Invitation to Combinatorial Topology

Author: Maurice Fréchet,Ky Fan

Publisher: Courier Corporation

ISBN: 0486147886

Category: Mathematics

Page: 136

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Elementary text, accessible to anyone with a background in high school geometry, covers problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, topological polygons, more. Includes 108 figures. 1967 edition.

Combinatorial Reciprocity Theorems: An Invitation to Enumerative Geometric Combinatorics

Author: Matthias Beck,Raman Sanyal

Publisher: American Mathematical Soc.

ISBN: 147042200X

Category: Combinatorial analysis

Page: 308

View: 6798

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Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.

Invitations to Geometry and Topology

Author: Martin R. Bridson

Publisher: Oxford University Press on Demand

ISBN: 9780198507727

Category: Mathematics

Page: 327

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This volume presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. The material is presented in a way that both graduate students and researchers should find accessible and enticing. The topics covered range from Morse theory and complex geometry theory to geometric group theory, and are accompanied by exercises that are designed to deepen the reader's understanding and to guide them in exciting directions for future investigation. The editors, M.R. Bridson and S.M. Salamon, have each written an article and are accompanied by A.J. Berrick; M.C. Crabb and A.J.B Potter; M. Eastwood and J. Sawon; M.A. Guest; N.J. Hitchin and J.Seade.

Gesammelte Abhandlungen / Collected Papers

Author: Hellmuth Kneser

Publisher: Walter de Gruyter

ISBN: 3110894513

Category: Mathematics

Page: 939

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Hellmuth Kneser (1898-1973) is the second of three mathematicians from consecutive generations of the Kneser family, all ofwhom made groundbreaking mathematical contributions on a wide range of topics. It was only in recent times that mathematicians recognized how Hellmuth Kneser’s work influenced the course of topology and the theory of several complex variables. For this book, presenting the entire collection of Kneser’s papers published in journals, experts in various areas have written English commentaries. Kneser’s articles are in German, with the exception of two papers written in French.

Groups

Topological, Combinatorial and Arithmetic Aspects

Author: Thomas Wolfgang Müller

Publisher: Cambridge University Press

ISBN: 9780521542876

Category: Mathematics

Page: 587

View: 5804

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In 1999 a number of eminent mathematicians were invited to Bielefeld to present lectures at a conference on topological, combinatorial and arithmetic aspects of (infinite) groups. The present volume consists of survey and research articles invited from participants in this conference. Topics covered include topological finiteness properties of groups, Kac-Moody groups, the theory of Euler characteristics, the connection between groups, formal languages and automata, the Magnus-Nielsen method for one-relator groups, atomic and just infinite groups, topology in permutation groups, probabilistic group theory, the theory of subgroup growth, hyperbolic lattices in dimension three, generalised triangle groups and reduction theory. All contributions are written in a relaxed and attractive style, accessible not only to specialists, but also to good graduate and post-graduate students, who will find inspiration for a number of basic research projects at various levels of technical difficulty.

Der Vierfarbensatz

Geschichte, topologische Grundlagen, und Beweisidee

Author: Rudolf Fritsch

Publisher: N.A

ISBN: 9783411151417

Category: Four-color problem

Page: 251

View: 4905

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An Invitation to Knot Theory

Virtual and Classical

Author: Heather A. Dye

Publisher: CRC Press

ISBN: 1498701655

Category: Mathematics

Page: 256

View: 9624

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The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra. The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.

Combinatorics and Commutative Algebra

Author: Richard P. Stanley

Publisher: Springer Science & Business Media

ISBN: 0817644334

Category: Mathematics

Page: 168

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* Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra: 1) The theory of invariants of a torus acting linearly on a polynomial ring, and 2) The face ring of a simplicial complex * In this new edition, the author further develops some interesting properties of face rings with application to combinatorics

Bridging Algebra, Geometry, and Topology

Author: Denis Ibadula,Willem Veys

Publisher: Springer

ISBN: 3319091867

Category: Mathematics

Page: 289

View: 4890

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Algebra, geometry and topology cover a variety of different, but intimately related research fields in modern mathematics. This book focuses on specific aspects of this interaction. The present volume contains refereed papers which were presented at the International Conference “Experimental and Theoretical Methods in Algebra, Geometry and Topology”, held in Eforie Nord (near Constanta), Romania, during 20-25 June 2013. The conference was devoted to the 60th anniversary of the distinguished Romanian mathematicians Alexandru Dimca and Ştefan Papadima. The selected papers consist of original research work and a survey paper. They are intended for a large audience, including researchers and graduate students interested in algebraic geometry, combinatorics, topology, hyperplane arrangements and commutative algebra. The papers are written by well-known experts from different fields of mathematics, affiliated to universities from all over the word, they cover a broad range of topics and explore the research frontiers of a wide variety of contemporary problems of modern mathematics.

The Heart of Mathematics, An Invitation to Effective Thinking

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467271675

Category: Education

Page: 52

View: 8502

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Facts101 is your complete guide to The Heart of Mathematics, An Invitation to Effective Thinking. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Maß und Kategorie

Author: J.C. Oxtoby

Publisher: Springer-Verlag

ISBN: 364296074X

Category: Mathematics

Page: 112

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Dieses Buch behandelt hauptsächlich zwei Themenkreise: Der Bairesche Kategorie-Satz als Hilfsmittel für Existenzbeweise sowie Die "Dualität" zwischen Maß und Kategorie. Die Kategorie-Methode wird durch viele typische Anwendungen erläutert; die Analogie, die zwischen Maß und Kategorie besteht, wird nach den verschiedensten Richtungen hin genauer untersucht. Hierzu findet der Leser eine kurze Einführung in die Grundlagen der metrischen Topologie; außerdem werden grundlegende Eigenschaften des Lebesgue schen Maßes hergeleitet. Es zeigt sich, daß die Lebesguesche Integrationstheorie für unsere Zwecke nicht erforderlich ist, sondern daß das Riemannsche Integral ausreicht. Weiter werden einige Begriffe aus der allgemeinen Maßtheorie und Topologie eingeführt; dies geschieht jedoch nicht nur der größeren Allgemeinheit wegen. Es erübrigt sich fast zu erwähnen, daß sich die Bezeichnung "Kategorie" stets auf "Bairesche Kategorie" be zieht; sie hat nichts zu tun mit dem in der homologischen Algebra verwendeten Begriff der Kategorie. Beim Leser werden lediglich grundlegende Kenntnisse aus der Analysis und eine gewisse Vertrautheit mit der Mengenlehre vorausgesetzt. Für die hier untersuchten Probleme bietet sich in natürlicher Weise die mengentheoretische Formulierung an. Das vorlie gende Buch ist als Einführung in dieses Gebiet der Analysis gedacht. Man könnte es als Ergänzung zur üblichen Grundvorlesung über reelle Analysis, als Grundlage für ein Se minar oder auch zum selbständigen Studium verwenden. Bei diesem Buch handelt es sich vorwiegend um eine zusammenfassende Darstellung; jedoch finden sich in ihm auch einige Verfeinerungen bekannter Resultate, namentlich Satz 15.6 und Aussage 20.4. Das Literaturverzeichnis erhebt keinen Anspruch auf Vollständigkeit. Häufig werden Werke zitiert, die weitere Literaturangaben enthalten.

Heart of Mathematics, An Invitation to Effective Thinking

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467256803

Category: Education

Page: 59

View: 1184

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Facts101 is your complete guide to Heart of Mathematics, An Invitation to Effective Thinking. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Books in Print Supplement, 2002-2003

A Midyear Publication Covering All New and Updated Titles Since the Production of Books in Print 2002-2003

Author: N.A

Publisher: N.A

ISBN: 9780835245661

Category: American literature

Page: N.A

View: 8572

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Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 4748

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Toric Topology

International Conference, May 29-June 3, 2006, Osaka City University, Osaka, Japan

Author: Megumi Harada

Publisher: American Mathematical Soc.

ISBN: 0821844865

Category: Mathematics

Page: 401

View: 6098

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Toric topology is the study of algebraic, differential, symplectic-geometric, combinatorial, and homotopy-theoretic aspects of a particular class of torus actions whose quotients are highly structured. The combinatorial properties of this quotient and the equivariant topology of the original manifold interact in a rich variety of ways, thus illuminating subtle aspects of both the combinatorics and the equivariant topology. Many of the motivations and guiding principles of the field are provided by (though not limited to) the theory of toric varieties in algebraic geometry as well as that of symplectic toric manifolds in symplectic geometry. This volume is the proceedings of the International Conference on Toric Topology held in Osaka in May-June 2006. It contains about 25 research and survey articles written by conference speakers, covering many different aspects of, and approaches to, torus actions, such as those mentioned above.Some of the manuscripts are survey articles, intended to give a broad overview of an aspect of the subject; all manuscripts consciously aim to be accessible to a broad reading audience of students and researchers interested in the interaction of the subjects involved. We hope that this volume serves as an enticing invitation to this emerging field.

The Four-Color Theorem

History, Topological Foundations, and Idea of Proof

Author: Rudolf Fritsch,Gerda Fritsch

Publisher: Springer Science & Business Media

ISBN: 1461217202

Category: Mathematics

Page: 260

View: 2874

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This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.