From Geometry To Topology Dover Books On Mathematics

From Geometry to Topology

2012-03-08

Introductory text for first-year math students uses intuitive approach, bridges the gap from familiar concepts of geometry to topology. Exercises and Problems. Includes 101 black-and-white illustrations. 1974 edition.

Author: H. Graham Flegg

Publisher: Courier Corporation

ISBN: 9780486138497

Category: Mathematics

Page: 208

View: 799

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Topology

1988

The book is not a collection of topics, rather it early employs the language of point set topology to define and discuss topological groups.

Author: George McCarty

Publisher: Dover Books on Mathematics

ISBN: 0486656330

Category: Mathematics

Page: 270

View: 706

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Covers sets and functions, groups, metric spaces, topologies, topological groups, compactness and connectedness, function spaces, the fundamental group, the fundamental group of the circle, locally isomorphic groups, more. 1967 edition.

Topology and Geometry for Physicists

2013-08-16

Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics.

Author: Charles Nash

Publisher: Courier Corporation

ISBN: 9780486318363

Category: Mathematics

Page: 320

View: 436

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Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research. "Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.

Elementary Topology

1990-01-01

This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence.

Author: Michael C. Gemignani

Publisher: Courier Corporation

ISBN: 0486665224

Category: Mathematics

Page: 270

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Topology is one of the most rapidly expanding areas of mathematical thought: while its roots are in geometry and analysis, topology now serves as a powerful tool in almost every sphere of mathematical study. This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence. In addition to superb coverage of the fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, and other essentials, Elementary Topology gives added perspective as the author demonstrates how abstract topological notions developed from classical mathematics. For this second edition, numerous exercises have been added as well as a section dealing with paracompactness and complete regularity. The Appendix on infinite products has been extended to include the general Tychonoff theorem; a proof of the Tychonoff theorem which does not depend on the theory of convergence has also been added in Chapter 7.

Elements of Point Set Topology

1991-01-01

Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates.

Author: John D. Baum

Publisher: Courier Corporation

ISBN: 9780486668260

Category: Mathematics

Page: 150

View: 802

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Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.

Experiments in Topology

2012-12-04

Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.

Author: Stephen Barr

Publisher: Courier Corporation

ISBN: 9780486152745

Category: Mathematics

Page: 210

View: 279

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A Geometric Introduction to Topology

1993

First course in algebraic topology for advanced undergraduates. Homotopy theory, the duality theorem, relation of topological ideas to other branches of pure mathematics. Exercises and problems. 1972 edition.

Author: Charles Terence Clegg Wall

Publisher: Courier Corporation

ISBN: 9780486678504

Category: Mathematics

Page: 168

View: 377

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Geometry

1988-01-01

Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Author: Daniel Pedoe

Publisher: Courier Corporation

ISBN: 0486658120

Category: Mathematics

Page: 449

View: 704

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Introduction to vector algebra in the plane; circles and coaxial systems; mappings of the Euclidean plane; similitudes, isometries, Moebius transformations, much more. Includes over 500 exercises.

Invitation to Combinatorial Topology

2012-08-13

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.

Author: Maurice Fréchet

Publisher: Courier Corporation

ISBN: 9780486147888

Category: Mathematics

Page: 136

View: 974

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Principles of Topology

2016-03-17

Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus.

Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 9780486810447

Category: Mathematics

Page: 336

View: 273

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Topology is a natural, geometric, and intuitively appealing branch of mathematics that can be understood and appreciated by students as they begin their study of advanced mathematical topics. Designed for a one-semester introduction to topology at the undergraduate and beginning graduate levels, this text is accessible to students familiar with multivariable calculus. Rigorous but not abstract, the treatment emphasizes the geometric nature of the subject and the applications of topological ideas to geometry and mathematical analysis. Customary topics of point-set topology include metric spaces, general topological spaces, continuity, topological equivalence, basis, subbasis, connectedness, compactness, separation properties, metrization, subspaces, product spaces, and quotient spaces. In addition, the text introduces geometric, differential, and algebraic topology. Each chapter includes historical notes to put important developments into their historical framework. Exercises of varying degrees of difficulty form an essential part of the text.

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