Coverage includes geometric transformations, models of the hyperbolic planes, and pseudospheres.

    Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.

    Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.

    Sufficient theoretical information is provided to enable applications of regression analysis to be carried out. Case studies are used to illustrate many of the statistical methods. There is coverage of composite designs for response surface studies and an introduction to the use of computer-generated optimal designs. The Holm procedure is featured, as well as the analysis of means of identifying important effects. This edition includes an expanded use of graphics: scatter plot matrices, three-dimensional rotating plots, paired comparison plots, three-dimensional response surface and contour plots, and conditional effects plots. An accompanying Student Solutions Manual works out problems in the text.

    As such, it is a fundamental and an essential tool in the study of differentiable manifolds.In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers.Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

    In The Curves of Life, Sir Theodore A. Cook (1867–1928), English author and editor, finds that the spiral or helix may lie at the core of life's first principle — that of growth. The spiral is fundamental to the structure of plants, shells, and the human body; to the periodicity of atomic elements and to an animal's horns; to microscopic DNA (the double helix) and to the Andromeda nebula.The Curves of Life portrays the significance of the spiral in 426 illustrations, from a Narwhal's tusk to Dürer's plan for a cylindrical helix. From the spiral in nature, science, and art, the author suggests ideas on the essence of beauty and man's response to it. "One of the chief beauties of the spiral as an imaginative conception is that it is always growing, yet never covering the same ground, so that it is not merely an explanation of the past, but is also a prophecy of the future."Martin Gardner, mathematician and author, said of The Curves of Life, "This is the classic reference on how the golden ratio applies to spirals and helices in nature."

    A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject.

    Jacobs' highly successful, distinctive text was revised on the basis of users' comments and ten years of classroom experience - perfecting an already acclaimed approach to teaching geometry.

    Intended for students of engineering and physical science as well as of pure mathematics.

    Biggs aims to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first section, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject that has strong links with the interaction models studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory. The structure of the volume is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of Additional Results are included at the end of each chapter, thereby covering most of the major advances in the past twenty years. This new and enlarged edition will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.

    The emphasis is on essential probabilistic reasoning, which is illustrated with a large number of samples. The fourth edition adds material related to mathematical finance as well as expansions on stable laws and martingales.From the reviews: "Almost thirty years after its first edition, this charming book continues to be an excellent text for teaching and for self study." -- STATISTICAL PAPERS

    Part I includes all the basic material found in a one semester introductory course in ordinary differential equations. Part II introduces students to certain specialized and more advanced methods, as well as providing a systematic introduction to fundamental theory.

    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.

    This book includes worked examples which are followed by matched problems. It contains exercises and applications.

    Written by two distinguished mathematicians, the expert treatment covers the essentials, incorporating important background materials, examples, and extensive notes.Geared toward advanced undergraduate and graduate students of mathematical programming, the text explores best approximation by algebraic polynomials in both discrete and continuous cases; the discrete problem, with and without constraints; the generalized problem of nonlinear programming; and the continuous minimax problem. Several appendixes discuss algebraic interpolation, convex sets and functions, and other topics. 1974 edition.

    In this third point, we wish to counterbalance a prevalent thesis that the impulse toward mathematical rigor was purely a response to the dialecticians' critique of foundations; on the contrary, we shall see that not until Eudoxus does there appear work which may be described as purely foundational in its intent. Through the examination of these problems, the present work will either alter or set in a new light virtually every standard thesis about the fourth-century Greek geometry. I. THE PRE-EUCLIDEAN THEORY OF INCOMMENSURABLE MAGNITUDES The Euclidean theory of incommensurable magnitudes, as preserved in Book X of the Elements, is a synthetic masterwork. Yet there are detect able seams in its structure, seams revealed both through terminology and through the historical clues provided by the neo-Platonist commentator Proclus."

    Suitable for courses that are designed for students who intend to teach mathematics.

    It covers problems associated with the special nature of plastic state and important applications of plasticity theory. 1971 edition.

    Prerequisites are minimal (calculus, linear algebra, and preferably some acquaintance with computer programming). Text includes many worked examples, problems, and an extensive bibliography. 1974 edition.