A Course On Set Theory PDF Download
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Author | : Ernest Schimmerling |
Publisher | : Cambridge University Press |
Total Pages | : 179 |
Release | : 2011-07-28 |
Genre | : Mathematics |
ISBN | : 1139501488 |
Download A Course on Set Theory Book in PDF, ePub and Kindle
Set theory is the mathematics of infinity and part of the core curriculum for mathematics majors. This book blends theory and connections with other parts of mathematics so that readers can understand the place of set theory within the wider context. Beginning with the theoretical fundamentals, the author proceeds to illustrate applications to topology, analysis and combinatorics, as well as to pure set theory. Concepts such as Boolean algebras, trees, games, dense linear orderings, ideals, filters and club and stationary sets are also developed. Pitched specifically at undergraduate students, the approach is neither esoteric nor encyclopedic. The author, an experienced instructor, includes motivating examples and over 100 exercises designed for homework assignments, reviews and exams. It is appropriate for undergraduates as a course textbook or for self-study. Graduate students and researchers will also find it useful as a refresher or to solidify their understanding of basic set theory.
Author | : Charles C Pinter |
Publisher | : Courier Corporation |
Total Pages | : 259 |
Release | : 2014-07-23 |
Genre | : Mathematics |
ISBN | : 0486497089 |
Download A Book of Set Theory Book in PDF, ePub and Kindle
"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"--
Author | : Daniel W. Cunningham |
Publisher | : Cambridge University Press |
Total Pages | : 265 |
Release | : 2016-07-18 |
Genre | : Mathematics |
ISBN | : 1107120322 |
Download Set Theory Book in PDF, ePub and Kindle
Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.
Author | : John P. Burgess |
Publisher | : Cambridge University Press |
Total Pages | : 82 |
Release | : 2022-03-10 |
Genre | : Philosophy |
ISBN | : 1108990053 |
Download Set Theory Book in PDF, ePub and Kindle
Set theory is a branch of mathematics with a special subject matter, the infinite, but also a general framework for all modern mathematics, whose notions figure in every branch, pure and applied. This Element will offer a concise introduction, treating the origins of the subject, the basic notion of set, the axioms of set theory and immediate consequences, the set-theoretic reconstruction of mathematics, and the theory of the infinite, touching also on selected topics from higher set theory, controversial axioms and undecided questions, and philosophical issues raised by technical developments.
Author | : Yiannis Moschovakis |
Publisher | : Springer Science & Business Media |
Total Pages | : 280 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475741537 |
Download Notes on Set Theory Book in PDF, ePub and Kindle
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 | : Robert R. Stoll |
Publisher | : Courier Corporation |
Total Pages | : 512 |
Release | : 2012-05-23 |
Genre | : Mathematics |
ISBN | : 0486139646 |
Download Set Theory and Logic Book in PDF, ePub and Kindle
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 | : Norman T. Hamilton |
Publisher | : Courier Dover Publications |
Total Pages | : 288 |
Release | : 2018-05-16 |
Genre | : Mathematics |
ISBN | : 0486830470 |
Download Set Theory: The Structure of Arithmetic Book in PDF, ePub and Kindle
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.
Author | : Winfried Just |
Publisher | : American Mathematical Soc. |
Total Pages | : 230 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821802666 |
Download Discovering Modern Set Theory. I: The Basics Book in PDF, ePub and Kindle
This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.
Author | : Nikolai Konstantinovich Vereshchagin |
Publisher | : American Mathematical Soc. |
Total Pages | : 130 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821827316 |
Download Basic Set Theory Book in PDF, ePub and Kindle
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.
Author | : D.C. Goldrei |
Publisher | : Routledge |
Total Pages | : 296 |
Release | : 2017-09-06 |
Genre | : Mathematics |
ISBN | : 1351460617 |
Download Classic Set Theory Book in PDF, ePub and Kindle
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.