Beginning with the background and very nature of probability theory, the book then proceeds through sample spaces, combinatorial analysis, fluctuations in coin tossing and random walks, the combination of events, types of distributions, Markov chains, stochastic processes, and more. The book's comprehensive approach provides a complete view of theory along with enlightening examples along the way.

    This brought about the crucial change in the concept of number that made possible modern science — in which the symbolic "form" of a mathematical statement is completely inseparable from its "content" of physical meaning. Includes a translation of Vieta's Introduction to the Analytical Art. 1968 edition. Bibliography.

    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.

    The topics range from elementary to advanced - from algebra, trigonometry and calculus to vector analysis, Bessel functions, Legendre polynomials, and elliptic integrals.

    

    It examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, finite sets and cardinal numbers, rational and real numbers, and other subjects. 1960 edition.

    Covering theoretical mechanics, this text contains 720 solved problems and covers topics such as vectors, velocity and acceleration, Newton's laws of motion, motion in a unified field, moving co-ordinate systems, rockets and collisions, space motion of rigid bodies and Hamiltonian theory.

    Part I treas length-preserving transformations, this volume treats shape-preserving transformations; and Part III treats affine and protective transformations. These classes of transformations play a fundamental role in the group-theoretic approach to geometry. As in the previous volume, the treatment is direct and simple. The introduction of each new idea is supplemented by problems whose solutions employ the idea just presented, and whose detailed solutions are given in the second half of the book.

    -- First edition (1968) sold more than 347,000 copies and was translated into nine languages-- Advanced calculus is a required course for over 163,000 students, including all math majors and many science and engineering majors-- Important new chapters, on Topology and LaPlace Transforms enhance the book's cross-disciplinary usage-- Contains essential new theorems with explanatory proofs

    Chung's A Course in Probability Theory, now in its third edition, has sustained its popularity for nearly 35 years. Originally developed from Dr. Chung's course at Stanford University, this book continues to be a successful tool for instructors and students alike.This third edition offers for the first time a supplement on Measure and Integral. This material has been used to supplement Dr. Chung's course for many years. It will assist students not previously exposed to this material and can also be sued as a review. The text is very flexible, offering instructors several different options in creating their syllabus, or in aligning it with current course design. It has been used successfully at over 75 universities since its initial publication.--back cover

    Impressed by the simplicity and mathematical elegance of the tableau point of view, the author focuses on it here.After preliminary material on tress (necessary for the tableau method), Part I deals with propositional logic from the viewpoint of analytic tableaux, covering such topics as formulas or propositional logic, Boolean valuations and truth sets, the method of tableaux and compactness.Part II covers first-order logic, offering detailed treatment of such matters as first-order analytic tableaux, analytic consistency, quantification theory, magic sets, and analytic versus synthetic consistency properties.Part III continues coverage of first-order logic. Among the topics discussed are Gentzen systems, elimination theorems, prenex tableaux, symmetric completeness theorems, and system linear reasoning.Raymond M. Smullyan is a well-known logician and inventor of mathematical and logical puzzles. In this book he has written a stimulating and challenging exposition of first-order logic that will be welcomed by logicians, mathematicians, and anyone interested in the field.

    Yitzhak Katznelson demonstrates the central ideas of harmonic analysis and provides a stock of examples to foster a clear understanding of the theory. This new edition has been revised to include several new sections and a new appendix.

    Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.

    Clayton's Principles of Stellar Evolution and Nucleosynthesis remains the standard work on the subject, a popular textbook for students in astronomy and astrophysics and a rich sourcebook for researchers. The basic principles of physics as they apply to the origin and evolution of stars and physical processes of the stellar interior are thoroughly and systematically set out. Clayton's new preface, which includes commentary and selected references to the recent literature, reviews the most important research carried out since the book's original publication in 1968.

    Research reviewed in the book include Berlekamp's algorithm for factoring polynomials (the first significant improvement on a classical mathematical problem in almost two centuries), and Berlekamp's algorithm for decoding Bose- Chaudhuri-Hocquenghem and Reed-Solomon codes. For the past 15 years, this coding algorithm has been used universally in algebraic decoders that correct multiple errors in communications or computer memory systems. Chapters include: Basic Binary Codes; Arithmetic Operations Modulo an Irreducible Binary Polynomial; The Number of Irreducible q-ary Polynomials of Given Degree; The Factorization of Polynomials Over Finite Fields; The Enumeration of Information Symbols in BCH Codes; appendices and references.

    This useful volume promises to be the salvation of those who, despite a distaste for math, need to use statistics in their work. Approaching the topic through logic and common sense rather than via complex mathematics, the author introduces the principle and applications of statistics, and teaches his reader to extract truth and draw valid conclusions from numerical data.An indispensable first chapter warns the reader on the ways he can be misled by numbers, and the ways in which numbers are used to misrepresent the truth (arithmetical errors, false percentages, fictitious precision, incomplete data, faulty comparisons, improper sampling, failure to allow for the effect of chance and misleading presentation). There follows a wealth of information on probability, sampling, averages and scatter, the design of investigations, significance tests — all presented in terms of specific, carefully worked out cases that make them both interesting and immediately understandable to the layman. The book is so entertaining, so eminently practical, that you'll gain expertise in the laws of chance, probability formulae, sampling methods, calculating the arithmetic mean and standard deviation, finding the geometric and the logarithmic mean, constructing an effective experiment or investigation using statistics, and a wide range of tests determining significance (zM test, X2 text, runs test for randomness and a number of others) and scores of other important skills — in a form so palatable you'll hardly realize how much you are learning, Scores of tables illustrate the text, and a complete table of squares and square roots is provided for your convenience. A handy guide to significance tests helps you to choose the test valid and appropriate for your data with speed and ease.Written with humor, clarity, and eminent good sense by a scientist of international reputation, this book is for anyone who wants to dispel the mystery of the numbers that pervade modern life, from news articles to literary criticism. For the biologist, sociologist, experimental psychologist or anyone whose profession requires the handling of a large mass of data, it will be of incalculable value.

    These volumes contain many extraordinary problems and sequences of problems, mostly from some time past, well worth attention today and tomorrow. Written in the early twenties by two young mathematicians of outstanding talent, taste, breadth, perception, perseverence, and pedagogical skill, this work broke new ground in the teaching of mathematics and how to do mathematical research. (Bulletin of the American Mathematical Society)

    This classic text focuses on pedagogy to enhance comprehension for students and make it more suitable for independent study.

    Traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers created by Hamilton and Grassmann to the final acceptance around 1910 of the modern system of vector analysis. Concentrates on vector addition and subtraction, the forms of vector multiplication, vector division (in those systems where it occurs), and the specification of vector types. 1985 corrected edition of 1967 original.