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© 2015,This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the EulerLagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integerorder integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of EulerLagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional SturmLiouville problems. Advanced Methods in the Fractional Calculus of Variations is a selfcontained text which will be useful for graduate students wishing to learn about fractionalorder systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering.

© 2015,This monograph provides a selfcontained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the RobinsonSchenstedKnuth algorithm and a method for proving Pólya's enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.

© 2015,Features the techniques, methods, and applications of calculus using realworld examples from business and economics as well as the life and social sciences An introduction to differential and integral calculus, Fundamentals of Calculus presents key topics suited for a variety of readers in fields ranging from entrepreneurship and economics to environmental and social sciences. Practical examples from a variety of subject areas are featured throughout each chapter and stepbystep explanations for the solutions are presented. Specific techniques are also applied to highlight important information in each section, including symbols interspersed throughout to further reader comprehension. In addition, the book illustrates the elements of finite calculus with the varied formulas for power, quotient, and product rules that correlate markedly with traditional calculus. Featuring calculus as the "mathematics of change," each chapter concludes with a historical notes section. Fundamentals of Calculus chapter coverage includes: Linear Equations and Functions The Derivative Using the Derivative Exponents and Logarithms Differentiation Techniques Integral Calculus Integrations Techniques Functions of Several Variables Series and Summations Applications to Probability Supplemented with online instructional support materials, Fundamentals of Calculus is an ideal textbook for undergraduate students majoring in business, economics, biology, chemistry, and environmental science.

© 2016,What gives statistics its unity as a science? Stephen Stigler sets forth the seven foundational ideas of statisticsâe"a scientific discipline related to but distinct from mathematics and computer science. Even the most basic ideaâe" aggregation , exemplified by averagingâe"is counterintuitive. It allows one to gain information by discarding information, namely, the individuality of the observations. Stiglerâe(tm)s second pillar, information measurement, challenges the importance of âeoebig dataâe by noting that observations are not all equally important: the amount of information in a data set is often proportional to only the square root of the number of observations, not the absolute number. The third idea is likelihood , the calibration of inferences with the use of probability. Intercomparison is the principle that statistical comparisons do not need to be made with respect to an external standard. The fifth pillar is regression , both a paradox (tall parents on average produce shorter children; tall children on average have shorter parents) and the basis of inference, including Bayesian inference and causal reasoning. The sixth concept captures the importance of experimental design âe"for example, by recognizing the gains to be had from a combinatorial approach with rigorous randomization. The seventh idea is the residual : the notion that a complicated phenomenon can be simplified by subtracting the effect of known causes, leaving a residual phenomenon that can be explained more easily. The Seven Pillars of Statistical Wisdom presents an original, unified account of statistical science that will fascinate the interested layperson and engage the professional statistician.

© 2015,This book examines the relationship between mathematics and data in the modern world. Indeed, modern societies are awash with data which must be manipulated in many different ways: encrypted, compressed, shared between users in a prescribed manner, protected from an unauthorised access and transmitted over unreliable channels. All of these operations can be understood only by a person with knowledge of basics in algebra and number theory. This book provides the necessary background in arithmetic, polynomials, groups, fields and elliptic curves that is sufficient to understand such reallife applications as cryptography, secret sharing, errorcorrecting, fingerprinting and compression of information. It is the first to cover many recent developments in these topics. Based on a lecture course given to thirdyear undergraduates, it is selfcontained with numerous worked examples and exercises provided to test understanding. It can additionally be used for selfstudy.

© 2017,NOTE: This edition features the same content as the traditional text in a convenient, threeholepunched, looseleaf version. Books a la Carte also offer a great valuethis format costs significantly less than a new textbook. Before purchasing, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson's MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products. For courses in introductory statistics. Putting It Together Statistics: Informed Decisions Using Data , Fifth Edition , gives students the tools to see a bigger picture and make informed choices. As a current introductory statistics instructor, Mike Sullivan III presents a text that is filled with ideas and strategies that work in today's classroom. His practical emphasis resonates with students and helps them see that statistics is connected, not only to individual concepts, but also with the world at large. MyStatLab for this edition takes advantage of data analytics to add additional exercises to high usage chapters. New Technology Support Videos show the author demonstrating easytofollow steps to solve a problem in several different formatsby hand, TI84, and StatCrunch(tm). Also available with MyStatLab MyStatLab from Pearson is the world's leading online resource for teaching and learning statistics; it integrates interactive homework, assessment, and media in a flexible, easytouse format. MyStatLab is a course management system that helps individual students succeed. It provides engaging experiences that personalize, stimulate, and measure learning for each student. Tools are embedded to make it easy to integrate statistical software into the course. And, it comes from an experienced partner with educational expertise and an eye on the future.

© 2016,This book introduces a theory of higher matrix factorizations for regular sequences and uses it to describe the minimal free resolutions of high syzygy modules over complete intersections. Such resolutions have attracted attention ever since the elegant construction of the minimal free resolution of the residue field by Tate in 1957. The theory extends the theory of matrix factorizations of a nonzero divisor, initiated by Eisenbud in 1980, which yields a description of the eventual structure of minimal free resolutions over a hypersurface ring. Matrix factorizations have had many other uses in a wide range of mathematical fields, from singularity theory to mathematical physics.

© 2015,From prehistory to the present, knots have been used for purposes both artistic and practical. The modern science of Knot Theory has ramifications for biochemistry and mathematical physics and is a rich source of research projects for undergraduate and graduate students and professionals alike. Quandles are essentially knots translated into algebra. This book provides an accessible introduction to quandle theory for readers with a background in linear algebra. Important concepts from topology and abstract algebra motivated by quandle theory are introduced along the way. With elementary selfcontained treatments of topics such as group theory, cohomology, knotted surfaces and more, this book is perfect for a transition course, an upperdivision mathematics elective, preparation for research in knot theory, and any reader interested in knots.

© 2011,Userfriendly and engaging introduction to elementary statistics. Written in a personal and informal style, this book helps readers make the leap from apprehension to comprehension of elementary statistics. Statistics For The Terrified , 5 e is intended as a supplemental text for undergraduate or graduate courses in statistics and research methods, as a refresher for students who have already taken a statistics course, or as a primer for new students of elementary statistics. Millions of people have math anxiety yet this is rarely taken into consideration in textbooks on statistics. This book presents selfhelp strategies that help people manage their math anxiety so they can relax and build confidence while learning statistics. After covering the essentials required for the journey into statistics, the remainder of the book presents an introduction to elementary statistics with a great deal of encouragement, support, stepbystep assistance, and numerous concrete examples, without lengthy theoretical discussions.

© 2016,This monograph contains a detailed exposition of the uptodate theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an Fspace, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.

© 2016,This book covers recent advances in Complex Automated Negotiations as a widely studied emerging area in the field of Autonomous Agents and MultiAgent Systems. The book includes selected revised and extended papers from the 7th International Workshop on AgentBased Complex Automated Negotiation (ACAN2014), which was held in Paris, France, in May 2014. The book also includes brief introductions about Agentbased Complex Automated Negotiation which are based on tutorials provided in the workshop, and brief summaries and descriptions about the ANAC'14 (Automated Negotiating Agents Competition) competition, where authors of selected finalist agents explain the strategies and the ideas used by them. The book is targeted to academic and industrial researchers in various communities of autonomous agents and multiagent systems, such as agreement technology, mechanism design, electronic commerce, related areas, as well as graduate, undergraduate, and PhD students working in those areas or having interest in them.

© 2016,What are the chances? This is the question we ask ourselves when we encounter the strangest and most seemingly impossible coincidences, like the woman who won the lottery four times or the fact that Lincoln's dreams foreshadowed his own assassination. But, when we look at coincidences mathematically, the odds are a lot better than any of us would have thought. In Fluke , mathematician Joseph Mazur takes a second look at the seemingly improbable, sharing with us an entertaining guide to the most surprising moments in our lives. He takes us on a tour of the mathematical concepts of probability, such as the law of large numbers and the birthday paradox, and combines these concepts with lively anecdotes of flukes from around the world. How do you explain finding your college copy of Moby Dick in a used bookstore on the Seine on your first visit to Paris? How can a jury be convinced beyond a reasonable doubt that DNA found at the scene of a heinous crime did not get there by some fluke? Should we be surprised if strangers named Maria and Francisco, seeking each other in a hotel lobby, accidentally meet the wrong Francisco and the wrong Maria, another pair of strangers also looking for each other? As Mazur reveals, if there is any likelihood that something could happen, no matterhow small, it is bound to happen to someone at some time. In Fluke , Mazur offers us proof of the inevitability of the sublime and the unexpected. He has written a book that will appeal to anyone who has ever wondered how all of the tiny decisions that happen in our lives add up to improbable wholes. A mustread for math enthusiasts and storytellers alike, Fluke helps us to understand the true nature of chance.

© 2016,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 X 2 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 Neyman Pearson 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,Leo Corry tells the story behind the idea of number, from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century.

© 2016,Forget everything you've been taught about math. In Burn Math Class , Jason Wilkes takes the traditional approach to how we learn mathwith its unwelcoming textbooks, unexplained rules, and authoritarian assertionsand sets it on fire. Focusing on how mathematics is created rather than on mathematical facts, Wilkes teaches the subject in a way that requires no memorization and no prior knowledge beyond addition and multiplication. From these simple foundations, Burn Math Class shows how mathematics can be (re)invented from scratch without preexisting textbooks and courses. We can discover math on our own through experimentation and failure, without appealing to any outside authority. When math is created free from arcane notations and pretentious jargon that hide the simplicity of mathematical concepts, it can be understood organicallyand it becomes fun! Following this unconventional approach, Burn Math Class leads the reader from the basics of elementary arithmetic to various "advanced" topics, such as timedilation in special relativity, Taylor series, and calculus in infinitedimensional spaces. Along the way, Wilkes argues that orthodox mathematics education has been teaching the subject backward: calculus belongs before many of its socalled prerequisites, and those prerequisites cannot be fully understood without calculus. Like the smartest, craziest teacher you've ever had, Wilkes guides you on an adventure in mathematical creation that will radically change the way you think about math. Revealing the beauty and simplicity of this timeless subject, Burn Math Class turns everything that seems difficult about mathematics upside down and sideways until you understand just how easy math can be.

© 2016,This book is intended to help researchers overcome the entrance barrier to Proper Generalized Decomposition (PGD), by providing a valuable tool to begin the programming task. Detailed Matlab Codes are included for every chapter in the book, in which the theory previously described is translated into practice. Examples include parametric problems, nonlinear model order reduction and realtime simulation, among others. Proper Generalized Decomposition (PGD) is a method for numerical simulation in many fields of applied science and engineering. As a generalization of ProperOrthogonal Decomposition or Principal Component Analysis to an arbitrary numberof dimensions, PGD is able to provide the analyst with very accurate solutionsfor problems defined in high dimensional spaces, parametric problems and evenrealtime simulation.

© 2016,This brief is concerned with tempered stable distributions and their associated Levy processes. It is a good text for researchers interested in learning about tempered stable distributions. A tempered stable distribution is one which takes a stable distribution and modifies its tails to make them lighter. The motivation for this class comes from the fact that infinite variance stable distributions appear to provide a good fit to data in a variety of situations, but the extremely heavy tails of these models are not realistic for most real world applications. The idea of using distributions that modify the tails of stable models to make them lighter seems to have originated in the influential paper of Mantegna and Stanley (1994). Since then, these distributions have been extended and generalized in a variety of ways. They have been applied to a wide variety of areas including mathematical finance, biostatistics,computer science, and physics.

© 2015,Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods. This important new work is edited by Miklós Bóna of the University of Florida where he is a member of the Academy of Distinguished Teaching Scholars. He received his Ph.D. in mathematics at Massachusetts Institute of Technology in 1997. Miklós is the author of four books and more than 65 research articles, including the awardwinning Combinatorics of Permutations. Miklós Bóna is an editorinchief for the Electronic Journal of Combinatoricsand Series Editor of the Discrete Mathematics and Its Applications Series for CRC Press/Chapman and Hall. The first two chapters provide a comprehensive overview of the most frequently used methods in combinatorial enumeration, including algebraic, geometric, and analytic methods. These chapters survey generating functions, methods from linear algebra, partially ordered sets, polytopes, hyperplane arrangements, and matroids. Subsequent chapters illustrate applications of these methods for counting a wide array of objects. The contributors for this book represent an international spectrum of researchers with strong histories of results. The chapters are organized so readers advance from the more general ones, namely enumeration methods, towards the more specialized ones. Topics include coverage of asymptotic normality in enumeration, planar maps, graph enumeration, Young tableaux, unimodality, logconcavity, real zeros, asymptotic normality, trees, generalized Catalan paths, computerized enumeration schemes, enumeration of various graph classes, words, tilings, pattern avoidance, computer algebra, and parking functions. This book will be beneficial to a wide audience. It will appeal to experts on the topic interested in learning more about the finer points, readers interested in a systematic and organized treatment of the topic, and novices who are new to the field.

© 2015,Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods. This important new work is edited by Miklós Bóna of the University of Florida where he is a member of the Academy of Distinguished Teaching Scholars. He received his Ph.D. in mathematics at Massachusetts Institute of Technology in 1997. Miklós is the author of four books and more than 65 research articles, including the awardwinning Combinatorics of Permutations. Miklós Bóna is an editorinchief for the Electronic Journal of Combinatoricsand Series Editor of the Discrete Mathematics and Its Applications Series for CRC Press/Chapman and Hall. The first two chapters provide a comprehensive overview of the most frequently used methods in combinatorial enumeration, including algebraic, geometric, and analytic methods. These chapters survey generating functions, methods from linear algebra, partially ordered sets, polytopes, hyperplane arrangements, and matroids. Subsequent chapters illustrate applications of these methods for counting a wide array of objects. The contributors for this book represent an international spectrum of researchers with strong histories of results. The chapters are organized so readers advance from the more general ones, namely enumeration methods, towards the more specialized ones. Topics include coverage of asymptotic normality in enumeration, planar maps, graph enumeration, Young tableaux, unimodality, logconcavity, real zeros, asymptotic normality, trees, generalized Catalan paths, computerized enumeration schemes, enumeration of various graph classes, words, tilings, pattern avoidance, computer algebra, and parking functions. This book will be beneficial to a wide audience. It will appeal to experts on the topic interested in learning more about the finer points, readers interested in a systematic and organized treatment of the topic, and novices who are new to the field.

© 2015,Teach Your Students Both the Mathematics of Numerical Methods and the Art of Computer Programming Introduction to Computational Linear Algebrapresents classroomtested material on computational linear algebra and its application to numerical solutions of partial and ordinary differential equations. The book is designed for senior undergraduate students in mathematics and engineering as well as firstyear graduate students in engineering and computational science. The text first introduces BLAS operations of types 1, 2, and 3 adapted to a scientific computer environment, specifically MATLAB®. It next covers the basic mathematical tools needed in numerical linear algebra and discusses classical material on Gauss decompositions as well as LU and Cholesky's factorizations of matrices. The text then shows how to solve linear least squares problems, provides a detailed numerical treatment of the algebraic eigenvalue problem, and discusses (indirect) iterative methods to solve a system of linear equations. The final chapter illustrates how to solve discretized sparse systems of linear equations. Each chapter ends with exercises and computer projects.

© 2015,A New York Times bestseller The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examplesfrom ice cream scoops and poker hands to measuring mountains and making magic squaresthis book empowers you to see the beauty, simplicity, and truly magical properties behind those formulas and equations that once left your head spinning. You'll learn the key ideas of classic areas of mathematics like arithmetic, algebra, geometry, trigonometry, and calculus, but you'll also have fun fooling around with Fibonacci numbers, investigating infinity, and marveling over mathematical magic tricks that will make you look like a math genius! A mathematician who is known throughout the world as the "mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand. In The Magic of Math , Benjamin does more than just teach skills: with a tip of his magic hat, he takes you on as his apprentice to teach you how to appreciate math the way he does. He motivates you to learn something new about how to solve for x, because there is real pleasure to be found in the solution to a challenging problem or in using numbers to do something useful. But what he really wants you to do is be able to figure out why, for that's where you'll find the real beauty, power, and magic of math. If you are already someone who likes math, this book will dazzle and amuse you. If you never particularly liked or understood math, Benjamin will enlighten you andwith a wave of his magic wandturn you into a math lover.

© 2015,This book is the English translation of Baumgart's thesis on the early proofs of the quadratic reciprocity law ("Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise"), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart's comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

© 2015,This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations, explaining the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the AuslanderReiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel's Theorem, the trichotomy and the Theorem of Kac  all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.

© 2015,College geometry students, professors interested in undergraduate research and secondary geometry teachers will find three rich environments in this textbook. The first chapter contains many of the standards of Euclidean college geometry. The second and third chapters introduce nonEuclidean models where some Euclidean rules hold and others do not. With emphases on constructions and proofs, the reader is encouraged to create the objects under investigation and verify the results with reasoning. Since both models of "bent" spaces exist in Euclidean geometry, the reader gains facility with Euclidean moves through the whole book, even while exploring nonEuclidean spaces. The book itself is meant to be unpacked, expanded and taken further, just like the problems it contains. Geometry by Construction challenges its readers to participate in the creation of mathematics. The questions span the spectrum from easy to newlypublished research and so are appropriate for a variety of students and teachers. From differentiation in a high school course through college classes and into summer research, any interested geometer will find compelling material. Teachers and professors might especially appreciate the way constructions provide openended questions which resist internet searches for solutions. College students should find the five refereed results from undergraduates like themselves encouraging. The active reader joins the mathematical tradition of a laboratory being a notebook plus a compass and ruler (or a dynamic geometry program on a computer.) New ideas await exploration and here are examples

© 2015,This book discusses the representation theory of symmetric groups, the theory of symmetric functions and the polynomial representation theory of general linear groups. The first chapter provides a detailed account of necessary representationtheoretic background. An important highlight of this book is an innovative treatment of the RobinsonSchenstedKnuth correspondence and its dual by extending Viennot's geometric ideas. Another unique feature is an exposition of the relationship between these correspondences, the representation theory of symmetric groups and alternating groups and the theory of symmetric functions. Schur algebras are introduced very naturally as algebras of distributions on general linear groups. The treatment of SchurWeyl duality reveals the directness and simplicity of Schur's original treatment of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.