The Banach–Tarski Paradox

Advance praise: '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 Advance praise: '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 Advance praise: '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 Review of previous edition: '... a readable and stimulating book.' Ward Henson, American Scientist