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Algebraic Topology

Algebraic Topology

  • Author: C. R. F. Maunder
  • Publisher: Courier Corporation
  • ISBN: 9780486691312
  • Category: Mathematics
  • Page: 375
  • View: 4081
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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.

Algebraic Topology

Algebraic Topology

Homology and Cohomology

  • Author: Andrew H. Wallace
  • Publisher: Courier Corporation
  • ISBN: 0486462390
  • Category: Mathematics
  • Page: 272
  • View: 4085
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Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.

A Combinatorial Introduction to Topology

A Combinatorial Introduction to Topology

  • Author: Michael Henle
  • Publisher: Courier Corporation
  • ISBN: 9780486679662
  • Category: Mathematics
  • Page: 310
  • View: 7942
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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.

Lehrbuch der Algebra

Lehrbuch der Algebra

Mit lebendigen Beispielen, ausführlichen Erläuterungen und zahlreichen Bildern

  • Author: Gerd Fischer
  • Publisher: Springer-Verlag
  • ISBN: 3834894559
  • Category: Mathematics
  • Page: 404
  • View: 5692
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Dieses ausführlich geschriebene Lehrbuch eignet sich als Begleittext zu einer einführenden Vorlesung über Algebra. Die Themenkreise sind Gruppen als Methode zum Studium von Symmetrien verschiedener Art, Ringe mit besonderem Gewicht auf Fragen der Teilbarkeit und schließlich als Schwerpunkt Körpererweiterungen und Galois-Theorie als Grundlage für die Lösung klassischer Probleme zur Berechnung der Nullstellen von Polynomen und zur Möglichkeit geometrischer Konstruktionen.

Principles of Topology

Principles of Topology

  • Author: Fred H. Croom
  • Publisher: Courier Dover Publications
  • ISBN: 0486810445
  • Category: Mathematics
  • Page: 336
  • View: 8378
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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.

An Introduction to Algebraic Topology

An Introduction to Algebraic Topology

  • Author: Andrew H. Wallace
  • Publisher: Courier Corporation
  • ISBN: 0486152952
  • Category: Mathematics
  • Page: 208
  • View: 2137
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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.

Algebra

Algebra

Aus dem Englischen übersetzt von Annette A’Campo

  • Author: Michael Artin
  • Publisher: Birkhäuser
  • ISBN: 9783764359386
  • Category: Mathematics
  • Page: 705
  • View: 2822
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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.

Foundations of Combinatorial Topology

Foundations of Combinatorial Topology

  • Author: L. S. Pontryagin
  • Publisher: Courier Corporation
  • ISBN: 0486406857
  • Category: Mathematics
  • Page: 112
  • View: 5143
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Concise, rigorous introduction to homology theory features applications to dimension theory and fixed-point theorems. Lucid coverage of the field includes examinations of complexes and their Betti groups, invariance of the Betti groups, and continuous mappings and fixed points. Proofs are presented in a complete and careful manner. A beneficial text for a graduate-level course, "this little book is an extremely valuable addition to the literature of algebraic topology." — The Mathematical Gazette.

Introduction to Topology

Introduction to Topology

Second Edition

  • Author: Theodore W. Gamelin,Robert Everist Greene
  • Publisher: Courier Corporation
  • ISBN: 0486320189
  • Category: Mathematics
  • Page: 256
  • View: 8113
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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.

Manifolds and Modular Forms

Manifolds and Modular Forms

  • Author: Friedrich Hirzebruch
  • Publisher: Springer-Verlag
  • ISBN: 3663140458
  • Category: Mathematics
  • Page: 212
  • View: 2798
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Topology

Topology

An Introduction to the Point-set and Algebraic Areas

  • Author: Donald W. Kahn
  • Publisher: Courier Corporation
  • ISBN: 9780486686097
  • Category: Mathematics
  • Page: 217
  • View: 1154
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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.

Galoissche Theorie

Galoissche Theorie

  • Author: Emil Artin
  • Publisher: N.A
  • ISBN: N.A
  • Category: Galois theory
  • Page: 86
  • View: 1824
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General Topology

General Topology

  • Author: Stephen Willard
  • Publisher: Courier Corporation
  • ISBN: 0486131785
  • Category: Mathematics
  • Page: 384
  • View: 8446
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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.

Understanding Topology

Understanding Topology

A Practical Introduction

  • Author: Shaun V. Ault
  • Publisher: JHU Press
  • ISBN: 142142407X
  • Category: Mathematics
  • Page: 416
  • View: 3109
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"Topology can present significant challenges for undergraduate students of mathematics and the sciences. 'Understanding topology' aims to change that. The perfect introductory topology textbook, 'Understanding topology' requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from chemical dynamics to determining the shape of the universe, will engage students in a way traditional topology textbooks do not"--

A Geometric Introduction to Topology

A Geometric Introduction to Topology

  • Author: Charles Terence Clegg Wall
  • Publisher: Courier Corporation
  • ISBN: 0486678504
  • Category: Mathematics
  • Page: 168
  • View: 4322
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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.

Elements of Point Set Topology

Elements of Point Set Topology

  • Author: John D. Baum
  • Publisher: Courier Corporation
  • ISBN: 0486668266
  • Category: Mathematics
  • Page: 150
  • View: 4263
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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.

Einführung in die Kategorientheorie

Einführung in die Kategorientheorie

Mit ausführlichen Erklärungen und zahlreichen Beispielen

  • Author: Martin Brandenburg
  • Publisher: Springer-Verlag
  • ISBN: 3662535211
  • Category: Mathematics
  • Page: 343
  • View: 7006
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Die Kategorientheorie deckt die innere Architektur der Mathematik auf. Dabei werden die strukturellen Gemeinsamkeiten zwischen mathematischen Disziplinen und ihren spezifischen Konstruktionen herausgearbeitet. Dieses Buch gibt eine systematische Einführung in die Grundbegriffe der Kategorientheorie. Zahlreiche ausführliche Erklärungstexte sowie die große Menge an Beispielen helfen beim Einstieg in diese verhältnismäßig abstrakte Theorie. Es werden viele konkrete Anwendungen besprochen, welche die Nützlichkeit der Kategorientheorie im mathematischen Alltag belegen. Jedes Kapitel wird mit einem motivierenden Text eingeleitet und mit einer großen Aufgabensammlung abgeschlossen. An Vorwissen muss der Leser lediglich ein paar Grundbegriffe des Mathematik-Studiums mitbringen. Die vorliegende zweite vollständig durchgesehene Auflage ist um ausführliche Lösungen zu ausgewählten Aufgaben ergänzt.

Basic Algebraic Topology

Basic Algebraic Topology

  • Author: Anant R. Shastri
  • Publisher: CRC Press
  • ISBN: 1466562447
  • Category: Mathematics
  • Page: 551
  • View: 8399
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Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and simplicial complexes. It then focuses on the fundamental group, covering spaces and elementary aspects of homology theory. It presents the central objects of study in topology visualization: manifolds. After developing the homology theory with coefficients, homology of the products, and cohomology algebra, the book returns to the study of manifolds, discussing Poincaré duality and the De Rham theorem. A brief introduction to cohomology of sheaves and Čech cohomology follows. The core of the text covers higher homotopy groups, Hurewicz’s isomorphism theorem, obstruction theory, Eilenberg-Mac Lane spaces, and Moore-Postnikov decomposition. The author then relates the homology of the total space of a fibration to that of the base and the fiber, with applications to characteristic classes and vector bundles. The book concludes with the basic theory of spectral sequences and several applications, including Serre’s seminal work on higher homotopy groups. Thoroughly classroom-tested, this self-contained text takes students all the way to becoming algebraic topologists. Historical remarks throughout the text make the subject more meaningful to students. Also suitable for researchers, the book provides references for further reading, presents full proofs of all results, and includes numerous exercises of varying levels.

Algebraic Geometry

Algebraic Geometry

  • Author: Solomon Lefschetz
  • Publisher: Courier Corporation
  • ISBN: 0486154726
  • Category: Mathematics
  • Page: 256
  • View: 4344
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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.

Concepts of Modern Mathematics

Concepts of Modern Mathematics

  • Author: Ian Stewart
  • Publisher: Courier Corporation
  • ISBN: 0486134954
  • Category: Mathematics
  • Page: 368
  • View: 5285
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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.