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Author : Thomas J. Jech
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.F/5 ( download)
Download or read book Lectures in Set Theory written by Thomas J. Jech and published by Lecture Notes in Mathematics. This book was released on 1971-09-23 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yiannis Moschovakis
Publisher : Springer Science & Business Media
ISBN 13 : 1475741537
Total Pages : 280 pages
Book Rating : 4.4/5 (757 download)
Download or read book Notes on Set Theory written by Yiannis Moschovakis and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
Author : Thomas J. Jech
Publisher :
ISBN 13 :
Total Pages : 137 pages
Book Rating : 4.:/5 (969 download)
Download or read book Lectures in set theory, with particular emphasis on the method of forcing written by Thomas J. Jech and published by . This book was released on 1971 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniel Ashlock
Publisher : Springer Nature
ISBN 13 : 3031024265
Total Pages : 233 pages
Book Rating : 4.0/5 (31 download)
Download or read book An Introduction to Proofs with Set Theory written by Daniel Ashlock and published by Springer Nature. This book was released on 2022-06-01 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid's algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor's Paradox, Russel's Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of Gödel's Incompleteness Theorems.
Author : Bernard Kolman
Publisher : Prentice Hall
ISBN 13 :
Total Pages : 488 pages
Book Rating : 4.:/5 (321 download)
Download or read book Discrete Mathematical Structures for Computer Science written by Bernard Kolman and published by Prentice Hall. This book was released on 1987 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text has been designed as a complete introduction to discrete mathematics, primarily for computer science majors in either a one or two semester course. The topics addressed are of genuine use in computer science, and are presented in a logically coherent fashion. The material has been organized and interrelated to minimize the mass of definitions and the abstraction of some of the theory. For example, relations and directed graphs are treated as two aspects of the same mathematical idea. Whenever possible each new idea uses previously encountered material, and then developed in such a way that it simplifies the more complex ideas that follow.
Author : George Tourlakis
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (99 download)
Download or read book Lectures in Logic and Set Theory written by George Tourlakis and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George Tourlakis
Publisher : Cambridge University Press
ISBN 13 : 9781139439435
Total Pages : 596 pages
Book Rating : 4.4/5 (394 download)
Download or read book Lectures in Logic and Set Theory: Volume 2, Set Theory written by George Tourlakis and published by Cambridge University Press. This book was released on 2003-02-13 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.
Author : George Tourlakis
Publisher : Cambridge University Press
ISBN 13 : 9780521168489
Total Pages : 0 pages
Book Rating : 4.1/5 (684 download)
Download or read book Lectures in Logic and Set Theory: Volume 2, Set Theory written by George Tourlakis and published by Cambridge University Press. This book was released on 2011-07-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).
Author : Joel David Hamkins
Publisher : MIT Press
ISBN 13 : 0262542234
Total Pages : 350 pages
Book Rating : 4.2/5 (625 download)
Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Author : Herbert B. Enderton
Publisher : Academic Press
ISBN 13 : 0080570429
Total Pages : 279 pages
Book Rating : 4.0/5 (85 download)
Download or read book Elements of Set Theory written by Herbert B. Enderton and published by Academic Press. This book was released on 1977-05-23 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.
Author : Thomas J. Jech
Publisher : Springer
ISBN 13 : 3540368825
Total Pages : 142 pages
Book Rating : 4.5/5 (43 download)
Download or read book Lectures in Set Theory written by Thomas J. Jech and published by Springer. This book was released on 2006-11-15 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mary Ellen Rudin
Publisher : American Mathematical Soc.
ISBN 13 : 082181673X
Total Pages : 82 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lectures on Set Theoretic Topology written by Mary Ellen Rudin and published by American Mathematical Soc.. This book was released on 1975-12-31 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey presents some recent results connecting set theory with the problems of general topology, primarily giving the applications of classical set theory in general topology and not considering problems involving large numbers. The lectures are completely self-contained--this is a good reference book on modern questions of general topology and can serve as an introduction to the applications of set theory and infinite combinatorics.
Author : Mary Tiles
Publisher : Courier Corporation
ISBN 13 : 0486138550
Total Pages : 258 pages
Book Rating : 4.4/5 (861 download)
Download or read book The Philosophy of Set Theory written by Mary Tiles and published by Courier Corporation. This book was released on 2012-03-08 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div
Author : Juris Steprans
Publisher : Springer
ISBN 13 : 3540467955
Total Pages : 233 pages
Book Rating : 4.5/5 (44 download)
Download or read book Set Theory and its Applications written by Juris Steprans and published by Springer. This book was released on 2006-11-14 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Set Theory and Applications meeting at York University, Ontario, featured both contributed talks and a series of invited lectures on topics central to set theory and to general topology. These proceedings contain a selection of the resulting papers, mostly announcing new unpublished results.
Author : Willard Van Orman Quine
Publisher : Harvard University Press
ISBN 13 : 9780674802070
Total Pages : 384 pages
Book Rating : 4.8/5 (2 download)
Download or read book Set Theory and Its Logic written by Willard Van Orman Quine and published by Harvard University Press. This book was released on 1969 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an extensively revised edition of W. V. Quine’s introduction to abstract set theory and to various axiomatic systematizations of the subject. The treatment of ordinal numbers has been strengthened and much simplified, especially in the theory of transfinite recursions, by adding an axiom and reworking the proofs. Infinite cardinals are treated anew in clearer and fuller terms than before. Improvements have been made all through the book; in various instances a proof has been shortened, a theorem strengthened, a space-saving lemma inserted, an obscurity clarified, an error corrected, a historical omission supplied, or a new event noted.
Author : Robert R. Stoll
Publisher : Courier Corporation
ISBN 13 : 0486139646
Total Pages : 512 pages
Book Rating : 4.4/5 (861 download)
Download or read book Set Theory and Logic written by Robert R. Stoll and published by Courier Corporation. This book was released on 2012-05-23 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Author : Xiang-dong Hou
Publisher : American Mathematical Soc.
ISBN 13 : 1470442892
Total Pages : 240 pages
Book Rating : 4.4/5 (74 download)
Download or read book Lectures on Finite Fields written by Xiang-dong Hou and published by American Mathematical Soc.. This book was released on 2018-06-07 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science. This book is a collection of selected topics in the theory of finite fields and related areas. The topics include basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields. The book is mostly self-contained, and the material covered is accessible to readers with the knowledge of graduate algebra; the only exception is a section on function fields. Each chapter is supplied with a set of exercises. The book can be adopted as a text for a second year graduate course or used as a reference by researchers.
