Search Results for "elementary-induction-on-abstract-structures-dover-books-on-mathematics"

Elementary Induction on Abstract Structures

Elementary Induction on Abstract Structures

  • Author: Yiannis N. Moschovakis
  • Publisher: Courier Corporation
  • ISBN: 0486152014
  • Category: Mathematics
  • Page: 240
  • View: 7826
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Well-written research monograph, recommended for students and professionals interested in model theory and definability theory. "Easy to use and a pleasure to read." — Bulletin of the American Mathematical Society. 1974 edition.

Contextual Approaches to Truth and the Strengthened Liar Paradox

Contextual Approaches to Truth and the Strengthened Liar Paradox

  • Author: Christine Schurz
  • Publisher: Walter de Gruyter
  • ISBN: 311032458X
  • Category: Philosophy
  • Page: 145
  • View: 8037
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The problem of truth and the liar paradox is one of the most extensive problems of philosophy. The liar paradox can be avoided by assuming a so-called theory of partial truth instead of a classical theory of truth. Theories of partial truth, however, cannot solve the so-called strengthened liar paradox, which is the problem that many semantic statements about the so-called strengthened liar cannot be true in a theory of partial truth. If such semantic statements were true in the theory, another paradox would emerge. To proponents of contextual accounts, which assume that the concept of truth is context-dependent, the strengthened liar paradox is the core of the liar problem. This book provides an overview of current contextual approaches to the strengthened liar paradox. For this purpose, the author investigates formal theories of truth that result from formal reconstructions of such contextual approaches.

Introduction to Logic

Introduction to Logic

and to the Methodology of Deductive Sciences

  • Author: Alfred Tarski
  • Publisher: Courier Corporation
  • ISBN: 0486318893
  • Category: Mathematics
  • Page: 272
  • View: 5168
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This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.

A Book of Abstract Algebra

A Book of Abstract Algebra

Second Edition

  • Author: Charles C Pinter
  • Publisher: Courier Corporation
  • ISBN: 0486474178
  • Category: Mathematics
  • Page: 384
  • View: 8331
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Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.

Elements of Abstract Algebra

Elements of Abstract Algebra

  • Author: Allan Clark
  • Publisher: Courier Corporation
  • ISBN: 0486140350
  • Category: Mathematics
  • Page: 224
  • View: 5005
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Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.

Algebra

Algebra

Chapter 0

  • Author: Paolo Aluffi
  • Publisher: American Mathematical Soc.
  • ISBN: 0821847813
  • Category: Algebra
  • Page: 713
  • View: 8276
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Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

Abstract and Concrete Categories

Abstract and Concrete Categories

The Joy of Cats

  • Author: Jiri Adamek,Jiří Adámek (ing.),Horst Herrlich,George E. Strecker
  • Publisher: N.A
  • ISBN: 9780486469348
  • Category: Mathematics
  • Page: 517
  • View: 4734
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This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases. A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

Mathematics for Algorithm and Systems Analysis

Mathematics for Algorithm and Systems Analysis

  • Author: Edward A. Bender,Stanley Gill Williamson
  • Publisher: Courier Corporation
  • ISBN: 0486442500
  • Category: Mathematics
  • Page: 248
  • View: 2519
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Discrete mathematics is fundamental to computer science, and this up-to-date text assists undergraduates in mastering the ideas and mathematical language to address problems that arise in the field's many applications. It consists of 4 units of study: counting and listing, functions, decision trees and recursion, and basic concepts of graph theory.

Discrete Mathematics with Applications

Discrete Mathematics with Applications

  • Author: Susanna S. Epp
  • Publisher: Cengage Learning
  • ISBN: 0495391328
  • Category: Mathematics
  • Page: 984
  • View: 8582
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Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, FOURTH EDITION provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Logic in Elementary Mathematics

Logic in Elementary Mathematics

  • Author: Robert M. Exner,Myron F. Rosskopf
  • Publisher: Courier Corporation
  • ISBN: 0486482219
  • Category: Mathematics
  • Page: 274
  • View: 8146
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"This accessible, applications-related introductory treatment explores some of the structure of modern symbolic logic useful in the exposition of elementary mathematics. Topics include axiomatic structure and the relation of theory to interpretation. No prior training in logic is necessary, and numerous examples and exercises aid in the mastery of the language of logic. 1959 edition"--

Set Theory and the Continuum Problem

Set Theory and the Continuum Problem

  • Author: Raymond M. Smullyan,Melvin Fitting
  • Publisher: N.A
  • ISBN: 9780486474847
  • Category: Mathematics
  • Page: 315
  • View: 7697
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A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.

A Short Course in Discrete Mathematics

A Short Course in Discrete Mathematics

  • Author: Edward A. Bender,S. Gill Williamson
  • Publisher: Courier Corporation
  • ISBN: 0486439461
  • Category: Mathematics
  • Page: 240
  • View: 9268
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What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 edition. Notation Index. Subject Index.

Mathematical Analysis

Mathematical Analysis

A Concise Introduction

  • Author: Bernd S. W. Schröder
  • Publisher: John Wiley & Sons
  • ISBN: 9780470226766
  • Category: Mathematics
  • Page: 584
  • View: 1383
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A self-contained introduction to the fundamentals of mathematical analysis Mathematical Analysis: A Concise Introduction presents the foundations of analysis and illustrates its role in mathematics. By focusing on the essentials, reinforcing learning through exercises, and featuring a unique "learn by doing" approach, the book develops the reader's proof writing skills and establishes fundamental comprehension of analysis that is essential for further exploration of pure and applied mathematics. This book is directly applicable to areas such as differential equations, probability theory, numerical analysis, differential geometry, and functional analysis. Mathematical Analysis is composed of three parts: ?Part One presents the analysis of functions of one variable, including sequences, continuity, differentiation, Riemann integration, series, and the Lebesgue integral. A detailed explanation of proof writing is provided with specific attention devoted to standard proof techniques. To facilitate an efficient transition to more abstract settings, the results for single variable functions are proved using methods that translate to metric spaces. ?Part Two explores the more abstract counterparts of the concepts outlined earlier in the text. The reader is introduced to the fundamental spaces of analysis, including Lp spaces, and the book successfully details how appropriate definitions of integration, continuity, and differentiation lead to a powerful and widely applicable foundation for further study of applied mathematics. The interrelation between measure theory, topology, and differentiation is then examined in the proof of the Multidimensional Substitution Formula. Further areas of coverage in this section include manifolds, Stokes' Theorem, Hilbert spaces, the convergence of Fourier series, and Riesz' Representation Theorem. ?Part Three provides an overview of the motivations for analysis as well as its applications in various subjects. A special focus on ordinary and partial differential equations presents some theoretical and practical challenges that exist in these areas. Topical coverage includes Navier-Stokes equations and the finite element method. Mathematical Analysis: A Concise Introduction includes an extensive index and over 900 exercises ranging in level of difficulty, from conceptual questions and adaptations of proofs to proofs with and without hints. These opportunities for reinforcement, along with the overall concise and well-organized treatment of analysis, make this book essential for readers in upper-undergraduate or beginning graduate mathematics courses who would like to build a solid foundation in analysis for further work in all analysis-based branches of mathematics.

A Profile of Mathematical Logic

A Profile of Mathematical Logic

  • Author: Howard DeLong
  • Publisher: Courier Corporation
  • ISBN: 0486139158
  • Category: Mathematics
  • Page: 320
  • View: 3328
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This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.

Book of Proof

Book of Proof

  • Author: Richard H. Hammack
  • Publisher: N.A
  • ISBN: 9780989472111
  • Category: Mathematics
  • Page: 314
  • View: 9133
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This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

The Origins of Cauchy's Rigorous Calculus

The Origins of Cauchy's Rigorous Calculus

  • Author: Judith V. Grabiner
  • Publisher: Courier Corporation
  • ISBN: 0486143740
  • Category: Mathematics
  • Page: 272
  • View: 7373
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This text examines the reinterpretation of calculus by Augustin-Louis Cauchy and his peers in the 19th century. These intellectuals created a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. 1981 edition.

Foundations of Mathematical Logic

Foundations of Mathematical Logic

  • Author: Haskell Brooks Curry
  • Publisher: Courier Corporation
  • ISBN: 9780486634623
  • Category: Mathematics
  • Page: 408
  • View: 7570
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Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.

Logic, Foundations of Mathematics, and Computability Theory

Logic, Foundations of Mathematics, and Computability Theory

Part One of the Proceedings of the Fifth International Congress of Logic, Methodology and Philosophy of Science, London, Ontario, Canada-1975

  • Author: Robert E. Butts,Jaakko Hintikka
  • Publisher: Springer Science & Business Media
  • ISBN: 9401011389
  • Category: Science
  • Page: 416
  • View: 4790
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The Fifth International Congress of Logic, Methodology and Philosophy of Science was held at the University of Western Ontario, London, Canada, 27 August to 2 September 1975. The Congress was held under the auspices of the International Union of History and Philosophy of Science, Division of Logic, Methodology and Philosophy of Science, and was sponsored by the National Research Council of Canada and the University of Western Ontario. As those associated closely with the work of the Division over the years know well, the work undertaken by its members varies greatly and spans a number of fields not always obviously related. In addition, the volume of work done by first rate scholars and scientists in the various fields of the Division has risen enormously. For these and related reasons it seemed to the editors chosen by the Divisional officers that the usual format of publishing the proceedings of the Congress be abandoned in favour of a somewhat more flexible, and hopefully acceptable, method of pre sentation. Accordingly, the work of the invited participants to the Congress has been divided into four volumes appearing in the University of Western Ontario Series in Philosophy of Science. The volumes are entitled, Logic, Foundations of Mathematics and Computability Theory, Foun dational Problems in the Special Sciences, Basic Problems in Methodol ogy and Linguistics, and Historical and Philosophical Dimensions of Logic, Methodology and Philosophy of Science.

Introduction to Smooth Manifolds

Introduction to Smooth Manifolds

  • Author: John M. Lee
  • Publisher: Springer Science & Business Media
  • ISBN: 0387217525
  • Category: Mathematics
  • Page: 631
  • View: 7187
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Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why

Sets for Mathematics

Sets for Mathematics

  • Author: F. William Lawvere,Robert Rosebrugh
  • Publisher: Cambridge University Press
  • ISBN: 9780521010603
  • Category: Mathematics
  • Page: 261
  • View: 2479
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In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.