Elementary Induction On Abstract Structures

Author: Yiannis N. Moschovakis
Publisher: Courier Corporation
ISBN: 0486152014
Size: 22.32 MB
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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

Author: Christine Schurz
Publisher: Walter de Gruyter
ISBN: 311032458X
Size: 71.20 MB
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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.

A Book Of Abstract Algebra

Author: Charles C Pinter
Publisher: Courier Corporation
ISBN: 0486474178
Size: 11.60 MB
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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

Author: Allan Clark
Publisher: Courier Corporation
ISBN: 0486140350
Size: 30.68 MB
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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.

Abstract And Concrete Categories

Author: Jiri Adamek
Publisher:
ISBN: 9780486469348
Size: 41.79 MB
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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.

Logic In Elementary Mathematics

Author: Robert M. Exner
Publisher: Courier Corporation
ISBN: 0486482219
Size: 38.85 MB
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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 The Structure Of Arithmetic

Author: Norman T. Hamilton
Publisher: Courier Dover Publications
ISBN: 0486830470
Size: 65.36 MB
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This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.

The Induction Book

Author: Steven H. Weintraub
Publisher: Courier Dover Publications
ISBN: 0486821234
Size: 23.29 MB
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Mathematical induction — along with its equivalents, complete induction and well-ordering, and its immediate consequence, the pigeonhole principle — constitute essential proof techniques. Every mathematician is familiar with mathematical induction, and every student of mathematics requires a grasp of its concepts. This volume provides an introduction and a thorough exposure to these proof techniques. Geared toward students of mathematics at all levels, the text is particularly suitable for courses in mathematical induction, theorem-proving, and problem-solving. The treatment begins with both intuitive and formal explanations of mathematical induction and its equivalents. The next chapter presents many problems consisting of results to be proved by induction, with solutions omitted to enable instructors to assign them to students. Problems vary in difficulty; the majority of them require little background, and the most advanced involve calculus or linear algebra. The final chapter features proofs too complicated for students to find on their own, some of which are famous theorems by well-known mathematicians. For these beautiful and important theorems, the author provides expositions and proofs. The text concludes with a helpful Appendix providing the logical equivalence of the various forms of induction.

Discrete Mathematics With Applications

Author: Susanna Epp
Publisher: Cengage Learning
ISBN: 0495391328
Size: 28.27 MB
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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.