Dense Sphere Packings
Dense Sphere Packings

Author: Thomas Callister Hales

Publisher: Cambridge University Press

Published: 2012-09-06

Total Pages: 286

ISBN-13: 0521617707

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The definitive account of the recent computer solution of the oldest problem in discrete geometry.

Algebraic Topology
Algebraic Topology

Author: J. F. Adams

Publisher: Cambridge University Press

Published: 1972-04-27

Total Pages: 309

ISBN-13: 0521080762

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This set of notes, for graduate students who are specializing in algebraic topology, adopts a novel approach to the teaching of the subject. It begins with a survey of the most beneficial areas for study, with recommendations regarding the best written accounts of each topic. Because a number of the sources are rather inaccessible to students, the second part of the book comprises a collection of some of these classic expositions, from journals, lecture notes, theses and conference proceedings. They are connected by short explanatory passages written by Professor Adams, whose own contributions to this branch of mathematics are represented in the reprinted articles.

Set Theory for the Working Mathematician
Set Theory for the Working Mathematician

Author: Krzysztof Ciesielski

Publisher: Cambridge University Press

Published: 1997-08-28

Total Pages: 256

ISBN-13: 9780521594653

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Presents those methods of modern set theory most applicable to other areas of pure mathematics.

Reversibility in Dynamics and Group Theory
Reversibility in Dynamics and Group Theory

Author: Anthony G. O'Farrell

Publisher: Cambridge University Press

Published: 2015-05-28

Total Pages: 295

ISBN-13: 1316195767

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Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention. The authors fix standard notation and terminology, establish the basic common principles, and illustrate the impact of reversibility in such diverse areas as group theory, differential and analytic geometry, number theory, complex analysis and approximation theory. As well as showing connections between different fields, the authors' viewpoint reveals many open questions, making this book ideal for graduate students and researchers. The exposition is accessible to readers at the advanced undergraduate level and above.

Dependence Logic
Dependence Logic

Author: Jouko Väänänen

Publisher: Cambridge University Press

Published: 2007-05-10

Total Pages: 52

ISBN-13: 1139465155

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Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka's independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic.

Random Graphs
Random Graphs

Author: Béla Bollobás

Publisher: Cambridge University Press

Published: 2001-08-30

Total Pages: 520

ISBN-13: 9780521797221

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This is a revised and updated version of the classic first edition.