Dover Books on Mathema 1.4tics – serie

This volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. Two chapters consider metric space and point-set topology; the other 2 chapters discuss algebraic topological material. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.

This unusually well-written, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations – equations which express the relationship between variables and their derivatives. In a disarmingly simple, step-by-step style that never sacrifices mathematical rigor, the authors – Morris Tenenbaum of Cornell University, and Harry Pollard of Purdue University – introduce and explain complex, critically-important concepts to undergraduate students of mathematics, engineering and the sciences.The book begins with a section that examines the origin of differential equations, defines basic terms and outlines the general solution of a differential equation-the solution that actually contains every solution of such an equation. Subsequent sections deal with such subjects as: integrating factors; dilution and accretion problems; the algebra of complex numbers; the linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas; and Picard's Method of Successive Approximations.The book contains two exceptional chapters: one on series methods of solving differential equations, the second on numerical methods of solving differential equations. The first includes a discussion of the Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation. Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. An abundance of solved problems and practice exercises enhances the value of Ordinary Differential Equations as a classroom text for undergraduate students and teaching professionals. The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians.Reprint of the Harper & Row, Publishers, 1963 edition.

Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.

This text focuses on the most widely used applications of mathematical methods, including those related to probability and statistics. The 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.

Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.

Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. "Thoroughly recommended." — Physics Bulletin. 1983 edition.

This major survey features the work of 18 outstanding mathematicians. Primary subjects include analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, and theories of probability and functions. Other topics include linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

This original anthology collects 10 of Weyl's less-technical writings that address the broader scope and implications of mathematics. Most have been long unavailable or not previously published in book form. Subjects include logic, topology, abstract algebra, relativity theory, and reflections on the work of Weyl's mentor, David Hilbert. 2012 edition.

This clear and well-developed approach to axiomatic set theory is geared toward upper-level undergraduates and graduate students. It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, and other subjects. 1960 edition.

This textbook for advanced courses in group theory focuses on finite groups, with emphasis on the idea of group actions. Early chapters identify important themes and establish the notation used throughout the book, and subsequent chapters explore the normal and arithmetical structures of groups as well as applications. Includes 679 exercises. 1978 edition.

Written by two of the most prominent figures in the field of graph theory, this comprehensive text provides a remarkably student-friendly approach. Geared toward undergraduates taking a first course in graph theory, its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.

Classic text leads from elementary calculus into more theoretic problems. Precise approach with definitions, theorems, proofs, examples and exercises. Topics include partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Numerous graded exercises with selected answers. 1961 edition.

This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers students at both high school and college levels an excellent mathematics workbook. Filled with rigorous problems, it assists students in developing and cultivating their logic and probability skills. 1974 edition.

"The best book available for non-mathematicians." — Contemporary Psychology. Superb nontechnical introduction to game theory and related disciplines, primarily as applied to the social sciences. Clear, comprehensive coverage of utility theory, 2-person zero-sum games, 2-person non-zero-sum games, n-person games, individual and group decision-making, much more. Appendixes. Bibliography. Graphs and figures.

Excellent introduction treats three 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.

This entertaining text is essential for anyone interested in game theory. Only a basic understanding of arithmetic is needed to grasp the necessary aspects of strategy games for two, three, four, and more players that feature two or more sets of inimical interests and a limitless array of zero-sum payoffs.

This well-respected text offers an accessible introduction to functional programming concepts and techniques for students of mathematics and computer science. The treatment is as nontechnical as possible, assuming no prior knowledge of mathematics or functional programming. Numerous exercises appear throughout the text, and all problems feature complete solutions. 1989 edition.