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© 2016,How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocketsized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

© 2016,Fractal geometry is a uniquely fascinating area of mathematics, exhibited in a range of shapes that exist in the natural world, from a simple broccoli floret to a majestic mountain range. In this essential primer, mathematician Michael Framea close collaborator with Benoit Mandelbrot, the founder of fractal geometryand poet Amelia Urry explore the amazing world of fractals as they appear in nature, art, medicine, and technology. Frame and Urry offer new insights into such familiar topics as measuring fractal complexity by dimension and the life and work of Mandelbrot. In addition, they delve into lessknown areas: fractals with memory, the Mandelbrot set in four dimensions, fractals in literature, and more. An inviting introduction to an enthralling subject, this comprehensive volume is ideal for learning and teaching.

© 2015,Posing the question "What exactly is a number?" a distinguished German mathematician presents this intriguing and accessible survey. Albrecht Beutelspacher ― founder of the renowned interactive mathematics museum, Mathematikum ― characterizes the wealth of experiences that numbers have to offer. In addition, he considers the many things that can be described by numbers and discusses which numbers possess special fascinations and pose lasting mysteries. Starting with natural numbers, the book examines representations of numbers, rational and irrational numbers, transcendental numbers, and imaginary and complex numbers. Readers will explore the history of numbers from Pythagoras to Fermat and discover such practical applications as cryptography and barcodes. A thoughtful and enlightening introduction to the past, present, and future of numbers, this volume will captivate mathematicians and nonmathematicians alike.

© 2016,UptoDate Guidance from One of the Foremost Members of the R Core Team Written by John M. Chambers, the leading developer of the original S software, Extending Rcovers key concepts and techniques in R to support analysis and research projects. It presents the core ideas of R, provides programming guidance for projects of all scales, and introduces new, valuable techniques that extend R. The book first describes the fundamental characteristics and background of R, giving readers a foundation for the remainder of the text. It next discusses topics relevant to programming with R, including the apparatus that supports extensions. The book then extends R's data structures through objectoriented programming, which is the key technique for coping with complexity. The book also incorporates a new structure for interfaces applicable to a variety of languages. A reflection of what R is today, this guide explains how to design and organize extensions to R by correctly using objects, functions, and interfaces. It enables current and future users to add their own contributions and packages to R.

© 2015,This volume is a sometimes serious and sometimes whimsical retrospective of Stata, its development, and its use over the last 30 years. The view from the inside opens with an essay by Bill Gould, Stata's president and cofounder, that discusses the challenges and concepts that guided the design and implementation of Stata. This is followed by an interview of Bill by Joe Newton that discusses Bill's early interest in computing, his early work on a program for matching prom dates in the days when you had to purchase time on computers, and further exploration of the guiding principles behind Stata. Finally, Sean Becketti, Stata's first employee, delves into the nottobemissed culture of Stata in its infancy. The view from the outside comprises 14 essays by prominent researchers and members of the Stata community. Most discuss Stata's use and evolution in disciplines such as behavioral sciences, business, economics, epidemiology, time series, political science, public health, public policy, veterinary epidemiology, and statistics. Some take a sweeping overview. Others are more intimate personal recollections. Mostly, we simply wanted to celebrate the relationship between Stata users and Stata software. We hope that this volume holds something interesting for everyone.

© 2016,Introduction to Enumerative and Analytic Combinatoricsfills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including errorcorrecting codes, properties of sequences, and magic squares. Strengthening the analytic flavor of the book, thisSecond Edition: Features a new chapter on analytic combinatorics and new sections on advanced applications of generating functions Demonstrates powerful techniques that do not require the residue theorem or complex integration Adds new exercises to all chapters, significantly extending coverage of the given topics Introduction to Enumerative and Analytic Combinatorics, Second Editionmakes combinatorics more accessible, increasing interest in this rapidly expanding field.

© 2016,For the past 500 years, gamblersled by mathematicians and scientistshave been trying to figure out how to pull the rug out from under Lady Luck. In The Perfect Bet , mathematician and awardwinning writer Adam Kucharski tells the astonishing story of how the experts have succeeded, revolutionizing mathematics and science in the process. The house can seem unbeatable. Kucharski shows us just why it isn't. Even better, he demonstrates how the search for the perfect bet has been crucial for the scientific pursuit of a better world.

© 2016,Packed with effective instructional strategies, this book explores why certain K5 students struggle with math and provides a framework for helping these learners succeed. The authors present empirically validated practices for supporting students with disabilities and others experiencing difficulties in specific areas of math, including problem solving, early numeracy, whole number operations, fractions, geometry, and algebra. Concrete examples, easytoimplement lessonplanning ideas, and connections to state standards, in particular the Common Core standards, enhance the book's utility. Also provided is invaluable guidance on planning and delivering multitiered instruction and intervention.

© 2015,Choose the Correct Solution Method for Your Optimization Problem Optimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, BroydenFletcherGoldfarbShanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible directions, genetic algorithms, particle swarm optimization (PSO), simulated annealing, ant colony optimization, and tabu search methods. The author shows how to solve nonconvex multiobjective optimization problems using simple modifications of the basic PSO code. The book also introduces multidisciplinary design optimization (MDO) architecturesone of the first optimization books to do soand develops software codes for the simplex method and affinescaling interior point method for solving linear programming problems. In addition, it examines Gomory's cutting plane method, the branchandbound method, and Balas' algorithm for integer programming problems. The author follows a stepbystep approach to developing the MATLAB® codes from the algorithms. He then applies the codes to solve both standard functions taken from the literature and realworld applications, including a complex trajectory design problem of a robot, a portfolio optimization problem, and a multiobjective shape optimization problem of a reentry body. This handson approach improves your understanding and confidence in handling different solution methods. The MATLAB codes are available on the book's CRC Press web page.

© 2015,The present volume provides a fascinating overview of geometrical ideas and perceptions from the earliest cultures to the mathematical and artistic concepts of the 20th century. It is the English translation of the 3rd edition of the wellreceived German book "5000 Jahre Geometrie," in which geometry is presented as a chain of developments in cultural history and their interaction with architecture, the visual arts, philosophy, science and engineering. Geometry originated in the ancient cultures along the Indus and Nile Rivers and in Mesopotamia, experiencing its first "Golden Age" in Ancient Greece. Inspired by the Greek mathematics, a new germ of geometry blossomed in the Islamic civilizations. Through the Oriental influence on Spain, this knowledge later spread to Western Europe. Here, as part of the medieval Quadrivium, the understanding of geometry was deepened, leading to a revival during the Renaissance. Together with parallel achievements in India, China, Japan and the ancient American cultures, the European approaches formed the ideas and branches of geometry we know in the modern age: coordinate methods, analytical geometry, descriptive and projective geometry in the 17th an 18th centuries, axiom systems, geometry as a theory with multiple structures and geometry in computer sciences in the 19th and 20th centuries. Each chapter of the book starts with a table of key historical and cultural dates and ends with a summary of essential contents of geometr y in the respective era. Compelling examples invite the reader to further explore the problems of geometry in ancient and modern times. The book will appeal to mathematicians interested in Geometry and to all readers with an interest in cultural history. From letters to the authors for the German language edition I hope it gets a translation, as there is no comparable work. Prof. J. GrattanGuinness (Middlesex University London) "Five Thousand Years of Geometry"  I think it is the most handsome book I have ever seen from Springer and the inclusion of so many color plates really improves its appearance dramatically! Prof. J.W. Dauben (City University of New York) An excellent book in every respect. The authors have successfully combined the history of geometry with the general development of culture and history. ... The graphic design is also excellent. Prof. Z. Nádenik (Czech Technical University in Prague)

© 2016,"There is nothing like it on the market...no others are as encyclopedic...the writing is exemplary: simple, direct, and competent." George W. Cobb, Professor Emeritus of Mathematics and Statistics, Mount Holyoke College Written in a direct and clear manner, Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times presents a comprehensive guide to the history of mathematical statistics and details the major results and crucial developments over a 200year period. Presented in chronological order, the book features an account of the classical and modern works that are essential to understanding the applications of mathematical statistics. Divided into three parts, the book begins with extensive coverage of the probabilistic works of Laplace, who laid much of the foundations of later developments in statistical theory. Subsequently, the second part introduces 20th century statistical developments including work from Karl Pearson, Student, Fisher, and Neyman. Lastly, the author addresses postFisherian developments. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times also features: A detailed account of Galton's discovery of regression and correlation as well as the subsequent development of Karl Pearson's X2 and Student's t A comprehensive treatment of the permeating influence of Fisher in all aspects of modern statistics beginning with his work in 1912 Significant coverage of NeymanPearson theory, which includes a discussion of the differences to Fisher's works Discussions on key historical developments as well as the various disagreements, contrasting information, and alternative theories in the history of modern mathematical statistics in an effort to provide a thorough historical treatment Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times is an excellent reference for academicians with a mathematical background who are teaching or studying the history or philosophical controversies of mathematics and statistics. The book is also a useful guide for readers with a general interest in statistical inference.

© 2015,Praise for the First Edition "This is a wellwritten and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory."  The Statistician Thoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, hypothesis testing, and simple linear regression. Encouraging readers to develop a deeper intuitive understanding of probability, the author presents illustrative geometrical presentations and arguments without the need for rigorous mathematical proofs. The Second Edition features interesting and practical examples from a variety of engineering and scientific fields, as well as: Over 880 problems at varying degrees of difficulty allowing readers to take on more challenging problems as their skill levels increase Chapterbychapter projects that aid in the visualization of probability distributions New coverage of statistical quality control and quality production An appendix dedicated to the use of Mathematica#65533; and a companion website containing the referenced data sets Featuring a practical and realworld approach, this textbook is ideal for a first course in probability for students majoring in statistics, engineering, business, psychology, operations research, and mathematics. Probability: An Introduction with Statistical Applications, Second Edition is also an excellent reference for researchers and professionals in any discipline who need to make decisions based on data as well as readers interested in learning how to accomplish effective decision making from data.

© 2015,The second edition enhanced with new chapters, figures, and appendices to cover the new developments in applied mathematical functions This book examines the topics of applied mathematical functions to problems that engineers and researchers solve daily in the course of their work. The text covers set theory, combinatorics, random variables, discrete and continuous probability, distribution functions, convergence of random variables, computer generation of random variates, random processes and stationarity concepts with associated autocovariance and cross covariance functions, estimation theory and Wiener and Kalman filtering ending with two applications of probabilistic methods. Probability tables with nine decimal place accuracy and graphical Fourier transform tables are included for quick reference. The author facilitates understanding of probability concepts for both students and practitioners by presenting over 450 carefully detailed figures and illustrations, and over 350 examples with every step explained clearly and some with multiple solutions. Additional features of the second edition of Probability and Random Processes are: Updated chapters with new sections on NewtonPepys' problem; Pearson, Spearman, and Kendal correlation coefficients; adaptive estimation techniques; birth and death processes; and renewal processes with generalizations A new chapter on Probability Modeling in Teletraffic Engineering written by Kavitha Chandra An eighth appendix examining the computation of the roots of discrete probabilitygenerating functions With new material on theory and applications of probability, Probability and Random Processes, Second Edition is a thorough and comprehensive reference for commonly occurring problems in probabilistic methods and their applications.

© 2014,In the ten years since the publication of the bestselling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Editionprovides comprehensive coverage of the main topics in pure and applied graph theory. This second editionover 400 pages longer than its predecessorincorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive singlesource guide to graph theory. It emphasizes quick accessibility to topics for nonexperts and enables easy crossreferencing among chapters.

© 2014,With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easytouse format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters. New to the Second Edition Separate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of matrices, generalized inverses, matrices over finite fields, invariant subspaces, representations of quivers, and spectral sets New chapters on combinatorial matrix theory topics, such as tournaments, the minimum rank problem, and spectral graph theory, as well as numerical linear algebra topics, including algorithms for structured matrix computations, stability of structured matrix computations, and nonlinear eigenvalue problems More chapters on applications of linear algebra, including epidemiology and quantum error correction New chapter on using the free and open source software system Sage for linear algebra Additional sections in the chapters on sign pattern matrices and applications to geometry Conjectures and open problems in most chapters on advanced topics Highly praised as a valuable resource for anyone who uses linear algebra, the first edition covered virtually all aspects of linear algebra and its applications. This edition continues to encompass the fundamentals of linear algebra, combinatorial and numerical linear algebra, and applications of linear algebra to various disciplines while also covering uptodate software packages for linear algebra computations.

© 2016,EasytoUse Reference and Software for Statistical Modeling and Testing Handbook of Statistical Distributions with Applications, Second Editionprovides quick access to common and specialized probability distributions for modeling practical problems and performing statistical calculations. Along with many new examples and results, this edition includes both the author's StatCalc software and R codes to accurately and easily carry out computations. New to the Second Edition Major changes in binomial, Poisson, normal, gamma, Weibull, exponential, logistic, Laplace, and Pareto distributions Updated statistical tests and intervals based on recent publications in statistical journals Enhanced PC calculator StatCalc with electronic help manuals R functions for cases where StatCalc is not applicable, with the codes available online This highly praised handbook integrates popular probability distribution models, formulas, applications, and software to help you compute a variety of statistical intervals. It covers probability and percentiles, algorithms for random number generation, hypothesis tests, confidence intervals, tolerance intervals, prediction intervals, sample size determination, and much more.

© 2016,Introduction to Abstract Algebra, Second Editionpresents abstract algebra as the main tool underlying discrete mathematics and the digital world. It avoids the usual groups first/rings first dilemma by introducing semigroups and monoids, the multiplicative structures of rings, along with groups. This new edition of a widely adopted textbook covers applications from biology, science, and engineering. It offers numerous updates based on feedback from first edition adopters, as well as improved and simplified proofs of a number of important theorems. Many new exercises have been added, while new study projects examine skewfields, quaternions, and octonions. The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. These three chapters provide a quick introduction to algebra, sufficient to exhibit irrational numbers or to gain a taste of cryptography. Chapters four through seven cover abstract groups and monoids, orthogonal groups, stochastic matrices, Lagrange's theorem, groups of units of monoids, homomorphisms, rings, and integral domains. The first seven chapters provide basic coverage of abstract algebra, suitable for a onesemester or twoquarter course. Each chapter includes exercises of varying levels of difficulty, chapter notes that point out variations in notation and approach, and study projects that cover an array of applications and developments of the theory. The final chapters deal with slightly more advanced topics, suitable for a secondsemester or thirdquarter course. These chapters delve deeper into the theory of rings, fields, and groups. They discuss modules, including vector spaces and abelian groups, group theory, and quasigroups. This textbook is suitable for use in an undergraduate course on abstract algebra for mathematics, computer science, and education majors, along with students from other STEM fields.

© 2015,Praise for the First Edition "...[t]he book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics."  MAA Reviews Thoroughly updated throughout, Introduction to Time Series Analysis and Forecasting, Second Edition presents the underlying theories of time series analysis that are needed to analyze timeoriented data and construct realworld short to mediumterm statistical forecasts. Authored by highlyexperienced academics and professionals in engineering statistics, the Second Edition features discussions on both popular and modern time series methodologies as well as an introduction to Bayesian methods in forecasting. Introduction to Time Series Analysis and Forecasting, Second Edition also includes: Over 300 exercises from diverse disciplines including health care, environmental studies, engineering, and finance More than 50 programming algorithms using JMP#65533;, SAS#65533;, and R that illustrate the theory and practicality of forecasting techniques in the context of timeoriented data New material on frequency domain and spatial temporal data analysis Expanded coverage of the variogram and spectrum with applications as well as transfer and intervention model functions A supplementary website featuring PowerPoint#65533; slides, data sets, and select solutions to the problems Introduction to Time Series Analysis and Forecasting, Second Edition is an ideal textbook upperundergraduate and graduatelevels courses in forecasting and time series. The book is also an excellent reference for practitioners and researchers who need to model and analyze time series data to generate forecasts.

© 2016,An uptodate version of the complete, selfcontained introduction to matrix analysis theory and practice Providing accessible and indepth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easytofollow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the stepbystep process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the MoorePenrose inverse; matrix differentiation; and the distribution of quadratic forms. An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features: * New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors * Additional problems and chapterend practice exercises at the end of each chapter * Extensive examples that are familiar and easy to understand * Selfcontained chapters for flexibility in topic choice * Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices Matrix Analysis for Statistics, Third Edition is an ideal textbook for upperundergraduate and graduatelevel courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics. James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott's research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.

© 2016,We use addition on a daily basisyet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite serieslong sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular formsthe analytic functions on the upper halfplane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem. Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.

© 2015,This book presents basic stochastic processes, stochastic calculus including L#65533;vy processes on one hand, and Markov and Semi Markov models on the other. From the financial point of view, essential concepts such as the Black and Scholes model, VaR indicators, actuarial evaluation, market values, fair pricing play a central role and will be presented. The authors also present basic concepts so that this series is relatively selfcontained for the main audience formed by actuaries and particularly with ERM (enterprise risk management) certificates, insurance risk managers, students in Master in mathematics or economics and people involved in Solvency II for insurance companies and in Basel II and III for banks.

© 2015,This book presents uptodate results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and nondensely defined functional differential equations and inclusions in separable Banach spaces or in Fr#65533;chet spaces. The tools used include classical fixed points theorems and the measureof noncompactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.