The Banach Tarski Paradox

Author: Stan Wagon
Publisher: Cambridge University Press
ISBN: 0521457041
Release Date: 1993-09-24
Genre: Mathematics

This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, and logic. It unifies the results of contemporary research on the paradox and presents several new results including some unusual paradoxes in hyperbolic space. It also provides up to date proofs and discusses many unsolved problems.

The Banach Tarski Paradox

Author: Grzegorz Tomkowicz
Publisher: Cambridge University Press
ISBN: 9781316571552
Release Date: 2016-06-14
Genre: Mathematics

The Banach–Tarski Paradox is a most striking mathematical construction: it asserts that a solid ball can be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large. This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, set theory, and logic. This new edition of a classic book unifies contemporary research on the paradox. It has been updated with many new proofs and results, and discussions of the many problems that remain unsolved. Among the new results presented are several unusual paradoxes in the hyperbolic plane, one of which involves the shapes of Escher's famous 'Angel and Devils' woodcut. A new chapter is devoted to a complete proof of the remarkable result that the circle can be squared using set theory, a problem that had been open for over sixty years.

Combinatorial Set Theory

Author: Lorenz J. Halbeisen
Publisher: Springer Science & Business Media
ISBN: 1447121732
Release Date: 2011-11-24
Genre: Mathematics

This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.

Combinatorial Group Theory and Applications to Geometry

Author: D.J. Collins
Publisher: Springer Science & Business Media
ISBN: 3540637044
Release Date: 1998-03-17
Genre: Mathematics

This book consists of two parts. The first part provides a comprehensive description of that part of group theory which has its roots in topology. The second more advanced part deals with recent work on groups relating to topological manifolds. It is a valuable guide to research in this field. The text contains numerous examples, sketches of proofs and open problems.

Encyclopaedia of Mathematics

Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9789401512886
Release Date: 2012-12-06
Genre: Mathematics

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Bulletin

Author:
Publisher:
ISBN: UOM:39015046023720
Release Date: 1985
Genre: Mathematics


Simon Stevin

Author:
Publisher:
ISBN: UCAL:B4189916
Release Date: 1986
Genre: Mathematics


International Mathematical News

Author:
Publisher:
ISBN: UOM:39015046596980
Release Date: 1985
Genre: Education

Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.