Algebraic Topology

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Author: C. R. F. Maunder

Publisher: Courier Corporation

ISBN: 9780486691312

Category: Mathematics

Page: 375

View: 2192

Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.

An Introduction to Algebraic Topology

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Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486152952

Category: Mathematics

Page: 208

View: 4889

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.

A Combinatorial Introduction to Topology

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Author: Michael Henle

Publisher: Courier Corporation

ISBN: 9780486679662

Category: Mathematics

Page: 310

View: 8166

Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

Introduction to Topology

Second Edition

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Author: Theodore W. Gamelin,Robert Everist Greene

Publisher: Courier Corporation

ISBN: 0486320189

Category: Mathematics

Page: 256

View: 6877

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.

Topology

An Introduction to the Point-set and Algebraic Areas

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Author: Donald W. Kahn

Publisher: Courier Corporation

ISBN: 9780486686097

Category: Mathematics

Page: 217

View: 621

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.

Principles of Topology

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Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 0486810445

Category: Mathematics

Page: 336

View: 5868

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.

Differentialgeometrie von Kurven und Flächen

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Author: Manfredo P. do Carmo

Publisher: Springer-Verlag

ISBN: 3322850722

Category: Technology & Engineering

Page: 263

View: 1321

Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

A Geometric Introduction to Topology

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Author: Charles Terence Clegg Wall

Publisher: Courier Corporation

ISBN: 0486678504

Category: Mathematics

Page: 168

View: 3877

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.

From Geometry to Topology

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Author: H. Graham Flegg

Publisher: Courier Corporation

ISBN: 0486138496

Category: Mathematics

Page: 208

View: 7660

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.

Topology

An Introduction with Application to Topological Groups

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Author: George McCarty

Publisher: Courier Corporation

ISBN: 0486450821

Category: Mathematics

Page: 288

View: 9793

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.

Algebraic Geometry

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Author: Solomon Lefschetz

Publisher: Courier Corporation

ISBN: 0486154726

Category: Mathematics

Page: 256

View: 3029

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

Partielle Differentialgleichungen

Eine Einführung

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Author: Walter A. Strauss

Publisher: Springer-Verlag

ISBN: 366312486X

Category: Mathematics

Page: 458

View: 8002

Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.

Elementary Topology

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Author: Michael C. Gemignani

Publisher: Courier Corporation

ISBN: 9780486665221

Category: Mathematics

Page: 270

View: 2812

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.

Liebe und Mathematik

Im Herzen einer verborgenen Wirklichkeit

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Author: Edward Frenkel

Publisher: Springer-Verlag

ISBN: 3662434210

Category: Mathematics

Page: 317

View: 9570

Introduction to Real Analysis

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Author: Michael J. Schramm

Publisher: Courier Corporation

ISBN: 0486131920

Category: Mathematics

Page: 384

View: 6834

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.

General Topology

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Author: Stephen Willard

Publisher: Courier Corporation

ISBN: 0486131785

Category: Mathematics

Page: 384

View: 7046

Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.

Elements of Point Set Topology

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Author: John D. Baum

Publisher: Courier Corporation

ISBN: 0486668266

Category: Mathematics

Page: 150

View: 1108

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.

An Introduction to Lebesgue Integration and Fourier Series

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Author: Howard J. Wilcox,David L. Myers

Publisher: Courier Corporation

ISBN: 9780486682938

Category: Mathematics

Page: 159

View: 3005

This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.

Homology Theory on Algebraic Varieties

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Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486799905

Category: Mathematics

Page: 128

View: 8130

Concise and authoritative monograph, geared toward advanced undergraduate and graduate students, covers linear sections, singular and hyperplane sections, Lefschetz's first and second theorems, the Poincaré formula, and invariant and relative cycles. 1958 edition.