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Complete works of ancient geometer feature such topics as the famous problems of the ratio of the areas of a cylinder and an inscribed sphere; the properties of conoids, spheroids, and spirals; more.

Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.

Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces - all in a single study. Detailed analyses. Problems. Bibliography. Index.

Only a basic understanding of arithmetic is needed to grasp these strategy games with two or more sets of inimical interests and a limitless array of zero-sum payoffs.

Twelve essays take a playful approach to mathematics, investigating the topology of a blanket, the odds of beating a superior tennis player, and how to distinguish between fact and fallacy.

Do you want to double or triple the speed with which you calculate? How to Calculate Quickly is a tried and true method for helping you in the mathematics of daily life--addition, subtraction, multiplication, division, and fractions. The author can awaken for you a faculty which is surprisingly dormant in accountants, engineers, scientists, businesspeople, and others who work with figures. This is "number sense"--or the ability to recognize relations between numbers considered as whole quantities. Lack of this number sense makes it entirely possible for a scientist to be proficient in higher mathematics, but to bog down in the arithmetic of everyday life. This book teaches the necessary mathematical techniques that schools neglect to teach: Horizontal addition, left to right multiplication and division, etc. You will learn a method of multiplication so rapid that you'll be able to do products in not much more time than it would take to write the problem down on paper. This is not a collection of tricks that work in only a very few special cases, but a serious, capably planned course of basic mathematics for self-instruction. It contains over 9,000 short problems and their solutions for you to work during spare moments. Five or ten minutes spent daily on this book will, within ten weeks, give you a number sense that will double or triple your calculation speed.

Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis.Customary topics of point-set topology include metric spaces, general topological spaces, continuity, topological equivalence, basis, subbasis, connectedness, compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces. In addition, the text introduces geometric, differential, and algebraic topology. Each chapter includes historical notes to put important developments into their historical framework. Exercises of varying degrees of difficulty form an essential part of the text.Dover (2015) republication of the edition originally published by Saunders College Publishing, Philadelphia, 1989, and by Cengage Learning Asia, 2002. See every Dover book in print atwww.doverpublications.com

Fundamentals of analytic function theory - plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.

Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Explores integrating factors; dilution and accretion problems; Laplace Transforms; Newton's Interpolation Formulas, more.

This fascinating, newly revised edition offers an overview of game theory, plus lucid coverage of two-person zero-sum game with equilibrium points; general, two-person zero-sum game; utility theory; and other topics.

A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.

Superb study of one of the most influential classics in mathematics examines the landmark 1859 publication entitled "On the Number of Primes Less Than a Given Magnitude," and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics.

The definitive book on tiling and geometric patterns, this magnificently illustrated volume features 520 figures and more than 100 tables. Accessible to anyone with a grasp of geometry, it offers numerous graphic examples of two-dimensional spaces covered with interlocking figures, in addition to related problems and references. Suitable for geometry courses as well as independent study, this inspiring book is geared toward students, professional mathematicians, and readers interested in patterns and shapes―artists, architects, and crystallographers, among others. Along with helpful examples from mathematics and geometry, it draws upon models from fields as diverse as crystallography, virology, art, philosophy, and quilting. The self-contained chapters need not be read in sequence, and each concludes with an excellent selection of notes and references. The first seven chapters can be used as a classroom text, and the final five contain fascinating browsing material, including detailed surveys of color patterns, groups of color symmetry, and tilings by polygons. The authors have also added a new Preface and Appendix to this second edition.Dover unabridged, corrected republication of the edition published by W. H. Freeman & Company, New York, 1987.See every Dover book in print atwww.doverpublications.com