From the reviews:"The book...is a thorough and very readable introduction to the arithmetic of function fields of one variable over a finite field, by an author who has made fundamental contributions to the field. It serves as a definitive reference volume, as well as offering graduate students with a solid understanding of algebraic number theory the opportunity to quickly reach the frontiers of knowledge in an important area of mathematics...The arithmetic of function fields is a universe filled with beautiful surprises, in which familiar objects from classical number theory reappear in new guises, and in which entirely new objects play important roles. Goss'clear exposition and lively style make this book an excellent introduction to this fascinating field." MR 97i:11062
The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph.
An exciting approach to the history and mathematics of number theory “. . . the author’s style is totally lucid and very easy to read . . .the result is indeed a wonderful story.” —Mathematical Reviews Written in a unique and accessible style for readers of varied mathematical backgrounds, the Second Edition of Primes of the Form p = x2+ ny2 details the history behind how Pierre de Fermat’s work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. Primes of the Form p = x2 + ny2, Second Edition focuses on addressing the question of when a prime p is of the form x2 + ny2, which serves as the basis for further discussion of various mathematical topics. This updated edition has several new notable features, including: • A well-motivated introduction to the classical formulation of class field theory • Illustrations of explicit numerical examples to demonstrate the power of basic theorems in various situations • An elementary treatment of quadratic forms and genus theory • Simultaneous treatment of elementary and advanced aspects of number theory • New coverage of the Shimura reciprocity law and a selection of recent work in an updated bibliography Primes of the Form p = x2 + ny2, Second Edition is both a useful reference for number theory theorists and an excellent text for undergraduate and graduate-level courses in number and Galois theory.
This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures. The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.
The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. Springer-Verlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of examples make the book an excellent text." (Mathematical Reviews)
This title was first published in 2003: This book provides an evaluation of the Gateshead Community Care Scheme which was devised as an alternative to residential and hospital care for frail elderly people. An important feature of the scheme was the decentralization of control of resources to individual social workers acting as care managers, with defined caseloads and expenditure limits to ensure accountability. The initial social social care scheme was subsequently extended to provide both health and social care to clients from a large general practice based in a health centre. The social care team was enlarged to include a nurse care manager and part-time doctor and physiotherapist. The study examines the operation of care management in both settings, the use of devolved budgets and services developed, the outcomes for clients and carers and the costs of care. Admissions to residential care were reduced and the elderly people who received the scheme’s support experienced a better quality of care and greater well-being when compared with elderly people receiving the usual range of services. This was achieved at no greater cost. The characteristics of those for whom the scheme was most appropriate are described. In addition, the pattern of development of the scheme as it was incorporated into the mainstream of the Social Services and after the implementation of the NHS and Community Care Act are examined. Final, the implications for the development of care management are considered.
This book studies when a prime p can be written in the form x2+ny2. It begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms. After exploring cubic and biquadratic reciprocity, the pace quickens with the introduction of algebraic number fields and class field theory. This leads to the concept of ring class field and a complete but abstract solution of p=x2+ny2. To make things more concrete, the book introduces complex multiplication and modular functions to give a constructive solution. The book ends with a discussion of elliptic curves and Shimura reciprocity. Along the way the reader will encounter some compelling history and marvelous formulas, together with a complete solution of the class number one problem for imaginary quadratic fields. The book is accessible to readers with modest backgrounds in number theory. In the third edition, the numerous exercises have been thoroughly checked and revised, and as a special feature, complete solutions are included. This makes the book especially attractive to readers who want to get an active knowledge of this wonderful part of mathematics.
For 50 years, Edward M. Purcell's classic textbook has introduced students to the world of electricity and magnetism. The third edition has been brought up to date and is now in SI units. It features hundreds of new examples, problems, and figures, and contains discussions of real-life applications. The textbook covers all the standard introductory topics, such as electrostatics, magnetism, circuits, electromagnetic waves, and electric and magnetic fields in matter. Taking a nontraditional approach, magnetism is derived as a relativistic effect. Mathematical concepts are introduced in parallel with the physics topics at hand, making the motivations clear. Macroscopic phenomena are derived rigorously from the underlying microscopic physics. With worked examples, hundreds of illustrations, and nearly 600 end-of-chapter problems and exercises, this textbook is ideal for electricity and magnetism courses. Solutions to the exercises are available for instructors at www.cambridge.org/Purcell-Morin.
This book presents papers given at a Conference on Inverse Scattering on the Line, held in June 1990 at the University of Massachusetts, Amherst. A wide variety of topics in inverse problems were covered: inverse scattering problems on the line; inverse problems in higher dimensions; inverse conductivity problems; and numerical methods. In addition, problems from statistical physics were covered, including monodromy problems, quantum inverse scattering, and the Bethe ansatz. One of the aims of the conference was to bring together researchers in a variety of areas of inverse problems which have seen intensive activity in recent years. scattering
This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.
In this work Schum develops a general theory of evidence as it is understood and applied across a broad range of disciplines and practical undertakings. He include insights from law, philosophy, logic, probability, semiotics, artificial intelligence, psychology and history.
The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held at the Institute for Advanced Study/Park City Mathematics Institute. The theme of the program was arithmetic algebraic geometry. The choice of lecture topics was heavily influenced by the recent spectacular work of Wiles on modular elliptic curves and Fermat's Last Theorem. The main emphasis of the articles in the volume is on elliptic curves, Galois representations, and modular forms. One lecture series offers an introduction to these objects. The others discuss selected recent results, current research, and open problems and conjectures. The book would be a suitable text for an advanced graduate topics course in arithmetic algebraic geometry.
An engaging, comprehensive, richly illustrated textbook about the atmospheric general circulation, written by leading researchers in the field. The book elucidates the pervasive role of atmospheric dynamics in the Earth System, interprets the structure and evolution of atmospheric motions across a range of space and time scales in terms of fundamental theoretical principles, and includes relevant historical background and tutorials on research methodology. The book includes over 300 exercises and is accompanied by extensive online resources, including solutions manuals, an animations library, and an introduction to online visualization and analysis tools. This textbook is suitable as a textbook for advanced undergraduate and graduate level courses in atmospheric sciences and geosciences curricula and as a reference textbook for researchers.
This advanced undergraduate-level text presents the quantum theory in terms of qualitative and imaginative concepts, followed by specific applications worked out in mathematical detail.
This book provides a comprehensive survey of modern molecular astrophysics. It includes an introduction to molecular spectroscopy and then addresses the main areas of current molecular astrophysics, including galaxy formation, star forming regions, mass loss from young as well as highlyevolved stars and supernovae, starburst galaxies plus the tori and discs near the central engines of active galactic nuclei. All chapters have been written by invited authors who are acknowledged experts in their fields. The thorough editorial process has ensured a uniformly high standard ofexposition and a coherent style. The book is unique in giving a detailed view of its wide-ranging subject. It will provide the standard introduction for research students in molecular astrophysics. The book will be read by research astronomers and astrophysicists who wish to broaden the basis oftheir knowledge or are moving their activities into this burgeoning field. It will enable chemists to learn the astrophysics most related to chemistry as well as instruct physicists about the molecular processes most important in astronomy.
Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics. Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.
Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition provides a sound, intuitive understanding of the basic concepts students need as they pursue careers in business, economics, and the life and social sciences. Students achieve success using this text as a result of the author's applied and real-world orientation to concepts, problem-solving approach, straight forward and concise writing style, and comprehensive exercise sets. More than 100,000 students worldwide have studied from this text!
This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.
The 5th edition of this classic textbook covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve that problem. End-of-chapter exercises are provided for all chapters. The material is organized into three separate parts. Part I offers a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. In turn, Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. As such, Parts II and III can easily be used without reading Part I and, in fact, the book has been used in this way at many universities. New to this edition are popular topics in data science and machine learning, such as the Markov Decision Process, Farkas’ lemma, convergence speed analysis, duality theories and applications, various first-order methods, stochastic gradient method, mirror-descent method, Frank-Wolf method, ALM/ADMM method, interior trust-region method for non-convex optimization, distributionally robust optimization, online linear programming, semidefinite programming for sensor-network localization, and infeasibility detection for nonlinear optimization.
In the past few years, the number of applications of tracers for in vivo biomedical studies has greatly increased. New analytical tools at the genetic and protein levels have spurred this growth, opening the door for a deeper understanding of metabolic events. This in turn promises to yield significant advances in the understanding and treatment of human disease. Now fully revised and expanded, Isotope Tracers in Metabolic Research, Second Edition is the established definitive text on stable and radioactive isotope tracers. In unique, multidisciplinary fashion, it presents comprehensive coverage of new methodological, mathematical, and theoretical approaches. This new Second Edition includes: All-new chapters on nuclear magnetic resonance, mass isotopomer analysis, and methods of protein metabolism analysis A completely updated categorized list of over 750 references Major advances in the development of mass isotopomer and positional isotopomer techniques, noninvasive isotope techniques for studying metabolic pathways, hyphenated techniques, and new tracer techniques The latest developments in quantification of DNA synthesis and mass spectrometry spurred by genome sequencing and proteomics New coverage of mathematical modeling Expanded coverage of microdialysis probes, laboratory procedures, and regulatory issues related to human studies In this complete guide to performing tracer studies, the authors systematically cover tracer selection, modeling considerations, sample derivitization, mass spectrometry analysis, and data interpretation. Problems and discussion questions highlight key points in each chapter. Isotope Tracers in Metabolic Research, Second Edition offers students and researchers a comprehensive, practical resource for utilizing the latest tracer methodologies.
Sybex is now the official publisher for Certified Wireless Network Professional, the certifying vendor for the CWSP program. This guide covers all exam objectives, including WLAN discovery techniques, intrusion and attack techniques, 802.11 protocol analysis. Wireless intrusion-prevention systems implementation, layer 2 and 3 VPNs used over 802.11 networks, and managed endpoint security systems. It also covers enterprise/SMB/SOHO/Public-Network Security design models and security solution implementation, building robust security networks, wireless LAN management systems, and much more.
A complete course in TeX that will be suitable for users of TeX who want to advance beyond the basics. The initial chapters introduce the essential workings of TeX and the later chapters cover a wide range of advanced topics such as macros, conditionals, tokens, leaders, file I/O, the line- and page-break algorithms, and output routines.
This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.
This volume is the third of three in a series surveying the theory of theta functions. Based on lectures given by the author at the Tata Institute of Fundamental Research in Bombay, these volumes constitute a systematic exposition of theta functions, beginning with their historical roots as analytic functions in one variable (Volume I), touching on some of the beautiful ways they can be used to describe moduli spaces (Volume II), and culminating in a methodical comparison of theta functions in analysis, algebraic geometry, and representation theory (Volume III).
This monograph develops the Gröbner basis methods needed to perform efficient state of the art calculations in the cohomology of finite groups. Results obtained include the first counterexample to the conjecture that the ideal of essential classes squares to zero. The context is J. F. Carlson’s minimal resolutions approach to cohomology computations.
Argues that Stonehenge's scientific purpose was to observe the setting midwinter sun, and that astronomical observations made by the ancient Britons were as rational and methodical as they are today.
This book provides a comprehensive introduction to Finsler geometry in the language of present-day mathematics. Through Finsler geometry, it also introduces the reader to other structures and techniques of differential geometry.Prerequisites for reading the book are minimal: undergraduate linear algebra (over the reals) and analysis. The necessary concepts and tools of advanced linear algebra (over modules), point set topology, multivariable calculus and the rudiments of the theory of differential equations are integrated in the text. Basic manifold and bundle theories are treated concisely, carefully and (apart from proofs) in a self-contained manner.The backbone of the book is the detailed and original exposition of tangent bundle geometry, Ehresmann connections and sprays. It turns out that these structures are important not only in their own right and in the foundation of Finsler geometry, but they can be also regarded as the cornerstones of the huge edifice of Differential Geometry.The authors emphasize the conceptual aspects, but carefully elaborate calculative aspects as well (tensor derivations, graded derivations and covariant derivatives). Although they give preference to index-free methods, they also apply the techniques of traditional tensor calculus.Most proofs are elaborated in detail, which makes the book suitable for self-study. Nevertheless, the authors provide for more advanced readers as well by supplying them with adequate material, and the book may also serve as a reference.
Community Pharmacy: Symptoms, Diagnosis and Treatment 3e builds on its established reputation as a trusted guide to differential diagnosis of symptoms commonly seen by Australian and New Zealand community pharmacists. The third edition has been carefully and thoroughly updated to reflect changes to over-the-counter drug scheduling and new over-the-counter drugs. In addition, the text highlights trends in pharmacy education and practice, with an emphasis on counselling, communication skills, evidence-based practice and customer requests specific to the Australian and New Zealand region. evolve Visit http://evolve.elsevier.com/AU/Newby/community/ for additional resources Lecturer resources Case studies Additional dermatology images Image collection Student resources Additional images for ophthalmology and dermatology Additional images of stings and bites Updated chapter 'Evidence-based pharmacy practice', which includes three new complex community pharmacy case studies Chapter on wound management, including images ‘Practice points’ – tips on how to counsel patients with respect to medications Wound management chapter on evolve Complex community pharmacy case studies Modified GRADE ratings incorporated throughout the chapters, which provide an assessment of the evidence supporting each therapeutic recommendation Expanded coverage of stings and bites
This Element is on new developments in the psychology of reasoning that raise or address philosophical questions. In traditional studies in the psychology of reasoning, the focus was on inference from arbitrary assumptions and not at all from beliefs, and classical binary logic was presupposed as the only standard for human reasoning. But recently a new Bayesian paradigm has emerged in the discipline. This views ordinary human reasoning as mostly inferring probabilistic conclusions from degrees of beliefs, or from hypothetical premises relevant to a purpose at hand, and as often about revising or updating degrees of belief. This Element also covers new formulations of dual-process theories of the mind, stating that there are two types of mental processing, one rapid and intuitive and shared with other animals, and the other slow and reflective and more characteristic of human beings. The final topic covered is the new developments and rationality.
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