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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.

I have endeavored to provide a comprehensive introduction to a wide - riety of statistical methods for the analysis of repeated measurements. I envision this book primarily as a textbook, because the notes on which it is based have been used in a semester-length graduate course I have taught since1991.Thiscourseisprimarilytakenbygraduatestudentsinbiostat- tics and statistics, although students and faculty from other departments have audited the course. I also anticipate that the book will be a useful r- erence for practicing statisticians. This assessment is based on the positive responses I have received to numerous short courses I have taught on this topic to academic and industry groups. Althoughmyintentistoprovideareasonablycomprehensiveoverviewof methodsfortheanalysisofrepeatedmeasurements,Idonotviewthisbook as a de?nitive "e;state of the art"e; compendium of research in this area. Some general approaches are extremely active areas of current research, and it is not feasible, given the goals of this book, to include a comprehensive summary and list of references. Instead, my focus is primarily on methods that are implemented in standard statistical software packages. As a result, thelevelofdetailonsometopicsislessthaninotherbooks,andsomemore recent methods of analysis are not included. One particular example is the topic of nonlinear mixed models for the analysis of repeated measurements (Davidian and Giltinan, 1995; Vonesh and Chinchilli, 1996). With respect to some of the more recent methods of analysis, I do attempt to mention some of the areas of current research.

The second half of the twentieth century saw an astonishing increase in computing power; today computers are unbelievably faster than they used to be, they have more memory, they can communicate routinely with remote machines all over the world - and they can fit on a desktop. But, despite this remarkable progress, the voracity of modem applications and user expectations still pushes technology right to the limit. As hardware engineers build ever-more-powerful machines, so too must software become more sophisticated to keep up. Medium- to large-scale programming projects need teams of people to pull everything together in an acceptable timescale. The question of how pro gram- mers understand their own tasks, and how they fit together with those of their colleagues to achieve the overall goal, is a major concern. Without that under- standing it would be practically impossible to realise the commercial potential of our present-day computing hardware. That programming has been able to keep pace with the formidable advances in hardware is due to the similarly formidable advances in the principles for design, construction and organisation of programs. The efficacy of these methods and principles speaks for itself - computer technology is all-pervasive - but even more telling is that they are beginning to feed back and inftuence hardware design as weIl. The study of such methods is called programming methodology, whose topics range over system-and domain-modelling, concurrency, object orientation, program specification and validation. That is the theme of this collection.

The following lecture notes correspond to a course taught for several years, first at the University of Paris-Nord (France) and then at the University of Bologna (Italy). They are mainly addressed to nonspecialists in the subject, and their purpose is to present in a pedagogical way most of the techniques used in the microlocal treatment of semiclassical problems coming from quantum physics. Both the standard Coo pseudodifferential calculus and the analytic microlocal analysis are developed, in a context that remains intentionally global so that only the relevant difficulties of the theory are encountered. The main original­ ity lies in the fact that we derive all the main features of analytic microlocal analysis from a single a priori estimate, which turns out to be elementary once the Coo pseudodifferential calculus is established. Various detailed exercises are given at the end of the main chapters, most of them being easily solvable by students. Besides illustrating the main results of the lecture, their aim is also to introduce the reader to various further developments of the theory, such as the functional calculus of pseudodifferential operators, properties of the analytic wave front set, Gevrey classes, the use of coherent states, the notion of semiclassical measures, WKB constructions. Applications to the study of the Schrodinger operator are also discussed in the text, so that they may help the understanding of new notions or general results where they appear by replacing them in the context of quantum mechanics.

This book is intended to provide a mathematical bridge from a general physics course to intermediate-level courses in classical mechanics, electricity and mag- netism, and quantum mechanics. The book begins with a short review of a few topics that should be familiar to the student from a general physics course. These examples will be used throughout the rest of the book to provide physical con- texts for introducing the mathematical applications. The next two chapters are devoted to making the student familiar with vector operations in algebra and cal- culus. Students will have already become acquainted with vectors in the general physics course. The notion of magnetic flux provides a physical connection with the integral theorems of vector calculus. A very short chapter on complex num- bers is sufficient to supply the needed background for the minor role played by complex numbers in the remainder of the text. Mathematical applications in in- termediate and advanced undergraduate courses in physics are often in the form of ordinary or partial differential equations. Ordinary differential equations are introduced in Chapter 5. The ubiquitous simple harmonic oscillator is used to il- lustrate the series method of solving an ordinary, linear, second-order differential equation. The one-dimensional, time-dependent SchrOdinger equation provides an illus- tration for solving a partial differential equation by the method of separation of variables in Chapter 6.

This book provides a theoretical background of branching processes and discusses their biological applications. Branching processes are a well-developed and powerful set of tools in the field of applied probability. The range of applications considered includes molecular biology, cellular biology, human evolution and medicine. The branching processes discussed include Galton-Watson, Markov, Bellman-Harris, Multitype, and General Processes. As an aid to understanding specific examples, two introductory chapters, and two glossaries are included that provide background material in mathematics and in biology. The book will be of interest to scientists who work in quantitative modeling of biological systems, particularly probabilists, mathematical biologists, biostatisticians, cell biologists, molecular biologists, and bioinformaticians. The authors are a mathematician and cell biologist who have collaborated for more than a decade in the field of branching processes in biology for this new edition.This second expanded edition adds new material published during the last decade, with nearly 200 new references. More material has been added on infinitely-dimensional multitype processes, including the infinitely-dimensional linear-fractional case. Hypergeometric function treatment of the special case of the Griffiths-Pakes infinite allele branching process has also been added. There are additional applications of recent molecular processes and connections with systems biology are explored, and a new chapter on genealogies of branching processes and their applications.Reviews of First Edition:"e;This is a significant book on applications of branching processes in biology, and it is highly recommended for those readers who are interested in the application and development of stochastic models, particularly those with interests in cellular and molecular biology."e; (Siam Review, Vol. 45 (2), 2003)"e;This book will be very interesting and useful for mathematicians, statisticians and biologists as well, and especially for researchers developing mathematical methods in biology, medicine and other natural sciences."e; (Short Book Reviews of the ISI, Vol. 23 (2), 2003)

Elementary number theory is concerned with the arithmetic properties of the ring of integers, Z, and its field of fractions, the rational numbers, Q. Early on in the development of the subject it was noticed that Z has many properties in common with A = IF[T], the ring of polynomials over a finite field. Both rings are principal ideal domains, both have the property that the residue class ring of any non-zero ideal is finite, both rings have infinitely many prime elements, and both rings have finitely many units. Thus, one is led to suspect that many results which hold for Z have analogues of the ring A. This is indeed the case. The first four chapters of this book are devoted to illustrating this by presenting, for example, analogues of the little theorems of Fermat and Euler, Wilson's theorem, quadratic (and higher) reciprocity, the prime number theorem, and Dirichlet's theorem on primes in an arithmetic progression. All these results have been known for a long time, but it is hard to locate any exposition of them outside of the original papers. Algebraic number theory arises from elementary number theory by con- sidering finite algebraic extensions K of Q, which are called algebraic num- ber fields, and investigating properties of the ring of algebraic integers OK C K, defined as the integral closure of Z in K.