But the dot, though perfect in every way, only had eyes for a wild and unkempt squiggle. All of the line's romantic dreams were in vain, until he discovered...angles! Now, with newfound self-expression, he can be anything he wants to be--a square, a triangle, a parallelogram....And that's just the beginning!First published in 1963 and made into an Academy Award-winning animated short film, here is a supremely witty love story with a twist that reveals profound truths about relationships--both human and mathematical--sure to tickle lovers of all ages.

    . . Nothing less than a major contribution to the scientific culture of this world." — The New York Times Book ReviewThis major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference."This is a masterful English translation of a stupendous and formidable mathematical masterpiece . . ." — Social Science

    These intriguing problems, collected from Gardner's Scientific American columns, involve knots, interlocking rings, rotations and reflections, logical paradox, two-dimensional universes, chess strategies, and gambling odds."Gardner conjures problems that are both profound and silly; exquisite truths and outrageous absurdities; paradoxes, anagrams, palindromes and party tricks. . . . He knows, better than most, how many amazing true things there are in the world."—Newsweek

    Morse theory was developed in the 1920s by mathematician Marston Morse. (Morse was on the faculty of the Institute for Advanced Study, and Princeton published his Topological Methods in the Theory of Functions of a Complex Variable in the Annals of Mathematics Studies series in 1947.) One classical application of Morse theory includes the attempt to understand, with only limited information, the large-scale structure of an object. This kind of problem occurs in mathematical physics, dynamic systems, and mechanical engineering. Morse theory has received much attention in the last two decades as a result of a famous paper in which theoretical physicist Edward Witten relates Morse theory to quantum field theory.Milnor was awarded the Fields Medal (the mathematical equivalent of a Nobel Prize) in 1962 for his work in differential topology. He has since received the National Medal of Science (1967) and the Steele Prize from the American Mathematical Society twice (1982 and 2004) in recognition of his explanations of mathematical concepts across a wide range of scienti.c disciplines. The citation reads, "The phrase sublime elegance is rarely associated with mathematical exposition, but it applies to all of Milnor's writings. Reading his books, one is struck with the ease with which the subject is unfolding and it only becomes apparent after re.ection that this ease is the mark of a master.?Milnor has published five books with Princeton University Press.

    This material is intended to contribute to a wider appreciation of the mathematical words "continuity and linearity." The book's purpose is to illuminate the meanings of these words and their relation to each other.

    The aim is to give treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Considerable attention is devoted to physical applications of variational methods, e.g., canonical equations, variational principles of mechanics, and conservation laws.the reader who merely wishes to become familiar with the most basic concepts and methods of the calculus of variations need only study the first chapter. Students wishing a more extensive treatment, however, will find the first six chapters comprise a complete university-level course in the subject, including the theory of fields and sufficient conditions for weak and strong extrema. Chapter seven considers the application of variational methods to the study of systems with infinite degrees of freedom, and Chapter eight deals with direct methods in the calculus of variations. The problems following each chapter were made specially for this English-language edition, and many of them comment further on corresponding parts of the text. Two appendices and suggestions for supplementary reading round out the text.Substantially revised and corrected by the translator, this inexpensive ne edition will be welcomed by advanced undergraduate and graduate students of mathematics and physics.

    Gives proofs of all the theoretical results used in modern sampling practice. New topics in this edition include the approximate methods developed for the problem of attaching standard errors or confidence limits to nonlinear estimates made from the results of surveys with complex plans.

    

    

    Topics include characterizing and comparing the measured performance of a material, product, or process; general considerations in planning experiments; statistical techniques for analyzing extreme-value data; use of transformations; and many other practical methods. 1966 edition. Index. 52 figures. 76 tables.

    History of Mathematics.

    The author will also improve the reasoning and methodology of the text by adding proofs of essential theorems in advanced calculus. Outdated chapters on very advanced topics like Complex Functions and Elliptic Integrals will be removed. Chapters and problems throughout the book will be updated to correspond to current advanced calculus courses. The book complements the undergraduate mathematics course required by math and many science and engineering majors, carefully follows standard textbooks, and serves as a complete and comprehensive review of the subject.