A Set Theory Workbook

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A Set Theory Workbook

Author : Iain Adamson
Publisher : Springer Science & Business Media
ISBN 13 : 0817681388
Total Pages : 145 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis A Set Theory Workbook by : Iain Adamson

Download or read book A Set Theory Workbook written by Iain Adamson and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a companion to A general topology workbook published by Birkhiiuser last year. In an ideal world the order of publication would have been reversed, for the notation and some of the results of the present book are used in the topology book and on the other hand (the reader may be assured) no topology is used here. Both books share the word Workbook in their titles. They are based on the principle that for at least some branches of mathematics a good way for a student to learn is to be presented with a clear statement of the definitions of the terms with which the subject is concerned and then to be faced with a collection of problems involving the terms just defined. In adopting this approach with my Dundee students of set theory and general topology I found it best not to differentiate too precisely between simple illustrative examples, easy exercises and results which in conventional textbooks would be labelled as Theorems.

A Book of Set Theory

Author : Charles C Pinter
Publisher : Courier Corporation
ISBN 13 : 0486497089
Total Pages : 259 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis A Book of Set Theory by : Charles C Pinter

Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Basic Set Theory

Author : Azriel Levy
Publisher : Courier Corporation
ISBN 13 : 0486150739
Total Pages : 418 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Basic Set Theory by : Azriel Levy

Download or read book Basic Set Theory written by Azriel Levy and published by Courier Corporation. This book was released on 2012-06-11 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.

Basic Set Theory

Author : Nikolai Konstantinovich Vereshchagin
Publisher : American Mathematical Soc.
ISBN 13 : 0821827316
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Basic Set Theory by : Nikolai Konstantinovich Vereshchagin

Download or read book Basic Set Theory written by Nikolai Konstantinovich Vereshchagin and published by American Mathematical Soc.. This book was released on 2002 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.

Problems and Theorems in Classical Set Theory

Author : Peter Komjath
Publisher : Springer Science & Business Media
ISBN 13 : 0387362193
Total Pages : 492 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Problems and Theorems in Classical Set Theory by : Peter Komjath

Download or read book Problems and Theorems in Classical Set Theory written by Peter Komjath and published by Springer Science & Business Media. This book was released on 2006-11-22 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.

Classic Set Theory

Author : D.C. Goldrei
Publisher : Routledge
ISBN 13 : 1351460609
Total Pages : 300 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Classic Set Theory by : D.C. Goldrei

Download or read book Classic Set Theory written by D.C. Goldrei and published by Routledge. This book was released on 2017-09-06 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.

A General Topology Workbook

Author : Iain T. Adamson
Publisher : Springer Science & Business Media
ISBN 13 : 0817681264
Total Pages : 156 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis A General Topology Workbook by : Iain T. Adamson

Download or read book A General Topology Workbook written by Iain T. Adamson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been called a Workbook to make it clear from the start that it is not a conventional textbook. Conventional textbooks proceed by giving in each section or chapter first the definitions of the terms to be used, the concepts they are to work with, then some theorems involving these terms (complete with proofs) and finally some examples and exercises to test the readers' understanding of the definitions and the theorems. Readers of this book will indeed find all the conventional constituents--definitions, theorems, proofs, examples and exercises but not in the conventional arrangement. In the first part of the book will be found a quick review of the basic definitions of general topology interspersed with a large num ber of exercises, some of which are also described as theorems. (The use of the word Theorem is not intended as an indication of difficulty but of importance and usefulness. ) The exercises are deliberately not "graded"-after all the problems we meet in mathematical "real life" do not come in order of difficulty; some of them are very simple illustrative examples; others are in the nature of tutorial problems for a conven tional course, while others are quite difficult results. No solutions of the exercises, no proofs of the theorems are included in the first part of the book-this is a Workbook and readers are invited to try their hand at solving the problems and proving the theorems for themselves.

Set Theory and Logic

Author : Robert R. Stoll
Publisher : Courier Corporation
ISBN 13 : 0486139646
Total Pages : 516 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Set Theory and Logic by : Robert R. Stoll

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 516 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.

Set Theory and the Continuum Hypothesis

Author : Paul J. Cohen
Publisher : Courier Corporation
ISBN 13 : 0486469212
Total Pages : 196 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Set Theory and the Continuum Hypothesis by : Paul J. Cohen

Download or read book Set Theory and the Continuum Hypothesis written by Paul J. Cohen and published by Courier Corporation. This book was released on 2008-12-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

Introduction to Set Theory

Author : Karel Hrbacek
Publisher :
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.3/5 (97 download)

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Book Synopsis Introduction to Set Theory by : Karel Hrbacek

Download or read book Introduction to Set Theory written by Karel Hrbacek and published by . This book was released on 1984 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Outline of Set Theory

Author : James M. Henle
Publisher : Springer Science & Business Media
ISBN 13 : 1461386802
Total Pages : 137 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis An Outline of Set Theory by : James M. Henle

Download or read book An Outline of Set Theory written by James M. Henle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable to ordinary mathematics majors. I use a recent modification of R. L. Moore's famous method developed in recent years by D. W. Cohen [1]. Briefly, in this new approach, projects are assigned to groups of students each week. With all the necessary assistance from the instructor, the groups complete their projects, carefully write a short paper for their classmates, and then, in the single weekly class meeting, lecture on their results. While the em phasis is on the student, the instructor is available at every stage to assure success in the research, to explain and critique mathematical prose, and to coach the groups in clear mathematical presentation. The subject matter of set theory is peculiarly appropriate to this style of course. For much of the book the objects of study are familiar and while the theorems are significant and often deep, it is the methods and ideas that are most important. The necessity of rea soning about numbers and sets forces students to come to grips with the nature of proof, logic, and mathematics. In their research they experience the same dilemmas and uncertainties that faced the pio neers.

Introduction to the Theory of Sets

Author : Joseph Breuer
Publisher : Courier Corporation
ISBN 13 : 0486154874
Total Pages : 130 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to the Theory of Sets by : Joseph Breuer

Download or read book Introduction to the Theory of Sets written by Joseph Breuer and published by Courier Corporation. This book was released on 2012-08-09 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.

Set Theory: The Structure of Arithmetic

Author : Norman T. Hamilton
Publisher : Courier Dover Publications
ISBN 13 : 0486830470
Total Pages : 289 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Set Theory: The Structure of Arithmetic by : Norman T. Hamilton

Download or read book Set Theory: The Structure of Arithmetic written by Norman T. Hamilton and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Set Theory for the Working Mathematician

Author : Krzysztof Ciesielski
Publisher : Cambridge University Press
ISBN 13 : 9780521594653
Total Pages : 256 pages
Book Rating : 4.5/5 (946 download)

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Book Synopsis Set Theory for the Working Mathematician by : Krzysztof Ciesielski

Download or read book Set Theory for the Working Mathematician written by Krzysztof Ciesielski and published by Cambridge University Press. This book was released on 1997-08-28 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents those methods of modern set theory most applicable to other areas of pure mathematics.

Classical Descriptive Set Theory

Author : Alexander Kechris
Publisher : Springer Science & Business Media
ISBN 13 : 1461241901
Total Pages : 419 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Classical Descriptive Set Theory by : Alexander Kechris

Download or read book Classical Descriptive Set Theory written by Alexander Kechris and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.

Labyrinth of Thought

Author : Jose Ferreiros
Publisher : Springer Science & Business Media
ISBN 13 : 9783764357498
Total Pages : 472 pages
Book Rating : 4.3/5 (574 download)

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Book Synopsis Labyrinth of Thought by : Jose Ferreiros

Download or read book Labyrinth of Thought written by Jose Ferreiros and published by Springer Science & Business Media. This book was released on 2001-11-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: "José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

An Introduction to Proofs with Set Theory

Author : Daniel Ashlock
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681738805
Total Pages : 251 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis An Introduction to Proofs with Set Theory by : Daniel Ashlock

Download or read book An Introduction to Proofs with Set Theory written by Daniel Ashlock and published by Morgan & Claypool Publishers. This book was released on 2020-06-24 with total page 251 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.