Bøker i Dover Books on Mathematics-serien

Two-part treatment discusses coordinates of points on a line, coordinates of points in a plane, coordinates of points in space, and peculiarities of four-dimensional space. Abundance of ingenious problems.

Suitable for introductory graduate-level courses and independent study, this text explores major themes of universal algebra: subdirect decompositions, direct decompositions, free algebras, and varieties of algebra. Includes problems and a bibliography. 1968 edition.

Widely praised for its clarity and thorough coverage, this comprehensive overview of mathematical logic is suitable for readers of many different backgrounds. Designed primarily for advanced undergraduates and graduate students of mathematics, the treatment also contains much of interest to advanced students in computer science and philosophy. An introductory section prepares readers for successive chapters on propositional logic and first-order languages and logic. Subsequent chapters shift in emphasis from an approach to logic from a mathematical point of view to the interplay between mathematics and logic. Topics include the theorems of Gödel, Church, and Tarski on incompleteness, undecidability, and indefinability; a rigorous treatment of recursive functions and recursive relations; computability theory; and Hilbert's Tenth Problem. Numerous exercises appear throughout the text, and an appendix offers helpful background on number theory.Dover (2013) republication of the edition published by PWS Publishing Company, Boston, 1995.See every Dover book in print atwww.doverpublications.com

This text for advanced undergraduate and graduate students presents a rigorous approach that also emphasizes applications. Encompassing more than the usual amount of material on the problems of computation with series, the treatment offers many applications, including those related to the theory of special functions. Numerous problems appear throughout the book.The first chapter introduces the elementary theory of infinite series, followed by a relatively complete exposition of the basic properties of Taylor series and Fourier series. Additional subjects include series of functions and the applications of uniform convergence; double series, changes in the order of summation, and summability; power series and real analytic functions; and additional topics in Fourier series. The text concludes with an appendix containing material on set and sequence operations and continuous functions. Dover (2014) republication of the edition originally published by Holt, Rinehart & Winston, New York, 1962.See every Dover book in print atwww.doverpublications.com

This introduction to calculus is designed for beginning college undergraduates majoring in mathematics as well as undergraduates pursuing other areas of science and engineering for whom calculus will be a vital tool. The three-part treatment begins by exploring the core of the calculus, concentrating on three basic ideas: the definite integral, the derivative, and the fundamental theorem of calculus. Part Two takes up topics such as the maximum and minimum of a function, Taylor's series, partial derivatives, differentiation of vectors, and Green's theorem in the plane. Part Three, which contains no further mathematical development, applies the techniques developed earlier to significant problems in the natural, social, and physical sciences. Appendixes supplement the treatment, offering helpful information on the rudiments of analytic geometry, real numbers, and functions. Numerous examples and exercises appear throughout the text, and solutions to the problems are available as free downloads from the Dover website. Dover (2016) republication of the edition originally published by McGraw-Hill, New York, 1967.See every Dover book in print atwww.doverpublications.com

This text assumes no knowledge of mathematical logic. Beginning with a nonstandard construction of the real number system, it leads students thorough the basic topics of elementary real analysis, topological spaces, and Hilbert space. Includes nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. 1977 edition.

Proceeds from general to special, including chapters on vector analysis on manifolds and integration theory.

Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices.

The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." -- John Stuart Mill.

Stimulating study of how abstract methods of pure mathematics can solve problems in applied math. Solving integral equations, finding Green's function, spectral representation of ordinary differential operators, more. Problems. Bibliography.