Algebraic Topology

Author: C. R. F. Maunder

Publisher: Courier Corporation

ISBN: 9780486691312

Category: Mathematics

Page: 375

View: 1178

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.
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A Combinatorial Introduction to Topology

Author: Michael Henle

Publisher: Courier Corporation

ISBN: 9780486679662

Category: Mathematics

Page: 310

View: 4060

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.
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An Introduction to Algebraic Topology

Author: Andrew H. Wallace

Publisher: Courier Corporation

ISBN: 0486152952

Category: Mathematics

Page: 208

View: 2658

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.
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Introduction to Topology

Second Edition

Author: Theodore W. Gamelin,Robert Everist Greene

Publisher: Courier Corporation

ISBN: 0486320189

Category: Mathematics

Page: 256

View: 9189

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.
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Topology

An Introduction to the Point-set and Algebraic Areas

Author: Donald W. Kahn

Publisher: Courier Corporation

ISBN: 9780486686097

Category: Mathematics

Page: 217

View: 5279

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.
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Principles of Topology

Author: Fred H. Croom

Publisher: Courier Dover Publications

ISBN: 0486810445

Category: Mathematics

Page: 336

View: 7557

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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Differentialgeometrie von Kurven und Flächen

Author: Manfredo P. do Carmo

Publisher: Springer-Verlag

ISBN: 3322850722

Category: Technology & Engineering

Page: 263

View: 3805

Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang
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A Geometric Introduction to Topology

Author: Charles Terence Clegg Wall

Publisher: Courier Corporation

ISBN: 0486678504

Category: Mathematics

Page: 168

View: 6785

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.
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Algebra

Aus dem Englischen übersetzt von Annette A’Campo

Author: Michael Artin

Publisher: Birkhäuser

ISBN: 9783764359386

Category: Mathematics

Page: 705

View: 6866

Important though the general concepts and propositions may be with which the modem and industrious passion for axiomatizing and generalizing has presented us, in algebra perhaps more than anywhere else, nevertheless I am convinced that the special problems in all their complexity constitute the stock and core of mathematics, and that to master their difficulties requires on the whole the harder labor. HERMANN WEYL Die Arbeit an diesem Buch begann vor etwa zwanzig Jahren mit Aufzeichnungen zur Ergänzung meiner Algebravorlesungen. Ich wollte einige konkrete Themen, wie Symmetrie, lineare Gruppen und quadratische Zahlkörper, ausführlicher be­ handeln als dies im vorgesehenen Text der Fall war, und darüberhinaus wollte ich den Schwerpunkt in der Gruppentheorie von den Permutationsgruppen auf Matrixgruppen verlagern. Ein anderes ständig wiederkehrendes Thema, nämlich Gitter, sind spontan aufgetaucht. Ich hoffte, der konkrete Stoff könne das Interesse der Studenten wecken und gleichzeitig die Abstraktionen verständlicher machen, kurz gesagt, sie sollten weiter kommen, indem sie beides gleichzeitig lernten. Das bewährte sich gut. Es dauerte einige Zeit, bis ich entschieden hatte, welche Themen ich behandeln wollte, und allmählich verteilte ich mehr und mehr Aufzeichnungen und ging schließlich dazu über, die ganze Vorlesung mit diesem Skript zu bestrei­ ten. Auf diese Weise ist ein Buch entstanden, das, wie ich meine, etwas anders ist als die existierenden Bücher. Allerdings haben mir die Probleme, die ich damit hatte, die einzelnen Teile des Buches zu einem Ganzen zusammenzufügen, einige Kopfschmerzen bereitet; ich kann also nicht empfehlen, auf diese Art anzufangen, ein Buch zu schreiben.
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From Geometry to Topology

Author: H. Graham Flegg

Publisher: Courier Corporation

ISBN: 0486138496

Category: Mathematics

Page: 208

View: 7998

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.
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Topology

An Introduction with Application to Topological Groups

Author: George McCarty

Publisher: Courier Corporation

ISBN: 0486450821

Category: Mathematics

Page: 288

View: 8765

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.
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Algebraic Geometry

Author: Solomon Lefschetz

Publisher: Courier Corporation

ISBN: 0486154726

Category: Mathematics

Page: 256

View: 5701

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.
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Partielle Differentialgleichungen

Eine Einführung

Author: Walter A. Strauss

Publisher: Springer-Verlag

ISBN: 366312486X

Category: Mathematics

Page: 458

View: 3641

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.
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Elementary Topology

Author: Michael C. Gemignani

Publisher: Courier Corporation

ISBN: 9780486665221

Category: Mathematics

Page: 270

View: 5043

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.
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Introduction to Real Analysis

Author: Michael J. Schramm

Publisher: Courier Corporation

ISBN: 0486131920

Category: Mathematics

Page: 384

View: 6179

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.
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General Topology

Author: Stephen Willard

Publisher: Courier Corporation

ISBN: 0486131785

Category: Mathematics

Page: 384

View: 1214

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.
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Elements of Point Set Topology

Author: John D. Baum

Publisher: Courier Corporation

ISBN: 0486668266

Category: Mathematics

Page: 150

View: 9193

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.
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Principia Mathematica.

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 8300

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Elementary Point-Set Topology

A Transition to Advanced Mathematics

Author: Andre L. Yandl,Adam Bowers

Publisher: Courier Dover Publications

ISBN: 048680349X

Category: Mathematics

Page: 256

View: 2449

This versatile, original approach, which focuses on learning to read and write proofs, serves as both an introductory treatment and a bridge between elementary calculus and more advanced courses. 2016 edition.
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