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© 2016,In 1936, when he was just twentyfour years old, Alan Turing wrote a remarkable paper in which he outlined the theory of computation, laying out the ideas that underlie all modern computers. This groundbreaking and powerful theory now forms the basis of computer science. In Turing's Vision , Chris Bernhardt explains the theory, Turing's most important contribution, for the general reader. Bernhardt argues that the strength of Turing's theory is its simplicity, and that, explained in a straightforward manner, it is eminently understandable by the nonspecialist. As Marvin Minsky writes, "The sheer simplicity of the theory's foundation and extraordinary short path from this foundation to its logical and surprising conclusions give the theory a mathematical beauty that alone guarantees it a permanent place in computer theory." Bernhardt begins with the foundation and systematically builds to the surprising conclusions. He also views Turing's theory in the context of mathematical history, other views of computation (including those of Alonzo Church), Turing's later work, and the birth of the modern computer. In the paper, "On Computable Numbers, with an Application to the Entscheidungsproblem ," Turing thinks carefully about how humans perform computation, breaking it down into a sequence of steps, and then constructs theoretical machines capable of performing each step. Turing wanted to show that there were problems that were beyond any computer's ability to solve; in particular, he wanted to find a decision problem that he could prove was undecidable. To explain Turing's ideas, Bernhardt examines three wellknown decision problems to explore the concept of undecidability; investigates theoretical computing machines, including Turing machines; explains universal machines; and proves that certain problems are undecidable, including Turing's problem concerning computable numbers.

© 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,The Math Myth expands on Andrew Hacker's scrutiny of some widely held assumptions: that mathematics broadens our minds; that mastery of arcane concepts  cosine, logarithms, the area of a sphere  will be needed for most jobs; that the Common Core's single format should be required of every student. He worries that a frenzied emphasis on STEM (science, technology, engineering, and mathematics) is diverting resources from other pursuits and subverting the spirit of the country.

© 2016,Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematicsbut, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twentyfirstcentury viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving wellknown theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries.

© 2015,Following hot on the heels of The Imitation Game , this is the first modern biography of Alan Turing by a member of the familyAlan's nephew, Sir Dermot Turing Alan Turing was an extraordinary man who crammed into a life of only 42 years the careers of mathematician, codebreaker, computer scientist, and biologist. He is widely regarded as a war hero grossly mistreated by his unappreciative country and it has become hard to disentangle the real man from the story. It is easy to cast him as a misfit, the stereotypical professor. But actually Alan Turing was never a professor, and his nickname "Prof" was given by his codebreaking friends at Bletchley Park. Now, Alan Turing's nephew, Dermot Turing, has taken a fresh look at the influences on Alan Turing's life and creativity, and the later creation of a legend. Dermot's vibrant and entertaining approach to the life and work of a true genius makes this a fascinating read. This unique family perspective features insights from secret documents only recently released to the UK National Archives and other sources not tapped by previous biographers, looks into the truth behind Alan's conviction for gross indecency, and includes previously unpublished photographs from the Turing family album.

© 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,When Critical Multiculturalism Meets Mathematics details the development and outcomes of a teacher professional development project that merged multiculturalism and mathematics. In six compact chapters the authors describe the impetus for their multiyear project and present rich case studies of nine teacher participants. The cases stand alone as compelling reading, yet Marshall et al. extend beyond their distinctiveness to explain the statistical data related to the project s broader impact. Emphasizing both qualitative and quantitative findings makes this book ideal for novice researchers interested in mixed method study. Likewise, the authors unveil the anatomy and a few complexities of conducting research in the real world contexts of schools including participant recruitment and resolution of unanticipated matters that can arise within research teams. A unique twist in the final chapter is Marshall et al. s critique of their own missteps as researchers, which are used skillfully and unobtrusively to proffer tips for future studies. They conclude by theorizing affirmed intersectionality, identified as the critical element that facilitated teachers recognition and acceptance of the compatibility between the study s two components."

© 2015,What do pure mathematicians do, and why do they do it? Looking beyond the conventional answersfor the sake of truth, beauty, and practical applicationsthis book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twentyfirst century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayy#65533;m to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

© 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,This monograph considers several wellknown mathematical theorems and asks the question, "Why prove it again?" while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues' Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials. Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians. Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.

© 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.