Now William Dunham gives them the attention they deserve.Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics.A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity.

    Generating functions have numerous applications in mathematics, especially in - Combinatorics - Probability Theory - Statistics - Theory of Markov Chains - Number Theory One of the most important and relevant recent applications of combinatorics lies in the development of Internet search engines whose incredible capabilities dazzle even the mathematically trained user.

    This is an introduction of mathematics history to mathematics students.

    "Categorical Data Analysis" was among those chosen.A valuable new edition of a standard reference"A 'must-have' book for anyone expecting to do research and/or applications in categorical data analysis."-"Statistics in Medicine on Categorical Data Analysis," First EditionThe use of statistical methods for categorical data has increased dramatically, particularly for applications in the biomedical and social sciences. Responding to new developments in the field as well as to the needs of a new generation of professionals and students, this new edition of the classic "Categorical Data Analysis" offers a comprehensive introduction to the most important methods for categorical data analysis.Designed for statisticians and biostatisticians as well as scientists and graduate students practicing statistics, "Categorical Data Analysis," Second Edition summarizes the latest methods for univariate and correlated multivariate categorical responses. Readers will find a unified generalized linear models approach that connects logistic regression and Poisson and negative binomial regression for discrete data with normal regression for continuous data. Adding to the value in the new edition is coverage of: Three new chapters on methods for repeated measurement and other forms of clustered categorical data, including marginal models and associated generalized estimating equations (GEE) methods, and mixed models with random effectsStronger emphasis on logistic regression modeling of binary and multicategory dataAn appendix showing the use of SAS for conducting nearly all analyses in the bookPrescriptions for how ordinal variables should be treated differently than nominal variablesDiscussion of exact small-sample proceduresMore than 100 analyses of real data sets to illustrate application of the methods, and more than 600 exercisesAn Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

    Nearly 1,000 entries have been added for this new edition covering everything from pure and applied mathematics to statistics. Also included are entries on mathematics of more general interest, such as fractals, game theory, and chaos. Providing succinct definitions and clear explanations to a wealth of terms, A Concise Oxford Dictionary of Mathematics also enables readers to make new discoveries as they browse and check cross-references. With explanatory figures, diagrams, and tables for ready reference to compliment the text, clear and precise definitions, with helpful examples, of a wide range of mathematical terms and concepts, and brief biographical sketches of the great mathematicians, this comprehensive dictionary will serve as an indispensable and trustworthy guide to the dynamic world of mathematics.

    Some of his works echo those of M.C. Escher in their meticulous rendering of shapes and patterns, while other pieces seem to be more visceral expressions of mathematical ideas. Stimulating to the imagination and to the eye, his rich and evocative work can be interpreted and appreciated in various ways - mathematical, aesthetic or emotional.

    This book covers areas such as ordered sets and lattices. A key feature of ordered sets, one which is emphasized in the text, is that they can be represented pictorially. Lattices are also considered as algebraic structures and hence a purely algebraic study is used to reinforce the ideas of homomorphisms and of ideals encountered in group theory and ring theory. Exposure to elementary abstract algebra and the rotation of set theory are the only prerequisites for this text. For the new edition, much has been rewritten or expanded and new exercises have been added.

    The writing is exceptionally lucid, as in the author's earlier books, … and the problems carefully selected for maximum interest and elegance." — Martin Gardner.This book is intended for people who liked geometry when they first encountered it (and perhaps even some who did not) but sensed a lack of intellectual stimulus and wondered what was missing, or felt that the play was ending just when the plot was finally becoming interesting.In this superb treatment, Professor Ogilvy demonstrates the mathematical challenge and satisfaction to be had from geometry, the only requirements being two simple implements (straightedge and compass) and a little thought. Avoiding topics that require an array of new definitions and abstractions, Professor Ogilvy draws upon material that is either self-evident in the classical sense or very easy to prove. Among the subjects treated are: harmonic division and Apollonian circles, inversion geometry, the hexlet, conic sections, projective geometry, the golden section, and angle trisection. Also included are some unsolved problems of modern geometry, including Malfatti's problem and the Kakeya problem.Numerous diagrams, selected references, and carefully chosen problems enhance the text. In addition, the helpful section of notes at the back provides not only source references but also much other material highly useful as a running commentary on the text.

    . . clear exposition of unusual and more advanced topics . . . Develops material to substantial level." — American Mathematical Monthly"Refreshingly different . . . an ideal training ground for the mathematical process of investigation, generalization, and conjecture leading to the discovery of proofs and counterexamples." — American Mathematical Monthly" . . . An excellent textbook for an undergraduate course." — Australian Computer JournalA stimulating view of mathematics that appeals to students as well as teachers, this undergraduate-level text is written in an informal style that does not sacrifice depth or challenge. Based on 20 years of teaching by the leading researcher in graph theory, it offers a solid foundation on the subject. This revised and augmented edition features new exercises, simplifications, and other improvements suggested by classroom users and reviewers. Topics include basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.

    Hyperbolic, parabolic, elliptic equations; wave propagation in space, heat conduction in space, special functions, more. Emphasis on mathematical formulation of problems, rigorous solutions, physical interpretation of results obtained. Problems. Appendixes. Tables.

    The powerful tools he forged from the ideas of modern algebra allowed him to penetrate classical problems with an unaccustomed depth, and brought new rigor to the intuitive proofs of the Italian School. The students he trained at Hopkins, and later at Harvard, are among the foremost mathematicians of our time.While what he called his real life is recorded in almost a hundred books and papers, this story of his unreal life is based upon Parikh s interviews with his family, colleagues, and students, and on his own memories from a series of tape-recorded interviews made a few years before his death in 1986.First published in 1991, The Unreal Life of Oscar Zariski was highly successful and widely praised, but has been out of print for many years. Springer is proud to make this book available again, introducing Oscar Zariski to a new generation of mathematicians."

    It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

    A beginning algebra textbook with instructions for the teacher on how to present the material to students.

    It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals. * Each topic is carefully explained and illustrated by examples and figures. * Includes all necessary mathematical background material. * Includes notes and references to enable the reader to pursue individual topics. * Features a wide selection of exercises, enabling the reader to develop their understanding of the theory. * Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers. Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. Also by Kenneth Falconer and available from Wiley: Techniques in Fractal Geometry ISBN 0-471-95724-0 Please click here to download solutions to exercises found within this title: http: //www.wileyeurope.com/fractal

    As a consequence, there is a wide demand for a survey of the results of mathematics. for an unconventional approach that would also make it possible to fill gaps in one's knowledge. We do not think that a mere juxtaposition of theorems or a collection of formulae would be suitable for this purpose, because this would over. emphasize the symbolic language of signs and letters rather than the mathematical idea, the only thing that really matters. Our task was to describe mathematical interrelations as briefly and precisely as possible. In view of the overwhelming amount of material it goes without saying that we did not just compile details from the numerous text-books for individual branches: what we were aiming at is to smooth out the access to the specialist literature for as many readers as possible. Since well over 700000 copies of the German edition of this book have been sold, we hope to have achieved our difficult goal. Colours are used extensively to help the reader. Important definitions and groups of formulae are on a yellow background, examples on blue, and theorems on red.

    Originally published in 1912, this classic has lost little of its scientific and didactic value, and is suitable for advanced undergraduate and graduate students of physics and historians of science.Part One describes the older formulation of statistico-mechanical investigations (kineto-statistics of the molecule). Part Two takes up the modern formulation of kineto-statistics of the gas model, and Part Three explores W. B. Gibbs's major work, Elementary Principles in Statistical Mechanics and its coverage of such topics as the problem of axiomatization in kineto-statistics, the introduction of canonical and microcanonical distributions, and the analogy to the observable behavior of thermodynamic systems. The book concludes with the authors' original notes, a series of useful appendixes, and a helpful bibliography.

    Drawing on the author's deep and personal understanding of three-dimensional space, it adopts an intuitive visual approach designed to develop heuristic tools of real use in applied contexts. Increasing activity in such areas as computer aided design and robotics calls for sophisticated methods to characterize solid objects. A wealth of mathematical research exists that can greatly facilitate this work yet engineers have continued to reinvent the wheel as they grapple with problems in three dimensional geometry. Solid Shape bridges the gap that now exists between technical and modern geometry and shape theory or computer vision, offering engineers a new way to develop the intuitive feel for behavior of a system under varying situations without learning the mathematicians' formal proofs. Reliance on descriptive geometry rather than analysis and on representations most easily implemented on microcomputers reinforces this emphasis on transforming the theoretical to the practical. Chapters cover shape and space, Euclidean space, curved submanifolds, curves, local patches, global patches, applications in ecological optics, morphogenesis, shape in flux, and flux models. A final chapter on literature research and an appendix on how to draw and use diagrams invite readers to follow their own pursuits in threedimensional shape.Solid Shape is included in the Artificial Intelligence series, edited by Patrick Winston, Michael Brady, and Daniel Bobrow

    Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases.A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

    Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.

    Much material was added or revised for this edition, which thoroughly establishes the theories of commutative fields and modules over a principal ideal domain.

    This book discusses two recent developments in this theory. The first uses the tool of extensive games to construct theories of bargaining in which time is modeled explicitly. The second applies the theory of bargaining to the study of decentralized markets. Rather than surveying the field, the authors present a select number of models, each of which illustrates a key point. In addition, they give detailed proofs throughout the book. It uses a small number of models, rather than a survey of the field, to illustrate key points, and includes detailed proofs given as explanations for the models. The text has been class-tested in a semester-long graduate course.

    These results have had far-reaching consequences in geometry, topology, and mathematical physics, and have proven to be a mainspring of current mathematical research. This book provides a lucid and accessible account of the modern study of the geometry of four-manifolds. Consequently, it will be required reading for all those mathematicians and theoretical physicists whose research touches on this topic. The authors present both a thorough treatment of the main lines of these developments in four-manifold topology--notably the definition of new invariants of four-manifolds--and also a wide-ranging treatment of relevant topics from geometry and global analysis. All of the main theorems about Yang-Mills instantons on four-manifolds are proven in detail. On the geometric side, the book contains a new proof of the classification of instantons on the four-sphere, together with an extensive discussion of the differential geometry of holomorphic vector bundles. At the end of the book the different strands of the theory are brought together in the proofs of results which settle long-standing problems in four-manifolds topology and which are close to the frontiers of current research. Co-author Donaldson is the 1994 co-recipient of the prestigious Crafoord Prize.

    It discusses the finite element method for both viscoplastic and rate-independent plastic solids, in addition to large deformation plasticity numerical methods for rate-based formulations and hyperelastic methods. 1990 edition.

    Its simple explanations of difficult subjects make it intuitively appealing to students in applied mathematics, physics, and engineering. It is also a fine reference for professionals. 1990 edition.

    Some have philosophers as their intended audience, some mathematicians, some computer scien tists. Although there is a common core to all such books, they will be very different in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer science formal logic turns up in a number of areas, from pro gram verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theo rem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but, not incompleteness issues. The first item to be addressed is, What are we talking about and why are we interested in it? We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject."

    

    This book aims to implement this structure, and then to develop those applications that have been central to the growth of the theory. The first three chapters provide an overview of differential geometry. Chapter 4 extensively analyzes the properties of a tetrad field, subsequently used in Chapter 5 to introduce spinors, in Chapter 8 to describe the geometry of congruences, and in Chapter 9 to define the physical measurements on a curved manifold. The coupling of fields and geometry is investigated in terms of lagrangeans in Chapter 6, and a detailed discussion of some exact solutions of the Einstein equations appears in Chapters 10 and 11.

    The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.

    They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide--more than 104,000 copies were bought of the prior edition--includes problems and examples using graphing calculators..

    It starts with a brief survey of the physics needed to follow the arguments - including quantum field theory, gauge theory and general relativity - to make sure all readers set off from the same starting point. Basic theory of vector spaces and topology is also included to make the book self-contained. Working from the basics to the more elaborate concepts of topology and geometry, all is carefully explained and illustrated with applications. Explicit calculations and diagrams clarify the abstract ideas involved. Many illustrations, exercises and problems are included. This book will be invaluable to advanced undergraduates and researchers in many areas of physics.

    It is designed for the two-term calculus-based mathematical statistics course at the junior level.

    

    Fisher, whose writings have had more influence on statistical theory and practice than any other 20th century statistician. It includes Statistical Methods for Research Workers, Statistical Methods and Scientific Inference, and The Design of Experiments, all republished in their entirety, with only minor corrections. An informative foreword by Dr. F. Yates, one of the author's closest colleagues and collaborators, discusses the key issues found in the texts, shedding new light on how Fisher's ideas have become mainstays of modern statistical practice.

    This elegant book has provided students and teachers with an excellent introduction to the field of graph theory for close to thirty years. Robin Wilson's revision adds strength to the book by updating the terminology and notation, bringing them in line with contemporary usage. Wilson has added new material on interval graphs, the traveling salesman problem, bracing frameworks, shortest route problems, and coloring maps on surfaces. Most of the diagrams in the book have been redrawn.

    Incorporating contemporary ideas, this introductory text assumes no knowledge of logic and no knowledge of set theory beyond the vague familiarity with curly brackets, union and intersection usually expected of an advanced mathematics student.

    The great strength of Revuz and Yor is the enormous variety of calculations carried out both in the main text and also (by implication) in the exercises. ... This is THE book for a capable graduate student starting out on research in probability: the effect of working through it is as if the authors are sitting beside one, enthusiastically explaining the theory, presenting further developments as exercises, and throwing out challenging remarks about areas awaiting further research..."Bull.L.M.S. 24, 4 (1992) Since the first edition in 1991, an impressive variety of advances has been made in relation to the material of this book, and these are reflected in the successive editions.

    The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

    Topics range from pre-calculus to vector analysis and from Fourier transforms to statistics.This third edition contains: A new chapter on business and financial mathematics - providing information on progressions, especially geometric progressions, which is the basis for many formulas related to annuities, growth of funds, and interest paymentsAdditional topics in statistics - including sample size calculations for testing differences and proportionsFeaturing numerical tables of probability distributions, the book also includes Discussions on formula listings and differential equationsFourier seriesLaplace and z-transformsVector analysisOrthogonal polynomialsMany other handbooks go too far in their attempts, essentially mimicking larger comprehensive texts they try to summarize. The result is a reference less detailed than the full texts and too big to be conveniently portable. Most scientists do not carry them.Through a careful selection of topics and detail, Pocket Book of Integrals and Mathematical Formulas truly meets the needs of engineers and scientists - a convenient, usable supplementary text providing worked examples where most necessary. Its comprehensive information and convenient arrangement of tables makes it an essential and easy to use reference.

    Perhaps the most novel feature of the book is its use of Kalman filtering together with econometric and time series methodology. From a technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. This technique was originally developed in control engineering but is becoming increasingly important in economics and operations research. The book is primarily concerned with modeling economic and social time series and with addressing the special problems that the treatment of such series pose.

    The author's aim is not to cover the standard material in a standard way, but to present results of applications in contemporary mathematics and to show the relevance of functional analysis to other areas. Unusual topics covered include geometry of finite-dimensional spaces, invariant subspace, fixed-point theorem, and the Bishop-Phelps theorem. An outstanding set of exercises run from the elementary to the challenging.

    The vision and purpose of the Series was - and still is - to provide tips, techniques, and algorithms for graphics programmers. All of the gems are written by programmers who work in the field and are motivated by a common desire to share interesting ideas and tools with their colleagues. Each volume provides a new set of innovative solutions to a variety of programming problems

    This new edition of a bestseller has been updated with Stata, R, and WinBUGS code as well as three new chapters on Bayesian analysis. Like its predecessor, this edition presents the theoretical background of generalized linear models (GLMs) before focusing on methods for analyzing particular kinds of data. It covers normal, Poisson, and binomial distributions; linear regression models; classical estimation and model fitting methods; and frequentist methods of statistical inference. After forming this foundation, the authors explore multiple linear regression, analysis of variance (ANOVA), logistic regression, log-linear models, survival analysis, multilevel modeling, Bayesian models, and Markov chain Monte Carlo (MCMC) methods.Using popular statistical software programs, this concise and accessible text illustrates practical approaches to estimation, model fitting, and model comparisons. It includes examples and exercises with complete data sets for nearly all the models covered.

    Eliot Porter's photographs of the natural world, spanning thirty-five years and five continents -- from an Antarctic ice floe to an American desert to an Icelandic lava field -- reveal in mesmerizing ways what scientists are beginning to see for themselves: the patterns, relations, and interactions present in nature's disorder and wildness. This is the perfect marriage of image and text -- brilliant full-color photographs by the preeminent nature photographer of his generation together with an illuminating essay by the widely praised author of Chaos.

    This edition has been revised and updated, the main difference being that the algorithms are presented in Turbo Pascal.

    A fully integrated work, The Physics of Fluid Turbulence approaches its subject as a universal phenomenon with a universal behavior. It includes a concise summary of the theory and practice of turbulence science up to 1960, followed by a detailed analysis of more recent developments inthis area, including a rigorous formulation of the turbulence problem as an example of a non-equilibrium statistical system with strong coupling, along with the application of renormalized perturbation theory. Designed for those new to the subject, the book will also be useful to those who arefamiliar with the study of turbulence but have not yet approached the subject utilizing the theoretical methods from quantum physics that are covered here.