Teachers of Mathematics (NCTM). These standards are the cornerstone of basic math principles that ensure the highest quality of learning for students. The rear of the book includes a Scope and Sequence of our content to NCTM's guidelines. Most Helpful Customer Reviews Pros: Tutor in a book - I have taught and tutored high school and college students in various topics such as algebra, calculus, statistics, probability, engineering, etc. for the past seven years. During this time I have come across a variety of books. Many of them are popular among students but in my opinion they are just a collection of solved problems and unsolved exercises. Even the solved problems leave students guessing about intermediate steps. No book in my opinion has so far made a sincere effort to help students develop the concepts of mathematics by guiding them in a step - by - step hands on approach. And this is where this book steps in. It solves the problems in elementary steps and in the process explains the concept very coherently. It is a tutor in a book! Arsenal of solutions - The authors seem to have done research on various types of problems which generally show up on tests and board exams and they have produced a detailed solution mechanism for each problem type. So, this does help students develop an arsenal of solutions to deal with different kinds of problems he/she might encounter on tests. Let's be honest here, at the high school level there are not infinite types of problems. Hence, to a certain extent Dr. Monroe's book has solved the ubiquitous uncertainty about different popular forms in which problems can show up on the exam. Variety of topics - Even though this is pretty much standard for all books, I like the organization of this book as far as presenting the topics is concerned. Dr. Monroe has tried to build up the students skills in a highly structured manner.Read more › This book should act as a supplement to your studying. Certain sections are quite thorough, while others only provide quick refreshers. Here is my take on each section: Essential Math Skills - This is a good, quick introduction to basic math skills, but I don't think that it will be useful for a high school student. Upon entering high school, a student should have mastered such topics as fractions and integers, and if he or she hasn't, then he or she is in trouble. Algebra I - You are inundated with information in this section, and although the explanations are clear, there are not enough examples. Algebra II - Dr. Monroe provides plenty of examples, and her step-by-step method of solving them is very clear and helpful. I liked how she details the four ways to solve systems of linear equations. Geometry - This chapter does not cover geometric proofs, which are fundamental to the subject. Trigonometry - A section on vectors would have been useful. Also, Dr. Monroe could have provided general instruction on how to use a graphing calculator to graph functions. Pre-Calculus - I liked the inclusion of word problems, which are sometimes left out in similar study aides. The chapter does lack sections on limits and polar coordinates. Calculus - This section could have been broadened to include more topics and flesh out certain concepts. It should be used only for a basic review of derivatives and integrals. Statistics - The section on Probability is very limited, and Probability is an integral part to the study of Statistics. This book is a summary of topics. Don't buy this book if you are looking for exercises and extend explanations. It covers a lot, but as I said ... once I got lost in one topic due to the brief explanation ... I was done! I had to look for other resources to see if I could understand. To me this book is more of a guide for professors and people that already know the topics than for somebody who is trying to learn by themselves. I'm only into the Exponential Functions section, but I must say, there are a few typos and incorrect formulas that made it necessary to consult online help. On the bright side, I discovered purplemath.com which is an excellent place to correct the mistakes in the book. To be more precise, the formulas for parabolas and ellipses were wrong. Also, the formula for the quotient rule of exponential equations was wrong...had to look them up. So, although I'm enjoying relearning math after many years out of high school, I must give this caveat: Pay close attention to what's written because, so far, there are some mistakes. Do I recommend this book ? Yes...but watch for the mistakes. I am a professional who left school a long, long time ago. I have been searching for a while for a good math book to refresh my skills and so far found that when it comes to math, finding a good book is as hard as the subject it self. Most books are cumbersome to use and part of school curricula that unless approached as a whole leave the reader feeling incomplete and uninformed. This little book is not perfect but it is a fair and balance refresher course. I like it.
GED Math Workbook (back cover) A solid review of math basics emphasizes topics that appear most frequently on the GED: number operations and number sense; ...Show synopsis(back cover) A solid review of math basics emphasizes topics that appear most frequently on the GED: number operations and number sense; measurement; geometry; algebra, functions and patterns; data analysis; statistics and probability Hundreds of exercises with answers A diagnostic test and four practice tests with answers Questions reflect math questions on the actual GED in format and degree of difficulty GED Math Workbook (Barron's Math Workbook for the Ged)...Good. GED Math Workbook (Barron's Math Workbook for the Ged
San Diego Tutor A San Diego-based in-home tutoring company, San Diego Tutor offers a Scholarship program for clients who can't afford high school math and science tutoring. ...more>> Saturday Academy Saturday Academy (SA) "gives kids learning experiences that get them excited about school, help them explore potential careers, discover their intellectual possibilities, and teach them to be lifelong learners." Targeting the youth and profesionals of ...more>> Saxon Publishers, Inc. - Harcourt Achieve Saxon publishes educational textbooks and other teaching materials for the primary and secondary education markets (Grades K-12) as well as for the home study market. The Saxon method of teaching math stresses "fundamentals." Site includes lists of inservices, ...more>> Science and Math Initiatives (SAMI) A database/clearinghouse of resources, funding, and curriculum for rural math and science teachers. List, search by title or description, or browse math resources by category. Originally a project of the Boulder Valley School District, Boulder, Colorado, ...more>> Sean's Home Page - Sean Mauch "For the past few years I have been working on an open source textbook. It contains material on calculus, functions of a complex variable, ordinary differential equations, partial differential equations and the calculus of variations...." This former ...more>> Shack's Math Problems - Michael Shackleford Pages of math problems ranging from basic math to differential equations. Each problem comes with a difficulty rating from one to four stars, roughly a measure of how much time it took Shackleford to do the problem. Includes answers and, usually, solutions.SHAREWARE.COM - CNET, Inc. Search more than 250,000 files in the former Virtual Software Library: first select the platform of your choice, then enter the word or filename to search for. You may also search for files in a specific archive here by first selecting the archive of ...more>> The Siluroid Curve - Dario de Judicibus Formulas, graphs, compass-and-straightedge constructions, derivatives, and more about this bi-quadratic, trilobate curve. Among the torpedo- or fish-shaped curve's curious properties: connecting its intersection with the generatrix or goniometric circle ...more>> SIMATH - Marc Conrad A computer algebra system, especially for number theory. Try out the online version of the SIMATH calculator simcalc; a more detailed overview is available as a .dvi file or you can download the TeX-Source of this file. ...more>> Sites with Problems Administered by Others - Math Forum Problems of the week or month: a page of annotated links to weekly/monthly problem challenges and archives hosted at the Math Forum but administered by others, and to problems and archives elsewhere on the Web, color-coded for the level(s) of the problems ...more>> Slide Show - Roxanne M. Byrne Slide shows on calculus concepts: limits, derivatives and rules, integration, and infinite series. Some of the slide shows can be downloaded as PowerPoint files; if you do not have PowerPoint on your computer, you can download a PowerPoint Viewer Zip ...more>> Smith's Stuff: Resources - Mark Smith Mark Smith shares resources that he has created as a high school teacher: games, mnemonics, activities, sketches, and more. Sign up for a free account if you'd like to share activities here as well. ...more>> Software for mathematics education - Piet van Blokland Software for mathematical education that draws on David Tall's philosophy of teaching: use Graphic Calculus to visualize, explore, and conceptualize the graph of a linear function; analyze the data and simulations included with VUStat to learn statistics ...more>> Spreading the Word - Keith Devlin (Devlin's Angle) History of and commentary on early calculus texts. "The first calculus text hit the shelves in 1696. They have been growing steadily in size (if not mathematical content) ever since. That first genre-setting volume was Guillaume Francois Antoine de l'Hospital's ...more>>
Practical Problems in Mathematics for Electricians, 9th Edition PRACTICAL PROBLEMS IN MATHEMATICS FOR ELECTRICIANS, 9E will give you the math skills you need to succeed in the electrical trade. It introduces you to the important math principles through problems designed for the electrical profession and offers you an excellent opportunity to develop and practice problem-solving skills while at the same time providing a valuable review of electrical terminology. This new edition uses the same straightforward writing style and simple, step-by-step explanations that made previous editions so reader-friendly. It minimizes theory and emphasizes problem-solving techniques and practice problems. This new edition also includes updated illustrations and information for a better learning experience than ever before! The book begins with basic arithmetic and then, once these basic topics have been mastered, progresses to algebra and concludes with trigonometry. Practical problems with real-world scenarios from the electrical field are used throughout, allowing you to apply key mathematical concepts while developing an awareness of basic electrical terms and practices. This is the perfect resource for students entering the electrical industry, or those simply looking to brush up on the necessary math84.95 Purchase Options Paperback $67.49 $67.49 Save $1716.49 from$16.49 Save up to $68.46! Rent thru 01/25/15 for $16.49 $16.49 Save $68.46! Rent thru 07/24/15 for $18.49 $18.49 Save $66.46! Rent thru 07/18/16 for $20.49 $20.49 Save $64.46! Rent thru 07/08/18 for $22.99 $22.99 Save $61
GMAT's Foundations of Math book provides a refresher of the basic math concepts tested on the GMAT. Designed to be user-friendly for all students, this book provides easy-to-follow explanations of fundamental math concepts and step-by-step application of these concepts to example problems. With nine chapters and over 600 practice problems, this book is an invaluable resource to any student who wants to cement their understanding and build their basic math skills for the GMAT. Special Features: Purchase of this book includes one year of access to additional online practice problems on ManhattanGMAT.com (accessible by inputting a unique code located in the back of each book).Other GMAT Preparation Guides (4th Edition): Number Properties: 978-0-9824238-4-4Fractions, Decimals, and Percents: 978-0-9824238-2-0Equations, Inequalities, and VIC's: 978-0-9824238-1-3Word Translations: 978-0-9824238-7-5 Geometry: 978-0-9824238-3-7Critical Reasoning: 978-0-9824238-0-6 Reading Comprehension: 978-0-9824238-5-1Sentence Correction: 978-0-9824238-6-8 Test Simulation Booklet 978-0-9790175-8-2
Bob Miller's Algebra for the Clueless - 2nd edition Summary: 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 c...show moreovers everything a you need to know to excel in Algebra I and II
The Pythagorean Relationship - MAT-956What does A-squared plus B-squared equals C-squared really mean? After teaching with hands-on activities, video demonstrations, animations, and comics, your students will be able to answer that question and apply the relationship in problem solving situations. This course is built around core propositions from the National Board for Professional Teaching Standards as well as national content standards
... More About This Book . Whether you're a student, parent, or teacher, this book will provide clarifying, encouraging help for any learner hoping to master Algebra 2. Related Subjects Meet the Author Mary Hansen received her B.A. in mathematics and her M.A.T. in education from Trinity University in San Antonio, Texas. She has taught mathematics and special education and has worked at the elementary school, high school, and college levels in Texas, North Carolina, and Kansas. She is the co-author of Algebra I: An Integrated Approach, Algebra 2: An Integrated Approach, and Geometry: An Integrated Approach, and she is the author of Business Math, 17th Edition. Mary currently works as an educational consultant and freelance
... More About This Book undergraduate text that reflects the importance of the heat equation in applied mathematics and mathematical modeling. The first two chapters of the book are introductory and summarize the essential elements of heat flow, diffusion, the mathematical formulation, and simple general results. The next two chapters develop exact analytical solutions, obtained by Laplace transforms and Fourier series, for infinite and finite media problems respectively. Other chapters deal with approximate analytical solutions based on the heat-balance integral method, numerical methods for the heat equation, and simple heat conduction moving boundary
Types of Courses Lecture: The traditional mathematics classes are formatted as an oral presentation. The instructor leads students through course material at the pace of the instructor. Lecture courses require students to purchase lecture note packets from the UM-Helena Bookstore. Most homework and exams are completed by submitting written work daily to the instructor at the beginning of class. Some lecture courses require the use of MathXL to complete homework and/or exams. Hybrid (HO): The hybrid class meets once a week. During the weekly meeting the instructor may lecture, answer student questions, have students work on homework and/or have students take an in class exam. The instructor sets the pace and schedule for the course. Students utilize MathXL to complete homework and exams electronically. Students in the hybrid class need regular internet access, MathXL, and the self-discipline to study and learn material independently. The instructor provides resources and the course pace for student success. Yet, the student must learn material by reading the electronic textbook, accessing videos and websites, attending a weekly class, and seeking assistance when needed. Self-Paced (SP): A self-paced class meets four days a week. Students progress through the course material at their own pace. Students meet in a computer lab each day, with an instructor present. The instructor is present to assist students with material, not lecture. The student must learn material by reading the electronic textbook, accessing videos and websites, attending class, and seeking assistance when needed. Students need to be self-disciplined to progress through the material at the recommended pace. If a student completes their mathematics course before the end of the semester their course is finished, and may choose to begin the next course at that point. Self-paced classes use MathXL for their homework and exams, so regular Internet access is needed. Online (O): Online courses are for students with the self-discipline to keep up with course material, learn independently, and have regular Internet access. Students progress through the material at their own pace. Students use MathXL to complete homework and exams. The instructor provides students with electronic resources to learn the course material.
Exercises I've discovered that simple exercises are exceptionally useful during a seminar to complete a student's understanding, so you'll find a set at the end of each chapter. Most exercises are designed to be easy enough that they can be finished in a reasonable amount of time in a classroom situation while the instructor observes, making sure that all the students are absorbing the material. Some exercises are more advanced to prevent boredom for experienced students. The majority are designed to be solved in a short time and test and polish your knowledge. Some are more challenging, but none present major challenges. (Presumably, you'll find those on your own – or more likely they'll find you
books.google.com - A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 continues the synthetic approach as it introduces Euclid's geometry... Course in Modern Geometries
Math Refresher 2014 Math Summer Refresher For many students, math courses are often gatekeepers. Two-thirds of the freshmen in the University of Alaska system enter college under-prepared. In other words, most freshmen need to take at least one developmental course before they can begin college level coursework. Part of the problem stems from the gap that exists between high school graduation requirements and Postsecondary education entry requirements. UAS is offering the chance to help close that gap for students by participating in the second annual UAS Summer Refresher Camp. What The Math Summer Refresher is a two week summer program for Juneau campus admitted students who have placed into MATH 055. The goals of Math Summer Refresher are to: Increase the mathematics placement scores of participants so that students can either move up to MATH 105 or successfully complete MATH 055, Provide participants with the social network and University contacts to support their success in their freshmen year at UAS.
.Read more... Abstract: An essential read for mathematicians, this volume looks beyond the syntax and semantics of Mathematica and other programs. It focuses on why they are necessary tools for anyone who engages in mathematics, as well as showing how to create better proofs.Read more... Reviews Editorial reviews Publisher Synopsis From the reviews: "There are two general approaches to computation: using computation as a numerical tool to approximate answers or using a computer algebra system to provide exact mathematical answers by symbolic manipulation. This book explores the second of these approaches, using the computer algebra system Mathematica. ... Though this work does teach students how to use Mathematica, it does so with the goal of providing new insights into basic mathematics, which can then be applied to more advanced mathematics. ... Summing Up: Recommended. Lower- and upper-division undergraduates." (D. Z. Spicer, Choice, Vol. 50 (7), March, 2013) "Three main chapters form the core of the book. In the first chapter, the authors talk about using a computer algebra system like Mathematica for problems in number theory ... . Chapters 2 and 3 are devoted to calculus and linear algebra, respectively. ... The mathematical content of the chapters is ... elementary and written in a style easily understandable by nonspecialists. ... a very good introduction for beginners to this interesting and important topic." (Kai Diethelm, ACM Computing Reviews, March, 2013)Read more... "."@en
Paperback Click on the Google Preview image above to read some pages of this book! Booktopia Comments Suitable For: Australian Capital Territory and New South Wales Book Description 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 addition to the successful New Century Maths series has been written for the new Mathematics General course commencing in 2013 in NSW. This book caters for the Mathematics General 1 HSC course in Year 12, for students heading towards the workforce or further training after school. This content-endorsed course is not HSC -examinable, providing mathematical skills for life. This book includes access to the NelsonNet teacher website of resources and downloadable chapter PDFs for schools that use New Century Maths 12 as a core resource. Select Bonus Resource Downloads to access the PowerPoint presentation "Exploring the new Mathematics General Syllabus" and a summary of course changes written by series editor Robert Yen. About the Author Sue Thomson is an experienced teacher and educational leader. She was head of mathematics at De La Salle Senior College, Cronulla, Director of Teaching and Learning at Hunter Valley Grammar School, an examination writer and assessor for the NSW Board of Studies, and a senior HSC marker. Judy Binns is head teacher of mathematics at Mulwaree High School in Goulburn and has taught at Homebush Boys High School. She has an interest in motivating students with learning difficulties and teaches the Applied Mathematics course at her school, based on the Mathematics General 1 syllabus. Judy has been co-writing the New Century Maths 7-8 series for 20 years, including new editions for the Australian Curriculum.
***************************************************** Math Xpander is Available for Free Download! Math Xpander is an interactive educational software package for school mathematics that allows students to learn by engaging in active exploration. HP, the inventor of the first handheld scientific calculator, developed this exciting educational software package that helps to advance education through innovative technology. Math Xpander was developed on the premise that technology should empower rather than be a complicated barrier to learning. Math Xpander's easy-to-use capabilities include a graphing environment that lets you sketch graphs directly on the screen. You can then convert a sketch to a genuine mathematical object by selecting from an extensive library of standard forms. You can even transform graphs directly with a stylus and observe the effects in graphic, numeric, and symbolic forms simultaneously. Math Xpander also includes a unique environment for creating and exploring geometric constructions. With it, you can transform geometric objects while watching measurements or calculations change. You can also impose or relax constraints in a construction or use the measurements or calculations to control geometric objects' attributes! In collaboration with Saltire Software Inc, HP is pleased to make this demonstration version of the Math Xpander software available to students and educators at this web address: Math Xpander runs on several Pocket PC devices, including the versatile HP Jornada 540 Series Color Pocket PC. Also available on the Saltire web site are two electronic lessons (E-lessons): an interactive periodic table of the elements, and a lesson exploring the composition of functions. All for free!
Students use Graphical Analysis to wirelessly collect, analyze, and share sensor data in science and math classrooms.... see more 'Graphical Analysis™ is a powerful tool for creating and analyzing graphs for science and math students. Use Graphical... see more 'Graphical Analysis™ is a powerful tool for creating and analyzing graphs for science and math students. Use Graphical Analysis to create graphs, modify scaling, make selections, create annotations and captions, and perform analysis with statistics and curve fits. Students can manually enter x,y data into a table, collect data using the built-in accelerometers, or connect wirelessly to a Vernier LabQuest 2 to work with Vernier sensors.Using Graphical Analysis with Vernier SensorsUsing a Vernier LabQuest 2 sensor interface or a computer running Logger Pro 3 (version 3.8.6 or newer), students can wirelessly connect to these data sources and view experimental data from Vernier sensors in a table or a graph. Multiple members of a lab group can connect at the same time while collecting data from any of over 80 compatible Vernier sensors. For more information, visit: needed, students can export data and graphs to create a lab report or send their finished work to the instructor. Students can export graphs to the Photo Gallery, Mail, Google Drive™, and third-party apps or print using an available printer. A CSV file of the data can be exported to third-party apps, email, or Google Drive.Key features• Display 1 or 2 graphs• Access data table with row-by-row entry and multiple columns• Auto-save data, graphs, annotations, statistics and curve fits• Draw predictions on a graph• Pinch to scale graph• Examine and select data• Perform curve fits, including linear, quadratic, natural exponent, and more• Create text annotations• Create graph titles• Export graphs and data• Explore included sample data filesAdditional features when used with LabQuest 2 and Logger Pro• Connect multiple student devices to a single data source via wireless networking• Collect data from multiple sensors simultaneously• Start/stop data collection remotely• Use with over 80 compatible Vernier sensors• Display sensor data as graphs or in a table'This app costs $4.99 'A comprehensively featured calculator that has become a favorite among adults and high school students around the world.... see more 'A comprehensively featured calculator that has become a favorite among adults and high school students around the world. Designed for a wide range of users, this calculator has large colorful buttons, optional high contrast, full VoiceOver support, and unique to this calculator; the option to use speech for answers, buttons names and formulas!''Features include: -------------------------- - Can read answers, entered numbers and formulas aloud.1,234.56 is spoken as "One thousand, two hundred and thirty four point five six.״ 2 + 3 x 5^2 is spoken as "two plus three multiply five squared.״ - Built in recording studio and script. Requires only 5 minutes to record a new voice. Recordings can be transferred between devices using Bluetooth.- Two entry modes, Standard and Formula. Standard mode emulates traditional calculators. Formula mode takes care of the order of operations for you. You enter a mathematical expression, complete with operators and parentheses (brackets), tap the = button, and the expression is evaluated. - The entire app is accessible to VoiceOver users. As you move your finger over the screen, the names of buttons are spoken to you. Double-tap to activate the selected button (or single tap with a second finger.) The calculator's voice will speak the calculation results. The iPad/iPhone's Home button can be triple-clicked to switch this mode of operation on and off. - Supports entry and display of Braille on supported devices (thanks to assistance from the Washington State School for the Blind.) - Numeric formatting of results: Max fraction digits (default), fixed fraction digits (useful for currency calculations), and max significant digits (useful for science and engineering lab work), plus international formatting. - Trigonometric, hyperbolic, logarithmic, permutations, combinations, factorial, powers, roots, percent and bit-wise operations, conversion between hexadecimal and decimal, random numbers. - Full support for fractions (simple and mixed), conversion to and from decimal, fraction reduction, and use of fractions with all operators. - Easy access to basic calculator functions, for those who rarely use scientific operations. - Paper log feature, designed particularly for classroom use. Calculations can be recorded with a timestamp to be viewed and emailed. - iPads get a user interface designed to make use of the large screen area. iPhones and iPod Touches get a user interface designed for the smaller screen. This includes large, easy to read scientific buttons, accessed on a scrolling panel. All the features of the iPad version are included in the smaller design. Customizable for each level of vision: -------------------------------------------- Normal to low vision: Large, clear buttons with optional speech. Low vision: High contrast display mode, with optional speech. No vision / blind: VoiceOver reads the button names before they are activated. The calculation results are spoken. Entry and display on refreshable Braille devices.'This app costs $4.99 'Please note the Lifesaver for iPad app abides exclusively by the UK resuscitation guidelines.Learning emergency life-saving... see more 'Please note the Lifesaver for iPad app abides exclusively by the UK resuscitation guidelines.Learning emergency life-saving skills made easy - learn anywhere, anytime, for free.Would you know what to do? Make lifesaving decisions in a crisis. Lifesaver is a movie you play like a game: it throws you into three situations where people are choking, and having cardiac arrests – make the right choices to save a life. YouPlease note the Lifesaver Mobile app abides exclusively by the UK resuscitation guidelines.Do it wrong, and see the consequences.DoTo ensure we deliver the highest quality experience, Lifesaver Mobile requires Android 4.0 and above, and currently supports... see more 'To ensure we deliver the highest quality experience, Lifesaver Mobile requires Android 4.0 and above, and currently supports the following devices:Samsung Galaxy S3Samsung Galaxy Note IILearning emergency life-saving skills made easy - learn anywhere, anytime, for free.Would you know what to do? Make... see more ' 'Thousands of people use SocialDiabetes to manage their Diabetes. With SocialDiabetes you take control of your diabetes in an... see more 'Thousands of people use SocialDiabetes to manage their Diabetes. With SocialDiabetes you take control of your diabetes in an easy and intuitive way. You remember what you ate one day, how much insulin you needed and how your blood sugar level was afterwards. 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Nobody knows your diabetes better than you.Use under the supervision of your doctor.'This is a free app
Fourier analysis and wavelet theory, the fundamental mathematical framework for the description of functions in the time and frequency domains, are the key elements for effective analysis of function properties, as well as for efficient implementation of computational methods. For this reason, it is very important in many application areas to find function descriptions that are localized both in time and frequency. In this course, attendees learned the mathematical concepts behind Fourier analysis and wavelets. These concepts are significant for researchers and developers alike, because they are involved in so many of the problems in computer graphics and image processing. Prerequisites Knowledge of linear algebra and calculus. Some familiarity with analysis of real and complex functions desirable. The course also assumed basic knowledge of signal and image processing. Topics Covered The main tools for function analysis in the frequency domain (the Fourier and Windowed Fourier Transforms), fundamental aspects of multiresolution analysis and its importance to the construction of wavelets, the main principles of computation with wavelets and their implementation, and various extensions of the basic wavelet transform.
Encyclopedia of Mathematics is a comprehensive one-volume encyclopedia designed for high school through early college students. More than 1,000 entries, more than 125 photographs and illustrations, and numerous essays cover the principal areas and issues that characterize this "new" area of science. This valuable resource unites disparate ideas and provides the meaning, history, context, and relevance behind each one. The easy-to-use format makes finding straightforward and natural answers to questions within arithmetic - such as algebra, trigonometry, geometry, probability, combinatorics, numbers, logic, calculus, and statistics - simple. Encyclopedia of Mathematics also gives historical context to mathematical concepts, with entries discussing ancient Arabic, Babylonian, Chinese, Egyptian, Greek, Hindu, and Mayan mathematics, as well as entries providing biographical descriptions of important people in the development of mathematics. Editorial Reviews Researcher, author, and educator Tanton has compiled this encyclopedia to share his enthusiasm for thinking about and doing mathematics. More than 800 alphabetically arranged entries present a wide variety of mathematical definitions, theorems, historical figures, formulas, examples, charts, and pictures. Many cross-references serve to connect concepts or extend a concept further. A mathematical time line listing major accomplishments is available following the entries, along with a list of current mathematics organizations. The bibliography contains print and Web resources, and the index is helpful in locating terms and concepts. Each entry varies in length depending on the term, concept, or person being described. Six longer essays describe the history of the branches of mathematics. The writing style is straightforward and readable and sometimes contains parenthetical notes that add background or context. If an entry contains a word or words in capital letters, that term or person is also an entry in the encyclopedia. Most Helpful Customer Reviews This remarkable book is not just a collection of facts about mathematics, but is a fairly detailed treatment (within the limits imposed by space considerations) of various mathematical terms and topics. It does not restrict itself to simple mathematics and devotes full attention to several advanced concepts, but is always clearly written. I really commend the author for including proofs for some of the more important theorems and results (e.g. proof of the fundamemtal theorem of algebra, derivation of the least-squares method, and many more). And yes, you will learn tons and tons of things from this excellent book. It is a must read for anybody interested in mathematics! Given these four, there is hardly a topic from among the current 495 math fields of study that isn't at least explained in enough detail to save LOTS of time on link expeditions. At minimum, these give head starts on alphabetized keywords that will quickly fill holes in any research project, class, or syllabus. Looking for divisibility rules for numbers that you didn't think had divisibility rules? Looking for names of symbols you didn't think had names? Dr. Tanton provides the facts and the explanations along with the stories behind the topics.
Math for Grownups by Laura Laing[3], a personal finance writer with a background in Mathematics and who once taught high school math for four years, is a book that seeks to reteach you all the arithmetic you forgot from school. And this book delivers on that simple promise. One of the common complaints about our educational system is that high school is mostly preparation for college. If you don't go to college, very few of the classes translate to real life (how many high schools offer any sort of personal finance education?). Even if you go to college, your high school classes are simply preparation for the college classroom, not college life. Nowhere is this more evident than in mathematics. You start with algebra, explaining in terms of X, Y, Z (and A, B, C when you need more variables), rather than more relatable terms (we do throw a bone in terms of "word problems," but that's generally not how it's taught). Algebra is preparation for trigonometry, which is preparation for calculus. There are few daily life uses for calculus. This book just repackages all that early arithmetic and puts it in terms that we deal with every day, from calculating a 15% tip to figuring out how much mulch you need for your 10′ x 5′ garden plot. It teaches you some shortcuts, like the Rule of 72[4], but mostly tackles daily math problems in a way that shows you why it was important to learn that stuff as a kid. As you can problem tell from my review, this isn't a life changing book on the level of The Richest Man in Babylon[5] but it's far more practical. If you're the type of person who isn't particularly good at math and often find yourself in tricky situations, this book is worth checking out. If you have a strong math background, you probably won't get much out of this book outside of a few shortcuts and more clever ways to solve a problem.
This program contains EVERYTHING! It has the following: absolute value, doubling time, number factorer, polynomial factorer, FOIL, half life, interest, linear equations, logs, parabolas, radical simplifier, synthetic substitution, quadratic formula, sequences, midpoint, and distance. What more could you ask for? It's also very user friendly and self explanitory! P.S. Improvements are made all the time so check for updates every once in a while!
We present two versions of a 3D function grapher--one on a white background, one on a black background. The user enters a formula for f(x,y) in terms of x and y and the applet draws its graph in 3D. T... More: lessons, discussions, ratings, reviews,... With this applet, students study the extrema of the function A cos^2 (t) + B cos(t) + C. A parabola is drawn with student-supplied coefficients and constant, and the unit circle is drawn below, so th... More: lessons, discussions, ratings, reviews,... Applet teaches an intuitive feel for the geometric length of sin(t) given the length of the hypotenuse and t. A crane is stationed on a ship. Its wire has the length of sin(t), where t is the angle ...Students write what they notice and wonder about a person riding a Ferris wheel, and then use TI-Nspire™ technology to measure quantities and develop a mathematical model describing the situation. More: lessons, discussions, ratings, reviews,... With this one-variable function grapher applet and function evaluator, users can rotate axis/axes, change scale, and translate by using mouse or by entering data. The web site also contains informatio
Math modeling handbook now available Apr 23, 2014 This is the cover of the free math modeling handbook published by the Society for Industrial and Applied Mathematics this month. Credit: SIAM Math comes in handy for answering questions about a variety of topics, from calculating the cost-effectiveness of fuel sources and determining the best regions to build high-speed rail to predicting the spread of disease and assessing roller coasters on the basis of their "thrill" factor. How does math do all that? That is the topic of a free handbook published by the Society for Industrial and Applied Mathematics (SIAM) this month: "Math Modeling: Getting Started and Getting Solutions." Finding a solution to any of the aforementioned problems—or the multitude of other unanswered questions in the real world—will likely involve the creation, application, and refinement of a mathematical model. A math model is a mathematical representation of a real-world situation intended to gain a qualitative or quantitative understanding in order to predict future behavior. Such predictions allow us to come up with novel findings, enable scientific advances, and make informed decisions. The handbook provides instructions and a process for building mathematical models using a variety of examples to answer wide-ranging questions. The inspiration for the handbook came from Moody's Mega Math (M3) Challenge, a high school applied math contest organized by SIAM. Despite the tremendous success of the nine-year-old Challenge, which is currently available to 45 U.S. states and Washington, D.C., organizers found that many participating students—high school juniors and seniors—were having trouble coming up with approaches and solutions to the open-ended realistic problems posed by the contest. Participants expressed their frustration in post-contest surveys and emails. "We have been enthusiastic about the high level of insight and analysis demonstrated by participants in the Challenge, especially the winning teams," says M3 Challenge Project Director Michelle Montgomery. "However, it became clear to us that, given the lack of modeling courses in most high school curricula, many of the participants did not have access to basic resources necessary to create a successful model. We came up with the handbook to give every participant these tools." This type of thinking created an "aha" moment, so to speak, for handbook authors Karen Bliss, Katie Fowler, and Ben Galluzzo, long-time Challenge judges who have been part of the contest's problem development team for the past two years. "All students, especially those interested in STEM disciplines, need as much practice in solving open-ended problems as possible, but they often do not get many chances to do that in school,"says Fowler, who is an associate professor of mathematics at Clarkson University. "Math modeling skills allow students to approach problems they initially may feel are outside of their comfort zone, and we want to give them the confidence to tackle them." Further motivated by a series of SIAM-National Science Foundation (NSF) workshops on the topic of math modeling across the curriculum, the trio began work on a modeling guide. What started as a pamphlet with step-by-step guidance about the modeling process grew into a 70-page, full color handbook, with a companion document that makes connections to the Common Core State Standards as well as easy-to-use reference cards for those who want to get straight to the crux of modeling. The guide is suitable for teachers as well as high school and undergraduate students interested in learning how to model. "Math modeling is challenging, but it's also surprisingly accessible. The guidebook is designed to remove perceived roadblocks by presenting modeling as a highly-creative iterative process in which multiple approaches—to the same problem—can lead to meaningful results," says Galluzzo, an assistant professor of mathematics at Shippensburg University. The handbook, as well as the Challenge itself, has another, more pressing goal: motivating our younger generation to pursue higher education and careers in science and math. "SIAM does a big service to the math community at large by giving high school students the opportunity to see how math is more than just a series of formulas and rote memorization," says Bliss, an assistant professor of mathematics at Quinnipiac University. "Students at all levels have the means to produce highly creative solutions to interesting problems. Seeing that math can be a powerful tool for solving truly important problems through M3 Challenge participation might be just enough to encourage a student to study math or another STEM discipline in college." Related Stories A paper written by four students from High Technology High School in Lincroft, New Jersey, entitled Ethanol: Not All It Seems To Be has been published in the January 2009 issue of The Mathematical Association of America
to provide a flexible approach to the college algebra and trigonometry curriculum that emphasizes real-world applications, this text integrates technology into the presentation without making it an end in itself, and is suitable for a variety of audiences. Mathematical concepts are presented in an informal manner that stresses meaningful motivation, careful explanations, and numerous examples, with an ongoing focus on real-world problem solving. Pedagogical elements including chapter opening applications, graphing explorations, technology tips, calculator investigations, and discovery projects are some of the tools students will use to master the material and begin applying the mathematics to solve real-world problems.
This activity builds on the previous activity, Limits with Tables. Students investigate limits using tools for controlling delta and epsilon, giving them a concrete, hands-on understanding of the form... More: lessons, discussions, ratings, reviews,... Download this Sketchpad file to investigate the concept of a limit numerically using tables. Students encounter a function that's undefined at a particular value of x, but whose limit exists at that v... More: lessons, discussions, ratings, reviews,... A Java applet that presents the formal, epsilon/delta definition of limits, with exercises and questions to answer with the applet. Includes a re-scalable presentation version with larger fonts. More: lessons, discussions, ratings, reviews,... An interactive applet and associated web page that demonstrate a bisector of a line segment. The applet shows a fixed line segment and another line that bisects it. The second line's endpoints ca
MAT-331 Calculus III Calculus III is an intensive, higher-level course in mathematics that builds on Calculus II. The course aims at serving the needs of a wide student audience, including students in engineering, mathematics, the physical and life sciences, and economics. It is constructed around multiple focal points with the intention of helping students become creative and efficient problem solvers. The course uses technology as a means of discovery for numerical, graphical and analytical solutions to problems. It also emphasizes communication skills and requires students to interpret, describe, discuss, justify and conjecture as they search for solutions to problems. Real-life applications provide links with students' everyday life. Topics covered include indeterminate forms, vector algebra and calculus in the plane and 3-space, analytic space geometry, multivariable functions, partial derivatives, gradients and real-world problems. Advisory: It is advisable to have knowledge equivalent to MAT 231 Calculus I and MAT 232 Calculus II in order to succeed in this course. Students are responsible for making sure they have this knowledge
Copyright 0 1996by Debra Anne Ross All rights reserved under the Pan-American and International Copyright Conventions. This book may not be reproduced, in whole or in part, in any form or by any means electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system now known or hereafter invented, without written permission from the publisher, The Career Press. MASTER m T H : BASICMATH AND PRE-ALGEBRA Cover design by The Visual Group Printed in the U.S.A.by Book-martPress To order this title, please call toll-free 1-800-CAREER-1(NJ and Canada: 201-848-0310)to order using VISA or Mastercard, or for further information on books from Career Press. Library of Congress Cataloging-in-PublicationData Ross, Debra h e , 1958 Master math :basic math and pre-algebra/ by Debra Anne Ross. p. cm. Includes index. 1. Mathematics. I. Title. ISBN 1-56414-214-0 (pbk.) QA39.2.R6547 1996 513.2-dc20 CIP 96-22992 Introduction Basic Math and Pre-Algebra is the first of three books in the Master Math series. The second and third books are entitled Algebra and Re-Calculus and Geo- metry. The Master Math series presents the general principles of mathematics from grade school through college including arithmetic, algebra, geometry, trigo- nometry, pre-calculus and introductory calculus. Basic Math and Pre-Algebra is a comprehensive arithmetic book that explains the subject matter in a way that makes sense to the reader. It begins with the most basic fundamental principles and progresses through more advanced topics to prepare a student for algebra. Basic Math and Be-Algebra explains the prin- ciples and operations of arithmetic, provides step-by- step procedures and solutions and presents examples and applications. Basic Math and Pre-Algebra is a reference book for grade school and middle school students that ex- plains and clarifies the arithmetic principles they are learningin school.It is also a comprehensivereference source for more advanced students learning algebra 1 Basic Math and Pre-Algebra and pre-calculus. Basic Math and Re-Algebra is inval- uable for students of all ages, parents, tutors and any- one needing a basic arithmetic reference source. The information provided in each book and in the series as a whole is progressive in difficulty and builds on itself, which allows the reader to gain per- spective on the connected nature of mathematics. The skills required to understand every topic presented are explained in an earlier chapter or book within the series. Each of the three books contains a complete table of contents, a comprehensive index, and the ta- bles of contents of the other two books in the series so that specific subjects, principles and formulas can be easily found. The books are written in a simple style that facilitates understanding and easy referencing of sought-afterprinciples, definitions and explanations. Basic Math and Pre-Algebra and the Master Math series are not replacements for textbooks but rather reference books providing explanations and per- spective. The Master Math series would have been in- valuable to me during my entire education from grade school through graduateschool.There is no other source that provides the breadth and depth of the Master Math series in a single book or series. Finally, mathematics is a language-the univer- sal language. A person struggling with mathematics should approach it in the same fashion he or she would approach learning any other language. If someone moves to a foreigncountry, he or she does not expect to know the language automatically. It takes practice and contact with a language in order to master it. 2 Introduction After a short time in the foreign country he or she would not say, "I do not know this language well yet. I must not have an aptitude for it." Yet many people have this attitude toward mathematics. If time is spent learning and practicing the principles, math- ematics will become familiar and understandable. Don't give up. 3 Basic Math and Pre-Algebra 1.1. Digits and the base ten system The system of numbers used for counting is based on groups of ten and is called the base ten system. Numbers are made up of digits that each correspond to a value. For example, the number 5,639,248 or five million, six hundred thirty-nine thousand, two hundred forty-eightrepresents: 5 millions, 6 hundred thousands, 3 ten thousands, 9 thousands, 2 hundreds, 4 tens, and 8 ones This number can also be written: 5,000,000 +600,000 +30,000 +9,000 +200 +40 +8 The ones digit indicates the number of ones, (1). The tens digit indicates the number of tens, (10). The hundreds digit indicates the number of The thousands digit indicates the number of The ten thousands digit indicates the number of tens The hundred thousands digit indicates the number of The millions digit indicates the number of millions, hundreds, (100). thousands, (1,000). of thousands, (10,000). hundreds of thousands, (100,000). (1,000,000). 6 Numbers and Their Operations 1.2. Whole numbers Whole numbers include zero and the counting numbers greater than zero. Negative numbers and numbers in the form of fractions, decimals, percents or exponents are not whole numbers. Whole numbers are depicted on the number line and include zero and numbers to the right of zero. I L I Whole Numbers = I I 1 ; > 0 1 2 3 4 5 6 7 8 Whole numbers can be written in the form of a set. WholeNumbers= (0,1,2, 3,4, 5, 6, 7, 8, 9,10,11,...) 1.3.Addition of whole numbers This section includes definitions, a detailed explanation of addition, and a detailed description of the standard addition technique. The symbol for addition is +. Addition is written 6 +2. The numbers to be added are called addends. 7 Basic Math and Pre-Algebra The answer obtained in addition is called the sum. The symbol for what the sum is equal to is the equal sign =. Note: The symbol for not equal is #. For any number n, the following is true: n +0 = n (Note that letters are often used to represent numbers.) A Detailed Explanation of Addition Consider the followingexamples: 5 + 3 = 8 34 + 76 = 110 439 + 278 = 717 5 + 3 + 2 = 1 0 33 + 28 + 56 = 117 456 + 235 + 649 = 1,340 To add numbers that have two or more digits, it is easier to write the numbers in a column format with ones, tens, hundreds, etc., aligned, then add each column. Example: Add 5 +3. 5 ones +3 ones 8 ones 8 Basic Math and Pre-Algebra A Detailed Description of the StandardAddition Technique An alternativeto separating the ones, tens, hundreds, etc., is to align the proper digits in columns (onesover ones, tens over tens, etc.).Then add each column,beginning with the ones, and carry-overdigits to the left. (Carry over the tens generated in the ones' column into the tens'column, carry over the hundreds generated in the tens' column into the hundreds' column,carry over the thousands generated in the hundreds'column into the thousands' columns,and so on.) Example: Add 35 +46. 35 +46 ? First add 5 +6 = 11,and carry over the 10 into the tens' column. 1 35 + 46 1 Add the tens'column. 12 Numbers and Their Operations 12 928 387 49 + 5 69 Add the hundreds, 1+9 +3 = 13hundreds. 12 928 387 49 + 5 1369 1.4. Subtraction of whole numbers This section includes definitions, a detailed explanation of subtraction, and a detailed description of the standard subtraction technique. Subtraction is the process of finding the difference between two numbers. The symbol for subtraction is -. Subtractionis written 6 - 2. 15 Basic Math and Pre-Algebra The number to be subtracted from is called the minuend. The number to be subtracted is the subtrahend. The answer obtained in subtraction is called the difference. Subtraction is the reverse of addition. If 2 +3 =5, then 5 - 2 = 3 or 5 - 3=2. For any number n, the following is true: n - 0 = n (Note that letters are often used to represent numbers.) To subtract more than two numbers, subtract the first two, then subtract the third number from the difference of the first two, and so on. Subtraction must be performed in the order that the numbers are listed. A Detailed Explanation of Subtraction Consider the examples: 6 - 2 = 4 26 - 8 18 10,322 - 899 = 9,423 To subtract numbers with two or more digits, it is easier to write the numbers in a column format with ones, tens, hundreds, etc., aligned, then subtract each column beginning with the ones. To subtract a digit in 16 Basic Math and Pre-Algebra To check the subtraction results, add the difference to the number that was subtracted. 9423 + 899 10,322 Note that if a larger number is subtracted from a smaller number, a negative number results. For example, 5 - 8 = -3 and 40 - 50 = -10. See Section 1.11 "Addition and subtraction of negative and positive integers." 1.5. Multiplicationofwhole numbers This section includes definitions, an explanation of multiplication, and a detailed description of the standard multiplication technique. Multiplication is a shortcut for addition. The symbols for multiplication are x, , 0 , ( >(). The numbers to be multiplied are called the multiplicand (thefirst number) and the multiplier (the second number). The answer obtained in multiplication is called the product. 22 Numbers and Their Operations Multiplication is written using the following symbols: 6 x 2 , 6 2,6 2, (6)(2) If you add 12 twelves, the answer is 144. 12+12+12+12+12+12+12+12+12+12+12+12 = 144 Adding 12 twelves is the same as multiplying twelve by twelve (12)(12)= 144 What is 3 times 2, (3)(2)?It is the value of 3 two times, or 3 +3 = 6. Equivalently, what is 2 times 3, (2)(3)?It is the value of 2 three times or, 2+2+2 = 6. What is 2 times 4 times 3? (2)(4)(3)= (2)(4 three times) = (2)(4+4+4)= (2)(12)= 24 Also, (2)(12)= 2 twelve times =2+2+2+2+2+2+2+2+2+2+2+2=24 23 Basic Math and Pre-Algebra Equivalently, 2 times 4 times 3 is: (2)(4)(3)= (4 two times)(3)= (4+4)(3) = (8)(3)= 8 three times = 8 +8 +8 = 24 The order in which numbers are multiplied does not afl'ect the result,just as the order in which numbers are added does not affect the result. If a number is multiplied by zero, that number is multiplied zero times and equals zero. For any number n, the followingis true: n x 0 = 0 (Note that letters are often used to represent numbers.) An Explanationof Multiplication Consider the followingexamples: 2 8 * 7 = ? 6,846 * 412 = ? 10 * 10 =? 10 * loo=? 10 * 1,000= ? To multiply numbers with two or more digits, it is easier to write the numbers in a column format. Then multiply each digit in the multiplicand (top number), beginning with the ones'digit, by each digit in the multiplier (bottom number), beginning with the ones' digit. 24 Numbers and Their Operations Note that alignment is important! Each partial product must be aligned with the right end of the multiplier digit. First, multiply the ones'digit in the multiplier with each digit in the multiplicand beginning with the ones' digit, 6 * 2 = 12,carry over the 1ten. 1 6846 x 412 2 Multiply the ones'digit in the multiplier with the tens' digit in the multiplicand, 4 * 2 = 8, then add the 1ten that was carried over (thereis nothing new to carry). 1 6846 x 412 92 Multiply the ones'digit in the multiplier with the hundreds'digit in the multiplicand, 8 * 2 = 16, (nothing carried over to add),carry over the 1thousand. I 1 6846 x 412 692 27 Basic Math and Pre-Algebra Multiply the ones'digit in the multiplier with the thousands'digit in the multiplicand, 6 * 2 = 12, add the 1thousand that was carried. 1 1 6846 x 412 13692 Resulting in the partial product aligned with the right end of the ones'digit of the multiplier. Next, multiply the tens' digit in the multiplier with the carry). 6846 x 412 ones'digit in the multiplicand, 6 * 1=6, (nothingto r with the ten 13692 6 Multiply the tens' digit in the mi ltipli digit in the multiplicand, 4 * 1=4, (nothingto add or cany). 6846 x 412 ? 13692 46 28 Numbers and Their Operations Multiply the tens' digit in the multiplier with the hundreds' digit in the multiplicand, 8 * 1= 8,(nothing to add or carry). 6846 x 412 13692 846 Multiply the tens' digit in the multiplier with the thousands' digit in the multiplicand, 6* 1=6,(nothing carried over to add). 6846 x 412 13692 6846 Resulting in the partial product aligned with the right end of the tens' digit of the multiplier. (Eachpartial product must be aligned with the right end of the multiplier digit.) Next, multiply the hundreds' digit in the multiplier with the ones'digit in the multiplicand, 6 * 4 = 24, and carry over the 2 to the tens'column. 29 Basic Math and Pre-Algebra 2 6846 x 412 13692 6846 4 Multiply the hundreds'digit in the multiplier with the tens' digit in the multiplicand, 4 * 4 = 16, add the 2 over the tens'column,and carry over the 1 to the hundreds'column. 12 6846 x 412 13692 6846 84 Multiply the hundreds'digit in the multiplier with the hundreds'digit in the multiplicand, 8 * 4 = 32, add the 1 over the hundreds'column,and carry over the 3 to the thousands'column. 312 6846 x 412 13692 6846 384 30 Numbers and Their Operations Multiply the hundreds' digit in the multiplier with the thousands' digit in the multiplicand, 6 * 4 = 24, and add the 3 over the thousands' column. 312 6846 x 412 13692 6846 27384 Resulting in the partial product aligned with the right end of the hundreds' digit of the multiplier. (Each partial product is aligned with the right end of the multiplier digit.) Next, add the three partial products for a total product. 6846 x 412 13692 6846 27384 2820552 Therefore, 6,846 * 412 = 2,820,552. 31 Numbers and Their Operations 1.6. Division of whole numbers This section provides definitions and describes in detail the long division format. Division evaluates how many times one number is present in another number. The symbolsfor division are +, /, r. The number that gets divided is called the dividend. The number that does the dividing (or divides into the dividend)is called the divisor. The answer obtained after division is called the quotient. Division is written 6 + 2, 6 ,(6)/(2),2 p . 2 Division is the inverse of multiplication. 2 * 3 = 6 , 6 + 2 = 3 , 6 + 3 = 2 Six divides by two three times or by three two times. 6 + 2 = 3 , 6 + 3 = 2 6 = 3 + 3 = 2 + 2 + 2 35 Basic Math and Pre-Algebra Because 6 +6 +6 +6 = 24, there are four sixes in 24. 6 * 4 =24 or 24 i 6 = 4 For any number n, the following is true: n + 0 = Undefined. (Note that letters are often used to represent numbers.). For any number n, the following is true: 0 + n =0 A Description of the Long Division Technique Example: 4,628 i5 =?. This division problem is easier to solve by writing it in a long division format. Divide the divisor (5) into the left digit(s)of the dividend. To do this, choose the smallestpart of the dividend the divisor will divide in to. Because 5 does not divide into 4, the next smallestpart of the dividend is 46. Estimate how many times 5 will divide into 46. First try 9. What is 5 * 9?5 * 9 =45, which is 1 less than 46. Write the 9 over the right end of the number it will divide into (46), and place 45 under the 46. (See Section 1.18 on rounding, truncating and estimating for assistance on estimating.) 36 Numbers and Their Operations 9?? 5)4628 45 Subtract 46 - 45. 9?? 5)4628 45 01 Bring down the next digit (2)to obtain the next number (12)to divide the 5 into. 9?? 5)4628 45 012 Estimate the most number of times 5 will divide into 12. The estimate is 2. Because, 5 * 2 = 10,(with a remainder of 2), 5 will divide into 12two times. Write the 2 over the right end of the number it will divide into (121,and place 10under 12. 37 Basic Math and Pre-Algebra 92? 5)4628 45 012 10- Subtract 12 - 10. 92? 5)4628 45 012 10 2 - Bring down the next digit (8)to obtain the next number (28)to divide 5 into. 92? 5)4628 45 012 10- 28 Estimate the most number of times 5 will divide into 28. The estimate is 5. Because 5 * 5 = 25,(with a remainder of 3),5 will divide into 28five times. Write the 5 over the right end of the number it will divide into (28),and place 25 under 28. 38 Numbers and Their Operations 925 5)4628 45 012 10- 28 25 Subtract 28 - 25. 925 5)4628 45 012 10- 28 25 3 There are no more numbers to bring down, therefore the division is complete, and 3 is the final remainder. Therefore, 4,628 + 5= 925plus a remainder of 3. To check division, multiply the quotient by the divisor and add the remainder to obtain the dividend. 39 Basic Math and Pre-Algebra 925 x 5 4625 Add the remainder. 4625 + 3 4628 Example: 160,476+ 364 = ?. Arrange in the long division format. 3641160476 Divide the divisor (364)into the left digits of the dividend. To do this, choose the smallest part of the dividend the divisor will divide in to. 364 will divide into 1,604.Estimate the most number of times 364 will divide into 1,604.The estimate is 4. 364 * 4 = 1,456with a remainder of 148. Write the 4 over the right end of the number it will divide into (1,604),and place 1,456under the 1,604. 4?? 364)160476 1456 Subtract 1,604 - 1,456. 40 Numbers and Their Operations 4?? 364)160476 1456 0148 Bring down the next digit (7)to obtain the next number (1,487)to divide 364 into. 4?? 364)160476 1456 01487 Estimate the most number oftimes 364 will divide into 1,487.The estimate is 4. 364 * 4 = 1,456with a remainder of 31. Write the 4 over the end of the number it will divide in to (1,487),andplace 1,456 under the 1,487. 44? 3641160476 1456 01487 1456 Subtract 1,487 - 1,456. 41 Basic Math and Pre-Algebra 44? 364)160476 1456 01487 1456 31 Bring down the next digit (6)to obtain the next number (316)to divide 364 into. 44? 3641160476 1456 01487 1456 316 Because 364 will not divide into 316, place a zero over the right end of 316. 440 364)160476 1456 01487 1456 316 316 becomes the remainder. Therefore, 160,476~364= 440 plusaremainderof316. 42 Numbers and Their Operations To check division, multiply the quotient by the divisor and add the remainder to obtain the dividend. 364 x 440 160160 Add the remainder. + 316 14560 1456 160160 160476 1.7. Divisibility,remainders,factors and multiples This section defines and gives examples of divisibility, remainders, factors and multiples. The divisibility of a number is determined by how many times that number can be divided evenly by another number. For example, 6is divisible by 2 because 2 divides into 6 a total of 3 times with no remainder. An example of a number that is not divisible by 2 is 5, because 2 divides into 5 a total of 2 times with 1 remaining. The remainder is the number left over when a number cannot be divided evenly by another number. 43 Basic Math and Pre-Algebra A smaller number is a factor of a larger number if the smaller number can be divided into the larger number without producing a remainder. Numbers that are multiplied together to produce a product are factors of that product. The factors of 6 .are6 and 1,or 2 and 3. 6 x 1 = 6 , 2 x 3 = 6 5 is not a factor of 6 because 6 + 5 = 1with a remainder of 1. The factors of 10are 2 and 5, or 10and 1,where: 10= (2)(5), 10= (10)(1) If a and b represent numbers, Where 2,3, a and b are factors of 6ab. A multiple of a number is any number that results after that number is multiplied with any number. Multiples of zero do not exist because any number multiplied by zero, including zero, results in zero. It is possible to create infinite multiples of numbers by simply multiplying them with other numbers. 44 Numbers and Their Operations The following are examples of multiples of the number 3: 35=15 3 2 = 6 34=12 320=60 Where 15,6,12and 60 are some of the multiples of 3. 1.8. Integers Integers include positive numbers and zero (whole numbers) and also negative numbers. The set of all integers is represented as follows: Integers = {...-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,...} Numbers that are not integers include numbers in the form of fractions, decimals,percents or exponents. Consecutiveintegers are integers that are arranged in an increasing order accordingto their size from the smallest to the largest without any integers missing in between. The following are examples of consecutive integers: {-10,-9,-8,-7) {0,1,2,3,4} {-2,-1,0,1,2,3,4,5) (99,100,101,102,103,104,105) 45 Basic Math and Pre-Algebra 1.9. Even and odd integers This section defines and provides examples of even integers and odd integers. Even integers are integers that can be divided evenly by 2. Even Integers = {...-6,-4,-2,0,2,4,6,8,...} Zero is an even integer. Odd integers are integers that cannot be divided evenly by 2, and therefore are not even. Odd Integers = {...-7,-5, -3, -1,1,3, 5,7, ...} Fractions are neither even nor odd. If division of two numbers yields a fraction the result is not odd or even. It is possible to immediately determine if a large number is even or odd by observing whether the digit in the ones position is even or odd. Consecutiveeven integers are even integers that are arranged in an increasing order accordingto their size without any integers missing in between. The following is an example of consecutive even integers: {-10,-8,-6,-4,-2,0, 2,4,6} Consecutiveodd integers are odd integers that are arranged in an increasing order accordingto their size without any integers missing in between. 46 Basic Math and Pre-Algebra If zero is multiplied by any number the result is zero: n * O = O Dividingby zero is "undefined": n + 0 =undefined Zero divided by a number (representedby letter n) is zero: 1.11. Addition and subtractionof negative and positive integers This section describes addition and subtraction of negative integers and positive integers. Remember the number line. -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 When numbers are added and subtracted, think of moving alongthe number line. Begin with the first number and move to the right or left depending on the sign of the second number and whether it is being added or subtracted to the first number. 48 Numbers and Their Operations To add a positive number, begin at the first number and move to the right the value of the second number. 2 + 1 = 3 T -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 -2+1 = -1 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 To add a negative number (subtract),begin at the first number and move to the left the value of the second number. 2+-1=1 ~ ~~~~ w -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 -2+-1= -3 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 To subtract a positive number, begin at the first number and move to the left the value of the second number. 2 - 1 = 1 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 49 Basic Math and Pre-Algebra A summary of the division rules are: (+) f (+) =+ (-)f (-)=+ (+)i(-)= - (-)i (+) = - 1.13. The real number line Real numbers include whole numbers, integers, fractions, decimals, rational numbers and irrational numbers. Real numbers can be expressed as the sum of a decimal and an integer. All real numbers except zero are either positive or negative. All real numbers correspond to points on the real number line and all points on the number line correspond to real numbers. The real number line reaches from negative infinity (-m) to positive infinity (v). < > -4 -3 -2 -1-.5 0 142 2 5/23n 4 Real numbers include -0.5,a,512 and 7r. (~3.14) All numbers to the left of zero are negative. All numbers to the right of zero are positive. 52 Numbers and Their Operations The distance between zero and a number on the number line is called the absolute value or the magnitude of the number. 1.14.Absolute value The absolute value is the distance between zero and the number on the number line. c > -4 -3 -2 -1-5 0 142 2 5/23 x 4 The absolute value is always positive or zero, never negative. The symbol for absolute value of a number represented by n is In I . Positive 4 and negative 4 have the same absolute value. 141 = 4 and 1-41 = 4 Properties of absolute value are (x and y represent numbers): 1x1 2 0 I x - y l = ly-XI 1x1 l y l = lxyl Ix+yl 1x1 + lyl (See Section 1.19for description of and 2.) 53 Basic Math and Pre-Algebra 1.15. Prime numbers A prime number is a number that can only be divided evenly (not producing a remainder)by itself and by 1. Forexample,7canonlybe dividedevenlyby 7andby 1. Examples of prime numbers are: {2,3,5,7,11,13,17,19,23} Zero and 1are not prime numbers. The only even prime number is 2. 1.16. Rational vs. irrational numbers In this section, rational numbers and irrational numbers are defined. A number is a rationaZ number if it can be expressed in the form of a fraction, d y , and the denominator is not zero. For example, 2 is a rational number because it can be expressed as the fraction Wl. Every integer can be expressed as a fraction and is a rational number. (Integer)/l or n/l Where n =any integer. 54 Numbers and Their Operations Whole numbers are included in the set of integers, and whole numbers are rational numbers. A number is an irrationd number if it is not a rational number and therefore cannot be expressed in the form of a fraction. Examples of irrational numbers are numbers that possess endless non-repeating digits to the right of the decimal point, such as, n = 3.1415...,and ./z= 1.414... 1.17. Complex numbers In this section, complex numbers, real numbers and imaginary numbers are defined, and addition, subtraction, multiplication and division of complex numbers are described. Complex numbers are numbers involving G,(see chapter on roots and radicals for a description of $>. There is no number that when squared equals -1.By definition ( a ) 2 should equal -1,but it does not, therefore the symbol i is introduced, such that: ./-x =i& Where x is a positive number and (i)2= -1. 55 Basic Math and Pre-Algebra For example, evaluate ( f i ) 2 . (&O=(i&)(i&) = (i)2(&)(&) = (i)2 &5) (5) = (-1)(5)= -5 Complex numbers are numbers involving i and are generally in the form: x +iy Where x and y are real numbers. In the expression,x +iy, x is called the real part and iy is called the imaginary part. A real number multiplied by i forms an imaginary number. (realnumber&) =imaginary number A real number added to an imaginary number forms a complex number. (real number) +(real number)(i)=complex number To add or subtract complex numbers, add or subtract the real parts and the imaginary parts separately. Example: Add (5+4i)+(3+2i). (5+4i)+(3+2i)= (5+3)+(4i+2i)=8+6i Example: Subtract (5+4i) - (3+2i). (5+4i) - (3+2i)=(5- 3) +(4i - 2i)= 2 +2i 56 Numbers and Their Operations Complex numbers are multiplied as ordinary binomials, and (i)2 is replaced by -1.(See Chapter 5, "Polynomials,"Section 5.4 for multiplication of polynomials in the second book of the Master Math series entitled Algebra.)To multiply binomials, each term in the first binomial is multiplied by each term in the second binomial, and like terms are combined (added). Example: Multiply (5+4i) x (3+2i). (5+4i)(3+2i) = (5)(3)+(5)(2i)+(4i)(3)+(4i)(2i) = 15+10i+12i+8(i)2= 15+22i +8(-1) = 15+22i - 8= (15 - 8)+22i = 7 +22i To divide complex numbers, first multiply the numerator and denominator by what is called the complex conjugate of the denominator. The complex conjugate of (3+2i) is (3- 2i), and the complex conjugate of (3- 2i) is (3+2i). The product of a complex number and its conjugate is a real number. Remember to replace (i)2by -1.(See chapters 5 entitled "Polynomials"and 6 entitled "AlgebraicFractions with Polynomial Fractions" for division and multiplication of polynomials and polynomial fractions in the second book of the Master Math series entitled Algebra.) 57 Numbers and Their Operations 1.18. Rounding,truncating and estimating numbers Quickly estimating the answer to a problem can be achieved by rounding the numbers that are to be added, subtracted,multiplied or divided,then adding, subtracting, multiplying or dividing the rounded numbers. Numbers can be rounded to the nearest ten, hundred, thousand, million, etc., dependingon their size. For example, estimate the sum of (38+43)by rounding. Round 38to the nearest ten. 40 Round 43 to the nearest ten. 40 The estimated sum is 40+40= 80 Compare the estimate with the actual sum. 38+43= 81 80is a good estimate of the actual value, 81. To round a number to the nearest ten, hundred, thousand, etc., the last retained digit should either be increased by one or left unchanged accordingto the followingrules: If the left most digit to be dropped is less than 5, leave the last retained digit unchanged. If the left most digit to be dropped is greater than 5, increase the last retained digit by one. 59 Basic Math and Pre-Algebra If the left most digit to be dropped is equal to 5, leave the last retained digit unchanged if it is even or increase the last retained digit by one if it is odd. Example: Round the following numbers to the nearest ten. 11 roundsto 10 65 roundsto 60 538 roundsto 540 65,236 rounds to 65,240 Example: Round the following numbers to the nearest hundred. 238 roundsto 200 650 roundsto 600 9,436 rounds to 9,400 750 roundsto 800 740 roundsto 700 Example: Round the following numbers to the nearest tenth. (See Chapter 3,"Decimals.") 5.01 rounds to 5.0 8.38 rounds to 8.4 9.55 rounds to 9.6 9.65 rounds to 9.6 60 Basic Math and Pre-Algebra Example: Estimate the sum of (56+68 +43) by rounding. Round each number and add the estimate. 60 +70 +40 = 170 Compare with the actual numbers. 56+68+43=167 Truncating rounds down to the smaller ten, hundred, thousand, etc. For example, 43 truncates to 40 768 truncatesto 760 1.19. Inequalities,>, <, 2, S Inequalities are represented by the symbols for greater than and less than, and describe expressions in which the value on one side of the symbol is greater than the value on the other side of the symbol. The symbol for greater than is > The symbol for less than is < The symbol for greater than or equal to is 2 The symbol for less than or equal to is I If a and b are numbers, a < b represents a is less than b, or a is to the left of b on the number line. 62 Numbers and Their Operations a > b represents a is greater than b, or a is to the right of b on the number line. a 1b represents a is less than or equal to b. a 2 b represents a is greater than or equal to b. a < c < b represents a is less than c and c is less than b. a > c > b represents a is greater than c and c is greater than b. Examples: 2 < 4 4 > 2 5 < 8 8 > 5 2 < 5 < 8 5 < 8 5 1 5 The number line below describesx > 1. If c is a positive number, then c > 0. For example, if c=5,then5>0. If d is a negative number, then d < 0. For example, if d = -5,then -5< 0. Example: If a,b and c represent numbers, and If a < b Then a + c < b + c Also a - c < b - c 63 Numbers and Their Operations Example: Ifa, b and d represent numbers, and If d<O Andif a < b Then ad>bd (If a negative number is multiplied, the inequality reverses.) Example: If a =2, b =3 and d = -4, and Because -4 < O And 2 < 3 Then (2)(-4) > (3)(-4) Equivalently -8> -12 (Remember, -12is to the left of -8on the number line.) Example: If a, b and d represent numbers, and If d<O Andif a > b Then a + d < b + d (If a negative number is divided, the inequality reverses.) Example: If a =4, b =6 and d = -2,and Because -2 < 0 And 4 < 6 Then 4 + -2 > 6 + -2 Equivalently -2 > -3 (Remember,-2 is to the right of -3on the number line.) 65 Basic Math and Pre-Algebra In summary, for an inequality: If a number is added to both sides, the inequality remains unchanged. If a number is subtracted from both sides, the inequality remains unchanged. If a positive number is multiplied, the inequality sign remains unchanged. If a positive number is divided, the inequality sign remains unchanged. If a negative number is multiplied, the inequality sign reverses. If a negative number is divided, the inequality sign reverses. 1.20. Factorial The factorial of a positive integer is the product of that integer and each consecutive positive integer from one to that number. The symbol for factorial is "!"(the explanation point). Examples of the factorial of numbers are: 5!= 1 * 2 * 3 * 4 * 5 = 120 7!= 1 * 2 * 3 * 4 * 5 * 6 * 7 =5,040 3!= 1 * 2 * 3 = 6 n! = 1* 2 * 3 * ...n O! = 1 by definition. 66 ChaPter 2 Fractions 2.1 Definitions 2.2 Multiplying fractions 2.3 Adding and subtracting fractions with common denominators 2.4 Adding and subtracting fractions with different denominators 2.5 Dividing fractions 2.6 Reducing fractions 2.7 Complex fractions, mixed numbers and improper 2.8 Adding and subtracting mixed numbers 2.9 Comparingfractions: Which is larger or smaller? fractions 2.1. Definitions A fraction is a number that is expressed in the a form a/bor - b' A fraction can also be defined as: 67 Basic Math and Pre-Algebra part section some or - whole' whole all If a pie is cut into 8pieces, then 2pieces are a fraction of the whole pie. - 2 pieces2 pieces whole pie - 8 pieces in whole pie The top number is the numerator, and the bottom number is the denominator. Numerator Denominator =Numerator + Denominator 5 Fractions express division. -= 5 + 8 8 Equivalent fractions are fractions that have equal value. The following are equivalent fractions: 112= 214= 418= 8/16= 16/32= 32/64 213 =416= 8/12= 16/24= 32/48 315 =6/10= 12/20=24/40= 48/80 2.2. Multiplying fractions To multiply fractions, multiply the numerators, multiply the denominators and place the product of the numerators over the product of the denominators. 68 Fractions For example, 9 5 3 9 x 5 ~ 3 135 2 8 4 2 x 8 ~ 4 64 - -- x - x - = - 2 x 3 6 12 3 3 4 3 x 4 12 2 - = - = -- x - = If the numerators are less than the denominators, then after multiplying,the value of the product will be less than the values of the original fractions.This is true because multiplying a number or fraction by a fraction is equivalentto taking a fraction of the first number or fraction. For example: If you have a piece of a pie (which means you have a fraction of a pie),then you eat a fractionof the piece, you have eaten less than a piece. In other words, you have eaten a fraction of a fraction. 2.3. Adding and subtracting fractions with common denominators To add or subtract two or more fractionsthat have the same denominators,simply add or subtract the numerators and place the sum or difference over the common denominator. 69 Basic Math and Pre-Algebra Examples: 9 5 3 9 + 5 + 3 - 17 8 8 8 8 8 - + - + - = - - 2.4. Adding and subtracting fractions with different denominators To add or subtract two or more fractions that have different denominators, a common denominator must be found. Then, each original fraction must be multiplied by multiplying-fractions that have their numerator equal to their denominator, so that new equivalent fractions are created that have the same common denominator. These fractions can then be added or subtracted as shown above.The procedure is: 1.Find a common denominator for two or more fractions by calculating multiples of each denominator until one number is obtained that is a multiple of each denominator. This is called a common multiple.For example, if there are two denominators, 4 and 6, the multiples of 4 are: 4,8, 12, 16, .., and the multiples of 6 are: 6, 12, 18,24,... The smallest number that is a multiple of both 4 and 6 is 12.Therefore, 12 is called the lowest common multiple and it is also the Lowest common denominator for 4 and 6. 70 Fractions 2. After the lowest common denominator is found, transform the original fractions into fractions with common denominators so that they can be added or subtracted. To do this, multiply each original fraction by a multiplying-fiaction that has its numerator equal to its denominator, so as to create new equivalent fractions that have the same common denominators. By having the numerator equal to the denominator in these mu1tiplying-fractions, the value of each of the original fractions remains unchanged. For example, (1/2)x (2/2) = (2/4),where 1/2 is the original fraction, 2/2 is the multiplying- fraction and 2/4 is the resulting equivalent fraction with its value equal to 1/2. To determine each multiplying-fraction, compare the new common denominator with the original denominators of each fraction, then create multiplying-fractions for each original fraction such that when the original denominator is multiplied with the multiplying-fraction'sdenominator, the resulting denominator is the common denominator. 3. After the equivalent fractions with their common denominators have been obtained, add or subtract the numerators and place the sum or difference over the common denominator. 4. Reduce the resulting fraction if it is possible, (see section below on reducing fractions). 71 Basic Math and Pre-Algebra For example, add 1/4+116=?. First, find the lowest common denominator. Multiples of4: 4,8, 12, 16, ... Multiples of 6: 6, 12, 18, ... The lowest common multiple and lowest common denominator is 12. Next, multiply each original fraction by a multiplying- fraction (with its numerator equal to its denominator) such that each equivalent fraction will have a denominator of 12. For the first fraction, because 4 x 3 = 12, 1/4+?/? =?/12 1/4 x 3/3 = 3/12 3/12 is equivalent to 1/4. For the second fraction,because 6 x 2 = 12, 1/6+?/? =?I12 1/6 x 2/2 = 2/12 2/12 is equivalent to 1/6. After the equivalent fractions with their common denominators have been obtained, add the numerators and place the sum over the common denominator. 3/12 +2/12 = 5/12 72 Fractions Example: Add ? 2 5 1 0 ? - + - + -9 5 3 -- - First, find the lowest common denominator. Multiples of 2: 2,4, 6, 8, 10, ... Multiples of 5: 5, 10, 15,20, ... Multiples of 10: 10,20, ... The lowest common multiple is 10,therefore the lowest common denominator is 10. (Notice that the smallest number that 2, 5, and 10 will all divide into is 10.)(Also, the factors of 10 are: (2)(5) and (1)(lO).) Next, multiply each original fraction by a multiplying- fraction (with its numerator equal to its denominator) such that each equivalent fraction will have a denominator of 10. For the first fraction, because 2 x 5 = 10: 9 5 45 2 5 10 - x - = - For the second fraction, because 5 x 2 = 10: 5 2 10 5 2 10 - x - = - For the third fraction, because 10x 1= 10: Fractions Therefore, the equation is: 9 x 4 - 5 x 1 - - -3 x 2 - 2 x 4 8 x 1 4 x 2 3 6 5 6 3 6 - 5 - 6 25 8 8 8 8 8 ----- _ - _ - - An alternative method for adding and subtracting two fractions is as follows: 1.Multiply the two denominators to find a common denominator. The result will be a common multiple of each, but not necessarily the lowest common multiple. Find the new numerator of the first fraction by multiplying the numerator of the first fraction with the original denominator of the second fraction. Find the new numerator of the second fraction by multiplying the numerator of the second fraction with the original denominator of the first fraction. 2. Then, add or subtract the new numerators and place the result over the common denominator. 3.Reduce the resulting fraction if it is possible (see section below on reducing fractions). 75 Basic Math and Pre-Algebra For example, add 1/2+314. Multiply denominators. 2 x 4 =8 The new common denominator is 8. The first new numerator is 1x 4=4. The second new numerator is 3 x 2 =6. The new equivalent fractions are: 4 6 10 8 8 8 - + - = - To reduce 10/8, divide 2 into both the numerator and the denominator. 1 0 / 2 5 8 / 2 4 - -- 2.5. Dividing fractions To divide fractions, turn the second fraction upside down to invert the numerator and denominator. (An inverted fraction is called a reciprocal.) Then, multiply the first fraction with the reciprocal fraction. 3 . 5 - 3 8 24 - 6 4 8 4 5 20 5 ---. ---x--=--- Where 815 is the reciprocal of 5/8. Multiplying the reciprocal is equivalent to dividing because: 76 Basic Math and Pre-Algebra Example: Reduce 30/40. Write the fraction in factored form and cancel the factors common to both the numerator and denominator. 3- 3 x 2 ~ 530 40 2 X 2 X 2 X 5 4 ----- Note that by inspection a 10 could have been canceled from both the numerator and the denominator. 2.7. Complex fractions,mixed numbers and improper fractions In this section, improper fractions, mixed numbers and complex fractions are defined, and methods for converting improper fractions to mixed numbers and converting mixed numbers to improper fractions are described. Every integer can be expressed as a fraction. For example, 6 = 6/1, 23 = 23/1. Improper fractions are fractions with their numerators larger than their denominators. Examples of improper fractions are: 13 6 12- - - 2 ' 1 ' 2 78 Fractions If a value is represented by an integer and a fraction, it is called a mixed number. A mixed number always has an integer and a fraction. The following are examples of mixed numbers: 1 3 6 - , 25- 2 4 An improper fraction can be expressed as a mixed number by dividing the numerator with the denominator. For example: 4 1 - -- 1- 3 3 4 1 3 3 Where - is the improper fraction and 1- is the mixed number. When performing calculations, it is generally easier to work with improper fractions than with mixed numbers. Mixed numbers are easily converted to improper fractions. Following are two methods used to convert mixed numbers into improper fractions. Method 1 1.Multiply the integer and the denominator. 2. Add the numerator to the result, which results in a new numerator. 79 Basic Math and Pre-Algebra 3. Place the new numerator over the original denominator. For example, convert 6 112to an improper fraction. Multiply the integer and the denominator. (6)(2)= 12 Add the numerator to the result to obtain the new numerator. 1+12= 13 Place the new numerator over the denominator to obtain the improper fraction. 13/2 Method 2 1.Find the common denominator. 2. Add the fractions. For example, convert 6 112to an improper fraction. 1 1 6 1 2 2 1 2 6 - = 6 + - = - + - The lowest common denominator is 2. Create equivalent fractions with common denominators of 2 and add. (112 does not need to be multiplied.) Therefore, 6 112 = 1312. Improper fractions are easily converted to mixed numbers by dividing the numerator with the denominator. 80 Fractions For example, convert 25/4 to a mixed fraction. Divide the numerator by the denominator. 25 + 4 = 6 plus a remainder of 1. Place the remainder over the divisor resulting in 6 1/4. To check the result, multiply the integer and the denominator. 6 x 4 =24 Add the numerator and place the result over the denominator. 24 +1 =25 25/4 is the original improper fraction. A complex:fraction has a fraction in the numerator or in the denominator or in both so that there is one or more fractions within a fraction. The following are examples of complexfractions (x and y represent numbers): 1 / 3 3 x + 2 / y 3- - 4 ' 4 / 5 ' 5 ' X / Y Complexfractions can be simplifiedby performing the indicated division of the fractions or sub-fractions. For example, simplifjlthe following (remember when dividing fractions, multiply the reciprocal). 1 / 3 1 1 4 1 1 1- = - + 4 4 - + - = - x - = - 4 3 3 1 3 4 1 2 81 Fractions Find a common denominator for the two improper fractions, 13/2 and 10314. 4 is a multiple of both 2 and 4. Multiply each fraction by a fraction with its numerator equal to its denominator such that the result is a common denominator of 4 in each fraction. Add the numerators and place the result over the common denominator. 1 3 x 2 103x1 2 x 2 4 x 1 + - 26 103 26+103 - 129 4 4 4 4 ----- -+- Therefore, 6 1/2 + 25 314 = 129/4. 2.9. Comparing fractions: Which is larger or smaller? In this section, methods for comparing the value of fractions are described. Two fractions can be directly compared if they have the same denominator. For example, which of the followingfractions is larger? 3/4 or 1/2? 83 Basic Math and Pre-Algebra Because 4 is a common multiple of both fractions, it is also a common denominator. To obtain a common denominator, multiply 3/4by 1/1and 1/2by 2/2. 1/2x 2/2=2/4 314x l/l= 3/4 The two fractions become: 3/4and 2/4 Because 3 > 2, 3/4> 2/4 To compare several fractions, rather than converting all of the fractions to the same denominator, it may be easier to compare two at a time. Which of the following are larger? 1/8or 3/4or 5/6? First, compare: 1/8and 3/4 The common denominator is 8. To obtain a common denominator, multiply 3/4by 2/2. 3/4x 2/2=6/8 The two fractions become: 84 Basic Math and Pre-Algebra To quickly assess whether one fraction is larger or smaller than another fraction, it may be useful to determine whether each fraction is larger or smaller than 112. The smaller the numerator is in comparison to the denominator, the smaller will be the value of fraction. 5/10 > 5/100 > 5/1000 > 5/10,000 > 5/100,000 > 5/1,000,000 58/59 is almost 1. 99/985,236is approximately one-tenthousandth. 86 ChaPter 3 Decimals 3.1 Definitions 3.2 Adding and subtracting decimals 3.3 Multiplying decimals 3.4 Dividing decimals 3.5 Rounding decimals 3.6 Comparing the size of decimals 3.7 Decimals and money 3.1. Definitions The decimal system and decimals are based on tenths or the number 10. The digits to the right of the decimal point are called decimal fi-actions. A decimal can be expressed in the form of a fraction, and a fraction can be expressed in the form of a decimal. 87 Basic Math and Pre-Algebra Decimals that do not have a digit to the left of the decimal point are written 0.95or .95.Inserting the zero before the decimal point prevents the viewer from mistaking .95for 95. The digits to the right of the decimal point correspond to tenths, hundredths, thousandths, ten thousandths,hundred thousandths, etc. For example, the digits in the number 48.35679correspond to: 4tens, 8ones. 3 tenths, 5 hundredths, 6thousandths, 7ten thousandths, 9hundred thousandths The decimal point is always present after the ones digit even though it may not be written. For example: 7 = 7.0 = 7.00= 7.000= 7.0000000 29 = 29.00= 29.0= 29.000000000 The following are examples of the equivalent forms of decimals and fractions: 0.1 = 1/10 0.01 = 1/100 0.001 = 1/1,000 0.0001 = 1/10,000 0.00001 = 1/100,000 Decimals have equivalent forms as fractions. For example, the decimal 0.5is equal to the fraction 5/10. This canbe provenby dividingthe fraction 5/10or 540. 88 Decimals Using the long division format: Insert the decimal point and a zero in the tenth position. 10 divides into 5.0,0.5times, then multiply 10 x 0.5 = 5.0. a 5 524 00 10& Therefore, 0.5 is equal to 5/10. In general, a fraction can be transformed into its decimal equivalent by dividing the numeratorby the denominator. (SeeSection 3.4,"Dividingdecimals.") a 5 110 0 0 1/2=2 L 2)1,0- 2)1.0 Therefore, 1/2=0.5. 89 Basic Math and Pre-Algebra Proper names that correspond to decimal fractions are used to describe measurements or quantities in various units such as grams, moles, seconds,liters, meters, etc. For example, if a scientist is measuring extremely small amounts of a chemical in grams, proper names for the following decimal quantities are: 0.1 = 10-1 = 100milligrams 0.01 = 10-2 = 10milligrams 0.001 = 10-3 = 1milligram 0.0001 = 10-4 = 100micrograms 0.00001 = 10-5 = 10micrograms 0.000001 = 10-6 = 1microgram 0.000000001 = 10-9 = lnanogram 0.000000000001 = 10-12 = 1picogram 0.000000000000001= 10-15 = 1femptogram 3.2. Adding and subtracting decimals To add or subtract decimals, align the decimal points, then proceed with the addition or subtraction (as if the decimal points are not there). To add decimals, arrange in column format, add each column beginning with the right column, and carry over digits to the next larger column as necessary. 90 Basic Math and Pre-Algebra 11 389.32 65.20 2.00 + .05 56.57 Add the hundreds' column. I1 389.32 65.20 2.00 + -05 456.57 Therefore, 389.32+65.2+2+0.05=456.57. To subtract decimals, arrange in column format, subtract each columnbeginning with the right column and borrow when necessary from the next larger column. If there are more than two numbers, subtract the first two, then subtract the third from the difference, and so on. Example: Subtract 23 - 3.89. Arrange in column format and subtract the hundredths'column. 92 Decimals 23.00 - 3.89 ? To borrow from the tenths' column, first borrow from the ones'column. Subtract the hundredths and tenths. 2 2 . {9}{10} - 3 . 8 9 . 1 1 To subtract the ones'column,first borrow from the tens'. Subtract the ones and tens. 1 9 . 1 1 Therefore, 23 - 3.89 = 19.11. 3.3. Multiplying decimals To multiply decimals, ignore the decimal points and multiply the numbers, then place the decimal point in the product so that there are the same number of digits to the right of the decimalpoint in the product as there are in the all of the numbers that were multiplied combined. 93 Basic Math and Pre-Algebra For example, if 2.2 and 0.3 are multiplied, because there are two digits to the right of the decimalpoints in 2.2 and 0.3(onefor each number),there must be two digits to the right of the decimal point in the product. Therefore, 2.2 x 0.3=0.66. Example: Multiply 35.268and 2.5. There are a total number of four digits to the right of the decimal points in these two numbers, therefore the product will have four digits to the right of the decimal point. Multiply the 5 in the multiplier with each number in the multiplicand beginning at the right. 35.268 x 2.5 176340 Multiply the 2 in the multiplier with each number in the multiplicand beginning at the right. 35.268 x 2.5 176340 70536 Add the partial products. 94 Decimals 35.268 X 2.5 176340 70536 Place the decimalpoint four digits from the right. Therefore, 35.268 x 2.5 = 88.1700. 3.4. Dividing decimals To divide decimals, arrange the numbers into the long division format, move the decimal point in the divisor to the right until there are no digits to the right of the decimal point, move the decimal point in the dividend the same number of places to the right so that the overall value of the division is unchanged (zeros may be inserted in the dividend as required), then divide using long division. The decimal point will be placed in the quotient above where it moved to in the dividend. Example: 10 + 0.5 =? Arrange the numbers into the long division format. 95 Basic Math and Pre-Algebra ? 0.5& Move the decimal point in the divisor and the dividend to the right until there are no digits to the right of the decimal point in the divisor (insert zeros as required). ? 5.)100 Divide 5 into 10. 2?. 5. )100 Subtract 10 - 10= 0, and bring down the last 0. 2?. 5.)100 U! 000 There is nothing for 5 to divide in to, so place a 0 above the last 0 in the dividend. 20. 5.)100 U! 000 Therefore, 10+ 0.5 = 20. 96 Decimals 3.5. Rounding decimals To round decimals, the last retained digit should either be increasedby one or left unchanged according to the followingrules: If the left most digit to be dropped is less than 5, leave the last retained digit unchanged. If the left most digit to be dropped is greater than 5, increase the last retained digit by one. If the left most digit to be dropped is equal to 5, leave the last retained digit unchanged if it is even or increase the last retained digit by one if it is odd. For example, round the followingto the nearest integer. 3.4 rounds to 3. 2.5 rounds to 2. 45.64 rounds to 46. Decimals may also be rounded to the nearest tenth, hundredth, thousandth, etc., depending on how many decimalplaces there are and the accuracyrequired. For example,round the following as specified. 45.689 rounded to the nearest tenth is 45.7. 1.9654rounded to the nearest hundredth is 1.96. 1.545454 rounded to the nearest thousandth is 1.545. 97 Basic Math and Pre-Algebra When solvingcomplexmathematical or engineering problems, it is important to retain the same number of "significant digits"in the intermediate and final results. The number of decimal places in the resulting numbers should not exceed the number of decimal places in the initial numbers because the resulting numbers cannot be known with greater accuracy than the original numbers. Therefore,depending on the least number of significant digits in the initial numbers, rounding intermediate and final results will be required to maintain the decimalplaces to ones, tenths, hundredths,thousandths, etc. For example, if 45.689 and 1.9654are added, the accuracy of the result cannot be greater than three decimal places. 45.689 +1.9654 = 47.6544= 47.654 3.6. Comparingthe size of decimals To comparethe value of two or more decimals to determine which decimal is a larger or smaller, the followingprocedure can be applied: 1.Place the decimals in a column. 2. Align the decimal points. 3. Fill in zeros to the right so that both decimals have the same number of digits to the right of the decimal point. 98 Decimals 4. The larger decimal will have the largest digit in the greatest column (thefarthest to the left). Example: Compare 0.00025 and 0.000098. Place the decimals in a column, align the decimal points, and fill in zeros. 0.000250 0.000098 The 2 in the ten-thousandths place is greater than the 9 in the hundred-thousandths place. Therefore: 0.000250 is larger than 0.000098. 3.7. Decimals and money There is a relationship between money and decimals because the money system is based on decimals. Dollars are represented by whole numbers and cents are represented by tenths and hundredths of a dollar. For example, $25.99 = 25 dollars and 99 cents. The following are equivalent: Ninety-nine hundredths of a dollar, 99 cents, 99/100 of a dollar, and 0.99 dollars. 99 Basic Math and Pre-Algebra Examples: 10cents is one tenth or 1/10of a dollar or 0.1 dollars. 70 cents is seven tenths or 7/10 of a dollar or 0.7 dollars. 1 cent is one hundredth or M O O of a dollar or 0.01 dollars. 6 cents is six hundredths or 61100of a dollar or 0.06 dollars. The amount, $0.50 is 1/2of a dollar. Similarly, the decimal 0.5 equals the fraction 1/2. The word cent refers to one hundred, (remember a century has 100years), and in money, cents refers to the number of hundredths. 100 Chapter 4 Percentages 4.1 Definitions 4.2 Figuring out the percents of numbers 4.3 Adding, subtracting,multiplying and dividing 4.4 Percent increase and decrease (percent change) 4.5 Simple and compound interest percents 4.1. Definitions Percent is defined as a rate or proportion per hundred, one one-hundredth,or M O O . The symbol for a percent is %. Apercent is a form of a fraction with its denominator equal to 100.To remember that percent is per one- hundred, think of a century, which has 100years. A percent can be convertedto a fraction or decimal.A percent can be reduced and manipulated like a fraction or decimal. 101 Basic Math and Pre-Algebra Percents of a number can also be determined by moving the decimal point according to the percent amount. The following examples represent percents of the number nine: 1%of9.Move the decimal to the left two digits. = 0.09 10%of 9.Move the decimalto the left one digit. = 0.9 100%of 9.The decimal does not move. = 9 1000%of 9. Move the decimalto the right one digit. = 90 10,000%of 9.Move the decimal to the right two digits. = 900 100,000% of 9. Move the decimal to the right three digits. = 9,000 The following are examples of percents of numbers: What is 6 percent of 30? 6 x U100 of 30 =6 x U100 x 30 = 6/100x 30= 180/100= 1.80 What is 5 percent of 20? 5 x 1/100of 20 = 5 x 1/100x 20 = 100/100= 1.00 What is 20 percent of 80? 20 x M O O of 80= 20 x 1/100x 80= 1600/100= 16 The examples above can also be solved using an alternative method. 104 Percentages What is 6 percent of 30? Because 1%of 30 is 0.30, and 6%is 6 times 1%, then 0.30x 6 = 1.80. What is 5 percent of 20? Because 10%of 20 is 2, and 5%is half of 10%, then half of 2 is 1. What is 20 percent of 80? Because 10%of 80 is 8, and 20%is 2 times 10%, then 8x 2 = 16. 4.3. Adding, subtracting,multiplying and dividing percents To add or subtract percents, simply add or subtract as with integers but keep track of the percent. For example, add or subtract the following: 26% +4%= 30% 158%- 6%= 152% 3%+16%+4%=23% For example, if you have 50%of your assets in stocks and 20%of your assets in bonds, then 70%of your assets are in stocks and bonds. 50%in stocks+20%in bonds= 70%in stocks and bonds 105 Percentages 4.4. Percent increase and decrease (percent change) In this section,percent change and discount are discussed. To determine the percent that a number has increased or decreased, the following equation is used: ?- - amount of increase or decrease (change) - original amount 100 This equation can also be written: amount of increase or decrease (change) (100) = percent change original amount Example: If the price of a house is discounted from $250,000 to,$200,000, what is the percent decrease or discount in the price? $50/000 (100)(100)= $250,000 - $200,000 $250,000 $250,000 = (0.2)(100) =20% 107 Percentages 4.5. Simple and compound interest Simple interest is generally computed annually, therefore the time it will take to earn a certain percent on money invested in a simple interest account is a year. Example: How much simple interest will $5,000 earn in a year and in 6 months at a rate of 4%? $5,000 x 4% = ($5,000)(0.04)= $200 will be earned in a year. In the first 6 months, $5,000will earn: $200 x (6 months)/(l2 months) = $200 x 1/22= $100 Therefore, in 6 months the $5,000becomes $5,100 and in one year the $5,000 becomes $5,200. Compound interest is compounded periodically during the year. To determine the compound interest, divide the interest rate by the number of times it is compounded in the year and apply it during each period. For example, if the interest rate is 4% and it is compounded semiannually, then 2%is applied to the principle every 6 months. If4%is compounded quarterly then 1%is applied to the principle every 3 months or four times a year. 109 Basic Math and Pre-Algebra Example: How much interest will $5,000 earn in six months and in a year at 4% interest compounded semi-annually? Divide the interest by the number of times it is compounded. 4% + 2 = 2% Apply 2% interest for the first 6-monthperiod. $5,000x 2% = ($5,000)(0.02)= $100 earned in 6 months. The second 6-monthperiod begins with $5,100. Apply 2% interest again for the second 6-monthperiod. $5,100 x 2%= ($5,100)(0.02)= $102 earned in the second 6-monthperiod. In 6 months the $5,000 becomes $5,100 And in one year the $5,000 becomes $5,202 Note that compound interest earns slightly more than simple interest for the same rate. 110 ChaPter 5 Converting Percentages, Fractions and Decimals 5.1 Converting fractions to percents 5.2 Convertingpercents to fractions 5.3 Converting fractions to decimals 5.4 Converting decimals to fractions 5.5 Converting percents to decimals 5.6 Converting decimals to percents 5.1. Convertingfractions to percents To convert a fraction to a percent, divide the numerator by the denominator, then multiply by 100. For example,convert 315 into a percent. Divide the numerator by the denominator using long division. 111 ConvertingPercentages,Fractions and Decimals 5.3. Convertingfractionsto decimals Toconvert a fraction to a decimal,divide the numerator by the denominator. For example,convert 3/5 into a decimal. Divide the numerator by the denominator using long division. ? l6 -3.0 0.0 5p = 5)3.0 Therefore,3/5=0.6. 5.4. Convertingdecimals to fractions Toconvert a decimal to a fraction,place the decimal-fractionover the tenth, hundredth, thousandth, ten-thousandth, hundred-thousandth,etc., that it corresponds to, then reduce the fraction. For example,convert the following decimals into their fractional form. 113 Converting Percentages, Fractions and Decimals 5.6. Convertingdecimalsto percents To convert a decimal to a percent, multiply by 100. Note that multiplying by 100is equivalent to moving the decimal point two places to the right. Example: Convert the decimal 0.25 to its percent form. Multiply 0.25 by 100. 0.25 x 100= 25% Two final notes: If two decimals are multiplied, the product will have the same number of digits to the right of its decimal point as in the multiplicand and multiplier combined. When convertingbetween fractions, percents and decimals, think about whether the result seems reasonable. For example, if the fraction 314 is converted to a percent and the result is 0.0075%,it does not seem reasonable that 0.0075%could be equivalent to three-fourths.Instead, 75%does seem reasonable. 117 Chanter 6 Ratios, Proportions and Variation 6.1 Definitions 6.2 Comparing ratios to fractions and percents 6.3 Variation and proportion 6.1. Definitions In this section,ratios and proportions are defined. Ratios depict the relation between two similar values with respect to the number of times the first contains the second. A ratio represents a comparison between two quantities. For example,if the ratio between apples and oranges in a fruit bowl is 3 to 2, then for every 3 applesthere are 2 oranges. Ratios are written 3 to 2, 3:2 and 3/2. The difference between ratios and fractions is that fractions represent part-per-whole,and ratios represent part-per-part. 118 Ratios, Proportions and Variation Proportions are a comparative relation between the size, quantity, etc., of objects or values. Mathematical proportions represent two equal ratios. For example, the following are equivalent: 1/2 =2/4, 1:2 =2:4, 112is proportional to 2/4, 1:2::2:4 Note that ina proportion,the product ofthe"extreme" outer numbers equals the product of the "mean" middle numbers. 1:2::2:4 can be written 1x 4 =2 x 2. When equivalent fractions, such as 112 = 214, are cross-multiplied(by multiplying the opposite numerators with the opposite denominators),the two products are always equal. This principle is useful when determining the quantity of one of the items when the ratio is known. For example, how many apples are there in a mixture containing 10oranges, if the ratio is 3 apples to 2 oranges? To solve this, set up the proportion: 3 apples - ? apples 2 oranges 10 oranges - Using cross-multiplicationthe equation becomes: 3 ~ 1 0 = 2 x ? 30=2x? Divide both sides by 2. 3012 = 1x ? 15 =? Therefore, there are 15 apples in this mixture. 119 Basic Math and Pre-Algebra 6.2. Comparing ratios to fractions and percents The differencebetween ratios and fractions is that fractions represent part-per-whole,and ratios represent part-per-part. Ratios can be expressed in the form of a fraction (or in the form of division). The definition of a ratio differs from that of a fraction but all the rules for manipulating fractions apply to ratios. The ratio 1to 2 (or 1:2 or 1/2)can be expressed as 50%or 0.50. Example: If Tom ate 3 pies for every 5 pies Ted ate, what is the ratio of pies eaten by Tom and Ted? Tom : Ted (3 pies) / (5pies) Tom ate 3/5the number of pies that Ted ate. Tom ate 3/5 = 0.60 = 60%of the number of pies that Ted ate. If a ratio of two values is known, the percent that one of the values is of the total can be determined by adding the parts to get the whole, placing the one value over the whole, and multiplying by 100. 120 Ratios, Proportions and Variation For example, what percent of the total number of pies did Tom and Ted eat? The ratio is (3pies) to (5pies), which represents partlpart. And the percent of the total number is (part/whole)(100). If the total number or whole is 3 pies +5 pies = 8 pies. Therefore, the percent of the total number of pies Tom ate is 3 pied8 pies = 3/8 = 0.375 and 0.373 x 100= 37.5% Also, the percent of the total number of pies Ted ate is 5 pies/8 pies = 5/8 = 0.625and 0.625x 100= 62.5% 6.3. Variation and proportion Variation describes how one quantity varies or changes as another quantity varies or changes. If as one number increases then decreases, another number increases then decreases simultaneously, the numbers are in direct variation or direct proportion to each other. The equation for direct variation or direct proportion is: 121 Basic Math and Pre-Algebra The k represents some constant number, and x and y represent numbers that vary directly.As x increases,y increases. As x decreases,y decreases. If as one number increasesthen decreases, another number decreasesthen increases simultaneously,the numbers are in indirect variation and are said to be inversely proportional.The equation for indirect variation representing inverselyproportional quantities is: xy =k which can be rearranged as y =Wx The k represents some constant number, and x and y represent numbers that vary indirectly. As x increases, y decreases.As x decreases, y increases. 122 Powers and Exponents 7.1 Definition of the exponent or power 7.2 Negative exponents 7.3 Multiplying exponents with the same base 7.4 Multiplying exponents with different bases 7.5 Dividing exponents with the same base 7.6 Dividing exponents with different bases 7.7 Raising a power of a base to a power 7.8 Distributing exponents into parenthesis 7.9 Addition of exponents 7.10 Subtraction of exponents 7.11 Exponents involvingfractions 7.1. Definition of the exponent or power An exponent represents a number that is multiplied by itself the number of times as the exponent or power defines. 123 Basic Math and Pre-Algebra The following exponent represents 2 raised to the 6th power: 26 =2 x 2 x 2x 2 x 2 x 2 =64 2 is called the base and 6 is the exponent or power. Examples of exponents are 26,257 and 21965. If a positive whole number is raised to a power greater than one, the result is a larger number. If a number (except zero) is raised to the 1stpower, the result is the number itself. 31 = 3. If a number is raised to the zero power, the result is 1. 3 0 = 1 aO= 1 a = any number except zero 00=undefined 7.2. Negative exponents In this section, negative numbers raised to even and odd powers and positive and negative numbers raised to negative powers are presented. If a negative number is raised to a positive even power, the result is a positive number. For example: (-2)' = (-2)(-2)(-2)(-2)(-2)(-2) = 64 124 Basic Math and Pre-Algebra 7.4. Multiplying exponentswith different bases To multiply exponents with different bases, each exponent must be expressed individually, then multiplied. The powers cannot be added directly. For example: 32 x 24= (3x 3)x (2x 2 x 2 x 2)=9x 16 = 144 ab x dC = abdc Where a, b, c and d represent numbers. To multiply exponents with different bases but the same power, the following law of exponents applies (a, b and c represent numbers): aCxbc=(axb)c Which can also be written: 7.5. Dividing exponents with the samebase To divide exponents with the same base, subtract the powers. 126 Basic Math and Pre-Algebra Consider the following examples (a,b and c represent numbers): (ab)2= (a2x b2)=a2b2 (2b)2=(22x b2)=4b2 If numbers or variables inside parenthesis are added or subtracted, the exponent outside cannot be distributed as above. Instead: (a+b)2= (a+b)*(a+b) =a2+ ab +ab +b2= a2+ 2ab +b2 (See multiplication of binomials in Chapter 5 of the second book in the Master Math series,Algebra.) 7.9. Addition of exponents To add exponents whether the base is the same or different, express each exponent individually,then add. The powers cannot be added directly. 130 Basic Math and Pre-Algebra Example: Express the followingfraction. abxc abc (2bP (22xb2) 4b2 = -(abY -- - A number raised to a negative power is equivalent to one-over that number. If a positive fraction is raised to a power, and the numerator is smaller than the denominator, the value of the resulting fraction is less. (1/2)2= (1/2)(1/2)= 114 Where 1/4< 112. If a positive fraction is raised to a power, and the numerator is larger than the denominator, the value of the resulting fraction is greater. (512)2= (5/2)(512)=2514 Where, 2514 > 512. Remember, 5/2 = 10/4. Consider the following examples with fractional exponents: 3112 = & 32/3=(3113)2 =(32)113 132 ChaPter 8 Logarithms 8.1 8.2 8.3 8.4 8.5 8.6 Definition of the logarithm Common (base ten) and natural logarithm Solving equations with logarithms or exponents Exponential form and logarithmic form Laws of logarithms: addition, subtraction, multiplication, division, power and radical Examples: the Richter scale, pH and radiometric dating 8.1. Definition of the logarithm The logarithm is the exponent of the power to which a base number must be raised to equal a given number. A logarithm is the inverse of an exponent. Each exponent has an inverse logarithm. 133 Basic Math and Pre-Algebra Consider the followingexponential equation (xand y represent numbers): x =a y Where a is an integer and is the base of the exponent. The inverse of this equation is: y =log,x Where a is the base of the logarithm. The inverse is obtained by taking the base a logarithm of both sides of the exponential equation. x =a y Because log,(a) cancels, the equation becomes: Example: Convert the exponential equation 24 = 16 to a logarithmic equation. Because the exponent has a power of 2, take the base 2 logarithm of both sides. Because log2(2)cancels, the equation becomes: 4 = log2(16) 134 Logarithms 8.2. Common (baseten) and natural logarithm The two most common logarithms are the common logarithm, also called the base ten logarithm, and the natural logarithm. The common or base ten logarithm is written: loglox or simply logx The natural logarithm is written: log& or lnx Where e = 2.71828182846. The relationship between the common logarithm and the natural logarithm can be written: Or equivalently: In x = (2.3026)logx 135 Basic Math and Pre-Algebra 8.3. Solving equations with logarithms or exponents To solve logarithmic equations, take the inverse or exponent. Example: Solve the equation y =log x for x. Because the base is 10,raise both sides of the equation by base 10. Because lO(10gio) cancels itself, lO(10gX) = x The equation becomes: 1 o y = x Example: Solve the equation y =In x for x. Because the base is e, raise both sides of the equation by e to isolate x. Because eln cancels itself, e(lnx)= x The equation becomes: 136 Logarithms To solve exponential equations, take the inverse or logarithm. Example: Solvethe equationy = 10xfor x. Because the base is 10,take log10 of both sides of the equation. logy =log(10.) Because loglo(10)cancels itself, log(1 0 ~ )=x The equation becomes: logy=x Example: Solve the equationy =e~ for x. Because the base is e, take In of both sides of the equation. In y =ln(ex) Because ln(e)cancels itself, ln(ex)=x The equation becomes: lny=x 137 Logarithms To approximate or compute numerical values of logarithms or exponents, refer to tables contained in mathematical handbooks and selected algebra books, or use the function keys of technical calculators. 8.5. Laws of logarithms:addition, subtraction, multiplication, division,power and radical The following are laws of logarithms (a represents any base): Also, note that: logb a = l/logab Where a and b represent numbers. Because a represents any base, these laws apply to base e (natural logarithms) or base ten (common logarithms). Proofs of the laws of logarithms can be found in selected algebra books. 139 Basic Math and Pre-Algebra 8.6. Examples: the Richter scale,pH and radiometric dating In this section, applicationsof logarithmic and exponential equationsfor the Richter scale,the pH scale and radioactive dating are presented. The Richter scale is a logarithmic scale that ranges from 1to 10and is used for indicatingthe intensity of an earthquake. The Richter scale was originated in 1931 by K. Wadati in Japan and was developed by Charles Richter in California in 1935.The Richter scale is a quantitative scale that measures wave amplitudes generated from ground shaking using a seismograph.Richter defined the magnitude of a local earthquake as the logarithm to base ten of the maximum seismic-waveamplitude (in thousandths of a millimeter)recorded on a standard seismograph at a distance of 100kilometersfrom the earthquake epicenter.Using the logarithmicscale, for each one unit increase in magnitude, the amplitude of the earthquake waves increase ten times. pH expressesthe acidity or basicity of a solution in terms of the pH (potency of hydrogen) scale.pH is defined as the negative of the logarithm of the hydrogen (or hydronium) ion concentration in an aqueous (water is the solvent)solution. pH = -log[H+] or pH = -log[H30+] 140 Logarithms For example, pure water that has a neutral pH of 7 has a hydrogen ion concentration of 1x10-7M or 10-7M (M is moles per liter). The logarithm of 10raised to the power -7is equal to -7. In an acidic solution, the H+concentration is greater than lO-7Mand less than the OH- concentration. An acidic solution with 1x10-4M of H+has a pH of 4. In a basic solution, the H+concentration is less than 10-7M and less than the OH- concentration. A basic solution with 35x10-10M of H+has a pH of 9.46. pH = -log[H+I=-10g[3.5x 10-101 = -(log[3.5]+log[lo-'ol) = -(0.54- 10)= -(-9.46)= 9.46 Radioactive substances are subject to exponential decay. The decay of radioactive substances is used to estimate the age of objects. For example, carbon-14 is used to estimate the age of plants and animals that were once alive by comparingthe ratio CVC12. (C-12is the more common form of carbon.) Carbon-14is produced in the atmosphere when high-energy neutrons (producedfrom cosmic rays collidingwith 141 Basic Math and Pre-Algebra atmospheric molecules)collide with the nuclei of nitrogen-14in the air. The carbon-14then reacts with oxygen to form carbon-14-carbondioxide. The carbon-14-carbondioxide is incorporated into plants through photosynthesis and into animals through ingestion of plants. m i l e a plant or animal is alive, the content of carbon-14 in its system is assumed to remain constant in small but measurable quantities.After the plant or animal has died, carbon- 14 can no longer be incorporated by photosynthesis or ingestion, and the carbon-14that is present begins to decay back to nitrogen-14 by emission of beta radiation (electrons). The half-life of carbon-14is 5,730 years, therefore after 5,730years half of the original amount of carbon- 14 in a given sample will have decayed back to nitrogen-14. (Note that radioactive dating techniques assume: (a)the rate of radioactive decay has remained constant over time; (b)the concentration of the radioactive substance that is naturally abundant today is equivalent to the concentration that was naturally abundant in the past; and (c) the substance did not interact with the environment so that there were no original atoms or decay products added or removed.) The equation for the mass of a substance at any time, t, can be derived as follows. If the half-life of a radioactive substance is t1/2 and its initial mass is c, 142 Logarithms then, in t1/2 units of time (years),the mass will reduce to c/2. The mass is given by y(tln)=ce-ktll2,therefore: Cancelingthe c's and taking the natural logarithm of both sides,the equation becomes: Because In e cancels itself, and because In(1/2)= -In2, the equation becomes: -ktln= -In2 Cancelingthe negative signs on both sides, and dividingboth sides by k,the equation becomes: t1i2= (In 2 ) k =(0.693)k so: t1/2 = (0.693)fk Multiplyingboth sides by k, and then dividingboth sides by t1/2, the equation becomes: k = (0.693)/t1/2 (SeeChapter 3 of Algebra, the second book in the Master Math series, for an explanation of solving equations using algebraic techniques.) 143 Basic Math and Fre-Algebra 1 Fraction of Nuclei Remaining 112 1I4 118 1/16 1 2 3 4 Time,Half-!ives The number of nuclei remainingis hdved during each half-life.The greatest decrease occurs during the first half-life andthe amount of decrease lessens with each succeedinghalf-life. 144 Basic Math and Pre-Algebra 9.1. Definitions A radical is written using the radical symbol, $. The number that the root is calculated for is inside the radical symbol. The word radical is derived from the Latin word rad,which means root. The number inside the radical symbol is called the radicand. In the case of JJE,x represents the radicand. Different roots of numbers exist. For example,for a number represented by x, possible roots are the square root, cubed root, fourth root, etc., represented by &, &,&,etc., respectively. An equivalent form of writing roots is ~ 1 ' 2 ,~ 1 ' 3 ,~ 1 ' 4 , where x represents any number. For example: v45x2 = (45X2P2 146 Roots and Radicals 9.2. The square root The square root of a number, is equal to a number that, when squared, equals the original number. For example, the square root of 4 is equal to 2, such that 22 equals 4. Also, (-2)2is equal to 4, so the square root of 4 could also be -2. If a number has two equal factors, then it has a square root. For example, 4 has factors 2 x 2. Aperfect square is a number that can be expressed as the product of two equal numbers or factors. The followingare perfect squares: 1,4,9,16,25, because they can be expressed as: 1x 1,2x 2,3 x 3,4x 4, and 5 x 5 respectively. The square root of 25 is k5, because 5 2 = (5)(5)or (-5)(-5)= 25. The radicaZ symbol, $,represents the positive square root. 147 Basic Math and Pre-Algebra It is not possible to find a perfect square root of a negative number such as J-4because when two identical numbers are multiplied together the result is always a positive number. 2 x 2 = 4 and -2x-2=4 (Note: See Section 1.17, "Complexnumbers,"for a discussion of A.) displayed. is commonly written &,with the "2" not The following are examples of square roots: 148 Roots and Radicals 9.3. Estimating square roots To determine the square root of a number that is not a perfect square: 1.Determine what two perfect squares the number is between. 2. Estimate the square root of the number to one decimal point accuracy (0.1). 3. Divide your estimate into the number (and evaluate to the nearest thousandth). 4. Find the average of the estimate and the quotient. 5. Check how good the estimate is by squaring the result. A technical calculator can also be used to estimate square roots. Example: Estimate the square root of 12. The two perfect squares this number is between are 9 and 16. Therefore,the is between 6and J16. Because &= 3 and J16=4, the between 3 and 4. must be 149 Basic Math and Pre-Algebra Estimate the square root of the number to one decimal point accuracy (0.1). Because 12is 3 away from 9and 4away from 16,the estimate is 3.4. Divide the estimate into 12and evaluate it to the nearest thousandth. Using a calculator 12 + 3.4 =3.529. Alternatively,using long division: 3.4p Move the decimalpoint to the right in both numbers so there is no decimal in the divisor. 34.j120.00 34 will divide into 120three times. Multiply 3 by 34 and subtract the result from 120. 3.??? 34.)120.000 102_ 18.0 Bring down the zero, divide 34into 18.0,multiply the result by 34,and subtract that result from 18.0. 150 Basic Math and Pre-Algebra Find the average of the estimate and the quotient. = 3.47 3.4 + 3.529 - 6.929- - Check how good the result is by squaring it: (3.47)2= 12.04. This process can be repeated to better the approximation by dividing 3.47 into 12 and proceeding as above. 9.4. The cubed root The cubed root of a positive number is the number that, when multiplied by itself three times, equals that number. For example, the cubed root of 8 written, 6 is equal to 2. This is true because, 23 = (2)(2)(2)= 8 Also: If a represents a number then: 152 Roots and Radicals 9.5. The fourth and fifth roots The fourth root of a positive number equals a number that when multiplied by itself four times equals the number. For example: Where a represents a number. The fifth root of a positive number equals a number that when multiplied by itself five times equals the number. For example: 6= V(2)(2)(2)(2)(2)= G = 2 153 Basic Math and Pre-Algebra 9.6. Simplifyingradicals by factoring To simplifyradicals by factoring, factor the radicand, look for perfect squares for square roots, or cubes for cubed roots, etc., and if multiple factors exist, bring each root out of the radical. For example, simplify the followingby factoring and reducing the radicals. There are no squared factors, so this radical cannot be reduced further. 154 Roots and Radicals 9,7. Multiplying radicals To multiply radicals, combine the numbers under one radical symbol, multiply and simplify. For example, multiply the following radicals: 9.8. Dividing radicals To divide radicals, combine Lie numbers under one radical symbol, divide and simplify. For example, divide the following radicals: (Notethat the 3 in the numerator canceled with the 3 in the denominator.) 155 Basic Math and Pre-Algebra 9.9. Radicals involving fractions To simplify a radical containing fractions or a fraction containing radicals, combine the radicands in each radical under one radical symbol,divide and simplify. For example, simplify the following radicals: 9.10. Rationalizing the denominator Rationalizing the denominator of a fraction containing radicals creates a fraction without any radicals in the denominator. To rationalize the denominator, simplify the radical in the denominator, multiply both the numerator and the denominator by the radical in the denominator (that will make the denominator'sradicand a perfect square),then simplify the fraction. 156 Chapter 10 Important Statistical Quantities 10.1 Average (arithmeticmean) 10.2 Median 10.3 Mode 10.4 Probability 10.5 Standard deviation, variance, histograms and distributions 1OeIe Average (arithmetic mean) In this section the average or arithmetic mean and the weighted average are defined. The average and the arithmetic mean are equivalent. To find the average of a group of numbers, add all of the numbers together and divide the sum by how many numbers there are. total sum of the numbers how many numbers there are Average = 159 Basic Math and Pre-Algebra Example: What is the average of {5,6,9,25}? The total sum is: 5 + 6 + 9 + 2 5 = 45 Divide the sum by how many numbers there are, or 4. 45 + 4 = 11.25 Example: What is the average of {9,6,6,9,25,25}? The total sum is: 9 + 6 + 6 + 9 + 2 5 + 2 5 = 80 Divide the sum by how many numbers there are, or 6. 80+ 6 = 13.333333.... Which rounds to 13.33. To solve a problem using the weighted average, each quantity is weighted (multiplied)by the number of items having that quantity. After multiplying each quantity by the number of items having that quantity, add the products and divide the sum by the total number of items. For example, what is the weighted average of the following: If'you purchase 5 shrubs and two cost $2 and three cost $7, what is the average cost per shrub? 160 Important Statistical Quantities To solve this problem as a weighted average, the two costs are weighted (multiplied)by the number of items and the products are added. 2($2)+3($7)= $25 $4 +$21 = $25 Then, divide the sum by the total number of shrubs. $25 + 5 = $5 Therefore, the average cost per shrub is $5. This problem can also be solved as a standard average. The total cost is: $2+$2+$7+$7+$7=$25 Divide the sum by the total number of shrubs, or 5. $25 + 5 = $5 Therefore, the average cost per shrub is $5. 10.2.Median The median is the value of the number in the middle of a sequential list of numbers. If there are two numbers in the middle, the median is the value of their average. There must be an equal number of numbers above and below the median. 161 Basic Math and Pre-Algebra To find the median of a group of numbers, list the numbers sequentially;the median is either the number in the middle, or the average of the two numbers in the middle. To find the median value of an odd number of numbers, list the numbers in an ordered sequence from least in value to greatest; the median is the number in the middle. For example: Find median of (5,7,3,10, I}. List in order. 1,3,5,7, 10 The middle number, or median, is 5. To find the median value of an even number of numbers, list the numbers in an ordered sequence from least in value to greatest; the median is the average of the two middle numbers. For example: Find median of (5, 7,3, 12, 10, l}. List in order. 1,3,5, 7,10,12 The middle two numbers are 5 and 7. The average of the middle two numbers is: - - -- 6 5 + 7 12 2 2 - Therefore, the median is 6. 162 Important Statistical Quantities 10.3. Mode The mode of a list of numbers is the number that occurs most frequently. Example: Find the mode of: {3,6,29,8,6,4,3,85,2,8,35,3,8,9}. It is easier to list the numbers sequentially. 2, 3,3,3,4, 6,634 8,8,9,29, 35, 85 The numbers 3 and 8 both occur three times, which is the greatest number of times. Therefore, 3 and 8 are both modes. As shown in this example,there can be more than one mode. If no number occurs more than once,then the mode does not exist for that list. 163 Basic Math and Pre-Algebra 10.4. Probability Probability defines the chances of some certain event occurring. The probability, p, is generally expressed as a fraction. Probability = number of possible ways total number of ways For example, if a cube has oneyellow face and five blue faces, what is the probability that the yellow face will land on top if the cube is tossed in the air? The answer is: p = 1/6 10.5. Standard deviation, variance, histograms and distributions In this section, standard deviation, variance, histograms and distributions are defined and explained. StandardDeviation andVariance Consider experimental data that has been collected where a measurement, xl, is made of a quantity x. If other measurements are made, we expect random error within our measurement that will be distributed around the correct value. The standard deviation and the variance represent the uncertainties associated with experimental attempts to determine the true value of some quantity. 164 Important Statistical Quantities The symbol for standard deviation is sigma 0 and the symbol for variance is 02. The standard deviation is a measure of the dispersion in a frequency distribution. It is equal to the square root of the mean of the squares of the deviations from the arithmetic mean of the distribution. The variance is the square of the standard deviation. The standard deviation is the square root of the variance. The standard deviation: G = fdo2 Where 02 is the variance. 1 Where: <x>is a weighted average over x of all possible values of x. x is the quantity that is being measured. xi represents the measurements made. N is the number of measurements made and i=l is the first measurement. 165 Basic Math and Pre-Algebra The sum (E)of all measurements from i=l to i=N is given by: i = l The LimN.>- represents the Limit as the number of measurements get larger and larger, (see Chapter 5, "Limits,"in the third book of the Master Muth series, Pre-CaZcuZus and Geometry).p represents the average of all possible measurements. The average is the sum of the values of the measurements divided by the total number of measurements, N. The variance (andfrom that the standard deviation) can be calculated using the equation: xave represents the average of the measurements (the experimental mean). 166 Important Statistical Quantities The Histogram,Binomial Distribution, Gaussian Distribution and Poisson Distribution If 100 measurements of the length of a football field are made, the measurements can be graphed in terms of a frequency distribution indicating the number of times each length was measured. A mean of the data points can be calculated and a standard deviation estimated. A histogram graph is used to depict the number of measurements recorded for each length. Frequency f Measurements x The curve represents an estimate distribution assuming infinite measurements could be made. The binomial distribution describes the probability of observingx for n attempts where only two mutually exclusive outcomes are possible. The probability for success in each attempt is p. A binomiaZ experiment is an experiment with n repeated attempts where: a)the attempts are independent; b) each attempt results in only two possible outcomes, success^' and "failure"; and c) the probability, p, of a success on each attempt, remains constant. x is the number of attempts that 167 Basic Math and Pre-Algebra result in success and has a binomial distribution with parameters p and n = 1,2, 3, ...The probability function is: p" (l-p)"-" n! x! (n-x)! P B = Where p =np and 02 = np(1 - p). (p represents the mean and 0 represents the standard deviation for the distribution of the hypothetical infinite population of all possible observations.) The total number of different sequences of attempts that contain x successes and n - x failures is: x! (n-x)! The Gaussian distribution or normal error distribution, is a bell-shaped curve and describes an expected distribution of random observations for a given experiment. In fact, it seems to describe the distribution of estimations of the parameters of most probability distributions. The Gaussian distribution is an approximation of the binomial distribution for the case where the number of possible different observations is large and the probability of successfor each measurement is large. The Gaussian distribution is useful for smooth symmetrical distributions with large n and infinite p. 168 Important Statistical Quantities (Notethat exp means raise to the exponent e.) The Poisson distribution represents an approximation to the binomial distribution for the case when the average number of successesis smaller than the possible number. The Poisson distribution is useful for describing small samples with large numbers of events that are difficult to observe. P, = -exp[-p]c1" X! 169
Just the facts (and figures) to understanding algebra. , polynomials, exponents and logarithms, conic sections, discrete math, word problemsand more. -Written in an easy-to-comprehend style to make math concepts approachable -Award-winning math teacher and author of The Complete Idiot's Guide® to Calculus and the bestselling advanced placement book in ARCO's "Master" series
As a sidetrack in this question it came up that it is important to have students read texts (in particular proofs) critically. As examples it is nice to have correct proofs at hand (presumably in the textbook/lecture notes), but also a variety of others: Proofs that are just plain wrong, like the nice "proof by induction" that all integers are larger than 10, just by omitting the base case Proofs that are wrong, but the result is actually right (missing cases, hidden assumptions, ...) Proofs that are right, but could be tightened up/simplified This is in part motivated by the classic by Kernighan and Plaugher "The Elements of Programming Style", where the authors show bad program snippets culled from textbooks and other published sources, dissect them and show how they should be written right, and why. I'm aware of Edward Barbeau's "Mathematical Fallacies, Flaws, and Flimflam" (MAA, 2000), but that targets more bad computation than bad proving. It it helps narrowing down, I'm mostly interested in combinatorics and discrete math. But approachable proofs, accessible to the relative layman (think students with Calculus I under their belt, often just taking Calculus II) in any area are quite welcome. Great question. There's a legend at my faculty that one of the professors used to give a wrong proof on the exam, and the students had to find the error. ;) – mborkMay 6 at 21:04 The book by Smith, Eggen, and St. Andre, Transition to Advanced Mathematics, has "proofs to grade" at the end of (nearly?) every exercise set. Lots on elementary set theory; perhaps not so many to do with combinatorics. – Michael E2May 6 at 21:29 @MichaelE2, sounds interesting, thanks! Will take a peek. – vonbrandMay 6 at 21:49 2 Answers 2 Students are, of course, the best source of "bad proofs". And while one can pull from assignments/homework, I find the best "bad proofs" are the ones students give on competition style problems. To that end, I usually photocopy our students' MAA Team Contest and Putnam responses before mailing them in. Then I can type up those responses and use them in our Intro to Proofs course.
Most independence debates start with the participants telling the audience what their conclusions are and then trying to get them over to their side. This is not a discussion. This is a membership drive.Denise Mina Our Price: £68.50 RRP £68.50 , Save £0.00 0 customer(s) reviewed this product Description Reviews Book Details Contents Crossing the River with Dogs: Problem Solving for College Students has been adapted from the popular high school text to provide an accessible and coherent college-level course in mathematical problem solving for adults. Crossing the River with Dogs: Problem Solving for College Students has been adapted from the popular high school text to provide an accessible and coherent college-level course in mathematical problem solving for adults. Focusing entirely on problem solving and using issues relevant to college students for examples, the authors continue their approach of explaining classic as well as non-traditional strategies through dialogs among fictitious students. This text is appropriate for a problem solving, liberal arts mathematics, mathematics for elementary teachers, or developmental mathematics course.
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).Our goal is to improve upon VisualBoyAdvance by integrating the best features from the various builds floating around. In order to uncompress the downloaded package, you need WinRAR or 7-Zip:
Abstract: One major part of the effort to reform secondary school mathematics is the project of changing the goal of studying school algebra from the mastery of symbolic manipulations to the ability to reason algebraically. Another major component of these reform efforts is the creation of opportunities for students to communicate within and about mathematics. The ability to generalize, especially when the generalization requires a major breakthrough in habits of mind, is one indication of algebraic reasoning. In this article, I describe generalization activity as an opportunity to learn about seventh graders' understanding of functions. A group of students who had studied functions modeled a multivariable situation. Through individual and group work, they designed, described, and discussed various representations for functions of 2 variables. Their modeling efforts allowed them to analyze their understanding of representations of quantities, relationships among quantities, and relationships among the representations of quantities in both single- and multivariable functions. The National Council of Teachers of Mathematics is the public voice of mathematics education, supporting teachers to ensure equitable mathematics learning of the highest quality for all students through vision, leadership, professional development, and research.
Weitere Ausgaben Kurzbeschreibung Erscheinungstermin: 18. März 2014 \| Reihe: For DummiesProduktbeschreibungen Buchrückseite Learn to: Solve tricky trig equations Graph functions and figure out formulas Use trigonometry to solve practical problems Your guide to getting an angle on sines, cosines, and tangents Confused by cosines? Perplexed by polynomials? Don't worry! This friendly guide takes the torture out of trigonometry by explaining everything in plain English, offering lots of easy-to-grasp examples, and adding a dash of humor and fun. You'll see the ways trig applies to everyday life, and how it's an important tool for a variety of careers. Start with basics — get up and running with an overview of trig functions, radians, and more Learn tricky trig functions — take things to the next level with SOH-CAH-TOA and circular functions Make trig work — get practical with trig, find out how to use your calculator for complex solutions, and solve trig equations Graph functions — figure out the basics of graphing sine, cosine, tangent, cotangent, and more Open the book and find: Definitions of trigonometry functions How to get down with Pythagoras and his theorem Ways to use Cartesian coordinates The lowdown on the sine, cosine, and tangent functions How to go 'round and 'round with circular functions The scoop on inverse trigonometry Details on graphing trig functions Ten basic identities and ten not-so-basic identities Über den Autor und weitere Mitwirkende Mary Jane Sterling is the author of Algebra I For Dummies and many other For Dummies titles. She has been teaching mathematics at Bradley University in Peoria, Illinois, for more than 30 years and has loved working with future business executives, physical therapists, teachers, and many others. I read the first edition and found it excellent. When this 2nd edition was announced, I purchased it feeling it might improve over the first edition. I was correct. This is an outstanding book for self-study. It is well written in essentially non-technical terms when compared to some other mathematics texts. It can be easily understood, even by those just beginning, or refreshing, their study of trigonometry. It defines terms clearly and understandably, and includes some examples to re-enforce the concepts presented. However, the number of examples provided is relatively sparse, and as is often said mathematics is -not- a spectator sport, it needs to be participated in to develop a meaningful understanding. The small number of worked examples, the lack of Chapter exercises, and the emphasis on statements made without proof are the text's primary weaknesses. For this reviewer, these deficiencies are compensated for by the presentation's excellence. Because of the lack of proofs, this should be considered an applied, rather than a pure, mathematics text. If you are interested is learning basic trig terminology and gaining a fundamental understanding of how trigonometric problems are solved, this is an excellent book (although, as noted, one with a shortage of solved examples, and thus one requiring a supplemental problem book, such as Kelley's excellent "The Humongous Book of Trigonometry Problems"). However, if you're primarily interested in understanding why certain trigonometric statements are true and how to prove these statements, this book is not a good choice. This edition modifies, augments, and corrects material from the first edition. As examples, the informative section on "Angles in circles" has been added between the "Chord and Tangent" and "Sectors" sections, retained from the first edition. In addition, the first edition presents an example for finding the area of a sector. In that example, the diameter is incorrectly used in place of the radius in calculations. That error has been corrected here. This book provides one of the clearest explanations of the six trigonometric functions. It presents these using a broad brush introduction in the first Chapter. It later expands and extends this introduction, using an explanation involving the sides of a right triangle. In a still later section, the trig functions are presented from a somewhat different perspective, based on the coordinates of a circle. This book's text as well as its equations and graphs display nicely on my Kindle DX. However, many equation displays on my Kindle HDX 7", HDX 8.9", PC and Android Kindle emulators are literally unreadable. Enlarging the font, sadly, only enlarges the text, but not these equations or graphs. The equations are still unreadable. Later Amazon Kindles appears to have a significant problem in displaying formulas, and this problem now appears pervasive. I am not aware (at the time of this review) of any current comment from Amazon about this issue, or even if they are aware of it and have a "fix" planned. Perhaps, one of Amazon's team will read this review and comment on this problem, present at the time of this posting. It appears ubiquitous in most Kindle editions of mathematics and science texts targeted for the HDXs and Kindle emulators. I do not have HDs or Paperwhites and so cannot comment on versions for those products; perhaps owners of these products will be kind enough to add comments here. Until this issue is fixed, I would gently recommend that any Kindle version of a mathematics or science text always be sampled on the target Kindle platform before purchase, and if this cannot be done, unless you are using a Kindle DX, the e-version be skipped in favor of the printed book. Bottom-line: This edition and the Kindle DX version can be highly recommended for applied users, but not for mathematicians, who would likely want a more "proof-oriented" text. This book deserves five stars for its content. Perhaps Amazon has implemented a solution to the formula display issue. However, I still found this same "formula" problem present in other Kindle books. If Amazon reads these reviews, may I gently suggest that until this problem is resolved, you consider -not- selling Kindle versions of any book containing formulas. If/when this display problem is fixed, please be kind enough to leave a comment with this review. Since Amazon now has an option for automatic updates available, we should then be able to see the correct display of these formulas on our Kindles and Kindle emulators. When/if I see Amazon's comment I would be pleased to check my HDX and Kindle emulator versions of this book for the proper formula display, and update this review accordingly. Until then, while this text is highly recommended in its book form, it cannot be recommended of any Kindle HDXs or any versions of Kindle emulator software. 2 von 2 Kunden fanden die folgende Rezension hilfreich 1.0 von 5 SternenTotal waste of money!!! Jumps over steps necessary for non math people to get it!24. Mai 2014 Von E. Milkes - Veröffentlicht auf Amazon.com Format:Taschenbuch\|Verifizierter Kauf I got this book as a refresher, because I had forgotten many of the concepts and wanted to brush up before tackling calculus. I assure you that not for the purpose of bragging, but so that you can believe that I'm fairly intelligent and can tell when something really stinks, I want to say at the outset that I have a degree from Brown University and a law degree from NYU. Despite my ability to understand complex language and the most convoluted gobbledygook, and more to the point, despite the fact that I was an A student in trigonometry in hight school, I consistently came up against brick walls of confusion with this book! I had to go to my son, a senior in high school, only to have him explain to me each time that the author had left out an important connection, or elemental explanation that would make sense of what she was saying. This happened about 4 times before I finally trashed the book! DONT WASTE YOUR MONEY!!! 1 von 1 Kunden fanden die folgende Rezension hilfreich 5.0 von 5 SternenTrig made fun and easy28. Mai 2014 Von A. Newsom - Veröffentlicht auf Amazon.com Format:Taschenbuch\|Verifizierter Kauf If you are like me and have had problems understanding trig, no matter how many times you've taken the classes - then this book is a must! Its informative and easy to follow, with a touch of humor and history well blended to keep your attention. It includes practical situations in which I never considered just how much trig is used in everyday occurances - from using angles in woodshops to how bearings are used in navigation - it is made fun and simple! - Heck if they used these books in college there'd be more people passing the classes than they'd have professors to teach them! 5.0 von 5 SternenVery good!16. Juni 2014 Von Patricia Cooper - Veröffentlicht auf Amazon.com Format:Taschenbuch\|Verifizierter Kauf Great study guide for college entry exams. Breaks it down..Easy to understand. We love all of the "Books For Dummies!"
MATLAB 7 für Ingenieure: Grundlagen und Programmierbeispiele, 5e This book provides a structured and systematic introduction to MATLAB. The book includes quick-reference tables with summaries of essential commands and functions. Also, the book demonstrates the functionality of MATLAB commands for interpolation, regression, linear equations, and graphical representation.
Textbooks To acquaint the student with the topics of equations, inequalities, rational expressions, exponents, logarithms, radicals, functions, graphs, and systems of equations. This course is designed to prepare students to take additional mathematics courses Calculator Requirement:Each student will need to have a graphing calculator available for some of the material of the course. The instructor will generally use a TI-83, TI-84 or TI-86, and recommends that the student use a TI calculator too.If a student has another brand, the instructor may not be able to help with any problems. If the student has a TI-89 (or TI-92) use will be restricted to those functions available on the TI-84.Cell phones or PDA'sare not acceptable.Cell phones and PDA's should be turned off and put away during all class periods, and especially during tests. Grading Standards See the attached course syllabus Final Exam 12/4/2010 10:30 - 12:30 Submission Format Policy Homework assignments should be done on 8 1/2 by 11 paper. The problems should be done neatly and in order, and if the assignment involves more than one page, the pages should be stapled together. Assignments should be done in pencil with all mistakes neatly and cleanly erased. It is recommended that the student solve the problems on scratch paper, and then copy the solution (not just the final answer) onto the homework sheets The teacher may give homework handouts, in which case the final answer should be placed in the underlined blank, if provided, and the work should be done neatly in the space between problems. Again, any misprints should be neatly and cleanly erased. Tests will be given in-class and will done on paper provided by the instructor. In-class quizzes may also be given. No make-ups will be given for quizzes, and tests will only be able to be made up for unavoidable reasons. If a student knows that he/she has a legitimate conflict with a scheduled test, that student should contact the instructor well in advance of the test to make arrangements for making up the assignment. If a student misses a test for an unavoidable reason, that student must contact the instructor no later than the first day that student returns to class (and preferably before that, if possibleAll tests and homework should be completed according to the schedule provided in the syllabus. No make-ups will be given for in-class quizzes or exercises (if any). If the instructor assigns problems to be worked outside class and handed in in class, then the problems are due at the beginning of the designated period (and each student should be prepared to hand the assignment in before taking his/her seat as the student enters the classroomStudents are expected to attend every session of the class. Recognizing that there are extenuating circumstances where students must miss an occasional class, the instructor will follow the Midwestern State University attendance policy as stated on page 78 of the Midwestern State University Undergraduate Catalog, Volume LXXVIII, Number 1, 2010-2012. In particular, the instructor will keep track of attendance and if a student accumulates four or more un-excused absences and is not taking the course seriously as evidenced by homework and tests, then the instructor reserves the right to use the policy to drop the student from the class An absence is defined as not being present for the entire period. Students who come in late or leave early may be counted absent for that class, unless they have made arrangements with the instructor in advance. Other Policies Use of cell phones for communication during class is forbidden. Students may not use cell phones or PDA's to communicate with other individuals inside or outside of the classroom. Any student found using a cell phone PDA, or computer during a test will be considered to be cheating, and will be subject to receiving a zero on the assignment. Students may use cell phones or cameras to copy material on the board, but communication during class is not permitted. Students may use personal computers to take notes during class, but again, communication with other people, surfing the web, or working on assignments for other classes is not permitted during this class. At the teacher's sole discretion, a cell phone, PDA or computer may be confiscated for the remainder of the class period. Entering the class late or leaving the class early is a disturbance to the other students and to the teacher. Each student is expected to treat the other students and the teacher with respect. Any student who is being disruptive to the class may be asked to leave the classroom and will be counted absent for that day. Grading:The final grade for the course will be determined by a combination of hour exams, exercises (some take-home and some in-class), and a final exam.Any take-home exercises will be due at the beginning of the period designated by the instructor.Late exercises will not be accepted. No makeup on in-class exercises will be given.The grade assigned will be determined by the grade scale listed below. InstrumentWeight\|Grade Scale ------------------------\|----------------- Hour Tests (4)68%\|90 - 100%A Exercises/Quizzes 10%\|80 -89%B Final Exam 22%\|70 -79%C \|60 -69%D Cheating:Each student is expected to do his or her own work on all graded assignments. ANY EVIDENCE OF CHEATING OR UNAUTHORIZED group effort WILL RESULT IN DISCIPLINARY ACTION which may range from a zero on the assignment to an F in the course.On homework assignments students may discuss the problems outside of class, but each student is expected to work out and understand the solutions to the problems.For some of the exercises done in class the teacher will let students work together, but not on tests. Note:Any student experiencing difficulty with this course has an obligation to himself and the rest of the class to seek help in mastering the material.The first step is to talk to the instructor.Putting it off will only make it worse.It has been the experience of the teacher that students who study together in groups outside class generally do better.Therefore the teacher encourages students to form study groups.It is permissible to work on homework problems outside class in study groups.However, simply to copy the answers derived by another student is not only self-defeating, but cheating.The Mathematics Department provides help sessions in Bolin 101 from 2:00 to 5:00 Monday through Thursday and 1:00 to 4:00 on Friday, starting the second week of classes and ending the last week of classes. This provides a good place to study and/or seek help. In accordance with the law, MSU provides students with documented disabilities academic accommodations. If you are a student with a disability, please contact me. Course Outline:The following is a tentative outline of the material to be covered in this course, and the pace at which it should be covered.Due to the fast pace, it is recommended that each student read the sections listed for each day prior to coming to class. Day Date Section(s) Day Date Section(s) Mon 8/22 1.1, 1.2 Fri 10/14 3.8 Wed 8/24 1.3 Mon 10/17 4.1 Fri 8/26 1.4 Wed 10/19 Test 3 3.1 – 3.8 Mon 8/29 1.5 Fri 10/21 4.2 Wed 8/31 1.5, 1.6 Mon 10/24 4.2, 4.3 Fri 9/02 1.6 Wed 10/26 4.3 Mon 9/05 Labor Day No Class Fri 10/28 4.4 Wed 9/07 2.1, 2.2 Mon 10/31 4.5 Fri 9/09 Test 1 1.1 – 1.6 Wed 11/02 5.1 Mon 9/12 2.2, 2.3 Fri 11/04 Test 4 4.1 – 4.5 Wed 9/14 2.3, 2.4 Mon 11/07 5.2 Fri 9/16 2.4, 2.5 Wed 11/09 5.3 Mon 9/19 2.5 Fri 11/11 5.4 Wed 9/21 2.6 Mon 11/14 5.5 Fri 9/23 2.6 Wed 11/16 5.6 Mon 9/26 3.1 Fri 11/18 5.6 Wed 9/28 Test 2 2.1 – 2.6 Mon 11/21 Test 5 5.1 – 5.6 Fri 9/30 3.2 Wed 11/23 Thanksgiving Holiday Mon 10/03 3.3 Fri 11/25 Thanksgiving Holiday Wed 10/05 3.4 Mon 11/28 7.1 Fri 10/07 3.5 Wed 11/30 7.1 Mon 10/10 3.6 Fri 12/02 Wind up Wed 10/12 3.7 Tuesday December 6, 2011 Final Exam 1:00 – 3:00 pm
Features Places combinatorial and graph-theoretical tools at the forefront of the development of matrix theory Fosters a better understanding of matrix theory by using graphs to explain basic matrix construction, formulas, computations, ideas, and results Presents material rarely found in other books at this level, including Gersgorin's theorem and its extensions, the Kronecker product of matrices, sign-nonsingular matrices, and the evaluation of the permanent matrix Includes a combinatorial argument for the classical Cayley–Hamilton theorem and a combinatorial proof of the Jordan canonical form of a matrix Describes several applications of matrices in electrical engineering, physics, and chemistry Summary Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices. After reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas. Editorial Reviews "The originality of the book lies – as its title indicates – in the use of combinatorial methods, specifically Graph Theory, in the treatment . . . An original and well-written textbook within whose pages even the most experienced reader should find something novel."
fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science.
More About This Textbook Overview The purpose of this book is to teach the basic principles of problem solving, including both mathematical and nonmathematical problems. This book will help students to ... translate verbal discussions into analytical data. learn problem-solving methods for attacking collections of analytical questions or data. build a personal arsenal of internalized problem-solving techniques and solutions. become ''armed problem solvers'', ready to do battle with a variety of puzzles in different areas of life. Taking a direct and practical approach to the subject matter, Krantz's book stands apart from others like it in that it incorporates exercises throughout the text. After many solved problems are given, a ''Challenge Problem'' is presented. Additional problems are included for readers to tackle at the end of each chapter. There are more than 350 problems in all. This book won the CHOICE Outstanding Academic Book Award for 1997. A Solutions Manual to most end-of-chapter exercises is
This is a free, open textbook that is part of the Connexions collection at Rice University. "This is a textbook for Basic... see more This is a free, open textbook that is part of the Connexions collection at Rice University. "This is a textbook for Basic Mathematics for community college students. The content in this book has been collected from three text books and modified, as specified by Robert Knight.״ This is a free, online textbook that is offered by the author. It is meant to cover exactly what the title says, and... see more This is a free, online textbook that is offered by the author. It is meant to cover exactly what the title says, and includes information on:Linear algebra, determinants, Gaussian elimination, LU, Cholesky;Affine geometry;Polynomials, PID's, UFD's; andBasic Topology, differential calculus. This is a free online course offered by the Saylor Foundation.'In this course, you will study basic algebraic operations and... see more This is a free online course offered by the Saylor Foundation.'In this course, you will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes the solutions to algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing of linear equations. You will apply these skills to solve real world problems (word problems). Each unit will have its own application problems, depending on the concepts you have been exposed to. This course is also intended to provide you with a strong foundation for intermediate algebra and beyond.This course will begin with a review of some math concepts formed in pre-algebra, such as order of operations and simplifying simple algebraic expressions to get your feet wet. You will then build on these concepts by learning more about functions, graphing of functions, evaluation of functions, and factorization. You will spend time on the rules of exponents and their applications in distribution of multiplication over addition/subtraction.' This lesson received an honorable mention in the 2010 SoftChalk Lesson Challenge.The objectives of this lesson are:3.1Graph... see more This lesson received an honorable mention in the 2010 SoftChalk Lesson Challenge.The objectives of this lesson are:3.1Graph ordered pairs on a rectangular coordinate system.3.2Find solutions to linear equations in two variables.Determine whether an ordered pair is a solution to a linear equation in two variables.3.3Graph a linear equation in two variables.Graph horizontal lines, vertical lines, and lines through the origin.3.4Find the intercepts of a line from the equation of the line.Use intercepts to graph a line.3.5Find the slope of a line from two points on the line.Graph a line given the slope and y-intercept.3.6Find the equation of a line given the slope and y-intercept of the line.Find the slope and y-intercept of a line given the equation of the line.Find the equation of a line given a point on the line and the slope of the line.Find the equation of a line given two points on the line. ״Big Calculator Free was designed to take full advantage of the iPad screen offering a large display and a paper tape to keep... see more ״Big Calculator Free was designed to take full advantage of the iPad screen offering a large display and a paper tape to keep track of your calculations. Need even larger buttons? Rotate to Portrait mode to fill the entire screen with just the calculator.FEATURES ★ Large, easy to press buttons ★ Paper tape so you can see your previous calculations ★ Change the font size of the paper tape to whatever is right for you ★ Email or Copy the contents of your paper tape ★ Memory Recall button changes to display your current memory value ★ Support for percentage, square root, squared, cubed plus all the basics ★ Backspace button ★ Store state when you exit - start off right where you left off ★ Number format based on your locale settings״This is a free appThis is a free textbook from BookBoon.'Blast into Math! A fun and rigorous introduction to pure mathematics, is suitable for... see more This is a free textbook fromAccording to Student PIRGS, "Book of Proof is an introduction to the language and methods of mathematical proofs. The text is... see more According to Student PIRGS, "Book of Proof is an introduction to the language and methods of mathematical proofs. The text is meant to bridge the computational courses that students typically encounter in their first years of college (such as calculus or differential equations) to more theoretical, proof-based courses such as topology, analysis and abstract algebra. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.Although this book may be more meaningful to the student who has had some calculus, there is no prerequisite other than a measure of mathematical maturity. The text is an expansion and refinement of the author's lecture notes developed over ten years of teaching proof courses at Virginia Commonwealth University. The text is catered to the program at VCU to an extent, but the author kept the larger audience of undergraduate mathematics students in mind. 'Brain Teaser measures the ability to differentiate, to analyze, to reason out, and to apply knowledge. It is one of the best... see more 'Brain Teaser measures the ability to differentiate, to analyze, to reason out, and to apply knowledge. It is one of the best ways to engage yourself as well as to check your intelligence.This version fixes all the issues reported by some users for previous version. We have tested each question / answer set for accuracy.HOW TO USE THIS APP ?=====================- To start, select the number of questions you want in the current session. - All the questions are in simple language. In each case 4 answers are given, and what you have to do is simply choose the right answer. - There is only one correct answer to each question. - Answer the current question to proceed to next question.SCORING / HIGH SCORE====================- The more you answer correctly more you will gain points.- You need to score at least 50% to get a chance in the High Score charts.- Keep track of your progress or compete with your friendsBENEFITS OF BRAIN TEASER=========================- Children can take this test for preparing aptitude test.- giving your brain a good exercise while you spend time in commute or a boring lecture ;)- fun to challenge your friends to beat your high score.- NO blinking ads means you can focus on the questions better.★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★ ★This is not just a game but a POWERFUL tool to practice, learn and develop MATHS and LOGIC skills.While anyone can attempt to play this game BUT if you are looking for a real tough set of questions which are actually asked in the Competitive examinations, then this app is a must have for you.'This app costs $0.99
Find a Lincolnwood StatisticsMany complicated geometries and initial/boundary conditions for differential equations render them impossible to be solved in closed form, and I often (like in my thesis) resort to designing a numerical algorithm for solving them on a computer. I have worked with constant coefficients equations ...
Discrete Mathematics With Graph Theory Discrete Mathematics with Graph Theory Summary For one or two term undergraduate courses in Discrete Mathematics for students of Mathematics and Computer Science. Adopting a user-friendly, conversationaland at times humorousstyle, these authors make the principles and practices of discrete mathematics as stimulating as possible while presenting comprehensive, rigorous coverage. Examples and exercises integrated throughout each chapter serve to pique student interest and bring clarity to even the most complex concepts. Above all, the book is designed to engage today's students in the interesting, applicable facets of modern mathematics.
Key Skills To excel at algebra problems, you'll need to hone some of your special algebra powers. That's right: you're basically a mathematical superhero. The world of crime is your Number Line, and Captain Irrational is your arch-enemy.
Summary Master mathematics the easy way. Improve your basic math skills with this course. This practical math course takes you from basic addition through algebra and trig. You'll apply mathematical analysis with confidence and ease, in situations that used to leave you helpless. You'll be in a power position, whether tackling cash register errors or major financial deals. This self-paced course requires no textbook or instructor. Never be intimidated by math again. With this practical math course, you'll master mathematics the easy way. You'll improve your math skills, from basic addition through algebra and trig, without the tedium you endured in school. After completion, you will easily add, subtract, multiply, divide, apply algebra, and apply trigonometry--with no paper or calculator. You'll apply mathematical analysis with confidence and ease. You will be able to negotiate salary, loans, and other financial deals from a power position, running numbers on the spot and getting the correct result every time. Approximate study time: 21 hours Benefits Does mathematics seem hard for you? This course uses proven techniques to show you how to overcome mathematical difficulty. Upon completion of this course, you will: No longer fear math, but rule it. Be able to add, subtract, multiply, and divide in your head--a 7 year old girl of average intelligence did exactly that with the information in this course. Be able to do algebra in your head--same girl,same thing. Apply mathematical analysis with confidence and ease. Negotiate salary, loans, and other financial deals from a power position. Never again be ripped off by shady sales offers that rely on manipulated numbers. Never again be fooled into voting for a candidate who makes unrealistic promises or whose plans will lower your standard of living. Be able to translate tax increases and government spending into the number of hours you work to pay for them. Improve your career outlook by having math skills and the analytical ability that comes with them. Awaken that part of your brain that performs mathematical calculations. Why Buy Gaining an intuitive understanding of mathematics and the ability to think quantitatively is of enormous benefit, personally and in business. Not just because you can solve math problems, but because you develop a very potent way of thinking and of solving all kinds of problems--even if they aren't math problems. And, of course, you need the math skills anyhow. Ten more reasons to buy this course and know this material: 10. Most people are uncomfortable with math--you want to be able to do math easily. 9. Math incompetence is a major source of stress. 8. Having this knowledge allows you to focus what you really want to do--rather than cope with math-related stress. 7. This course is a lot quicker than sitting through a semester of college. 6. This course focuses on what you really need to know, in a way you can understand. 5. Poor time math performance can haunt you for life. Good math performance can provide life-long benefits by allowing you to get the best deal, manage your finances, and so on. 4. This knowledge helps you make the right decisions. 3. The right approach to math saves time and energy. 2. By taking this course, you gain insight into specifics of making math easy for you to do. and the number one reason to buy this course and learn this material... 1. You owe it to yourself to know this information. Why limit yourself to a continual state of math-related dependence on others, when this knowledge can put you in charge? TOC FAQs Questions Answers This looks really interesting but I can't figure out what you are sending or how you are sending it. These are downloadable files. In other words, you get download instructions as soon as the buying part is done and you get the files right away. What is it that I'm going to get and how? Is it a file that I'll download? Is it mailed? As soon as your purchase is complete, you will receive download instructions both on screen and via e-mail. You download self-extracting zip file that contains the course material. Depending on the course, the individual files will be in the rich text format or in the e-book format. Most materials are in the easier-to-handle rich text format. Are we talking about a lot of pages for me to read? Here's something that pleasantly surprises most people about these. If you look at a typical $99 professional book, most of it is filler. These courses don't have the filler. Ditto for $995 seminars covering the same information. Our courses get right to the meat, saving you the effort of wading through pages of nonsense. We don't mass up the high overhead of generating the filler, and we pass the savings on to our customers. Do your courses on project management prepare me for the various certification routes of the Project Management Institute? No. The material does not focus on exam preparation. It focuses on improving your real-world skills. However, what you learn will not impede certification. Are you one of the approved (by PMI) course providers? No. We are not affiliated with the Project Management Institute, although we may consider going that direction. Our goal is not to make you spend a lot of money learning how to answer test questions. Our goal is to teach you how to do your job better. How long does each of your courses take? It depends on the student. These courses are essentially white papers with exercises to help you relate the information to what you are doing now. You can read the material in each course in under an hour. But, how long it takes to digest it and apply it is up to you. Do I have to buy books in addition to your course material? Will those books have to be bought from you? To both questions, no. You don't have to buy anything else. Each course stands on its own. What if your course material is not clear? Are your course writers available for clarification? Since it is not possible to read all material at one shot, and collect all questions at the same time, will the course writers be available as needed or on a one time basis? a. It will be clear. b. Yes. c. Your success is important. If you have a question that is germane to the material, and not a probe for free consulting services, we will help you understand the material. We have kept the prices low, because not everyone can afford $995 for a two-day seminar that amounts to little more than a book promo. This is not a book promo. What if I have other questions? We'll answer to whatever extent is reasonable. It may be possible that you will ask questions that require developing a new course--some aspect of successful project management we didn't cover and that is not part of the normal project management training regimen. In that case, you would get the new course for free. Do you have other courses? Yes, and we are developing more. You can always write to us with specific needs, and we will adjust our product development accordingly. Also, it's a good idea to check Mindconnection on a regular basis, just to see what is new. Who writes these courses? That depends on the subject. For example, Dr. Jay Prince wrote the behavior courses based on his experience as a licensed therapist. All of the courses are well-researched and devoid of pseudoscience. Most are written by a subject matter expert. All are reviewed by a professional editor for clarity and succinctness. Do your courses qualify for employer reimbursement? Possibly not, because they are not accredited. Then again, our cost is very low. So, you must ask yourself if that small amount is worth investing into the skills you need to keep yourself employed and employable. The goal here is not to pile up paper credits. The goal is to get the information you would ordinarily get only from a lifetime of working in project management--if even then. We save you "classroom time" in the "school of hard knocks." You will recover your investment (and then some), simply because you will be that much better at what you do. How much time can I reasonably expect to save, once I use the principles in your time management course? That depends on how you presently approach your work. The typical student can expect to increase productivity by 50%. If you look at the way most people do their work, and then work your way through the course, you'll see why this is so. The author of that course works three full-time jobs and is Chair for one non-profit and acting Chair for another. Yet, he manages to excel in all of these roles while still maintaining outstanding health and enjoyment of life. More Info How many times have you looked at a math problem and felt your stomach churn? Do you make mistakes filing your taxes? Do car salesmen and other hard pressure people work you over with voodoo math you feel defenseless to counter? Help is here. Do you feel better math skills will help you do better on your job? Would better math skills improve the way you invest your money? Spend your money? Do you encounter everyday situations where you just wish you could "do the math?" Do you have difficulty sifting through election promises? Help is here. Do you fear your kids will grow up math-illiterate, instead of being able to shine on their SATs? Would you like to set an example for your kids, help them win a scholarship, and feel competent in this basic life skill? Help is here. This practical math course takes you from basic addition through algebra and trig. No, you won't encounter a bunch of mysterious symbols or mathematical jargon to memorize. You will learn how to do the math. Without getting a headache from it. The first thing we must do to overcome math phobia is to recognize that math is orderly, predictable, and logical. There's really nothing mysterious about it. Mathematics is, after all, the study of relationships between quantities--numbers. In its essence, it's a way of counting things. Two will always be two, and four will always be four. The rules of math are far simpler than the rules of English, yet most of us speak and write with far more comfort than we feel when doing math. Put another way, math should be easy for you because you have already shown competence in something much more complicated and confusing than math will ever be. The leaders of our public schools decided at some point that children in third grade would understand math quickly, if the textbooks explained math by using words the children did not understand. That makes about as much sense as trying to teach kids by saying, "You know that feeling you get after running a major international corporation for a few years? That's the basis for today's math lesson." This despicably stupid approach to teaching has made millions of American children feel stupid as they study math. This is how I felt, decades ago. You may have felt the same way. It's clear to me now what distribution means and what associating means, and so you could explain to me math concepts in terms of "distributive" or "associative" properties, but attempting that with kids whose ages are in the single digits is preposterous. This is what has set the stage for poor math performance in adults who would otherwise be adept at mathematical calculations. If math is hard for you, it's not your fault. But you can do something about it, thanks to this course. In this course, we don't use big words in some misguided attempt to impress administrators while leaving the student to twist in the breeze. Nor do we even consider the complex gyrations that pass for methods of solving math problems. Those gyrations just about require a PhD in astrophysics to understand, and applying them to four-digit addition and subtraction is completely irrational. Using an irrational approach to teach the logic of math may fit well with the government way of doing things, but it's not a way of accomplishing the goal of teaching math. Many of us have suffered math phobia as a result of such a mismatch, but that doesn't mean you have to suffer now. Help is here. This course gives you the knowledge to correct that mismatch, overcome that phobia, and enjoy the power of being able to do practical math with ease. Why can't school textbooks make math this easy? Not to mention, it's actually fun now. I add stuff up in my head while other people are pecking away on their calculator app and just grin when they say "How did you do that?" My main reason for buying this was so I could stop having trouble with multiplication (fumble fingers and I get the wrong answer on my computer). But now I'm doing algebra without so much as a paper and pen! And it's easy! I no longer fear math, 1.26.2012 Reviewer: Tina Rampel (Cedar Rapids, IA) I bought this course out of desperation and due to some bad things that happened due to my poor math skills. I was really afraid of math, but after taking this course I don't find it intimidating or difficult. The material was very clear, but I would also have liked audio to go with it. Very helpful math course, 12.9.2011 Reviewer: Renee Connelly (Arlingto, TX) I've always hated math and have not been very good at it. But earlier this year our operations manager announced he'd be retiring. I really wanted that job and had dinner with the ops man to discuss my chances of being promoted. My lack of math jumped out as a deal killer, but the ops man encouraged me to self-study and gain those skills. This didn't seem possible, but like I said I really wanted that job so with his confidence in me helping I bought a couple of math books. And promptly got frustrated. When my son asked me what I was upset about, that led to looking online and I found this course. It actually cost less than the books I'd bought. And I had ZERO frustration. So now I actually have that job. It's tougher than I thought it would be, but I love it. The math is absolutely not a problem, and that means I can focus on other issues. What's really funny is I pop out numbers at people without using any paper and they think I've always been this good at math! Outstanding!, 2.25.2011 Reviewer: Jared Brown (Detroit, MI) I hated math in school, and this caused me a lot of problems in life. I finally decided enough was enough and to do something about my math phobia and lack of math skills. This math course was surprisingly easy. No jargon or mysterious concepts. Just good explanations and enough sample problems for me to see I was learning the material.
Graded Exercises in Pure Mathematics (Graded Exercises in Advanced Level Mathematics) for an Amazon Gift Card of up to £0.25, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more Book DescriptionMore About the Author Product Description Book Description A wide-ranging collection of exercises for homework, practice and revision. This series covers all areas of A and AS level mathematics, including optional topics, and has been designed for the new specifications brilliant - it is not a textbook but a book full of questions to help you practise in preparation for your Maths exams. As Maths A-level has been divided up into so many modules, often students will not have had enough practice to consolidate their knowledge. This book does it for you. At the beginning of each topic there is a summary of key points to help you with the questions. The questions are arranged in increasing difficulty, allowing no gaps in the foundation needed to attempt the more challenging questions. There are even past questions from as far back as 1964, and also a few past STEP questions slipped in to challenge the more able mathematician. If you're willing to sit down and attempt the majority of this book, then I can assure you that's 80% of revision done! Now all you need is to do past papers from your exam board and you're done. Maths at A-level is all about practice - and no other book (that I have found) does it better! Buy it if you want an A. I have worked my way through this book over the past year. I think this has made me more secure in my knowledge of maths and it has given me a range of practice questions at all levels to be able to work my way through the different grades with. I didn't want to spend this much money but it's really worth it. I'd say if you only buy one book for A-level maths, make it this one. Oh and as other people have said the answers are generally correct, which makes a change in an A-level maths book.
The Calculus 2 Advanced Tutor: Learning By Example DVD Series teaches students through step-by-step example problems that progressively become more difficult. This DVD covers ratios and root tests of series convergence in calculus, including what a ratio and root test is and why it is a central topic in calculus. Grades 9-12. 53 minutes on DVD.
Manassas, VA GeDuring this level course, students gain proficiency in solving linear equations, inequalities, and systems of linear equations. New concepts include solving quadratic equations and inequalities, exploring conics, investigating polynomials, and applying/using matrices to organize and interpret data. Students will also investigate exponential and logarithmic functions at Herndon Center where I taught Pre-Algebra, U.S History, and Basic Skills.
For this matter and motion worksheet, pupils solve 4 different problems that relate to determining the matter and motion of a function problem. First, they find the limit of a as n to infinity and then, determine whether each series converges or diverges. Then, students determine the first three non zero terms of the Maclaurin Series for a function. In this graphing functions worksheet, students solve and complete 16 various types of problems. First, they evaluate each of the limits provided. Then, students graph each of the functions and their asymptotes as given. In this Calculus instructional activity, 12th graders are provided with practice problems for their exam. Topics covered include limits, derivatives, area bounded by a curve, minimization of cost, and the volume of a solid of revolution. The four page document contains seventeen multiple choice questions. Answers are not included. In this calculus instructional activity, students find the derivative of a given function, evaluate limits, and integrals, and find the area of a region. The one page interactive instructional activity contains eight multiple choice questions and is self checking. The typical introductory environmental questions are asked in this two-page worksheet. Emerging ecologists define populations, limiting factors, carrying capacity, and trophic levels. They analyze a population graph and consider the impact of humans on the biogeochemical cycles. Give your middle school or high school life science class these 20 questions to answer for homework. Pupils explore and practice the concepts of the limit of a function, approaches of an arbitrary constant and functions of infinity. They investigate the vertical and horizontal asymptotes of a rational function, graphically, numerically and symbolically. Students are introduced to stoichiometric relationships in chemical equations with a Trail Mix activity before performing a lab to reinforce stoichiometry. Students complete the unit with a lab about limiting reactants in chemical reactions. In this college level calculus worksheet, students evaluate the given limits or show that the limit does not exist. Students determine the derivative of the given functions. The two page worksheet contains twenty-six problems. Answers are not included. Students explore the success of members of racial and ethnic minorities in the business world through discussing a related New York Times article. They interview successful people in various professions who would be considered minority. Students examine the issue of tribal sovereignty for Native Americans. Following a mock trial simulation based on the case of Johnson v. McIntosh, they write opinion papers based on the results of the Supreme Court decision in 1823. Students hypothesize as to the spread of dandelion seeds and its effectiveness. Throughout the remaining lesson, students experiment and discuss their results. This usually leads to a discussion of natural selection, populations, exponential growth, etc. In this college level calculus worksheet, students determine if a limit exists and if so, find it, and solve differential equations. The one page worksheet contains seven problems. Answers are not provided. Work on stoichiometry with this worksheet, which focuses on the concept of limiting reactants. It provides the concentrations and amounts of reactants in particular situations. Your students then give amounts of products, reactants used, and molarity of the solutions involved.
Elementary Algebra (Paperback), 1st Edition The early introduction of fundamental algebraic concepts through numerous interactive examples and a wide variety of exercises shows students how to translate English phrases into mathematical symbols. Tussy and Gustafson's fully integrated learning process is designed to expand students' reasoning abilities and teach them how to read, write, and think mathematically69
Videos Will Help Students "Ace" Math 02/01/97 Ace-Math, an award-winning video tutorial series, is suited for students trying to grasp fundamental mathematical concepts, parents who want to help their child with their homework, or people who need to brush up on math skills for a specialized license or test. There are nine separate series, each with many individual videos: Basic Mathematical Skills, Pre-Algebra, Algebra I, Algebra II, Advanced Algebra, Trigonometry, Calculus, Geometry, and Probability and Statistics. Each series except Algebra I consists of 30-minute videotapes explaining various concepts. Algebra I has 16 hour-long videos. For only $29.95, Ace-Math purchasers get a 30-minute tape with the right to make two back-up copies. This lets educators keep the tape in the learning center and let students check out a copy to take home -- with the added security of another back-up copy! These innovative tapes have been purchased by institutions such as NASA, the U.S. Coast Guard and IBM, and are in use at institutions such as the Los Angeles Public Library and New York Public Library.Video Resources Software, Miami, FL, (888) ACE-MATH
David Gay and David Lovelock Department of Mathematics University of Arizona Tucson, Arizona 85721 This program will evalute complex expressions, find the n th roots of a complex number (n < 9), and graphically display complex numbers. This program also has games involving addition, subtraction, complex conjugates, multiplication, division, and recipricals (all of complex numbers).
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more

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