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

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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

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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.

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

An Invitation to Knot Theory

Virtual and Classical

Author: Heather A. Dye

Publisher: CRC Press

ISBN: 1315360098

Category: Mathematics

Page: 256

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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.

The Heart of Mathematics, An Invitation to Effective Thinking

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467271675

Category: Education

Page: 52

View: 340

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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.

Bridging Algebra, Geometry, and Topology

Author: Denis Ibadula,Willem Veys

Publisher: Springer

ISBN: 3319091867

Category: Mathematics

Page: 289

View: 7996

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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.

Heart of Mathematics, An Invitation to Effective Thinking

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467256803

Category: Education

Page: 59

View: 8770

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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: 5447

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Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 6582

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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.

Der Vierfarbensatz

Geschichte, topologische Grundlagen, und Beweisidee

Author: Rudolf Fritsch

Publisher: N.A

ISBN: 9783411151417

Category: Four-color problem

Page: 251

View: 7069

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Surveys in General Topology

Author: George M. Reed

Publisher: Academic Press

ISBN: 148326386X

Category: Mathematics

Page: 572

View: 4864

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Surveys in General Topology presents topics relating to general topology ranging from closed mappings and ultrafilters to covering and separation properties of box products. Ordered topological spaces and the use of combinatorial techniques in functional analysis are also considered, along with product spaces and weakly compact subsets of Banach spaces. Applications of stationary sets in topology are presented as well. Comprised of 15 chapters, this volume begins with an analysis of some of the techniques and results in the area of closed mappings, followed by a discussion on the theory of ultrafilters. The reader is then introduced to the question of when a box product of compact spaces is paracompact, and how badly a box product of compact or metrizable spaces can fail to be normal. Subsequent chapters focus on the transfinite dimension; the properties of metacompactness, submetacompactness, and subparacompactness; the dimension of ordered topological spaces; the use of combinatorial techniques for the treatment and solution of fundamental problems in functional analysis, particularly in the isomorphic theory of Banach spaces; and order-theoretic base axioms. This monograph will be of significant value both to researchers in general topology and to mathematicians outside the field who wish an overview of current topics and techniques.

Algebraic Topology

A First Course

Author: William Fulton

Publisher: Springer Science & Business Media

ISBN: 1461241804

Category: Mathematics

Page: 430

View: 9253

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To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

International mathematical news

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

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Issues for Dec. 1952- include section: Nachrichten der Österreichischen Mathematischen Gesellschaft.