Bøger udgivet af Springer New York

Why would anyone bid $3. 25 in an auction where the prize is a single dollar bill? Can one "e;game"e; explain the apparent irrationality behind both the arms race of the 1980s and the libretto of Puccini's opera Tosca? How can one calculation suggest the president has 4 percent of the power in the United States federal system while another s- gests that he or she controls 77 percent? Is democracy (in the sense of re?ecting the will of the people) impossible? Questionslikethesequitesurprisinglyprovideaveryniceforumfor some fundamental mathematical activities: symbolic representation and manipulation, model-theoretic analysis, quantitative represen- tionandcalculation,anddeductionasembodiedinthepresentationof mathematical proof as convincing argument. We believe that an ex- sure to aspects of mathematics such as these should be an integral part of a liberal arts education. Our hope is that this book will serve as a text for freshman-sophomore level courses, aimed primarily at students in the humanities and social sciences, that will provide this sort of exposure. A number of colleges and universities already have interdisciplinary freshman seminars where this could take place. Most mathematics texts for nonscience majors try to show that mathematics can be applied to many different disciplines. A student's viii PREFACE interest in a particular application, however, often depends on his or hergeneralinterestintheareainwhichtheapplicationistakingplace. Our experience at Union College and Williams College has been that there is a real advantage in having students enter the course knowing that virtually all the applications will focus on a single discipline-in this case, political science.

A book on any mathematical subject above textbook level is not of much value unless it contains new ideas and new perspectives. Also, the author may be encouraged to include new results, provided that they help the reader gain newinsightsandarepresentedalongwithknownoldresultsinaclearexposition. Itis with this philosophy that Iwrite this volume. The two subjects, Dirichlet series and modular forms, are traditional, but I treat them in both orthodox and unorthodox ways. However, I try to make the book accessible to those who are not familiar with such topics, by including plenty of expository material. More speci?c descriptions of the contents will be given in the Introduction. To some extent, this book has a supplementary nature to my previous book Introduction to the Arithmetic Theory of Automorphic Functions, published by Princeton University Press in 1971, though I do not write the present book with that intent. While the 1971 book grew out of my lectures in various places, the essential points of this new book have never been presented publicly or privately. I hope that it will draw an audience as large as that of the previous book.

Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions.With 116 examples, 54 figures, and 167 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. The revised second edition includes new sections on extreme value copulas, tail dependence, and quasi-copulas.

Can be used as a graduate textContains many exercisesContains new results

This book is intended to complement my Elements oi Algebra, and it is similarly motivated by the problem of solving polynomial equations. However, it is independent of the algebra book, and probably easier. In Elements oi Algebra we sought solution by radicals, and this led to the concepts of fields and groups and their fusion in the celebrated theory of Galois. In the present book we seek integer solutions, and this leads to the concepts of rings and ideals which merge in the equally celebrated theory of ideals due to Kummer and Dedekind. Solving equations in integers is the central problem of number theory, so this book is truly a number theory book, with most of the results found in standard number theory courses. However, numbers are best understood through their algebraic structure, and the necessary algebraic concepts- rings and ideals-have no better motivation than number theory. The first nontrivial examples of rings appear in the number theory of Euler and Gauss. The concept of ideal-today as routine in ring the- ory as the concept of normal subgroup is in group theory-also emerged from number theory, and in quite heroic fashion. Faced with failure of unique prime factorization in the arithmetic of certain generalized "e;inte- gers"e; , Kummer created in the 1840s a new kind of number to overcome the difficulty. He called them "e;ideal numbers"e; because he did not know exactly what they were, though he knew how they behaved.

This series is directed to healthcare professionals who are leading the tra- formation of health care by using information and knowledge. Launched in 1988 as Computers in Health Care, the series offers a broad range of titles: some addressed to specific professions such as nursing, medicine, and health administration; others to special areas of practice such as trauma and radiology. Still other books in the series focus on interdisciplinary issues, such as the computer-based patient record, electronic health records, and networked healthcare systems. Renamed Health Informatics in 1998 to reflect the rapid evolution in the discipline now known as health informatics, the series will continue to add titles that contribute to the evolution of the field. In the series, eminent experts, serving as editors or authors, offer their accounts of innovations in health informatics. Increasingly, these accounts go beyond hardware and software to address the role of information in influencing the transformation of healthcare delivery systems around the world. The series also incre- ingly focuses on "e;peopleware"e; and the organizational, behavioral, and so- etal changes that accompany the diffusion of information technology in health services environments.

Pell's equation is an important topic of algebraic number theory that involves quadratic forms and the structure of rings of integers in algebraic number fields. The history of this equation is long and circuitous, and involved a number of different approaches before a definitive theory was found. There were partial patterns and quite effective methods of finding solutions, but a complete theory did not emerge until the end of the eighteenth century. The topic is motivated and developed through sections of exercises which allow the student to recreate known theory and provide a focus for their algebraic practice. There are also several explorations that encourage the reader to embark on their own research. Some of these are numerical and often require the use of a calculator or computer. Others introduce relevant theory that can be followed up on elsewhere, or suggest problems that the reader may wish to pursue. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject. Edward Barbeau is Professor of Mathematics at the University of Toronto. He has published a number of books directed to students of mathematics and their teachers, including Polynomials (Springer 1989), Power Play (MAA 1997), Fallacies, Flaws and Flimflam (MAA 1999) and After Math (Wall & Emerson, Toronto 1995).

On several occasions I and colleagues have found ourselves teaching a o- semester course for students at the second year of graduate study in ma- ematics who want to gain a general perspective on Jordan algebras, their structure, and their role in mathematics, or want to gain direct experience with nonassociative algebra. These students typically have a solid grounding in ?rst¿year graduate algebra and the Artin¿Wedderburn theory of assoc- tive algebras, and a few have been introduced to Lie algebras (perhaps even Cayley algebras, in an o?hand way), but otherwise they have not seen any nonassociative algebras. Most of them will not go on to do research in non- sociative algebra, so the course is not primarily meant to be a training or breeding ground for research, though the instructor often hopes that one or two will be motivated to pursue the subject further. This text is meant to serve as an accompaniment to such a course. It is designed ?rst and foremost to be read by students on their own without assistance by a teacher. It is a direct mathematical conversation between the author and a reader whose mind (as far as nonassociative algebra goes) is a tabula rasa. In keeping with the tone of a private conversation, I give more heuristicandexplanatorycommentthanisusualingraduatetextsatthislevel (pep talks, philosophical pronouncements on the proper way to think about certain concepts, historical anecdotes, mention of some mathematicians who have contributed to our understanding of Jordan algebras, etc.

The subject of local dynamical systems is concerned with the following two questions: 1. Given an nn matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di?erential equations having a rest point at the origin with linear part Ax, that is, all systems of the form x ? = Ax+*** , n where x? R and the dots denote terms of quadratic and higher order. 2. Describethebehavior(neartheorigin)ofallsystemsclosetoasystem of the type just described. To answer these questions, the following steps are employed: 1. A normal form is obtained for the general system with linear part Ax. The normal form is intended to be the simplest form into which any system of the intended type can be transformed by changing the coordinates in a prescribed manner. 2. An unfolding of the normal form is obtained. This is intended to be the simplest form into which all systems close to the original s- tem can be transformed. It will contain parameters, called unfolding parameters, that are not present in the normal form found in step 1. vi Preface 3. The normal form, or its unfolding, is truncated at some degree k, and the behavior of the truncated system is studied.

One cannot build or understand a modern operating system unless one knows the principles of concurrent programming. This volume is a collection of 19 original papers on the invention and origins of concurrent programming, illustrating the major breakthroughs in the field from the mid 1960s to the late 1970s. All of them are written by the pioneers in concurrent programming, including Brinch Hansen himself, and have introductions added that summarize the papers and put them in perspective. This anthology is an essential reference for professional programmers, researchers, and students of electrical engineering and computer science. A familiarity with operating system principles is assumed.

Overview The motivation of this text lies in what we believe is the inadequacy of current frameworks to reason about the ?ow of data in imperative programs. This inadequacy clearly shows up when dealing with the individual side effects of loop iterations. - deed, we face a paradoxical situation where, on the one hand, a typical program spends most of its execution time iterating or recursing on a few lines of codes, and, on the other hand, current optimization frameworks are clumsy when trying to capture the effects of each incarnation of these few lines-frameworks we inherited from designs made decades ago. The reasons are manyfold, but one of them stands out: The same concepts have been used, on the one hand, to represent and manipulate programs internally in compilers and, on the other hand, to allow us humans to reason about optimizations. Unfortunately, these two uses have different aims and constraints. An example of such a situation is given by control-?ow graphs of basic blocks, which have been - tremely useful in practice as an internal representation of programs, but which are not always adequate or convenient to formally think about programs and specify their transformations. In some cases, de?nitions based on control-?ow graphs can be overly restrictive. Dominance, studied in Chapter 4, is a good example.

Respiratory cytopathology is indispensable in the workup of patients suspected of having lung cancer requiring cytologic evaluation and is used increasingly in immunocompromised patients for the identification of infectious diseases. Currently, there is no single text devoted exclusively to Pulmonary Cytology. Color Atlas of Pulmonary Cytopathology is the only text to include, under one cover, up-to-date information on every aspect of Respiratory Cytopathology. The atlas includes techniques of bronchoscopy, brochoalveolar lavage, and fine needle aspiration biopsy, a detailed section on cytopreparatory techniques, liberal use of images on histomorphology to complement cytology, emphasis on diagnostic pitfalls, a detailed section on cytopathology of non-neoplastic conditions, unusual and uncommon lesions, cytology of metastatic lung cancers to other body sites, and a section on pediatric pulmonary cytology. Abundantly illustrated with over 1300 color images on 108 plates, the atlas presents not only the usual cytohistologic patterns of various disease entities, but also focuses on differential diagnostic problems and depicts the differentiating features. Over 75 tables summarize cytologic criteria and differentiating features. A must-have reference for cytotechnology students, cytotechnologists, pathologists, pathology residents, cytopathologists, as well as pulmonologists.