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A Short Course in Automorphic Functions (Dover Books on Mathematics)
by Joseph LehnerThis concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous groups. Author Joseph Lehner begins by elaborating on the theory of discontinuous groups by the classical method of Poincaré, employing the model of the hyperbolic plane. The necessary hyperbolic geometry is developed in the text. Chapter two develops automorphic functions and forms via the Poincaré series. Formulas for divisors of a function and form are proved and their consequences analyzed. The final chapter is devoted to the connection between automorphic function theory and Riemann surface theory, concluding with some applications of Riemann-Roch theorem. <p> The book presupposes only the usual first courses in complex analysis, topology, and algebra. Exercises range from routine verifications to significant theorems. Notes at the end of each chapter describe further results and extensions, and a glossary offers definitions of terms.
Square Summable Power Series (Dover Books on Mathematics)
by James Rovnyak Louis De BrangesThis text for advanced undergraduate and graduate students introduces Hilbert space and analytic function theory, which is centered around the invariant subspace concept. The book's principal feature is the extensive use of formal power series methods to obtain and sometimes reformulate results of analytic function theory. The presentation is elementary in that it requires little previous knowledge of analysis, but it is designed to lead students to an advanced level of performance. This is achieved chiefly through the use of problems, many of which were proposed by former students. The book's tried-and-true approach was developed from the authors' lecture notes on courses taught at Lafayette College, Bryn Mawr College, and Purdue University.
The Theory of Spinors
by Élie CartanThe French mathematician Élie Cartan (1869-1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities.The book is divided into two parts. The first is devoted to generalities on the group of rotations in n-dimensional space and on the linear representations of groups, and to the theory of spinors in three-dimensional space. Finally, the linear representations of the group of rotations in that space (of particular importance to quantum mechanics) are also examined. The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space). While the basic orientation of the book as a whole is mathematical, physicists will be especially interested in the final chapters treating the applications of spinors in the rotation and Lorentz groups. In this connection, Cartan shows how to derive the "Dirac" equation for any group, and extends the equation to general relativity.One of the greatest mathematicians of the 20th century, Cartan made notable contributions in mathematical physics, differential geometry, and group theory. Although a profound theorist, he was able to explain difficult concepts with clarity and simplicity. In this detailed, explicit treatise, mathematicians specializing in quantum mechanics will find his lucid approach a great value.
Two-Person Game Theory
by Anatol Rapoport"Game theory is an intellectual X-ray. It reveals the skeletal structure of those systems where decisions interact, and it reveals, therefore, the essential structure of both conflict and cooperation." -- Kenneth BouldingThis fascinating and provocative book presents the fundamentals of two-person game theory, a mathematical approach to understanding human behavior and decision-making, Developed from analysis of games of strategy such as chess, checkers, and Go, game theory has dramatic applications to the entire realm of human events, from politics, economics, and war, to environmental issues, business, social relationships, and even "the game of love." Typically, game theory deals with decisions in conflict situations.Written by a noted expert in the field, this clear, non-technical volume introduces the theory of games in a way which brings the essentials into focus and keeps them there. In addition to lucid discussions of such standard topics as utilities, strategy, the game tree, and the game matrix, dominating strategy and minimax, negotiated and nonnegotiable games, and solving the two-person zero-sum game, the author includes a discussion of gaming theory, an important link between abstract game theory and an experimentally oriented behavioral science. Specific applications to social science have not been stressed, but the methodological relations between game theory, decision theory, and social science are emphasized throughout.Although game theory employs a mathematical approach to conflict resolution, the present volume avoids all but the minimum of mathematical notation. Moreover, the reader will find only the mathematics of high school algebra and of very elementary analytic geometry, except for an occasional derivative. The result is an accessible, easy-to-follow treatment that will be welcomed by mathematicians and non-mathematicians alike.
Variational Methods for Eigenvalue Problems: An Introduction to the Weinstein Method of Intermediate Problems (Second Edition) (Mathematical Expositions #10)
by S. H. GouldThe first edition of this book gave a systematic exposition of the Weinstein method of calculating lower bounds of eigenvalues by means of intermediate problems. From the reviews of this edition and from subsequent shorter expositions it has become clear that the method is of considerable interest to the mathematical world; this interest has increased greatly in recent years by the success of some mathematicians in simplifying and extending the numerical applications, particularly in quantum mechanics. Until now new developments have been available only in articles scattered throughout the literature: this second edition presents them systematically in the framework of the material contained in the first edition, which is retained in somewhat modified form.
100 Great Problems of Elementary Mathematics
by Heinrich Dörrie"The collection, drawn from arithmetic, algebra, pure and algebraic geometry and astronomy, is extraordinarily interesting and attractive." -- Mathematical GazetteThis uncommonly interesting volume covers 100 of the most famous historical problems of elementary mathematics. Not only does the book bear witness to the extraordinary ingenuity of some of the greatest mathematical minds of history -- Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and many others -- but it provides rare insight and inspiration to any reader, from high school math student to professional mathematician. This is indeed an unusual and uniquely valuable book.The one hundred problems are presented in six categories: 26 arithmetical problems, 15 planimetric problems, 25 classic problems concerning conic sections and cycloids, 10 stereometric problems, 12 nautical and astronomical problems, and 12 maxima and minima problems. In addition to defining the problems and giving full solutions and proofs, the author recounts their origins and history and discusses personalities associated with them. Often he gives not the original solution, but one or two simpler or more interesting demonstrations. In only two or three instances does the solution assume anything more than a knowledge of theorems of elementary mathematics; hence, this is a book with an extremely wide appeal.Some of the most celebrated and intriguing items are: Archimedes' "Problema Bovinum," Euler's problem of polygon division, Omar Khayyam's binomial expansion, the Euler number, Newton's exponential series, the sine and cosine series, Mercator's logarithmic series, the Fermat-Euler prime number theorem, the Feuerbach circle, the tangency problem of Apollonius, Archimedes' determination of pi, Pascal's hexagon theorem, Desargues' involution theorem, the five regular solids, the Mercator projection, the Kepler equation, determination of the position of a ship at sea, Lambert's comet problem, and Steiner's ellipse, circle, and sphere problems.This translation, prepared especially for Dover by David Antin, brings Dörrie's "Triumph der Mathematik" to the English-language audience for the first time.
The Advanced Geometry of Plane Curves and Their Applications (Dover Books on Mathematics)
by C. Zwikker"Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." -- British Journal of Applied PhysicsThis study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves.Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves -- cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others -- receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.
Africa: A Geographical Study (Routledge Revivals)
by Alan B Mountjoy Clifford EmbletonFirst published in 1965, Africa provides a geographical, political, economic and social description of the continent. Contemporary Africa is a continent of change and revolutions. The diversity and limitations of the African environment gives us a fuller understanding of the explosive dynamism of the African economic and social scene. This book will be of interest to students of geography, economy, anthropology and political science.
Applied Complex Variables (Dover Books on Mathematics)
by John W. DettmanAnalytic function theory is a traditional subject going back to Cauchy and Riemann in the 19th century. Once the exclusive province of advanced mathematics students, its applications have proven vital to today's physicists and engineers. In this highly regarded work, Professor John W. Dettman offers a clear, well-organized overview of the subject and various applications -- making the often-perplexing study of analytic functions of complex variables more accessible to a wider audience.The first half of Applied Complex Variables, designed for sequential study, is a step-by-step treatment of fundamentals, presenting superior coverage of concepts of complex analysis, including the complex number plane; functions and limits; the Cauchy-Riemann conditions for differentiability; Riemann surfaces; the definite integral; power series; meromorphic functions; and much more. The second half provides lucid exposition of five important applications of analytic function theory, each approachable independently of the others: potential theory; ordinary differential equations; Fourier transforms; Laplace transforms; and asymptotic expansions. Helpful exercises are included at the end of each topic in every chapter. The two-part structure of Applied Complex Variables affords the college instructor maximum classroom flexibility. Once fundamentals are mastered, applications can be studied in any sequence desired. Depending on how many are selected for study, Professor Dettman's impressive text is ideal for either a one- or two-semester course. And, of course, the ambitious student possessing a knowledge of basic calculus will find its straightforward approach rewarding to his independent study efforts.Applied Complex Variables is a cogent, well-written introduction to an important and exciting branch of advanced mathematics -- serving both the theoretical needs of the mathematics specialist and the applied math needs of the physicist and engineer. Students and teachers alike will welcome this timely, moderately priced reissue of a widely respected work.
Calculus On Manifolds
by Michael SpivakThis little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.
Calculus On Manifolds
by Michael SpivakThis little book is especially concerned with those portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.<P><P> Advisory: Bookshare has learned that this book offers only partial accessibility. We have kept it in the collection because it is useful for some of our members. To explore further access options with us, please contact us through the Book Quality link on the right sidebar. Benetech is actively working on projects to improve accessibility issues such as these.
Concepts of Probability Theory: Second Revised Edition
by Paul E. PfeifferThis approach to the basics of probability theory employs the simple conceptual framework of the Kolmogorov model, a method that comprises both the literature of applications and the literature on pure mathematics. The author also presents a substantial introduction to the idea of a random process. Intended for college juniors and seniors majoring in science, engineering, or mathematics, the book assumes a familiarity with basic calculus.After a brief historical introduction, the text examines a mathematical model for probability, random variables and probability distributions, sums and integrals, mathematical expectation, sequence and sums of random variables, and random processes. Problems with answers conclude each chapter, and six appendixes offer supplementary material. This text provides an excellent background for further study of statistical decision theory, reliability theory, dynamic programming, statistical game theory, coding and information theory, and classical sampling statistics.
Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization
by Rufus IsaacsOne of the definitive works in game theory, this fascinating volume offers an original look at methods of obtaining solutions for conflict situations. Combining the principles of game theory, the calculus of variations, and control theory, the author considers and solves an amazing array of problems: military, pursuit and evasion, games of firing and maneuver, athletic contests, and many other problems of conflict.Beginning with general definitions and the basic mathematics behind differential game theory, the author proceeds to examinations of increasingly specific techniques and applications: dispersal, universal, and equivocal surfaces; the role of game theory in warfare; development of an effective theory despite incomplete information; and more. All problems and solutions receive clearly worded, illuminating discussions, including detailed examples and numerous formal calculations.The product of fifteen years of research by a highly experienced mathematician and engineer, this volume will acquaint students of game theory with practical solutions to an extraordinary range of intriguing problems.
Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with Applications (Dover Books on Mathematics)
by A. H. ZemanianThis well-known text provides a relatively elementary introduction to distribution theory and describes generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. Suitable for a graduate course for engineering and science students or for an advanced undergraduate course for mathematics majors. 1965 edition.
Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics)
by Frederick MostellerCan you solve the problem of "The Unfair Subway"? Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain. Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to challenge the mathematically inclined. From "The Flippant Juror" and "The Prisoner's Dilemma" to "The Cliffhanger" and "The Clumsy Chemist," they provide an ideal supplement for all who enjoy the stimulating fun of mathematics. Professor Frederick Mosteller, who teaches statistics at Harvard University, has chosen the problems for originality, general interest, or because they demonstrate valuable techniques. In addition, the problems are graded as to difficulty and many have considerable stature. Indeed, one has "enlivened the research lives of many excellent mathematicians." Detailed solutions are included. There is every probability you'll need at least a few of them.
A First Course in Partial Differential Equations: with Complex Variables and Transform Methods
by H. F. WeinbergerThis popular text was created for a one-year undergraduate course or beginning graduate course in partial differential equations, including the elementary theory of complex variables. It employs a framework in which the general properties of partial differential equations, such as characteristics, domains of independence, and maximum principles, can be clearly seen. The only prerequisite is a good course in calculus.Incorporating many of the techniques of applied mathematics, the book also contains most of the concepts of rigorous analysis usually found in a course in advanced calculus. These techniques and concepts are presented in a setting where their need is clear and their application immediate. Chapters I through IV cover the one-dimensional wave equation, linear second-order partial differential equations in two variables, some properties of elliptic and parabolic equations and separation of variables, and Fourier series. Chapters V through VIII address nonhomogeneous problems, problems in higher dimensions and multiple Fourier series, Sturm-Liouville theory, and general Fourier expansions and analytic functions of a complex variable. The last four chapters are devoted to the evaluation of integrals by complex variable methods, solutions based on the Fourier and Laplace transforms, and numerical approximation methods. Numerous exercises are included throughout the text, with solutions at the back.
Fringe Benefits, Labour Costs and Social Security (Routledge Revivals)
by G. L. Reid D. J. RobertsonOriginally published in 1965, this book is concerned with an important yet neglected part of economic life ‘fringe benefits’ which employers provide for and on behalf of their employees apart from wages and salaries. The book sets out results of an inquiry into the costs of supplementary labour costs for manual workers, with an account of the various influences which help to explain differences in expenditure by different firms. The book then gives comparative figures for Western European countries and considers some of the economic effects of the European levels of supplementary labour costs. The situation in the USA is discussed, as is the relationship of employer-financed welfare schemes and State social security programmes. Chapters on pensions, sick pay and redundancy payments are included as well as those dealing with the history of paid holidays and subsidized welfare facilities such as canteens.
From Fourier Analysis and Number Theory to Radon Transforms and Geometry
by Hershel M. Farkas Robert C. Gunning Marvin I. Knopp B. A. TaylorA memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis's contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore. A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.
The General Theory of Dirichlet's Series (Dover Books on Mathematics)
by G. H. Hardy Marcel RieszThis classic work explains the theory and formulas behind Dirichlet's series and offers the first systematic account of Riesz's theory of the summation of series by typical means. Its authors rank among the most distinguished mathematicians of the twentieth century: G. H. Hardy is famous for his achievements in number theory and mathematical analysis, and Marcel Riesz's interests ranged from functional analysis to partial differential equations, mathematical physics, number theory, and algebra.Following an introduction, the authors proceed to a discussion of the elementary theory of the convergence of Dirichlet's series, followed by a look at the formula for the sum of the coefficients of a Dirichlet's series in terms of the order of the function represented by the series. They continue with an examination of the summation of series by typical means and of general arithmetic theorems concerning typical means. After a survey of Abelian and Tauberian theorems and of further developments of the theory of functions represented by Dirichlet's series, the text concludes with an exploration of the multiplication of Dirichlet's series.
Geometric Algebra (Dover Books on Mathematics)
by Emil ArtinThis concise classic presents advanced undergraduates and graduate students in mathematics with an overview of geometric algebra. The text originated with lecture notes from a New York University course taught by Emil Artin, one of the preeminent mathematicians of the twentieth century. The Bulletin of the American Mathematical Society praised Geometric Algebra upon its initial publication, noting that "mathematicians will find on many pages ample evidence of the author's ability to penetrate a subject and to present material in a particularly elegant manner."Chapter 1 serves as reference, consisting of the proofs of certain isolated algebraic theorems. Subsequent chapters explore affine and projective geometry, symplectic and orthogonal geometry, the general linear group, and the structure of symplectic and orthogonal groups. The author offers suggestions for the use of this book, which concludes with a bibliography and index.
Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables
by Milton Abramowitz Irene A. StegunDespite the increasing use of computers, the basic need for mathematical tables continues. Tables serve a vital role in preliminary surveys of problems before programming for machine operation, and they are indispensable to thousands of engineers and scientists without access to machines. Because of automatic computers, however, and because of recent scientific advances, a greater variety of functions and a higher accuracy of tabulation than have been available until now are required.In 1954, a conference on mathematical tables, sponsored by M.I.T. and the National Science Foundation, met to discuss a modernization and extension of Jahnke and Emde's classical tables of functions. This volume, published 10 years later by the U.S. Department of Commerce, is the result. Designed to include a maximum of information and to meet the needs of scientists in all fields, it is a monumental piece of work, a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems.The book contains 29 sets of tables, some to as high as 20 places: mathematical constants; physical constants and conversion factors (6 tables); exponential integral and related functions (7); error function and Fresnel integrals (12); Bessel functions of integer (12) and fractional (13) order; integrals of Bessel functions (2); Struve and related functions (2); confluent hypergeometric functions (2); Coulomb wave functions (2); hypergeometric functions; Jacobian elliptic and theta functions (2); elliptic integrals {9); Weierstrass elliptic and related functions; parabolic cylinder functions {3); Mathieu functions (2); spheroidal wave functions (5); orthogonal polynomials (13); combinatorial analysis (9); numerical interpolation, differentiation and integration (11); probability functions (ll); scales of notation (6); miscellaneous functions (9); Laplace transforms (2); and others.Each of these sections is prefaced by a list of related formulas and graphs: differential equations, series expansions, special functions, and other basic relations. These constitute an unusually valuable reference work in themselves. The prefatory material also includes an explanation of the numerical methods involved in using the tables that follow and a bibliography. Numerical examples illustrate the use of each table and explain the computation of function values which lie outside its range, while the editors' introduction describes higher-order interpolation procedures. Well over100 figures illustrate the text.In all, this is one of the most ambitious and useful books of its type ever published, an essential aid in all scientific and engineering research, problem solving, experimentation and field work. This low-cost edition contains every page of the original government publication.
The Hindu-Arabic Numerals (Dover Books on Mathematics)
by David Eugene Smith Louis Charles KarpinskiThe numbers that we call Arabic are so familiar throughout Europe and the Americas that it can be difficult to realize that their general acceptance in commercial transactions is a matter of only the last four centuries and they still remain unknown in parts of the world.In this volume, one of the earliest texts to trace the origin and development of our number system, two distinguished mathematicians collaborated to bring together many fragmentary narrations to produce a concise history of Hindu-Arabic numerals. Clearly and succinctly, they recount the labors of scholars who have studied the subject in different parts of the world; they then assess the historical testimony and draw conclusions from its evidence. Topics include early ideas of the origin of numerals; Hindu forms with and without a place value; the symbol zero; the introduction of numbers into Europe by Boethius; the development of numerals among Arabic cultures; and the definitive introduction of numerals into Europe and their subsequent spread. Helpful supplements to the text include a guide to the pronunciation of Oriental names and an index.
A History of Geometrical Methods (Dover Books on Mathematics)
by Julian Lowell CoolidgeFull and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons between older and newer methods, and his references to over 600 primary and secondary sources make this book an invaluable reference. 1940 edition.
How to Gamble If You Must: Inequalities for Stochastic Processes (Dover Books on Mathematics)
by Leonard J. Savage Prof. William Sudderth Lester E. Dubins Prof. David GilatThis classic of advanced statistics is geared toward graduate-level readers and uses the concepts of gambling to develop important ideas in probability theory. The authors have distilled the essence of many years' research into a dozen concise chapters. "Strongly recommended" by the Journal of the American Statistical Association upon its initial publication, this revised and updated edition features contributions from two well-known statisticians that include a new Preface, updated references, and findings from recent research. Following an introductory chapter, the book formulates the gambler's problem and discusses gambling strategies. Succeeding chapters explore the properties associated with casinos and certain measures of subfairness. Concluding chapters relate the scope of the gambler's problems to more general mathematical ideas, including dynamic programming, Bayesian statistics, and stochastic processes.
Information Theory
by Robert B. AshExcellent introduction treats 3 major areas: analysis of channel models and proof of coding theorems; study of specific coding systems; and study of statistical properties of information sources. Appendix summarizes Hilbert space background and results from the theory of stochastic processes. Advanced undergraduate to graduate level. Bibliography.