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© 2001,This book 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.

© 2007,This is a brand new edition of an essential work on Bayesian networks and decision graphs. It is an introduction to probabilistic graphical models including Bayesian networks and influence diagrams. The reader is guided through the two types of frameworks with examples and exercises, which also give instruction on how to build these models. Structured in two parts, the first section focuses on probabilistic graphical models, while the second part deals with decision graphs, and in addition to the frameworks described in the previous edition, it also introduces Markov decision process and partially ordered decision problems.

© 2015,What does mathematics have to do with poetry? Seemingly, nothing. Mathematics deals with abstractions while poetry with emotions. And yet, the two share something essential: Beauty. "Euclid alone has looked on beauty bare, " says the title of a poem by Edna St. Vincent Millay."Mathematics, Poetry and Beauty" tries to solve the secret of the similarity between the two domains. It tries to explain how a mathematical argument and a poem can move us in the same way. Mathematical and poetic techniques are compared, with the aim of showing how they evoke the same sense of beauty.The reader may find that, as Bertrand Russell said, "Mathematics, rightly viewed, possesses not only truth, but supreme beauty  a beauty hold and austere, like that of sculpture ... sublimely pure, and capable of a stern perfection such as only the greatest art can show."

© 2015,The first volume in this groundbreaking series focuses on the origins and early development of numerical cognition in nonhuman primates, lower vertebrates, human infants, and preschool children. The text will help readers understand the nature and complexity of these foundational quantitative concepts and skills along with evolutionary precursors and early developmental trajectories. Brings together and focuses the efforts and research of multiple disciplines working in math cognition. The contributors bring vast knowledge and experience to bear on resolving extant substantive and methodological challenges to help advance the field of basic number processing. Introductory sections and summaries will be included to provide background for nonspecialist readers.

© 2014,With this volume of Video Aided Instruction's "HiSET Review" series, even the most "mathphobic" among us can learn how to succeed on the "Mathematics" section of the HiSET exam. Your dynamic instructor shows you stepbystep solutions to hundreds of practice questions at the chalkboard. Along the way, he explains every math concept in plain English, so you can easily master the essentials of arithmetic, algebra, geometry, and data analysis  and learn foolproof techniques for tackling even the most challenging problems. It's like having your own private math tutor! The number of American adults who didn't finish high school is truly staggering. Some wish they could get a "second chance" by earning their high school equivalency credential, but many find the HiSET exam too intimidating. They're overwhelmed by the thought of having to learn or relearn school subjects by plodding through dry textbooks or sitting through tedious classes. Well, if any of this sounds familiar, you're in luck! Now you can study with the HiSET experts  on your schedule and at your pace. With over 30 years' experience preparing students for high school equivalency exams, Video Aided Instruction has made getting that passing score easier than ever before. Our comprehensive "HiSET Review" series is the ultimate resource for conquering the exam. Featuring real teaching by real teachers, these developmental study programs start with the basics, develop your skills, and take the stress out of learning. "The Complete HiSET Review Series" includes 4 volumes of test preparation: * "HiSET Review: Language Arts Steps 123" (Item #VAI5281) * "HiSET Review: Mathematics Steps 123" (Item #VAI5282) * "HiSET Review: Science Steps 123" (Item #VAI5283) * "HiSET Review: Social Studies Steps 123" (Item #VAI5284) With this userfriendly DVD series, you'll learn how to succeed on the "Language Arts  Reading," "Language Arts  Writing," "Mathematics," "Science," and "Social Studies" sections of the HiSET exam! Each jampacked review course begins with Step 1, where you'll review basic literacy skills in reading, writing, math, science, and social studies (e.g., how to find the main idea of a reading passage; how to identify common sentence structure errors; how to work with fractions, decimals, and percents; how to use context to define unfamiliar scientific terms; and how to understand the causes and effects of historical events). Then, in Step 2, you'll continue improving your abilities and build on what you've learned as you tackle more complex material (e.g., how to make inferences from a text; how to recognize when subjects and verbs don't agree; how best to organize your ideas before writing an essay; how to solve quadratic equations; how to interpret scientific graphs; and how to make sense of political cartoons). And finally, in Step 3, you'll tie everything together and learn the more advanced concepts you'll likely be tested on (e.g., how to compare multiple reading passages; how to sound smart in your own writing; how to calculate volume and surface area of 3D solids; how to evaluate the results of scientific studies; and how to analyze historical documents). Along the way, you'll work through a large variety of exercises so you can fill in any "gaps" in your knowledge and get extensive practice in the various subjects tested. Your easytofollow instructors reveal insider secrets about what the testmakers are looking for and proven strategies for answering every type of question you're likely to encounter on your test. By the end of these programs, you'll feel competent, comfortable, and confident when you walk into that exam room! So don't let your lack of a high school diploma hold you back  a brighter future is now within your reach. Let Video Aided Instruction be your guide! 9 DVDs/19 Hrs. 45 Mins. Item #VAI5282. Volume 2 of Video Aided Instruction's 4Volume "HiSET Review" Series.

© 2006,Many everyday situations require basic math literacy  whether you're following a recipe in your kitchen, sharing a candy bar at the movie theater, making change at a hardware store, or calculating interest at the bank. Although lots of people know their multiplication and division, they still find the basic math areas of fractions, decimals, and percents very confusing. Now you can master these fundamentals  and build a solid foundation for effective calculator use and future math study  with Video Aided Instruction's "Basic Math: Fractions, Decimals, Percents"! Perfect for middle school students through adult learners, this extraordinary program features real teaching by a real teacher! Your master teacher's friendly demeanor and engaging delivery make him easy to listen to and to learn from. And his uncanny ability to explain basic math concepts in plain English makes them easy to understand. You'll feel like part of his classroom as he works at the chalkboard, showing you the stepbystep solutions to hundreds of problems! Now it's easier than ever to earn high test marks in school or relearn forgotten mathematics  all with your own private teacher! Four DVDs/7 Hrs. 53 Mins. Total. Item #VAI1701.

© 2006,Having trouble with those x's and y's? Now every student can make sense of firstyear algebra with Video Aided Instruction's "Algebra 1." The ultimate resource for middle school students through adult learners, this set covers the standard topics taught in Algebra 1, Elementary Algebra, and Beginning Algebra classes and is jampacked with hundreds of practice questions and proven strategies for tackling even the most challenging problems.Video Aided Instruction's "Algebra 1" is your key to conquering firstyear algebra! An essential prerequisite to advanced math courses, our "Algebra 1" set covers: order of operations; signed numbers; evaluating algebraic expressions; monomials; polynomials; firstdegree equations & inequalities; applications of firstdegree equations; factoring; fractions; radicals; quadratic equations; applications of quadratic equations; graphs & equations of straight lines; and systems of linear equations & inequalities.Now it's easier than ever to overcome math anxiety, earn high grades in school, or relearn forgotten math  all with your own private teacher!

© 2007,From logarithmic equations to the law of cosines, Video Aided Instruction's "Algebra 2 & Trigonometry" can help every student make sense of secondyear algebra and trig. The ultimate resource for high school students through adult learners, this set covers the standard algebra and trigonometry topics taught in Algebra 2 and Intermediate Algebra classes and is jampacked with hundreds of practice questions and strategies for tackling even the toughest problems.A crucial followup to our "Algebra 1" course, Video Aided Instruction's extensive "Algebra 2 & Trigonometry" set covers: factoring & operations on rational expressions; real numbers & radicals; the complex numbers; quadratic equations; graphs of quadratic functions, relations, & equations; exponential functions; logarithmic functions; trigonometry of the right triangle; trigonometric functions of angles of any size (general angle); trigonometric graphs; generalized trigonometric relationships; trigonometric equations; and trigonometric applications.Now it's easier than ever to overcome math anxiety, earn high grades in school, or relearn forgotten math  all with your own private teacher!Five DVDs/10 Hrs. Total. Item #VAI1752.

© 2007,The fundamentals of probability are integrated into diverse math courses taught in high school and college. Now every student can master introductory probability quickly and easily with Video Aided Instruction's "Probability." The ultimate resource for high school students, college students, and adult learners, this set covers the standard probability topics taught in math classes and is jampacked with practice questions and strategies for tackling even the most confusing problems.Chances are, students will find Video Aided Instruction's "Probability" the perfect tool for mastering introductory probability! This exceptional set covers: introduction to probability; simple probability; joint probability; the addition rule; the multiplication rule; counting principles; permutations; probability & permutations; combinations; probability & combinations; binomial distribution; conditional probability; Bayes? Rule; and expected value of a probability distribution.Now it's easier than ever to overcome math anxiety, earn high grades in school, or relearn forgotten math  all with your own private teacher!Two DVDs/4 Hrs. Total. Item #VAI1779.

© 2006,Precalculus includes a wide variety of topics drawn from algebra, geometry, and trigonometry that pave the way for studying calculus. Now you can master this demanding course quickly and easily with Video Aided Instruction's "Precalculus." The ultimate resource for high school students, college students, and adult learners, this program covers the standard topics taught in precalculus and college algebra classes and is jampacked with practice questions and strategies for tackling even the most challenging problems.Video Aided Instruction's "Precalculus" will help you develop those allimportant math skills that lay the groundwork for calculus. An essential prerequisite to our "Calculus I" and "Calculus II" sets, our "Precalculus" course covers: functions and graphs; analytic geometry; polynomial equations; systems of equations; matrices; determinants; exponential and logarithmic functions; inverse trigonometric functions; and polar coordinates.Now it's easier than ever to overcome math anxiety, earn high grades in school, or relearn forgotten math  all with your own private teacher!

© 2006,Calculus just got a lot less intimidating! Now you can master an entire year's worth of collegelevel calculus quickly and easily with Video Aided Instruction's "Calculus I" and "Calculus II." The ultimate resource for AP high school students, college students, and adult learners, these sets cover the standard topics taught in calculus classes and are jampacked with practice questions and strategies for tackling even the most challenging problems. These programs are also perfect for students of physics, economics, engineering, and other fields.Video Aided Instruction's "Calculus I" is your key to conquering that first semester of calculus! An essential prerequisite to our "Calculus II" set, our "Calculus I" set covers: equations of straight lines; functions; limits; derivatives; graphing; applications of differentiation; simple integrals; applications of integration; logarithmic and exponential functions; trigonometric functions; inverse trigonometric functions; and methods of integration.Now it's easier than ever to overcome math anxiety, earn high grades in school, or relearn forgotten math  all with your own private teacher!

© 2006,Calculus just got a lot less intimidating! Now you can master an entire year's worth of collegelevel calculus quickly and easily with Video Aided Instruction's "Calculus I" and "Calculus II." The ultimate resource for AP high school students, college students, and adult learners, these sets cover the standard topics taught in calculus classes and are jampacked with practice questions and strategies for tackling even the most challenging problems. These programs are also perfect for students of physics, economics, engineering, and other fields.Video Aided Instruction's "Calculus I" is your key to conquering that first semester of calculus! An essential prerequisite to our "Calculus II" set, our "Calculus I" set covers: equations of straight lines; functions; limits; derivatives; graphing; applications of differentiation; simple integrals; applications of integration; logarithmic and exponential functions; trigonometric functions; inverse trigonometric functions; and methods of integration.Now it's easier than ever to overcome math anxiety, earn high grades in school, or relearn forgotten math  all with your own private teacher!

© 2007,Statistics isn't just for math majors: now it's taught in high school, and it's even a required course for many college degrees in psychology, sociology, business, economics, engineering, and other fields! Now every student can master this course quickly and easily with Video Aided Instruction's "Statistics." The ultimate resource for AP high school students, college students, and adult learners, this set covers the standard topics taught in introductory stats classes and is jampacked with practice questions and strategies for tackling even the most complicated problems.The numbers don't lie: Video Aided Instruction's bestselling "Statistics" course helps even the most mathchallenged students excel! Our "Statistics" set covers: definitions; review of summation notation; descriptive statistics; data presentation: tables & charts; normal distribution & sampling distribution of the mean; confidence intervals & sample size determination; onesample tests of hypothesis; testing differences between the means of two groups; testing for proportions & chisquare tests; and analysis of variance.

© 2015,Regression Analysis: Unified Concepts, Practical Applications, Computer Implementation is a concise and innovative book that gives a complete presentation of applied regression analysis in approximately onehalf the space of competing books. With only the modest prerequisite of a basic (noncalculus) statistics course this text is appropriate for the widest possible audience including college juniors, seniors and firstyear graduate students in business and statistics, as well as professionals in business and industry. The book is able to accommodate this wide audience because of the unique, integrative approach that is taken to the teaching of regression analysis. Whereas other regression books cover regression in four chapters, beginning with a statistical review, followed by chapters on simple linear regression, matrix algebra and multiple regression, this book introduces regression and covers both simple linear regression and multiple regression in single cohesive chapter. This is made possible through an efficient, integrative discussion of the two techniques. Additionally, in the same chapter (Chapter Two) basic statistical and matrix algebra concepts are introduced as needed In order to facilitate instruction. This approach avoids the needless repetition that is often found in longer treatments of the subject, while serving to bring a collective focus to students of widely varying mathematical backgrounds.

© 2015,A ClassroomTested, Alternative Approach to Teaching Math for Liberal Arts Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decisionmaking situations that progress from recreational problems to important contemporary applications develop the criticalthinking skills of nonscience and nontechnical majors. The logical underpinnings of this textbook were developed and refined throughout many years of classroom feedback and in response to commentary from presentations at national conferences. The text's five units focus on graphs, logic, probability, voting, and cryptography. The authors also cover related areas, such as operations research, game theory, number theory, combinatorics, statistics, and circuit design. The text uses a core set of common representations, strategies, and algorithms to analyze diverse games, puzzles, and applications. This unified treatment logically connects the topics with a recurring set of solution approaches. Requiring no mathematical prerequisites, this book helps students explore creative mathematical thinking and enhance their own criticalthinking skills. Students will acquire quantitative literacy and appreciation of mathematics through the text's unified approach and wide range of interesting applications.

© 2014,The focus of this book is on the birth and historical development of permutation statistical methods from the early 1920s to the near present. Beginning with the seminal contributions of R.A. Fisher, E.J.G. Pitman, and others in the 1920s and 1930s, permutation statistical methods were initially introduced to validate the assumptions of classical statistical methods. Permutation methods have advantages over classical methods in that they are optimal for small data sets and nonrandom samples, are datadependent, and are free of distributional assumptions. Permutation probability values may be exact, or estimated via moment or resamplingapproximation procedures. Because permutation methods are inherently computationallyintensive, the evolution of computers and computing technology that made modern permutation methods possible accompanies the historical narrative. Permutation analogs of many wellknown statistical tests are presented in a historical context, including multiple correlation and regression, analysis of variance, contingency table analysis, and measures of association and agreement. A nonmathematical approach makes the text accessible to readers of all levels.

© 2014,A book from the standup mathematician that makes math fun again! Math is boring, says the mathematician and comedian Matt Parker. Part of the problem may be the way the subject is taught, but it's also true that we all, to a greater or lesser extent, find math difficult and counterintuitive. This counterintuitiveness is actually part of the point, argues Parker: the extraordinary thing about math is that it allows us to access logic and ideas beyond what our brains can instinctively dothrough its logical tools we are able to reach beyond our innate abilities and grasp more and more abstract concepts. In the absorbing and exhilarating Things to Make and Do in the Fourth Dimension , Parker sets out to convince his readers to revisit the very math that put them off the subject as fourteenyearolds. Starting with the foundations of math familiar from school (numbers, geometry, and algebra), he reveals how it is possible to climb all the way up to the topology and to fourdimensional shapes, and from there to infinityand slightly beyond. Both playful and sophisticated , Things to Make and Do in the Fourth Dimension is filled with captivating games and puzzles, a buffet of optional handson activities that entices us to take pleasure in math that is normally only available to those studying at a university level. Things to Make and Do in the Fourth Dimension invites us to relearn much of what we missed in school and, this time, to be utterly enthralled by it.

© 2014,Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausenvon Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p adic measures; the EulerMaclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of exponential sums expressed by generalized Bernoulli numbers; the relation between ideal classes of orders of quadratic fields and equivalence classes of binary quadratic forms; class number formula for positive definite binary quadratic forms; congruences between some class numbers and Bernoulli numbers; simple zeta functions of prehomogeneous vector spaces; Hurwitz numbers; Barnes multiple zeta functions and their special values; the functional equation of the double zeta functions; and polyBernoulli numbers. An appendix by Don Zagier on curious and exotic identities for Bernoulli numbers is also supplied. This book will be enjoyable both for amateurs and for professional researchers. Because the logical relations between the chapters are loosely connected, readers can start with any chapter depending on their interests. The expositions of the topics are not always typical, and some parts are completely new.

© 2014,This book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus  such as the real numbers, differentiation and integration, mean value theorems, the exponential function  are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for π. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization. More Calculus of a Single Variable is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for selfstudy by students, instructors, and, indeed, all connoisseurs of ingenious calculations.

© 2014,This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous workedout examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.

© 2014,Analysis (sometimes called Real Analysis or Advanced Calculus) is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible atfirst. This book aims to ensure that no student need be unprepared. It is not like other Analysis books. It is not a textbook containing standard content. Rather, it is designed to be read before arriving at university and/or before starting an Analysis course, or as a companion text once a courseis begun. It provides a friendly and readable introduction to the subject by building on the student's existing understanding of six key topics: sequences, series, continuity, differentiability, integrability and the real numbers. It explains how mathematicians develop and use sophisticated formalversions of these ideas, and provides a detailed introduction to the central definitions, theorems and proofs, pointing out typical areas of difficulty and confusion and explaining how to overcome these. The book also provides study advice focused on the skills that students need if they are to build on this introduction and learn successfully in their own Analysis courses: it explains how to understand definitions, theorems and proofs by relating them to examples and diagrams, how to thinkproductively about proofs, and how theories are taught in lectures and books on advanced mathematics. It also offers practical guidance on strategies for effective study planning. The advice throughout is research based and is presented in an engaging style that will be accessible to students whoare new to advanced abstract mathematics.

© 2014,Or that Asian Americans are most susceptible to heart attacks on the fourth day of the month? Or that drinking a full pot of coffee every morning will add years to your life, but one cup a day increases the risk of pancreatic cancer? All of these "facts" have been argued with a straight face by credentialed researchers and backed up with reams of data and convincing statistics.As Nobel Prizewinning economist Ronald Coase once cynically observed, "If you torture data long enough, it will confess." Lying with statistics is a timehonored con. In Standard Deviations, economics professor Gary Smith walks us through the various tricks and traps that people use to back up their own crackpot theories. Sometimes, the unscrupulous deliberately try to mislead us. Other times, the wellintentioned are blissfully unaware of the mischief they are committing. Today, data is so plentiful that researchers spend precious little time distinguishing between good, meaningful indicators and total rubbish. Not only do others use data to fool us, we fool ourselves.With the breakout success of Nate Silver's The Signal and the Noise, the once humdrum subject of statistics has never been hotter. Drawing on breakthrough research in behavioral economics by luminaries like Daniel Kahneman and Dan Ariely and taking to task some of the conclusions of Freakonomics author Steven D. Levitt, Standard Deviations demystifies the science behind statistics and makes it easy to spot the fraud all around.