Bücher veröffentlicht von Springer New York

This book documents the history of pi from the dawn of mathematical time to the present. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet accessible, mathematics. The articles on pi collected herein include selections from the mathematical and computational literature over four millennia, a variety of historical studies on the cultural significance of the number, and an assortment of anecdotal, fanciful, and simply amusing pieces.For this new edition, the authors have updated the original material while adding new material of historical and cultural interest. There is a substantial exposition of the recent history of the computation of digits of pi, a discussion of the normality of the distribution of the digits, new translations of works by Viete and Huygen, as well as Kaplansky's never-before-published "Song of Pi."From the reviews of earlier editions:"Few mathematics books serve a wider potential readership than does a source book and this particular one is admirably designed to cater for a broad spectrum of tastes: professional mathematicians with research interest in related subjects, historians of mathematics, teachers at all levels searching out material for individual talks and student projects, and amateurs who will find much to amuse and inform them in this leafy tome. The authors are to be congratulated on their good taste in preparing such a rich and varied banquet with which to celebrate pi."- Roger Webster for the Bulletin of the LMS"The judicious representative selection makes this a useful addition to one's library as a reference book, an enjoyable survey of developments and a source of elegant and deep mathematics of different eras."- Ed Barbeau for MathSciNet"Full of useful formulas and ideas, it is a vast source of inspiration to any mathematician, A level and upwards-a necessity in any maths library."- New Scientist

The aim of this book is to provide a concise treatment of some topics from group theory and representation theory for a one term course. It focuses on the non-commutative side of the field emphasizing the general linear group as the most important group and example. The book will enable graduate students from every mathematical field, as well as strong undergraduates with an interest in algebra, to solidify their knowledge of group theory. The reader should have a familiarity with groups, rings, and fields, along with a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to expose the reader to additional topics.

...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had expressed so forcefully. This was combined with the elegance and understanding with which Artin had lectured...Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach spaces to topological group theory...It is, in my view, the most influential text in algebra of the twentieth century.- Saunders MacLane, Notices of the AMSHow exciting it must have been to hear Emil Artin and Emmy Noether lecture on algebra in the 1920's, when the axiomatic approach to the subject was amazing and new! Van der Waerden was there, and produced from his notes the classic textbook of the field. To Artin's clarity and Noether's originality he added his extraordinary gift for synthesis. At one time every would-be algebraist had to study this text. Even today, all who work in Algebra owe a tremendous debt to it; they learned from it by second or third hand, if not directly. It is still a first-rate (some would say, the best) source for the great range of material it contains.- David Eisenbud, Mathematical Sciences Research InstituteVan der Waerden's book Moderne Algebra, first published in 1930, set the standard for the unified approach to algebraic structures in the twentieth century. It is a classic, still worth reading today.- Robin Hartshorne, University of California, Berkeley

Based on courses given at the Ecole Polytechnique in France, this book covers not only the fundamental physics of semiconductors, but also discusses the operation of electronic and optical devices based on semiconductors. It is aimed at students with a good background in mathematics and physics, and is equally suited for graduate-level courses in condensed-matter physics as for self-study by engineers interested in a basic understanding of semiconductor devices.

The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 "explorations" invite the reader to investigate research problems and related topics.

Discrete mathematics is quickly becoming one of the most important areas of mathematical research, with applications to cryptography, linear programming, coding theory and the theory of computing. This book is aimed at undergraduate mathematics and computer science students interested in developing a feeling for what mathematics is all about, where mathematics can be helpful, and what kinds of questions mathematicians work on. The authors discuss a number of selected results and methods of discrete mathematics, mostly from the areas of combinatorics and graph theory, with a little number theory, probability, and combinatorial geometry. Wherever possible, the authors use proofs and problem solving to help students understand the solutions to problems. In addition, there are numerous examples, figures and exercises spread throughout the book.Lszl Lovsz is a Senior Researcher in the Theory Group at Microsoft Corporation. He is a recipient of the 1999 Wolf Prize and the Gdel Prize for the top paper in Computer Science. Jzsef Pelikn is Professor of Mathematics in the Department of Algebra and Number Theory at Etvs Lornd University, Hungary. In 2002, he was elected Chairman of the Advisory Board of the International Mathematical Olympiad. Katalin Vesztergombi is Senior Lecturer in the Department of Mathematics at the University of Washington.

Over the last 30 years graph theory has evolved into an important math­ ematical tool in the solution of a wide variety of problems in many areas of society. The purpose of this book is to present selected topics from this theory that have been found useful and to point out various applications. Some important theoretical topics have been omitted as they are not es­ sential for the applications in Part II. Hence Part I should not be seen as a well-rounded treatise on the theory of graphs. Some effort has been made to present new applications that do not use merely the notation and ter­ minology of graphs but do actually implement some mathematical results from graph theory. It has been written for final undergraduate year or first year graduate students in engineering, mathematics, computer science, and operations research, as well as researchers and practitioners with an inter­ est in graph theoretic modelling. Suggested plans for the reading of the book by people with these interests are given later. The book comprises two parts. The first is a brief introduction to the mathematical theory of graphs. The second is a discussion on the applications of this material to some areas in the subjects previously mentioned. It is, of course, possi­ ble to read only the first part to attempt to gain an appreciation of the mathematical aspects of graph theory. However even the purest of mathe­ maticians is strongly recommended to delve seriously into the second part.

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.

Biology undergraduates, medical students and life-science graduate students often have limited mathematical skills. Similarly, physics, math and engineering students have little patience for the detailed facts that make up much of biological knowledge. Teaching computational neuroscience as an integrated discipline requires that both groups be brought forward onto common ground. This book does this by making ancillary material available in an appendix and providing basic explanations without becoming bogged down in unnecessary details. The book will be suitable for undergraduates and beginning graduate students taking a computational neuroscience course and also to anyone with an interest in the uses of the computer in modeling the nervous system.

Arguably the most intricate dynamic object in the universe, the human brain is an unsounded source of wonder for the scienti?c community. The primary aim of this book is to provide both students and established - vestigators in the growing area of neuroscience with an appreciation of the roles that mathematics may play in helping to understand this en- maticorgan. Alongwithdiscussionsofresultsobtainedbytheneuroscience community, emphasis is placed on suggesting fruitful research problems for those planning to embark on mathematical studies in neuroscience. To make the overall perspectives understandable to philosophers and psychologists, essential features of the discussions are presented in ordinary English, with more detailed mathematical comments in appendices and footnotes. Although it attempts to maintain both clarity and biological relevance, this is not a text on the anatomy of nerve systems; thus readers should bring some knowledge of neurophysiology through other courses, associated studies, or laboratory research. It is a guiding theme throughout the book that the brain is organized into several quite di?erent levels of dynamic activity. As will be seen, these levels are hierarchically structured, beginning with the molecular dynamics ofintrinsicmembraneproteinsandproceedingupward,throughtheswit- ing properties of active membrane patches and synapses, the emergence of impulses on active ?bers, overall properties of individual neurons, and the growth of functional assemblies of interacting neurons, to the global - namics of a brain. At each level of description, reality turns di?erent facets of her mystery to us, and diverse phenomena make their contributions to the brain's collective behavior.

This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces.

Agriculture is more than farming. It is a highly spe­ The entire system is increasingly consumer cialized, internationally industrialized, and produc­ driven, with market power shifting to the retail tive food and fiber system. Its many components outlets as they respond to consumer preferences have an interdependent future, the sum total of rather than to urgings from food manufacturers. which is the industry's future. The production sector is still primarily a response mechanism adjusting cost structures where pos­ The complexity of agriculture extends through­ sible in line with "given" market prices. Keys to out the economy, making it increasingly vulnerable profit and survivability throughout the system lie in to political, social, and institutional forces. Al­ product/service differentiation, superior manage­ though one can summarize the future of agriculture ment (finance in particlar), use of relevant technol­ more than is done here, to do so would lose the ogies, and effective communication of all kinds.

Ecosystem management requires a planning and decision-making process that places land use in its appropriate ecological context. Because ecological assessments must be conducted at various spatial scales and across jurisdictional boundaries, approaches to assessment must be compatible and consistent with each other. A Guidebook for Integrated Ecological Assessment analyzes methods and provides standards and protocols for assessment and the integration of data.

Statistical performance evaluation has assumed an increasing amount of importance as we seek to design more and more sophisticated communication and information processing systems. The ability to predict a proposed system's per- formance before one constructs it is an extremely cost effective design tool. This book is meant to be a first-year graduate level introduction to the field of statistical performance evaluation. It is intended for people who work with sta- tistical performance evaluation including engineers, computer scientists and applied mathematicians. As such, it covers continuous time queueing theory (chapters 1-4), stochastic Petri networks (chapter 5), discrete time queueing theory (chapter 6) and recent network traffic modeling work (chapter 7). There is a short appendix at the end of the book that reviews basic probability theory. This material can be taught as a complete semester long course in performance evalua- tion or queueing theory. Alternatively, one may teach only chapters 2 and 6 in the first half of an introductory computer networking course, as is done at Stony Brook. The second half of the course could use a more protocol oriented text such as ones by Saadawi [SAAD] or Stallings [STALl What is new in the third edition of this book? In addition to the well received material of the second edition, this edition has three major new features.

Grothendieck¿s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.