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| Author | : Krzysztof Ciesielski |
| Publisher | : Cambridge University Press |
| Total Pages | : 256 |
| Release | : 1997-08-28 |
| Genre | : Mathematics |
| ISBN | : 9780521594653 |
Presents those methods of modern set theory most applicable to other areas of pure mathematics.
| Author | : Saunders Mac Lane |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 320 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475747217 |
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.
| Author | : Paul J. Cohen |
| Publisher | : Courier Corporation |
| Total Pages | : 196 |
| Release | : 2008-12-09 |
| Genre | : Mathematics |
| ISBN | : 0486469212 |
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.
| Author | : |
| Publisher | : Univalent Foundations |
| Total Pages | : 484 |
| Release | : |
| Genre | : |
| ISBN | : |
| Author | : Joseph Breuer |
| Publisher | : Courier Corporation |
| Total Pages | : 130 |
| Release | : 2012-08-09 |
| Genre | : Mathematics |
| ISBN | : 0486154874 |
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.
| Author | : Winfried Just |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 230 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 0821802666 |
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 | : Peter Komjath |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 492 |
| Release | : 2006-11-22 |
| Genre | : Mathematics |
| ISBN | : 0387362193 |
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.
| Author | : Charles C Pinter |
| Publisher | : Courier Corporation |
| Total Pages | : 259 |
| Release | : 2014-07-23 |
| Genre | : Mathematics |
| ISBN | : 0486497089 |
"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 | : Stephen Pollard |
| Publisher | : Courier Dover Publications |
| Total Pages | : 196 |
| Release | : 2015-07-15 |
| Genre | : Mathematics |
| ISBN | : 0486797147 |
This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.
| Author | : Nikolai Konstantinovich Vereshchagin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 130 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821827316 |
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.
