A First Course in Topology

An Introduction to Mathematical Thinking

Author: Robert A Conover

Publisher: Courier Corporation

ISBN: 0486780015

Category: Mathematics

Page: 272

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Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com

A First Course in Topology

Continuity and Dimension

Author: John McCleary

Publisher: American Mathematical Soc.

ISBN: 0821838849

Category: Mathematics

Page: 211

View: 1953

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How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time.The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.

Topology

An Introduction to the Point-set and Algebraic Areas

Author: Donald W. Kahn

Publisher: Courier Corporation

ISBN: 9780486686097

Category: Mathematics

Page: 217

View: 8612

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Comprehensive coverage of elementary general topology as well as algebraic topology, specifically 2-manifolds, covering spaces and fundamental groups. Problems, with selected solutions. Bibliography. 1975 edition.

Introduction to Analysis

Author: Maxwell Rosenlicht

Publisher: Courier Corporation

ISBN: 0486134687

Category: Mathematics

Page: 272

View: 5645

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Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

An Introduction to Algebraic Topology

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486152952

Category: Mathematics

Page: 208

View: 7197

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This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.

Introduction to Topology

Third Edition

Author: Bert Mendelson

Publisher: Courier Corporation

ISBN: 0486135098

Category: Mathematics

Page: 224

View: 3394

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Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

An Introduction to Algebraic Structures

Author: Joseph Landin

Publisher: Courier Corporation

ISBN: 0486150410

Category: Mathematics

Page: 272

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This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.

Topology

An Introduction with Application to Topological Groups

Author: George McCarty

Publisher: Courier Corporation

ISBN: 0486450821

Category: Mathematics

Page: 288

View: 7977

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This stimulating introduction employs the language of point set topology to define and discuss topological groups. It examines set-theoretic topology and its applications in function spaces as well as homotopy and the fundamental group. Well-chosen exercises and problems serve as reinforcements. 1967 edition. Includes 99 illustrations.

A Geometric Introduction to Topology

Author: Charles Terence Clegg Wall

Publisher: Courier Corporation

ISBN: 0486678504

Category: Mathematics

Page: 168

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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.

Mathematics and Logic

Author: Mark Kac,Stanislaw M. Ulam

Publisher: Courier Corporation

ISBN: 0486670856

Category: Philosophy

Page: 170

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Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."

Introductory Real Analysis

Author: A. N. Kolmogorov,S. V. Fomin

Publisher: Courier Corporation

ISBN: 0486134741

Category: Mathematics

Page: 416

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Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.

Introduction to Topology

Second Edition

Author: Theodore W. Gamelin,Robert Everist Greene

Publisher: Courier Corporation

ISBN: 0486320189

Category: Mathematics

Page: 256

View: 4137

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This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

Introduction to Graph Theory

Author: Richard J. Trudeau

Publisher: Courier Corporation

ISBN: 0486318664

Category: Mathematics

Page: 224

View: 4228

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Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.

Elementary Point-Set Topology

A Transition to Advanced Mathematics

Author: Andre L. Yandl,Adam Bowers

Publisher: Courier Dover Publications

ISBN: 0486811018

Category: Mathematics

Page: 256

View: 9834

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In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations. "This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America

Geometry: A Comprehensive Course

Author: Dan Pedoe

Publisher: Courier Corporation

ISBN: 0486131734

Category: Mathematics

Page: 464

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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.

A First Course in Geometry

Author: Edward T Walsh

Publisher: Courier Corporation

ISBN: 048679668X

Category: Mathematics

Page: 400

View: 4507

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Suitable for college courses, this introductory text covers the language of mathematics, geometric sets of points, separation and angles, triangles, parallel lines, similarity, polygons and area, circles, and space and coordinate geometry. 1974 edition.

Principles of Topology

Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 0486801543

Category: Mathematics

Page: 336

View: 933

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Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.

Introduction to Real Analysis

Author: Michael J. Schramm

Publisher: Courier Corporation

ISBN: 0486131920

Category: Mathematics

Page: 384

View: 9664

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This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.

Introduction to Topology

Author: V. A. Vasilʹev

Publisher: American Mathematical Soc.

ISBN: 0821821628

Category: Mathematics

Page: 149

View: 6468

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This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, intersection index, etc. The author notes, ``The lecture note origins of the book left a significant imprint on its style. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs.'' He concludes, ``As a rule, only those proofs (or sketches of proofs) that are interesting per se and have important generalizations are presented.''

Concepts of Modern Mathematics

Author: Ian Stewart

Publisher: Courier Corporation

ISBN: 0486134954

Category: Mathematics

Page: 368

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In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts of groups, sets, subsets, topology, Boolean algebra, and other mathematical subjects. 200 illustrations.