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by J. L. Bell (Author)Topos theory has led to unexpected connections between classical and constructive mathematics. This text explores Lawvere and Tierney's concept of topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. A virtually self-contained introduction, this volume presents toposes as the models of theories -- known as local set theories -- formulated within a typed intuitioni...
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by Charles Loewner (Author)Professor of Mathematics at Stanford University from 1950 until his death in 1968, Charles Loewner occasionally taught as a Visiting Professor at the University of California at Berkeley. After his 1955 course at Berkeley on continuous groups, Loewner's lectures were reproduced in the form of mimeographed notes. The professor had intended to develop these notes into a book, but the project was still in formative stages at the time of his death. The 1971 edition comp...
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by Joseph Louis Lagrange (Author), Thomas J. McCormack (Translator)One of the eighteenth century's greatest mathematicians, Lagrange made significant contributions to all fields of analysis and number theory. He survived the French Revolution to deliver these lectures in 1795 at the cole Normale, a training school for teachers. An exemplar among elementary expositions, Lagrange's talks feature both originality of thought and elegance of expression.The five lectures begin with discussions of ...
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by Jerome Spanier (Author), Ely M. Gelbard (Author)This two-part treatment introduces the general principles of the Monte Carlo method within a unified mathematical point of view, applying them to problems in neutron transport. It describes several efficiency-enhancing approaches, including the method of superposition and simulation of the adjoint equation based on reciprocity.The first half of the book presents an exposition of the fundamentals of Monte Carlo methods, examining discrete and ...
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by Jacob Lubliner (Author)The aim of Plasticity Theory is to provide a comprehensive introduction to the contemporary state of knowledge in basic plasticity theory and to its applications. It treats several areas not commonly found between the covers of a single book: the physics of plasticity, constitutive theory, dynamic plasticity, large-deformation plasticity, and numerical methods, in addition to a representative survey of problems treated by classical methods, such as elastic-plastic pr...
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by H. S. M. Coxeter (Author)Polytopes are geometrical figures bounded by portions of lines, planes, or hyperplanes. In plane (two dimensional) geometry, they are known as polygons and comprise such figures as triangles, squares, pentagons, etc. In solid (three dimensional) geometry they are known as polyhedra and include such figures as tetrahedra (a type of pyramid), cubes, icosahedra, and many more; the possibilities, in fact, are infinite H. S. M. Coxeter's book is the foremost book avail...
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by Anthony E. Labarre (Author)Geared toward those who have studied elementary calculus and intend to progress to more advanced mathematics, this book stresses concepts rather than techniques. It emphasizes the simplest setting of basic theorems so that students may progress from "one-space" to ""n"-space" calculus.An introductory section by the author reviews the roles of sets, relations, and functions. Subsequent chapters explore real numbers, the limit concept, useful theorems, continuity, ...
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by Georgi E. Shilov (Author), Richard a. Silverman (Author)This introduction to linear algebra and functional analysis offers a clear expository treatment, viewing algebra, geometry, and analysis as parts of an integrated whole rather than separate subjects. All abstract ideas receive a high degree of motivation, and numerous examples illustrate many different fields of mathematics. Abundant problems include hints or answers.Author BiographySoviet mathematician Georgi E. Shilov (1917-75) was ...
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by Emil Artin (Author), Arthur N. Milgram (Editor)In the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications.The first section d...
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by David F. Belding (Author), Kevin J. Mitchell (Author)This introduction to basic analysis presents a careful development of the real number system and the theory of calculus on the real line, extending the theory to real and complex planes. Designed as a first encounter with rigorous, formal mathematics for students with one year of calculus, the work features extended discussions of key ideas and detailed proofs of difficult theorems.Authors David F. Belding and Kevin J. Mitchell are Profe...
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by Leonard J. Savage (Author)With the 1954 publication of his Foundations of Statistics, in which he proposed a basis that takes into account not only strictly objective and repetitive events, but also vagueness and interpersonal differences, Leonard J. Savage opened the greatest controversy in modern statistical thought. His theory of the foundations, connected with the personalistic interpretation of probability, challenged the then dominant frequentist school. In the first seven chapters o...
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by John D. Pryce (Author)Introduction to the themes of mathematical analysis, geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elementary Fourier analysis. Numerous exercises and worked examples.1973 edition.Author BiographyJohn D. Pryce is a Mathematics Professor at England's Cranfield University. Number of Pages: 320 Dimensions: 0.7 x 8.4 x 5.4 IN Illustrated: Yes Publication Date: October 20, 2011
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by Tullio Levi-Civita (Author)Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.Part one opens with considerations of functional determinants and matrices, advanci...
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by Nikolai Nikolaevich Vorob'ev (Author)Fibonacci numbers date back to an 800-year-old problem concerning the number of offspring born in a single year to a pair of rabbits. This book offers the solution and explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. A discussion of the "golden section" rectangle, in which the lengths of the sides can be expressed as a ration of two successive Fibonacci numbers, draws upon attempts by ancient and medieval...
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by G. E. Shilov (Author), B. L. Gurevich (Author)This graduate-level textbook and monograph defines the functions of a real variable through consistent use of the Daniell scheme, offering a rare and useful alternative to customary approaches. The treatment can be understood by any reader with a solid background in advanced calculus, and it features many problems with hints and answers. The exposition is fresh and sophisticated, declared Sci-Tech Book News, and will engage the interest of acc...
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by Bradford Henry Arnold (Author)This volume concentrates on the structure of Boolean algebras and rings as developed through simpler algebraic systems. The algebra of logic and set theory appears as applications or illustrations throughout, and numerous problems form an integral part of the text. No prior knowledge of Boolean algebra is necessary. The text begins with a consideration of some concepts of intuitive logic. Subsequent chapters introduce Boolean functions, basic ordered sets, and...
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by John Horton Conway (Author)World-famous mathematician John H. Conway based this classic text on a 1966 course he taught at Cambridge University. Geared toward graduate students of mathematics, it will also prove a valuable guide to researchers and professional mathematicians.His topics cover Moore's theory of experiments, Kleene's theory of regular events and expressions, Kleene algebras, the differential calculus of events, factors and the factor matrix, and the theory of operators. Addit...
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by Y. a. Rozanov (Author)This book, a concise introduction to modern probability theory and certain of its ramifications, deals with a subject indispensable to natural scientists and mathematicians alike. Here the readers, with some knowledge of mathematics, will find an excellent treatment of the elements of probability together with numerous applications. Professor Y. A. Rozanov, an internationally known mathematician whose work in probability theory and stochastic processes has received wi...
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by Anthony J. Pettofrezzo (Author)This book presents an elementary and concrete approach to linear algebra that is both useful and essential for the beginning student and teacher of mathematics. Here are the fundamental concepts of matrix algebra, first in an intuitive framework and then in a more formal manner. A Variety of interpretations and applications of the elements and operations considered are included. In particular, the use of matrices in the study of transformations of the plane i...
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by Hans Schwerdtfeger (Author)This book should be in every library, and every expert in classical function theory should be familiar with this material. The author has performed a distinct service by making this material so conveniently accessible in a single book. -- Mathematical ReviewSince its initial publication in 1962, Professor Schwerdtfeger's illuminating book has been widely praised for generating a deeper understanding of the geometrical theory of analytic functions as well as of th...
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by Gertrude Ehrlich (Author)A text in abstract algebra for undergraduate mathematics majors, this volume contains enough material for a two-semester course. It presents extensive coverage of set theory, groups, rings, modules, vector spaces, and fields. Examples, definitions, theorems, and proofs appear throughout, along with numerous practice exercises at the end of each section. 1991 edition.Author BiographyGertrude Ehrlich is a Professor Emerita in the Department of Mathematics at the Univ...
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by R. W. Hamming (Author)This book by a prominent mathematician is appropriate for a single-semester course in applied numerical analysis for computer science majors and other upper-level undergraduate and graduate students. Although it does not cover actual programming, it focuses on the applied topics most pertinent to science and engineering professionals.An extensive range of topics includes round-off and function evaluation, real zeros of a function, simultaneous linear equations and mat...
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by Gilbert Helmberg (Author)Starting with a definition of Hilbert space and its geometry, this text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-adjoint operators. Familiarity with analysis and analytic geometry is the only prerequisite. Extensive appendixes complement the text. 1969 edition. Number of Pages: 346 Dimensions: 0.73 x 9.18 x 6.23 IN Illustrated: Yes Publication Date: June 11, 2008
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by Edward R. Scheinerman (Author), Daniel H. Ullman (Author), Claude Berge (Foreword by)This volume explores the various ways in which integer-valued graph theory concepts can be modified to derive nonintegral values. It explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics, including fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and additional subjec...
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by J. M. Cordier (Author), T. Porter (Author)This in-depth treatment uses shape theory as a ""case study"" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. 1989 edition. Number of Pages: 210 Dimensions: 0.4 x 9.19 x 6.27 IN Illustrated: Yes Publication Date: May 19, 2008
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by Élie Cartan (Author)The French mathematician Élie Cartan (1869-1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically ...
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by Thomas J. Jech (Author)Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and consequences of the axiom of choice. Each chapter contains several problems, graded according to difficulty, and concludes with some historical remarks.An introduction to the use of the axiom of choice is followed by explorations of consistency, permutation models, and independence. Subsequent chapters examine embedding theorems, models with finite suppo...
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by N. G. De Bruijn (Author)A reader looking for interesting problems tackled often by highly original methods, for precise results fully proved, and for procedures fully motivated, will be delighted. -- Mathematical Reviews.Asymptotics is not new. Its importance in many areas of pure and applied mathematics has been recognized since the days of Laplace. Asymptotic estimates of series, integrals, and other expressions are commonly needed in physics, engineering, and other fields. Unfortunately...
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by Avner Friedman (Author)This accessible and self-contained treatment provides even readers previously unacquainted with parabolic and elliptic equations with sufficient background to understand research literature. Author Avner Friedman -- Director of the Mathematical Biosciences Institute at The Ohio State University -- offers a systematic and thorough approach that begins with the main facts of the general theory of second order linear parabolic equations. Subsequent chapters explore asym...
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by Z. a. Melzak (Author)Intended for students of many different backgrounds with only a modest knowledge of mathematics, this text features self-contained chapters that can be adapted to several types of geometry courses. Only a slight acquaintance with mathematics beyond the high-school level is necessary, including some familiarity with calculus and linear algebra. This text's introductions to several branches of geometry feature topics and treatments based on memorability and relevance. Th...
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by Robert B. Ash (Author)This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus.Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, ...
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by Roland Deaux (Author), Howard Eves (Translator)Geared toward readers unfamiliar with complex numbers, this text explains how to solve the kinds of problems that frequently arise in the applied sciences, especially electrical studies. To assure an easy and complete understanding, it develops topics from the beginning, with emphasis on constructions related to algebraic operations.The three-part treatment begins with geometric representations of complex numbers and proceeds to an in-depth su...