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© 2015,This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numbers, while the second details several other number representations. Each chapter ends with exercises to review the key points. Topics covered include interval arithmetic, fixedpoint numbers, floating point numbers, big integers and rational arithmetic. This book is for anyone who develops software including software engineerings, scientists, computer science students, engineering students and anyone who programs for fun.

© 2015,In a surprising sequence of developments, the longest increasing subsequence problem, originally mentioned as merely a curious example in a 1961 paper, has proven to have deep connections to many seemingly unrelated branches of mathematics, such as random permutations, random matrices, Young tableaux, and the corner growth model. The detailed and playful study of these connections makes this book suitable as a starting point for a wider exploration of elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians. The specific topics covered are the VershikKerovLoganShepp limit shape theorem, the BaikDeiftJohansson theorem, the TracyWidom distribution, and the corner growth process. This exciting body of work, encompassing important advances in probability and combinatorics over the last forty years, is made accessible to a general graduatelevel audience for the first time in a highly polished presentation.

© 2015,This lavishly illustrated book provides a handson, stepbystep introduction to the intriguing mathematics of symmetry. Instead of breaking up patterns into blocksa sort of potatostamp methodFrank Farris offers a completely new waveform approach that enables you to create an endless variety of rosettes, friezes, and wallpaper patterns: dazzling art images where the beauty of nature meets the precision of mathematics. Featuring more than 100 stunning color illustrations and requiring only a modest background in math, Creating Symmetry begins by addressing the enigma of a simple curve, whose curious symmetry seems unexplained by its formula. Farris describes how complex numbers unlock the mystery, and how they lead to the next steps on an engaging path to constructing waveforms. He explains how to devise waveforms for each of the 17 possible wallpaper types, and then guides you through a host of other fascinating topics in symmetry, such as colorreversing patterns, threecolor patterns, polyhedral symmetry, and hyperbolic symmetry. Along the way, Farris demonstrates how to marry waveforms with photographic images to construct beautiful symmetry patterns as he gradually familiarizes you with more advanced mathematics, including group theory, functional analysis, and partial differential equations. As you progress through the book, you'll learn how to create breathtaking art images of your own. Fun, accessible, and challenging, Creating Symmetry features numerous examples and exercises throughout, as well as engaging discussions of the history behind the mathematics presented in the book.

© 2015,This book provides the first comprehensive treatment of Benford's law, the surprising logarithmic distribution of significant digits discovered in the late nineteenth century. Establishing the mathematical and statistical principles that underpin this intriguing phenomenon, the text combines uptodate theoretical results with overviews of the law's colorful history, rapidly growing body of empirical evidence, and wide range of applications. An Introduction to Benford's Law begins with basic facts about significant digits, Benford functions, sequences, and random variables, including tools from the theory of uniform distribution. After introducing the scale, base, and suminvariance characterizations of the law, the book develops the significantdigit properties of both deterministic and stochastic processes, such as iterations of functions, powers of matrices, differential equations, and products, powers, and mixtures of random variables. Two concluding chapters survey the finitely additive theory and the flourishing applications of Benford's law. Carefully selected diagrams, tables, and close to 150 examples illuminate the main concepts throughout. The text includes many open problems, in addition to dozens of new basic theorems and all the main references. A distinguishing feature is the emphasis on the surprising ubiquity and robustness of the significantdigit law. This text can serve as both a primary reference and a basis for seminars and courses.

© 2015,Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together many of the world's leading experts on Benford's law to demonstrate the many useful techniques that arise from the law, show how truly multidisciplinary it is, and encourage collaboration. Beginning with the general theory, the contributors explain the prevalence of the bias, highlighting explanations for when systems should and should not follow Benford's law and how quickly such behavior sets in. They go on to discuss important applications in disciplines ranging from accounting and economics to psychology and the natural sciences. The contributors describe how Benford's law has been successfully used to expose fraud in elections, medical tests, tax filings, and financial reports. Additionally, numerous problems, background materials, and technical details are available online to help instructors create courses around the book. Emphasizing common challenges and techniques across the disciplines, this accessible book shows how Benford's law can serve as a productive meeting ground for researchers and practitioners in diverse fields.

© 2015,Scientific progress depends on good research, and good research needs good statistics. But statistical analysis is tricky to get right, even for the best and brightest of us. You'd be surprised how many scientists are doing it wrong. Statistics Done Wrong is a pithy, essential guide to statistical blunders in modern science that will show you how to keep your research blunderfree. You'll examine embarrassing errors and omissions in recent research, learn about the misconceptions and scientific politics that allow these mistakes to happen, and begin your quest to reform the way you and your peers do statistics. You'll find advice on: Asking the right question, designing the right experiment, choosing the right statistical analysis, and sticking to the plan How to think about p values, significance, insignificance, confidence intervals, and regression Choosing the right sample size and avoiding false positives Reporting your analysis and publishing your data and source code Procedures to follow, precautions to take, and analytical software that can help Scientists: Read this concise, powerful guide to help you produce statistically sound research. Statisticians: Give this book to everyone you know. The first step toward statistics done right is Statistics Done Wrong .

© 2010,Designed for a onesemester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis  providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative workedout examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook http://www.elsevierdirect.com/product.jsp'isbn=9780123749550 * Student Solutions Manual To come * Instructors Solutions Manual To come Appropriate rigor for a onesemester advanced calculus course Presents modern materials and nontraditional ways of stating and proving some results Includes precise historical notes throughout the book outstanding feature is the collection of exercises in each chapter Provides coverage of exponential function, and the development of trigonometric functions from the integral

© 2015,The techniques presented here are useful for solving mathematical contest problems in algebra and analysis. Most of the examples and exercises that appear in the book originate from mathematical Olympiad competitions around the world. In the first four chapters the authors cover material for competitions at high school level. The level advances with the chapters. The topics explored include polynomials, functional equations, sequences and an elementary treatment of complex numbers. The final chapters provide a comprehensive list of problems posed at national and international contests in recent years, and solutions to all exercises and problems presented in the book. It helps students in preparing for national and international mathematical contests form high school level to more advanced competitions and will also be useful for their first year of mathematical studies at the university. It will be of interest to teachers in college and university level, and trainers of the mathematical Olympiads.

© 2015,Did you grow up thinking math is boring? It's time to reconsider. This book will teach you everything you ever wondered about numbersand more. How and why did human beings first start using numbers at the dawn of history? Would numbers exist if we Homo sapiens weren't around to discover them? What's so special about weird numbers like pi and the Fibonacci sequence? What about rational, irrational, real, and imaginary numbers? Why do we need them? Two veteran math educators explain it all in ways even the most math phobic will find appealing and understandable. You'll never look at those squiggles on your calculator the same again.

© 2014,Manifolds fall naturally into two classes depending on whether they can be fitted with a distance measuring function or not. The former, metrisable manifolds, and especially compact manifolds, have been intensively studied by topologists for over a century, whereas the latter, nonmetrisable manifolds, are much more abundant but have a more modest history, having become of increasing interest only over the past 40 years or so. The first book on this topic, this book ranges from criteria for metrisability, dynamics on nonmetrisable manifolds, Nyikos's Bagpipe Theorem and whether perfectly normal manifolds are metrisable to structures on manifolds, especially the abundance of exotic differential structures and the dearth of foliations on the long plane. A rigid foliation of the Euclidean plane is described. This book is intended for graduate students and mathematicians who are curious about manifolds beyond the metrisability wall, and especially the use of Set Theory as a tool.

© 2015,Probability comes of age with this, the first dictionary of probability and its applications in English, which supplies a guide to the concepts and vocabulary of this rapidly expanding field. Besides the basic theory of probability and random processes, applications covered here include financial and insurance mathematics, operations research (including queueing, reliability, and inventories), decision and game theory, optimization, time series, networks, and communication theory, as well as classic problems and paradoxes. The dictionary is reliable, stable, concise, and cohesive. Each entry provides a rigorous definition, a sketch of the context, and a reference pointing the reader to the wider literature. Judicious use of figures makes complex concepts easier to follow without oversimplifying. As the only dictionary on the market, this will be a guiding reference for all those working in, or learning, probability together with its applications.

© 2015,The numbers one through nine have remarkable mathematical properties and characteristics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? Are there really "six degrees of separation" between all pairs of people? And how can any map need only four colors to ensure that no regions of the same color touch? In Single Digits , Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics. Each chapter focuses on a single digit, beginning with easy concepts that become more advanced as the chapter progresses. Chamberland covers vast numerical territory, such as illustrating the ways that the number three connects to chaos theory, an unsolved problem involving Egyptian fractions, the number of guards needed to protect an art gallery, and problematic election results. He considers the role of the number seven in matrix multiplication, the Transylvania lottery, synchronizing signals, and hearing the shape of a drum. Throughout, he introduces readers to an array of puzzles, such as perfect squares, the four hats problem, Strassen multiplication, Catalan's conjecture, and so much more. The book's short sections can be read independently and digested in bitesized chunksespecially good for learning about the Ham Sandwich Theorem and the Pizza Theorem. Appealing to high school and college students, professional mathematicians, and those mesmerized by patterns, this book shows that single digits offer a plethora of possibilities that readers can count on.

© 2015,Professor Bard has provided a valuable service by carefully explaining everything an undergraduate student of mathematics, or a teacher of these topics, needs to get started with Sage quickly and easily. It will also be useful for any student or teacher of another STEM discipline. There is an excellent mix of the most frequently used commands, along with warnings about common pitfalls or caveats. I highly recommend it for anyone new to Sage, or who desires an overview of the system's impressive capabilities. Robert A. Beezer, University of Puget Sound This book is a sort of ``Missing Manual'' that explains how Sage can be used in a range of standard mathematics courses, instead of targeting specialists like much existing Sage documentation. The depth of content is very impressive, and describesin a single coherent narrativehow to successfully use Sage for a wide swath of undergraduate applied topics. William Stein, University of Washington, Seattle As the opensource and free competitor to expensive software like MapleTM, MathematicaR, Magma, and MATLABR, Sage offers anyone with access to a web browser the ability to use cuttingedge mathematical software and display his or her results for others, often with stunning graphics. This book is a gentle introduction to Sage for undergraduate students toward the end of Calculus II (singlevariable integral calculus) or higherlevel course work such as Multivariate Calculus, Differential Equations, Linear Algebra, or Math Modeling. The book assumes no background in computer science, but the reader who finishes the book will have learned about half of a first semester Computer Science I course, including large parts of the Python programming language. The audience of the book is not only math majors, but also physics, engineering, finance, statistics, chemistry, and computer science majors.

© 2015,This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more projectstyle sections have been added. Investigations of Euler's computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book's cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Review of the first edition: "This is a dangerous book. Understanding Analysis is so wellwritten and the development of the theory so w ellmotivated that exposing students to it could well lead them to expect such excellence in all their textbooks. ... Understanding Analysis is perfectly titled; if your students read it, that's what's going to happen. ... This terrific book will become the text of choice for the singlevariable introductory analysis course ... "  Steve Kennedy, MAA Reviews

© 2011,Algebra, Second Edition , by Michael Artin, provides comprehensive coverage at the level of an honorsundergraduate or introductorygraduate course. The second edition of this classic text incorporates twenty years of feedback plus the author's own teaching experience. This book discusses concrete topics of algebra in greater detail than others, preparing readers for the more abstract concepts; linear algebra is tightly integrated throughout.

© 2015,At its heart, mathematics is about numbers, our fundamental tools for understanding the world. In Professor Stewart's Incredible Numbers , Ian Stewart offers a delightful introduction to the numbers that surround us, from the common (Pi and 2) to the uncommon but no less consequential (1.059463 and 43,252,003,274,489,856,000). Along the way, Stewart takes us through prime numbers, cubic equations, the concept of zero, the possible positions on the Rubik's Cube, the role of numbers in human history, and beyond! An unfailingly genial guide, Stewart brings his characteristic wit and erudition to bear on these incredible numbers, offering an engaging primer on the principles and power of math.

© 1993,This book is intended for anyone, regardless of discipline, who is interested in the use of statistical methods to help obtain scientific explanations or to predict the outcomes of actions, experiments or policies. Much of G. Udny Yule's work illustrates a vision of statistics whose goal is to investigate when and how causal influences may be reliably inferred, and their comparative strengths estimated, from statistical samples. Yule's enterprise has been largely replaced by Ronald Fisher's conception, in which there is a fundamental cleavage between experimental and non experimental inquiry, and statistics is largely unable to aid in causal inference without randomized experimental trials. Every now and then members of the statistical community express misgivings about this turn of events, and, in our view, rightly so. Our work represents a return to something like Yule's conception of the enterprise of theoretical statistics and its potential practical benefits. If intellectual history in the 20th century had gone otherwise, there might have been a discipline to which our work belongs. As it happens, there is not. We develop material that belongs to statistics, to computer science, and to philosophy; the combination may not be entirely satisfactory for specialists in any of these subjects. We hope it is nonetheless satisfactory for its purpose.

© 2015,Who first presented Pascal's triangle? (It was not Pascal.) Who first presented Hamiltonian graphs? (It was not Hamilton.) Who first presented Steiner triple systems? (It was not Steiner.) The history of mathematics is a wellstudied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to have been largely overlooked. This book goes some way to redress this and serves two main purposes: 1) it constitutes the first booklength survey of the history of combinatorics; and 2) it assembles, for the first time in a single source, researches on the history of combinatorics that would otherwise be inaccessible to the general reader. Individual chapters have been contributed by sixteen experts. The book opens with an introduction by Donald E. Knuth to two thousand years of combinatorics. This is followed by seven chapters on early combinatorics, leading from Indian and Chinese writings on permutations to lateRenaissance publications on the arithmetical triangle. The next seven chapters trace the subsequent story, from Euler's contributions to such wideranging topics as partitions, polyhedra, and latin squares to the 20th century advances in combinatorial set theory, enumeration, and graph theory. The book concludes with some combinatorial reflections by the distinguished combinatorialist, Peter J. Cameron. This book is not expected to be read from cover to cover, although it can be. Rather, it aims to serve as a valuable resource to a variety of audiences. Combinatorialists with little or no knowledge about the development of their subject will find the historical treatment stimulating. A historian of mathematics will view its assorted surveys as an encouragement for further research in combinatorics. The more general reader will discover an introduction to a fascinating and too little known subject that continues to stimulate and inspire the work of scholars today.

© 2013,Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the "fractal revolution" that occurred in mathematics in the 20th century, presents the "new geometry" of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects ofeconomics.This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics.

© 2014,This book provides a thorough introduction to the formal foundations and practical applications of Bayesian networks. It provides an extensive discussion of techniques for building Bayesian networks that model realworld situations, including techniques for synthesizing models from design, learning models from data, and debugging models using sensitivity analysis. It also treats exact and approximate inference algorithms at both theoretical and practical levels. The author assumes very little background on the covered subjects, supplying indepth discussions for theoretically inclined readers and enough practical details to provide an algorithmic cookbook for the system developer.