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Author: Stan Wagon
Publisher: Cambridge University Press
ISBN: 9780521457040
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Asserting that a solid ball may be taken apart into many pieces that can be rearranged to form a ball twice as large as the original, the Banach-Tarski paradox is examined in relationship to measure and group theory, geometry and logic.
Author: Stan Wagon
Publisher: Cambridge University Press
ISBN: 9780521457040
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Asserting that a solid ball may be taken apart into many pieces that can be rearranged to form a ball twice as large as the original, the Banach-Tarski paradox is examined in relationship to measure and group theory, geometry and logic.
Author: Grzegorz Tomkowicz
Publisher: Cambridge University Press
ISBN: 1316570568
Category : Mathematics
Languages : en
Pages : 367
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Book Description
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.
Author: Ian Stewart
Publisher: Basic Books
ISBN: 0465056881
Category : Mathematics
Languages : en
Pages : 321
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Book Description
Acclaimed writer and mathematician Ian Stewart's third miscellany of mathematical curios and conundrums. In Professor Stewart's Casebook of Mathematical Mysteries, acclaimed mathematician Ian Stewart presents an enticing collection of mathematical curios and conundrums. With a new puzzle on each page, this compendium of brainteasers will both teach and delight. Guided by stalwart detective Hemlock Soames and his sidekick, Dr. John Watsup, readers will delve into almost two hundred mathematical problems, puzzles, and facts. Tackling subjects from mathematical dates (such as Pi Day), what we don't know about primes, and why the Earth is round, this clever, mind-expanding book demonstrates the power and fun inherent in mathematics.
Author: Tibor Bisztriczky
Publisher: Springer Science & Business Media
ISBN: 9401109249
Category : Mathematics
Languages : en
Pages : 515
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Book Description
The aim of this volume is to reinforce the interaction between the three main branches (abstract, convex and computational) of the theory of polytopes. The articles include contributions from many of the leading experts in the field, and their topics of concern are expositions of recent results and in-depth analyses of the development (past and future) of the subject. The subject matter of the book ranges from algorithms for assignment and transportation problems to the introduction of a geometric theory of polyhedra which need not be convex. With polytopes as the main topic of interest, there are articles on realizations, classifications, Eulerian posets, polyhedral subdivisions, generalized stress, the Brunn--Minkowski theory, asymptotic approximations and the computation of volumes and mixed volumes. For researchers in applied and computational convexity, convex geometry and discrete geometry at the graduate and postgraduate levels.
Author: Alan L. T. Paterson
Publisher: American Mathematical Soc.
ISBN: 0821809857
Category : Mathematics
Languages : en
Pages : 474
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Book Description
The subject of amenability has its roots in the work of Lebesgue at the turn of the century. In the 1940s, the subject began to shift from finitely additive measures to means. This shift is of fundamental importance, for it makes the substantial resources of functional analysis and abstract harmonic analysis available to the study of amenability. The ubiquity of amenability ideas and the depth of the mathematics involved points to the fundamental importance of the subject. This book presents a comprehensive and coherent account of amenability as it has been developed in the large and varied literature during this century. The book has a broad appeal, for it presents an account of the subject based on harmonic and functional analysis. In addition, the analytic techniques should be of considerable interest to analysts in all areas. In addition, the book contains applications of amenability to a number of areas: combinatorial group theory, semigroup theory, statistics, differential geometry, Lie groups, ergodic theory, cohomology, and operator algebras. The main objectives of the book are to provide an introduction to the subject as a whole and to go into many of its topics in some depth. The book begins with an informal, nontechnical account of amenability from its origins in the work of Lebesgue. The initial chapters establish the basic theory of amenability and provide a detailed treatment of invariant, finitely additive measures (i.e., invariant means) on locally compact groups. The author then discusses amenability for Lie groups, "almost invariant" properties of certain subsets of an amenable group, amenability and ergodic theorems, polynomial growth, and invariant mean cardinalities. Also included are detailed discussions of the two most important achievements in amenability in the 1980s: the solutions to von Neumann's conjecture and the Banach-Ruziewicz Problem. The main prerequisites for this book are a sound understanding of undergraduate-level mathematics and a knowledge of abstract harmonic analysis and functional analysis. The book is suitable for use in graduate courses, and the lists of problems in each chapter may be useful as student exercises.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 588
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Book Description
Author: Kossuth Lajos Tudományegyetem. Matematikai Intézet
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 740
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Book Description
Author: Roger C. Lyndon
Publisher:
ISBN:
Category : Combinatorial group theory
Languages : en
Pages : 364
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Book Description
Author: James E. Humphreys
Publisher: Cambridge University Press
ISBN: 9780521436137
Category : Mathematics
Languages : en
Pages : 222
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Book Description
This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 342
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Book Description
