the banach tarski paradox encyclopedia of mathematics and its applications

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The Banach Tarski Paradox

Author : Stan Wagon
ISBN : 0521457041
Genre : Mathematics
File Size : 31. 3 MB
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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
ISBN : 9781107042599
Genre : Mathematics
File Size : 63. 24 MB
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The Banach-Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.


Author : Henryk Minc
ISBN : 0521302269
Genre : Mathematics
File Size : 87. 68 MB
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The purpose of this book, which was first published in 1978, is to give a complete account of the theory of permanents, their history and applications. This volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt. The work also contains many results stated without formal proofs. This book can be used as a textbook at the advanced undergraduate or graduate level. The only prerequisites are a standard undergraduate course in the theory of matrices and a measure of mathematical maturity.

Theory Of Matroids

Author : Neil White
ISBN : 9780521309370
Genre : Mathematics
File Size : 87. 98 MB
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The theory of matroids is unique in the extent to which it connects such disparate branches of combinatorial theory and algebra as graph theory, lattice theory, design theory, combinatorial optimization, linear algebra, group theory, ring theory and field theory. Furthermore, matroid theory is alone among mathematical theories because of the number and variety of its equivalent axiom systems. Indeed, matroids are amazingly versatile and the approaches to the subject are varied and numerous. This book is a primer in the basic axioms and constructions of matroids. The contributions by various leaders in the field include chapters on axiom systems, lattices, basis exchange properties, orthogonality, graphs and networks, constructions, maps, semi-modular functions and an appendix on cryptomorphisms. The authors have concentrated on giving a lucid exposition of the individual topics; explanations of theorems are preferred to complete proofs and original work is thoroughly referenced. In addition, exercises are included for each topic.

Combinatorial Set Theory

Author : Lorenz J. Halbeisen
ISBN : 1447121732
Genre : Mathematics
File Size : 83. 46 MB
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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.

Nonnegative Matrices And Applications

Author : R. B. Bapat
ISBN : 0521571677
Genre : Mathematics
File Size : 87. 81 MB
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This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.

Combinatorial Group Theory And Applications To Geometry

Author : D.J. Collins
ISBN : 3540637044
Genre : Mathematics
File Size : 89. 35 MB
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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.

Special Functions

Author : George E. Andrews
ISBN : 0521789885
Genre : Mathematics
File Size : 58. 2 MB
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An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

Model Theory

Author : Wilfrid Hodges
ISBN : 0521304423
Genre : Mathematics
File Size : 72. 11 MB
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Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.

Philosophy Of Mathematics

Author :
ISBN : 0080930581
Genre : Philosophy
File Size : 70. 78 MB
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One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

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