- Table View
- List View
N-Person Game Theory: Concepts and Applications (Dover Books on Mathematics)
by Anatol RapoportN-person game theory provides a logical framework for analyzing contests in which there are more than two players or sets of conflicting interests-anything from a hand of poker to the tangled web of international relations. In this sequel to his Two-Person Game Theory, Dr. Rapoport provides a fascinating and lucid introduction to the theory, geared towards readers with little mathematical background but with an appetite for rigorous analysis.Following an introduction to the necessary mathematical notation (mainly set theory), in Part I the author presents basic concepts and models, including levels of game-theoretic analysis, individual and group rationality, the Von Neumann-Morgenstern solution, the Shapley value, the bargaining set, the kernel, restrictions on realignments, games in partition function form, and Harsanyi's bargaining model. In Part II he delves into the theory's social applications, including small markets, large markets, simple games and legislatures, symmetric and quota games, coalitions and power, and more.This affordable new edition will be welcomed by economists, political scientists, historians, and anyone interested in multilateral negotiations or conflicts, as well as by general readers with an interest in mathematics, logic, or games.
On Formally Undecidable Propositions of Principia Mathematica and Related Systems (Dover Books on Mathematics)
by Kurt GödelIn 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics.The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument.This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.
Practical Statistics Simply Explained
by Dr Russell LangleyFor those who need to know statistics but shy away from math, this book teaches how to extract truth and draw valid conclusions from numerical data using logic and the philosophy of statistics rather than complex formulae. Lucid discussion of averages and scatter, investigation design, more. Problems with solutions.
Probability, Statistics, and Decision for Civil Engineers (Dover Books on Engineering)
by Jack R Benjamin C. Allin CornellDesigned as a primary text for civil engineering courses, as a supplementary text for courses in other areas, or for self-study by practicing engineers, this text covers the development of decision theory and the applications of probability within the field. Extensive use of examples and illustrations helps readers develop an in-depth appreciation for the theory's applications, which include strength of materials, soil mechanics, construction planning, and water-resource design. A focus on fundamentals includes such subjects as Bayesian statistical decision theory, subjective probability, and utility theory. This makes the material accessible to engineers trained in classical statistics and also provides a brief elementary introduction to probability. The coverage also addresses in detail the methods for analyzing engineering economic decisions in the face of uncertainty. An Appendix of tables makes this volume particularly useful as a reference text.
Real Analysis
by Truman Arthur Botts Edward James McShaneThis text offers upper-level undergraduates and graduate students a survey of practical elements of real function theory, general topology, and functional analysis. Beginning with a brief discussion of proof and definition by mathematical induction, it freely uses these notions and techniques. The maximality principle is introduced early but used sparingly; an appendix provides a more thorough treatment. The notion of convergence is stated in basic form and presented initially in a general setting. The Lebesgue-Stieltjes integral is introduced in terms of the ideas of Daniell, measure-theoretic considerations playing only a secondary part. The final chapter, on function spaces and harmonic analysis, is deliberately accelerated. Helpful exercises appear throughout the text. 1959 edition.
Ruler and the Round: Classic Problems in Geometric Constructions (Dover Books on Mathematics)
by Nicholas D. KazarinoffAlthough easy to comprehend and fun to do, many geometric constructions defy completion with just a ruler and a compass. This book takes an intriguing look at the most famous of these "impossible" constructions. In exploring ground rules, history, and angle trisection, the first part considers angle trisection and bird migration, constructed points, analytic geometry, algebraic classification of constructible numbers, fields of real numbers, cubic equations, and marked ruler, quadratix, and hyperbola (among other subjects). The second part treats nonconstructible regular polygons and the algebra associated with them; specifically, irreducibility and factorization, unique factorization of quadratic integers, finite dimensional vector spaces, algebraic fields, and nonconstructible regular polygons. High school and college students as well as amateur mathematicians will appreciate this stimulating and provocative book, and its glimpses into the crucial role geometry plays in a wide range of mathematical applications.
Science and Method
by Henri PoincaréThis classic by the famous mathematician defines the basic methodology and psychology of scientific discovery, particularly regarding mathematics and mathematical physics. Drawing on examples from many fields, it explains how scientists analyze and choose their working facts, and it explores the nature of experimentation, theory, and the mind. 1914 edition.
A Source Book in Mathematics
by David Eugene SmithThis work presents, in English translation, the great discoveries in mathematics from the Renaissance to the end of the nineteenth century. You are able to read the writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others, exactly as the world saw them for the first time. Succinct selections from 125 different treatises and articles, most of them unavailable elsewhere in English, offer a vivid, firsthand story of the growth of mathematics.
Speed Mathematics Simplified (Dover Books on Mathematics)
by Edward StoddardThis entertaining, easy-to-follow book is ideal for anyone who works with numbers and wants to develop greater speed, ease, and accuracy in doing mathematical calculations. In an inspiring introduction, science writer Edward Stoddard offers important suggestions for mastering an entirely new system of figuring. Without having to discard acquired information about mathematical computation, students build on the knowledge they already have, "streamline" these techniques for rapid use and then combine them with classic shortcuts.Initially, readers learn to master a basic technique known as the Japanese "automatic" figuring method — the principle behind the abacus. This method enables users to multiply without carrying, divide with half the written work of long division, and mentally solve mathematical problems that usually require pencil and paper or a calculator. Additional chapters explain how to build speed in addition and subtraction, how to check for accuracy, master fractions, work quickly with decimals, handle percentages, and much more. A valuable asset for people in business who work with numbers on a variety of levels, this outstanding book will also appeal to students, teachers, and anyone looking for a reliable way to improve skill and speed in doing basic arithmetic.
Straight Lines, Parallel Lines, Perpendicular Lines (Young Math Books)
by Mannis Charosh Enrico ArnoUsing an imaginative approach to basic principles, this book invites the reader to explore, to understand, and to enjoy the principles of mathematics.
Theory of Linear Operators in Hilbert Space
by I. M. Glazman N. I. AkhiezerThis classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.
A Treatise on the Differential Geometry of Curves and Surfaces (Dover Books on Mathematics)
by Luther Pfahler EisenhartCreated especially for graduate students, this introductory treatise on differential geometry has been a highly successful textbook for many years. Its unusually detailed and concrete approach includes a thorough explanation of the geometry of curves and surfaces, concentrating on problems that will be most helpful to students. 1909 edition.
Winter Walk in the City (In The City Ser.)
by Cathy Goldberg FishmanFollow this adventure through the city in the winter, and peek into the windows to explore multicultural winter holidays.