It discusses new results, along with applications of probability theory to a variety of problems. The book contains many exercises and is suitable for use as a textbook on graduate-level courses involving data analysis. Aimed at readers already familiar with applied mathematics at an advanced undergraduate level or higher, it is of interest to scientists concerned with inference from incomplete information.

    With a new introduction, three new chapters, modernized language and methods throughout, and an appendix of challenging and enjoyable practice problems, Calculus Made Easy has been thoroughly updated for the modern reader.

    "A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven PinkerProbing the life and work of Kurt Gödel, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.

    Harmonograph is an introduction to the evolution of simple harmonic theory, from the discoveries of Pythagoras to diatonic tuning and equal temperament. Beautiful drawings show the octave as triangle, the fifth as pentagram; diagrams show the principles of harmonics, overtones, and the monochord. Anthony Ashton examines the phenomenon of resonance in Chladni patterns, describes how to build a harmonograph of your own, and provides tables of world tuning systems. This inspiring book will appeal to musicians, mathematicians, designers, and artists alike.

    Therefore, this book provides the fundamental concepts and techniques of real analysis for readers in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations and extend ideas to a new context. Like the first two editions, this edition maintains the same spirit and user-friendly approach with some streamlined arguments, a few new examples, rearranged topics, and a new chapter on the Generalized Riemann Integral.

    Dozens of examples in innumeracy show us how it affects not only personal economics and travel plans, but explains mis-chosen mates, inappropriate drug-testing, and the allure of pseudo-science.

    There are equally many advanced textbooks which delve into the far reaches of statistical theory, while bypassing practical applications. But between these two approaches is an unfilled gap, in which theory and practice merge at an intermediate level. Professor M. G. Bulmer's Principles of Statistics, originally published in 1965, was created to fill that need. The new, corrected Dover edition of Principles of Statistics makes this invaluable mid-level text available once again for the classroom or for self-study.Principles of Statistics was created primarily for the student of natural sciences, the social scientist, the undergraduate mathematics student, or anyone familiar with the basics of mathematical language. It assumes no previous knowledge of statistics or probability; nor is extensive mathematical knowledge necessary beyond a familiarity with the fundamentals of differential and integral calculus. (The calculus is used primarily for ease of notation; skill in the techniques of integration is not necessary in order to understand the text.)Professor Bulmer devotes the first chapters to a concise, admirably clear description of basic terminology and fundamental statistical theory: abstract concepts of probability and their applications in dice games, Mendelian heredity, etc.; definitions and examples of discrete and continuous random variables; multivariate distributions and the descriptive tools used to delineate them; expected values; etc. The book then moves quickly to more advanced levels, as Professor Bulmer describes important distributions (binomial, Poisson, exponential, normal, etc.), tests of significance, statistical inference, point estimation, regression, and correlation. Dozens of exercises and problems appear at the end of various chapters, with answers provided at the back of the book. Also included are a number of statistical tables and selected references.

    (The also-rans that year included Tom Wolfe, Verlyn Klinkenborg, and Oliver Sacks.) Hayes's work in this genre has also appeared in such anthologies as The Best American Magazine Writing, The Best American Science and Nature Writing, and The Norton Reader. Here he offers us a selection of his most memorable and accessible pieces--including "Clock of Ages"--embellishing them with an overall, scene-setting preface, reconfigured illustrations, and a refreshingly self-critical "Afterthoughts" section appended to each essay.

    Each chapter opens with a surprising insight—not a mathematic formula, but a common observation. From there, the authors leapfrog over math and anecdote toward profound ideas about nature, art, and music. Coincidences is a book for lovers of puzzles and posers of outlandish questions, lapsed math aficionados and the formula-phobic alike.

    Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).

    The material is arranged chronologically beginning with archaic origins and covers Egyptian, Mesopotamian, Greek, Chinese, Indian, Arabic and European contributions done to the nineteenth century and present day. There are revised references and bibliographies and revised and expanded chapters on the nineteeth and twentieth centuries.

    Written by two of the best-known names in categorical logic, Conceptual Mathematics is the first book to apply categories to the most elementary mathematics. It thus serves two purposes: first, to provide a key to mathematics for the general reader or beginning student; and second, to furnish an easy introduction to categories for computer scientists, logicians, physicists, and linguists who want to gain some familiarity with the categorical method without initially committing themselves to extended study.

    A timeless introduction to the field and a landmark in symbolic logic, showing that classical logic can be treated algebraically.

    Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

    It offers a comprehensive and accessible treatment of the theory of algorithms and complexity—the elegant body of concepts and methods developed by computer scientists over the past 30 years for studying the performance and limitations of computer algorithms. The book is self-contained in that it develops all necessary mathematical prerequisites from such diverse fields such as computability, logic, number theory and probability.