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This treatment of extreme value theory is unique in book literature in that it focuses on some beautiful theoretical results along with applications. All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion so that in the final chapter even the most recent developments in the theory can be understood.Key to the presentation is the concentration on the probabilistic and statistical aspects of extreme values without major emphasis on such related topics as regular variation, point processes, empirical distribution functions, and Brownian motion.The work is an excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity.

This book introduces the theory of modular forms with an eye toward the Modularity Theorem:All rational elliptic curves arise from modular forms. The topics covered include¿ elliptic curves as complex tori and as algebraic curves,¿ modular curves as Riemann surfaces and as algebraic curves, ¿ Hecke operators and Atkin¿Lehner theory, ¿ Hecke eigenforms and their arithmetic properties, ¿ the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms, ¿ elliptic and modular curves modulo p and the Eichler¿Shimura Relation, ¿ the Galois representations associated to elliptic curves and to Hecke eigenforms.As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory.A First Course in Modular Forms is written for beginning graduate students and advanced undergraduates. It does not require background in algebraic number theory or algebraic geometry, and it contains exercises throughout.Fred Diamond received his Ph.D from Princeton University in 1988 under the direction of Andrew Wiles and now teaches at King's College London. Jerry Shurman received his Ph.D from Princeton University in 1988 under the direction of Goro Shimura and now teaches at Reed College.

Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems. Precise estimates and excursions into the theoretical background makes this workbook valuable to both the applied sciences and mathematics fields. As a bonus in its last chapter the book includes a collection of rare and useful pieces of literature, such as the summary of the Perturbation theory of Matrices.Detailed illustrations, stimulating examples and exercises as well as a clear explanation of the underlying theory makes this workbook ideal for senior undergraduate and beginning graduate students in applied mathematics as well as science and engineering fields.

Statistical Physics bridges the properties of a macroscopic system and the microscopic behavior of its constituting particles, otherwise impossible due to the giant magnitude of Avogadro's number. Numerous systems of today's key technologies - such as semiconductors or lasers - are macroscopic quantum objects; only statistical physics allows for understanding their fundamentals. Therefore, this graduate text also focuses on particular applications such as the properties of electrons in solids with applications, and radiation thermodynamics and the greenhouse effect.

This book is the first serious attempt to gather all of the available theory of  "e;nonharmonic Fourier series"e; in one place, combining published results with new results by the authors. 

The indications and use of shoulder arthroplasty has dramatically increased over the last decade, and this trend will continue in the future. The average age of our population is increasing, yet there is a strong desire to remain active and viable. The majority of people will not accept limitation of a joint function that compromises their life styles if a reasonable surgical solution is available. Our knowledge of disease processes has broadened and improved our understanding about how best to manage these problem's cli- cally. Technology and innovation have provided us with options that were not possible before. However, a successful shoulder arthroplasty depends not only on knowledge and modern technology but also on sound clinical judgment, accurate surgical technique, and appropriate postoperative rehabilitation. This book provides a comprehensive approach to dealing with the most common indications for shoulder arthroplasty. In addition, it p- vides insight into some of the more complex problems. Detailed inf- mation concerning preoperative evaluation, approaches, technology, surgical technique, and postoperative therapy will allow the surgeon to make decisions that will help his patient remain active. We thank the contributing authors for their work and commitment to this project. We appreciate the time they took from their practices and more importantly their families to complete this volume and provide an extraordinary text.

Evolutionary Computation for Optimization and Modeling is an introduction to evolutionary computation, a field which includes genetic algorithms, evolutionary programming, evolution strategies, and genetic programming. The text is a survey of some application of evolutionary algorithms. It introduces mutation, crossover, design issues of selection and replacement methods, the issue of populations size, and the question of design of the fitness function. It also includes a methodological material on efficient implementation. Some of the other topics in this book include the design of simple evolutionary algorithms, applications to several types of optimization, evolutionary robotics, simple evolutionary neural computation, and several types of automatic programming including genetic programming. The book gives applications to biology and bioinformatics and introduces a number of tools that can be used in biological modeling, including evolutionary game theory. Advanced techniques such as cellular encoding, grammar based encoding, and graph based evolutionary algorithms are also covered. This book presents a large number of homework problems, projects, and experiments, with a goal of illustrating single aspects of evolutionary computation and comparing different methods. Its readership is intended for an undergraduate or first-year graduate course in evolutionary computation for computer science, engineering, or other computational science students. Engineering, computer science, and applied math students will find this book a useful guide to using evolutionary algorithms as a problem solving tool.

The book is the first English translation of John Wallis's Arithmetica Infinitorum (1656), a key text on the seventeenth-century development of the calculus. Accompanied with annotations and an introductory essay, the translation makes Wallis's work fully available for the first time to modern readers. It shows how Wallis drew on some of the most important new ideas from the preceding twenty years, and took them forward to lay the foundations on which Newton was to build. Above all, the book displays the crucial mid-seventeenth-century shift from geometry to arithmetic and algebra as the primary language of mathematics.

This text is an elementary introduction to differential geometry. Although it was written for a graduate-level audience, the only requisite is a solid back- ground in calculus, linear algebra, and basic point-set topology. The first chapter covers the fundamentals of differentiable manifolds that are the bread and butter of differential geometry. All the usual topics are cov- ered, culminating in Stokes' theorem together with some applications. The stu- dents' first contact with the subject can be overwhelming because of the wealth of abstract definitions involved, so examples have been stressed throughout. One concept, for instance, that students often find confusing is the definition of tangent vectors. They are first told that these are derivations on certain equiv- alence classes of functions, but later that the tangent space of ffi.n is "e;the same"e; n as ffi. . We have tried to keep these spaces separate and to carefully explain how a vector space E is canonically isomorphic to its tangent space at a point. This subtle distinction becomes essential when later discussing the vertical bundle of a given vector bundle.

I had great pleasure in reading Philippe Refregier's book on the theory of noise and its applications in physics. The main aim of the book is to present the basic ideas used to characterize these unwanted random signals that obscure information content. To this end, the author devotes a sigificant part of his book to a detailed study of the probabilistic foundations of fluctuation theory. Following a concise and accurate account of the basics of probability the- ory, the author includes a detailed study of stochastic processes, emphasizing the idea of the correlation function, which plays a key role in many areas of physics. Physicists often assume that the noise perturbing a signal is Gaussian. This hypothesis is justified if one can consider that the noise results from the superposition of a great many independent random perturbations. It is this fact that brings the author to discuss the theory underlying the addition of random variables, accompanied by a wide range of illustrative examples. Since noise affects information, the author is naturally led to consider Shannon's information theory, which in turn brings him to the altogether fundamental idea of entropy. This chapter is completed with a study of com- plexity according to Kolmogorov. This idea is not commonly discussed in physics and the reader will certainly appreciate the clear presentation within these pages.

TheclassicaltheoryofFourierseriesandintegrals,aswellasLaplacetra- forms, is of great importance for physical and technical applications, and its mathematical beauty makes it an interesting study for pure mathema- cians as well. I have taught courses on these subjects for decades to civil engineeringstudents,andalsomathematicsmajors,andthepresentvolume can be regarded as my collected experiences from this work. There is, of course, an unsurpassable book on Fourier analysis, the tr- tise by Katznelson from 1970. That book is, however, aimed at mathem- ically very mature students and can hardly be used in engineering courses. Ontheotherendofthescale,thereareanumberofmore-or-lesscookbo- styled books, where the emphasis is almost entirely on applications. I have felt the need for an alternative in between these extremes: a text for the ambitious and interested student, who on the other hand does not aspire to become an expert in the ?eld. There do exist a few texts that ful?ll these requirements (see the literature list at the end of the book), but they do not include all the topics I like to cover in my courses, such as Laplace transforms and the simplest facts about distributions.

Categorical data arise often in many fields, including biometrics, economics, management, manufacturing, marketing, psychology, and sociology. This book provides an introduction to the analysis of such data. The coverage is broad, using the loglinear Poisson regression model and logistic binomial regression models as the primary engines for methodology. Topics covered include count regression models, such as Poisson, negative binomial, zero-inflated, and zero-truncated models; loglinear models for two-dimensional and multidimensional contingency tables, including for square tables and tables with ordered categories; and regression models for two-category (binary) and multiple-category target variables, such as logistic and proportional odds models.All methods are illustrated with analyses of real data examples, many from recent subject area journal articles. These analyses are highlighted in the text, and are more detailed than is typical, providing discussion of the context and background of the problem, model checking, and scientific implications. More than 200 exercises are provided, many also based on recent subject area literature. Data sets and computer code are available at a web site devoted to the text. Adopters of this book may request a solutions manual from: textbooks@springer-ny.com. Jeffrey S. Simonoff is Professor of Statistics at New York University. He is author of Smoothing Methods in Statistics and coauthor of A Casebook for a First Course in Statistics and Data Analysis, as well as numerous articles in scholarly journals. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute.

As I glance out my window in the early morning, I can see beads of droplets gracing a spider web. The film of dew that has settled on the threads is unstable and breaks up spontaneously into droplets. This phenomenon has implications for the treatment of textile fibers (the process known as "e;oiling"e;), glass, and carbon. It is no less important when applying mascara! I take my morning shower. The moment I step out, I dry off by way of evaporation (which makes me feel cold) and by dewetting (the process by which dry areas form spontaneously and expand on my skin). As I rush into my car under a pelting rain, my attention is caught by small drops stuck on my windshield. I also notice larger drops rolling down and others larger still that, like snails, leave behind them a trail of water. I ask myself what the difference is between these rolling drops and grains of sand tumbling down an incline. I wonder why the smallest drops remain stuck. The answers to such questions do help car manufacturers treat the surface of glass and adjust the tilt of windshields.

I ?nd it impossible to write a preface to this work, without discovering a little of the enthusiasm which I have contracted from an attention to it. Joseph Priestley. The History and Present State of Electricity. It is generally considered bad form in writing, unless on matters autob- graphic,tomakeunbridleduseoftheperpendicularpronoun. Thereaderof the present book, however, may well wonder why one would want to study 1 the life and works of Thomas Bayes, 'this strangely neglected topic' , and it is only by a reluctant use of the ?rst person singular on the part of the author that this legitimate question can be answered. It was in the late 1960s that my interest in various aspects of subjective probability was awakened by some of the papers of I. J. ('Jack') Good, and this was followed by the reading of works such as Harold Je?reys's Theory of Probability. In many of these the (apparently simple) result known as Bayes's Theorem played a pivotal rE ole, and it struck me that it might be interesting to ?nd out a bit more about Thomas Bayes himself. In trying to satisfy this curiosity in spasmodic periods over many years I discovered that little information seemed to be available. Writings by John D.

Sample data alone never suffice to draw conclusions about populations. Inference always requires assumptions about the population and sampling process. Statistical theory has revealed much about how strength of assumptions affects the precision of point estimates, but has had much less to say about how it affects the identification of population parameters. Indeed, it has been commonplace to think of identification as a binary event - a parameter is either identified or not - and to view point identification as a pre-condition for inference. Yet there is enormous scope for fruitful inference using data and assumptions that partially identify population parameters. This book explains why and shows how. The book presents in a rigorous and thorough manner the main elements of Charles Manski's research on partial identification of probability distributions. One focus is prediction with missing outcome or covariate data. Another is decomposition of finite mixtures, with application to the analysis of contaminated sampling and ecological inference. A third major focus is the analysis of treatment response. Whatever the particular subject under study, the presentation follows a common path. The author first specifies the sampling process generating the available data and asks what may be learned about population parameters using the empirical evidence alone. He then ask how the (typically) setvalued identification regions for these parameters shrink if various assumptions are imposed. The approach to inference that runs throughout the book is deliberately conservative and thoroughly nonparametric. Conservative nonparametric analysis enables researchers to learn from the available data without imposing untenable assumptions. It enables establishment of a domain of consensus among researchers who may hold disparate beliefs about what assumptions are appropriate. Charles F. Manski is Board of Trustees Professor at Northwestern University. He is author of Identification Problems in the Social Sciences and Analog Estimation Methods in Econometrics. He is a Fellow of the American Academy of Arts and Sciences, the American Association for the Advancement of Science, and the Econometric Society.

Je tiens impossible de connaitre les parties sans connaitre le tout, non plus que de connaitre le tout sans connaitre particulierement les parties -Pascal The eterna[ mystery of the world is its comprehensibility -Einstein This book deals with the application of mathematical tools to the study of physiological systems. It is directed toward an audience of physiologists, physicians, physicists, kinesiologists, psychologists, engineers, mathemati- cians, and others interested in finding out more about the complexities and subtleties of rhythmic physiological processes from a theoretical per- spective. We have attempted to give a broad view of the underlying notions behind the dynamics of physiological rhythms, sometimes from a theoretical perspective and sometimes from the perspective of the experimentalist. This book can be used in a variety of ways, ranging from a more tra- ditional approach such as a textbook in a biomathematics course (at either the advanced undergraduate or graduate level) to a research re- source in which someone interested in a particular problem might look at the corresponding discussion here to guide their own thinking. We hope that researchers at all levels will find inspiration from the way we have dealt with particular research problems to tackle completely new areas of investigation, or even approach these in totally new ways.