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© 2014,This book provides an introduction to the topic of transcendental numbers for upperlevel undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker's theorem, Schanuel's conjecture, and Schneider's theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.

© 2014,Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.

© 2014,The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modernday number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.

© 2014,This book focuses on the way in which the problem of the motion of bodies has been viewed and approached over the course of human history. It is not another traditional history of mechanics but rather aims to enable the reader to fully understand the deeper ideas that inspired men, first in attempting to understand the mechanisms of motion and then in formulating theories with predictive as well as explanatory value. Given this objective, certain parts of the history of mechanics are neglected, such as fluid mechanics, statics and astronomy after Newton. On the other hand, due attention is paid, for example, to the history of thermodynamics, which has its own particular point of view on motion. Inspired in part by historical epistemology, the book examines the various views and theories of a given historical period (synchronic analysis) and then makes comparisons between different periods (diachronic analysis). In each period, one or two of the most meaningful contributions are selected for particular attention, instead of presenting a long inventory of scientific achievements.

© 2014,Teaching Math, Science, and Technology in Schools Today: Guidelines for Engaging Both Eager and Reluctant Learners offers unique, engaging, and thoughtprovoking ideas. The activities open imaginative doors to learning and provide opportunities for all learners. It surveys today s most important trends and dilemmas while explaining how collaboration and critical thinking can be translated into fresh classroom practices. Questions, engagement, and curiosity are viewed as natural partners for mathematical problem solving, scientific inquiry, and learning about technology. Like the Common Core State Standards, the book builds on the social nature of learning to provide suggestions for both eager and reluctant learners. The overall goal of the book is to deepen the collective conversation, challenge thinking, and provide some uptodate tools for teachers so they can help reverse the steady erosion of math, science, and technology understanding in the general population."

© 2015,Highdimensional data appear in many fields, and their analysis has become increasingly important in modern statistics. However, it has long been observed that several wellknown methods in multivariate analysis become inefficient, or even misleading, when the data dimension p is larger than, say, several tens. A seminal example is the wellknown inefficiency of Hotelling's T2test in such cases. This example shows that classical large sample limits may no longer hold for highdimensional data; statisticians must seek new limiting theorems in these instances. Thus, the theory of random matrices (RMT) serves as a muchneeded and welcome alternative framework. Based on the authors' own research, this book provides a firsthand introduction to new highdimensional statistical methods derived from RMT. The book begins with a detailed introduction to useful tools from RMT, and then presents a series of highdimensional problems with solutions provided by RMT methods.

© 2014,Quaternions are a number system that has become increasingly useful for representing the rotations of objects in threedimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and selfcontained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

© 2007,Learn to program SAS by example If you like learning by example, then Learning SAS by Example: A Programmer's Guide makes it easy to learn SAS programming. In an instructive and conversational tone, author Ron Cody clearly explains each programming technique and then illustrates it with one or more reallife examples, followed by a detailed description of how the program works. The text is divided into four major sections: Getting Started; DATA Step Processing; Presenting and Summarizing Your Data; and Advanced Topics. Subjects addressed include: Reading data from external sources Learning details of DATA step programming Subsetting and combining SAS data sets Understanding SAS functions and working with arrays Creating reports with PROC REPORT and PROC TABULATE Learning to use the SAS Output Delivery System Getting started with the SAS macro language Introducing PROC SQL You can test your knowledge and hone your skills by solving the problems at the end of each chapter. (Solutions to oddnumbered problems are located at the back of this book. Solutions to all problems are available to instructors by visiting Ron Cody's author page for details.) This book is intended for beginners and intermediate users. Readers should know how to enter and submit a SAS program from their operating system. This book is part of the SAS Press program.

© 2014,What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenthcentury mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the DedekindPeano axioms and ends with the construction of the real numbers. The core CantorDedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a yearlong course at the upperundergraduate level. For shorter onesemester or onequarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via selfstudy.

© 2014,In Professor Stewart's Casebook of Mathematical Mysteries , acclaimed mathematician Ian Stewart presents an enticing collection of mathematical curios and conundrums. With a new puzzle on each page, this compendium of brainteasers will both teach and delight. Guided by stalwart detective Hemlock Soames and his sidekick, Dr. John Watsup, readers will delve into almost two hundred mathematical problems, puzzles, and facts. Tackling subjects from mathematical dates (such as Pi Day), what we don't know about primes, and why the Earth is round, this clever, mindexpanding book demonstrates the power and fun inherent in mathematics.

© 2014,Past, Present, and Future of Statistical Science was commissioned in 2013 by the Committee of Presidents of Statistical Societies (COPSS) to celebrate its 50th anniversary and the International Year of Statistics. COPSS consists of five charter member statistical societies in North America and is best known for sponsoring prestigious awards in statistics, such as the COPSS Presidents' award. Through the contributions of a distinguished group of 50 statisticians who are past winners of at least one of the five awards sponsored by COPSS, this volume showcases the breadth and vibrancy of statistics, describes current challenges and new opportunities, highlights the exciting future of statistical science, and provides guidance to future generations of statisticians. The book is not only about statistics and science but also about people and their passion for discovery. Distinguished authors present expository articles on a broad spectrum of topics in statistical education, research, and applications. Topics covered include reminiscences and personal reflections on statistical careers, perspectives on the field and profession, thoughts on the discipline and the future of statistical science, and advice for young statisticians. Many of the articles are accessible not only to professional statisticians and graduate students but also to undergraduate students interested in pursuing statistics as a career and to all those who use statistics in solving realworld problems. A consistent theme of all the articles is the passion for statistics enthusiastically shared by the authors. Their success stories inspire, give a sense of statistics as a discipline, and provide a taste of the exhilaration of discovery, success, and professional accomplishment.

© 2014,What is algebra? For some, it is an abstract language of x's and y's. For mathematics majors and professional mathematicians, it is a world of axiomatically defined constructs like groups, rings, and fields. Taming the Unknown considers how these two seemingly different types of algebra evolved and how they relate. Victor Katz and Karen Parshall explore the history of algebra, from its roots in the ancient civilizations of Egypt, Mesopotamia, Greece, China, and India, through its development in the medieval Islamic world and medieval and early modern Europe, to its modern form in the early twentieth century. Defining algebra originally as a collection of techniques for determining unknowns, the authors trace the development of these techniques from geometric beginnings in ancient Egypt and Mesopotamia and classical Greece. They show how similar problems were tackled in Alexandrian Greece, in China, and in India, then look at how medieval Islamic scholars shifted to an algorithmic stage, which was further developed by medieval and early modern European mathematicians. With the introduction of a flexible and operative symbolism in the sixteenth and seventeenth centuries, algebra entered into a dynamic period characterized by the analytic geometry that could evaluate curves represented by equations in two variables, thereby solving problems in the physics of motion. This new symbolism freed mathematicians to study equations of degrees higher than two and three, ultimately leading to the present abstract era. Taming the Unknown follows algebra's remarkable growth through different epochs around the globe.

© 2014,This book is a popularized reference for students looking to work with spatialized data, but who do not have the advanced statistical theoretical basics.

© 2014,This is the second volume of the book on the proof of Fermat's Last Theorem by Wiles and Taylor (the first volume is published in the same series; see MMONO/243). Here the detail of the proof announced in the first volume is fully exposed. The book also includes basic materials and constructions in number theory and arithmetic geometry that are used in the proof. In the first volume the modularity lifting theorem on Galois representations has been reduced to properties of the deformation rings and the Hecke modules. The Hecke modules and the Selmer groups used to study deformation rings are constructed, and the required properties are established to complete the proof. The reader can learn basics on the integral models of modular curves and their reductions modulo $p$ that lay the foundation of the construction of the Galois representations associated with modular forms. More background materials, including Galois cohomology, curves over integer rings, the Neron models of their Jacobians, etc., are also explained in the text and in the appendices.

© 2015,This is the second edition of the popular book on using R for statistical analysis and graphics. The authors, who run a popular blog supplementing their books, have focused on adding many new examples to this new edition. These examples are presented primarily in new chapters based on the following themes: simulation, probability, statistics, mathematics/computing, and graphics. The authors have also added many other updates, including a discussion of RStudioa very popular development environment for R.

© 2014,R is open source statistical computing software. Since the R core group was formed in 1997, R has been extended by a very large number of packages with extensive documentation along with examples freely available on the internet. It offers a large number of statistical and numerical methods and graphical tools and visualization of extraordinarily high quality. R was recently ranked in 14th place by the Transparent Language Popularity Index and 6th as a scripting language, after PHP, Python, and Perl. The book is designed so that it can be used right away by novices while appealing to experienced users as well. Each article begins with a data example that can be downloaded directly from the R website. Data analysis questions are articulated following the presentation of the data. The necessary R commands are spelled out and executed and the output is presented and discussed. Other examples of data sets with a different flavor and different set of commands but following the theme of the article are presented as well. Each chapter predents a handsonexperience. R has superb graphical outlays and the book brings out the essentials in this arena. The end user can benefit immensely by applying the graphics to enhance research findings. The core statistical methodologies such as regression, survival analysis, and discrete data are all covered. Addresses data examples that can be downloaded directly from the R website No other source is needed to gain practical experience Focus on the essentials in graphical outlays

© 2014,This title is written for the numerate nonspecialist, and hopesto serve three purposes. First it gathers mathematical materialfrom diverse but related fields of order statistics, records,extreme value theory, majorization, regular variation andsubexponentiality. All of these are relevant for understanding fattails, but they are not, to our knowledge, brought together in asingle source for the target readership. Proofs that give insightare included, but for most fussy calculations the reader isreferred to the excellent sources referenced in the text.Multivariate extremes are not treated. This allows us to presentmaterial spread over hundreds of pages in specialist texts intwenty pages. Chapter 5 develops new material on heavy taildiagnostics and gives more mathematical detail. Since variances andcovariances may not exist for heavy tailed joint distributions,Chapter 6 reviews dependence concepts for certain classes of heavytailed joint distributions, with a view to regressing heavy tailedvariables. Second, it presents a new measure of obesity. The most populardefinitions in terms of regular variation and subexponentialityinvoke putative properties that hold at infinity, and thiscomplicates any empirical estimate. Each definition captures somebut not all of the intuitions associated with tail heaviness.Chapter 5 studies two candidate indices of tail heaviness based onthe tendency of the mean excess plot to collapse as data areaggregated. The probability that the largest value is more thantwice the second largest has intuitive appeal but its estimator hasvery poor accuracy. The Obesity index is defined for a positiverandom variable X as: Ob(X) = P (X1 +X4 > X2 +X3X1 ≤ X2 ≤ X3 ≤X4), Xi independent copies of X. For empirical distributions, obesity is defined bybootstrapping. This index reasonably captures intuitions of tailheaviness. Among its properties, if α > 1 then Ob(X) Third and most important, we hope to convince the reader thatfat tail phenomena pose real problems; they are really out thereand they seriously challenge our usual ways of thinking abouthistorical averages, outliers, trends, regression coefficients andconfidence bounds among many other things. Data on flood insuranceclaims, crop loss claims, hospital discharge bills, precipitationand damages and fatalities from natural catastrophes drive thispoint home. While most fat tailed distributions are"bad", research in fat tails is one distribution whosetail will hopefully get fatter.

© 2014,Everyone thinks kids hate math. But the truth is, kids don't hate maththey hate worksheets! Writing down equations takes fine motor skills that young children haven' yet developed, making the process of learning math difficult and tedious. Math done mentally, or verbal math, makes math fun. Children see math problems as a game and a challenge. In the second edition of this pioneering educational bestseller, handwriting is removed from math problems to help children cement fundamental mathematical skills so that they may solve problems without having to do any writing at all. Developed as a supplement to traditional math education, the lesson is completely comprehensive, stepbystep, and leaves no area undone. The first book of the series introduces children to the basic concept of adding and subtracting, and works its way up to math problems involving numbers with double digits. The book is meant for children between the ages of 5 and 7.

© 2014,Everyone thinks kids hate math. But the truth is, kids don't hate maththey hate worksheets! Writing down equations takes fine motor skills that young children haven' yet developed, making the process of learning math difficult and tedious. Math done mentally, or verbal math, makes math fun. Children see math problems as a game and a challenge. In the second edition of this pioneering educational bestseller, handwriting is removed from math problems to help children cement fundamental mathematical skills so that they may solve problems without having to do any writing at all. Developed as a supplement to traditional math education, the lesson is completely comprehensive, stepbystep, and leaves no area undone. The second book of the series is meant for children between the ages of 7 and 8.

© 2014,Everyone thinks kids hate math. But the truth is, kids don't hate maththey hate worksheets! Writing down equations takes fine motor skills that young children haven' yet developed, making the process of learning math difficult and tedious. Math done mentally, or verbal math, makes math fun. Children see math problems as a game and a challenge. In the second edition of this pioneering educational bestseller, handwriting is removed from math problems to help children cement fundamental mathematical skills so that they may solve problems without having to do any writing at all. Developed as a supplement to traditional math education, the lesson is completely comprehensive, stepbystep, and leaves no area undone. The third book of the series is meant for children between the ages of 8 and 10.

© 2014,"A firstrate survey of the world of mathematics...Great reading for the intellectually curious," ( Kirkus Reviews ) from the bestselling author of Here's Looking at Euclid a dazzling new book that turns even the most complex math into a brilliantly entertaining read. From triangles, rotations, and power laws, to cones, curves, and the dreaded calculus, Alex Bellos takes you on a journey of mathematical discovery with his signature wit and limitless enthusiasm. He sifts through more than 30,000 survey submissions to uncover the world's favorite number and meets a mathematician who looks for universes in his garage. He attends the World Mathematical Congress in India and visits the engineer who designed the first rollercoaster loop. "Channeling the spirit of Martin Gardner...Bellos introduces fascinating characters, from the retired cab driver in Tucson whose hobby is factoring prime numbers, to swashbuckling astronomer Tycho Brahe, who lost his nose in a duel over a math formula. Through intriguing characters, lively prose, and thoroughly accessible mathematics, Bellos deftly shows readers why math is so important, and why it can be so much fun" ( Publishers Weekly , starred review). Get hooked on math as Bellos delves deep into humankind's turbulent relationship with numbers, revealing how they have shaped the world we live in.

© 2014,Initial training in pure and applied sciences tends to present problemsolving as the process of elaborating explicit closedform solutions from basic principles, and then using these solutions in numerical applications. This approach is only applicable to very limited classes of problems that are simple enough for such closedform solutions to exist. Unfortunately, most reallife problems are too complex to be amenable to this type of treatment. Numerical Methods  a Consumer Guide presents methods for dealing with them. Shifting the paradigm from formal calculus to numerical computation, the text makes it possible for the reader to ·nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp; discover how to escape the dictatorship of those particular cases that are simple enough to receive a closedform solution, and thus gain the ability to solve complex, reallife problems; ·nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp; understand the principles behind recognized algorithms used in stateoftheart numerical software; ·nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp; learn the advantages and limitations of these algorithms, nbsp;to facilitate the choice of which preexisting bricks to assemble for solving a given problem; and ·nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp;nbsp; acquire methods that allow a critical assessment of numerical results. nbsp; Numerical Methods  a Consumer Guide will be of interest to engineers and researchers who solve problems numerically with computers or supervise people doing so, and to students of both engineering and applied mathematics.

© 2014,It is hard to imagine a more original and insightful approach to classical mechanics. Most physicists would regard this as a wellworn and settled subject. But Mark Levi's treatment sparkles with freshness in the many examples he treats and his unexpected analogies, as well as the new approach he brings to the principles. This is inspired pedagogy at the highest level. Michael Berry, Bristol University, UK How do you write a textbook on classical mechanics that is fun to learn from? Mark Levi shows us the way with his new book: ``Classical Mechanics with Calculus of Variations and Optimal Control: An Intuitive Introduction.'' The combination of his unique point of view with his physical and geometrical insights and numerous instructive examples, figures and problem sets make it a pleasure to work through. Paul Rabinowitz, University of Wisconsin This is a refreshingly low key, downtoearth account of the basic ideas in EulerLagrange and HamiltonJacobi theory and of the basic mathematical tools that relate these two theories. By emphasizing the ideas involved and relegating to the margins complicated computations and messy formulas, he has written a textbook on an ostensibly graduate level subject that second and third year undergraduates will find tremendously inspiring. Victor Guillemin, MIT This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the ``tennis racket paradox''; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

© 2014,Galileo Galilei said he was "reading the book of nature" as he observed pendulums swinging, but he might also simply have tried to draw the numbers themselves as they fall into networks of permutations or form loops that synchronize at different speeds, or attach themselves to balls passing in and out of the hands of good jugglers. Numbers are, after all, a part of nature. As such, looking at and thinking about them is a way of understanding our relationship to nature. But when we do so in a technical, professional way, we tend to overlook their basic attributes, the things we can understand by simply "looking at numbers." Tom Johnson is a composer who uses logic and mathematical models, such as combinatorics of numbers, in his music. The patterns he finds while "looking at numbers" can also be explored in drawings. This book focuses on such drawings, their beauty and their mathematical meaning. The accompanying comments were written in collaboration with the mathematician Franck Jedrzejewski.

© 2014,Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a crosssection of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the massproduction automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone. This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe. Mathematics is one of mankind's oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.