Bøger i Dover Books on Mathematics serien

This text examines the reinterpretation of calculus by Augustin-Louis Cauchy and his peers in the 19th century. These intellectuals created a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.

"This book is well-written and the bibliography excellent," declared Mathematical Reviews of John Knopfmacher's innovative study. The three-part treatment applies classical analytic number theory to a wide variety of mathematical subjects not usually treated in an arithmetical way. The first part deals with arithmetical semigroups and algebraic enumeration problems; Part Two addresses arithmetical semigroups with analytical properties of classical type; and the final part explores analytical properties of other arithmetical systems.Because of its careful treatment of fundamental concepts and theorems, this text is accessible to readers with a moderate mathematical background, i.e., three years of university-level mathematics. An extensive bibliography is provided, and each chapter includes a selection of references to relevant research papers or books. The book concludes with an appendix that offers several unsolved questions, with interesting proposals for further development.Dover (2015) corrected and enlarged republication of the edition originally published by North-Holland Publishing Company, Amsterdam, and the American Elsevier Publishing Company, Inc., New York, 1975.See every Dover book in print atwww.doverpublications.com

This stimulating collection -- complete with instructive solutions -- involves numbers, equations, polygons, and polyhedra as well as more amusing and practical subjects, from picnic hams to rooks on a chessboard.

Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.

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

Concise, highly focused review offers everything high school and beginning college students need to know to handle problems in probability and statistics. Rigorously tested examples and coherent explanations, presented in an easy-to-follow format.

Classic overview for advanced undergraduates and graduate students of mathematics explores affine and projective geometry, symplectic and orthogonal geometry, general linear group, and structure of symplectic and orthogonal groups. 1957 edition.

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

Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include Some Theorems and Concepts of Graph Theory, Topological Concepts in Graph Theory, Graphical Reconstruction, and other introductory talks. A series of invited lectures follows, featuring presentations by other authorities on the faculty of University College as well as visiting scholars. These include Extremal Problems in Graph Theory by Paul Erdös, Complete Bipartite Graphs: Decomposition into Planar Subgraphs, by Lowell W. Beineke, Graphs and Composite Games, by Cedric A .B. Smith, and several others.Dover (2015) republication of the edition published by Holt, Rinehart & Winston, Inc., New York, 1967.See every Dover book in print atwww.doverpublications.com

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

This best-of compilation features 101 of the most entertaining and challenging math puzzles from Dover's vast collections. No advanced knowledge of mathematics is necessary, just solid thinking and puzzle-solving skills. Includes complete solutions.