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Banach-tarski Paradox, Paperback by Tomkowicz, Grzegorz; Wagon, Stan, Brand N...
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- Book Title
- Banach-tarski Paradox
- ISBN
- 9781107617315
- Subject Area
- Mathematics
- Publication Name
- Banach-Tarski Paradox
- Item Length
- 9.1 in
- Publisher
- Cambridge University Press
- Subject
- Probability & Statistics / General, Algebra / General, Mathematical Analysis
- Series
- Encyclopedia of Mathematics and Its Applications Ser.
- Publication Year
- 2019
- Type
- Textbook
- Format
- Trade Paperback
- Language
- English
- Item Height
- 0.8 in
- Features
- Revised
- Item Width
- 6 in
- Item Weight
- 21.2 Oz
- Number of Pages
- 366 Pages
關於產品
Product Information
The Banach-Tarski Paradox is the most surprising result in mathematics. This new edition of a classic book offers a comprehensive, accessible presentation, with many related results, especially connections to non-Euclidean geometry, to squaring the circle, and even to some art by Escher. This material is suited to projects for undergraduates or masters students.
Product Identifiers
Publisher
Cambridge University Press
ISBN-10
1107617316
ISBN-13
9781107617315
eBay Product ID (ePID)
27038747427
Product Key Features
Publication Name
Banach-Tarski Paradox
Format
Trade Paperback
Language
English
Features
Revised
Subject
Probability & Statistics / General, Algebra / General, Mathematical Analysis
Series
Encyclopedia of Mathematics and Its Applications Ser.
Publication Year
2019
Type
Textbook
Subject Area
Mathematics
Number of Pages
366 Pages
Dimensions
Item Length
9.1 in
Item Height
0.8 in
Item Width
6 in
Item Weight
21.2 Oz
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
Series Volume Number
Series Number 163
Lc Classification Number
Qa248.W22 2019
Edition Description
Revised Edition
Reviews
"Several spectacular results have been proved since the first edition of this book ... All these results and problems are presented in a penetrating and lucid way in this new edition." Jan Mycielski, University of Colorado, Boulder, from the Foreword, "This is the second edition of this classic and comprehensive monograph on paradoxical decompositions. What adds to the special appeal of this topic is the diversity of methods and the connection to several fields including set theory, group theory, measure theory, geometry, algebra, and discrete mathematics. The previous edition of this book stimulated a large amount of research. The present volume also includes these developments and furthermore discusses the solutions to some of the problems that were solved in the past thirty years, including the realization of the Banach-Tarski paradox with pieces having the Baire property and Tarski's circle squaring problem." Miklos Laczkovich, University College London, "The new edition of The Banach-Tarski Paradox, by Grzegorz Tomkowicz and Stan Wagon, is a welcome revisiting and extensive reworking of the first edition of the book. Whether you are new to the topic of paradoxical decompositions, or have studied the phenomenon for years, this book has a lot to offer. I recommend buying two copies of the book, one for the office and one for the home, because studying the book carefully (perhaps in a series of working seminars) will be worthwhile, and casually browsing through the book in your spare time will be simply a lot of fun." Joseph Rosenblatt, Department Chair, Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, "Wagon's classic book on the Banach-Tarski paradox has been updated with Tomkowicz to include major advances over the last thirty years. It remains the definitive source for both newcomers to the subject and experts who want to broaden their knowledge. The book provides a basic introduction to the field with clear exposition and important historical background. It includes complete proofs of the Banach-Tarski paradox and related results. It continues with an extensive survey of more advanced topics. This is far and away the best resource for beginners and experts on the strangest result in all of mathematics." Matthew Foreman, University of California, Irvine, 'For some people the book will be over by page 36, because by then one has seen full treatments of the results of Hausdor and of Banach and Tarski. These people are short-sighted; there is much fascinating mathematics to be learned from the further developments. As the recent result of Marks and Unger shows, there is probably still much to discover. Indeed, the book contains some very interesting questions that still await solution.' Klaas Pieter Hart, Mathematical Reviews, 'In 1985 Stan Wagon wrote The Banach-Tarski Paradox, which not only became the classic text on paradoxical mathematics, but also provided vast new areas for research. The new second edition, co-written with Grzegorz Tomkowicz, a Polish mathematician who specializes in paradoxical decompositions, exceeds any possible expectation I might have had for expanding a book I already deeply treasured. The meticulous research of the original volume is still there, but much new research has also been included ... I should also mention that this book is beautifully illustrated.' John J. Watkins, MAA Reviews
Table of Content
Part I. Paradoxical Decompositions, or the Nonexistence of Finitely Additive Measures: 1. Introduction; 2. The Hausdorff paradox; 3. The Banach-Tarski paradox: duplicating spheres and balls; 4. Hyperbolic paradoxes; 5. Locally commutative actions: minimizing the number of pieces in a paradoxical decomposition; 6. Higher dimensions; 7. Free groups of large rank: getting a continuum of spheres from one; 8. Paradoxes in low dimensions; 9. Squaring the circle; 10. The semigroup of equidecomposability types; Part II: Finitely Additive Measures, or the Nonexistence of Paradoxical Decompositions: 11. Transition; 12. Measures in groups; 13. Applications of amenability; 14. Growth conditions in groups and supramenability; 15. The role of the axiom of choice.
Copyright Date
2019
Dewey Decimal
511.3/22
Dewey Edition
23
Illustrated
Yes
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