A Geometric Introduction to Topology


Author: Charles Terence Clegg Wall
Publisher: Courier Corporation
ISBN: 0486678504
Category: Mathematics
Page: 168
View: 9353

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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.

A Combinatorial Introduction to Topology


Author: Michael Henle
Publisher: Courier Corporation
ISBN: 9780486679662
Category: Mathematics
Page: 310
View: 5210

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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.

From Geometry to Topology


Author: H. Graham Flegg
Publisher: Courier Corporation
ISBN: 0486138496
Category: Mathematics
Page: 208
View: 5428

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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.

Principles of Topology


Author: Fred H. Croom
Publisher: Courier Dover Publications
ISBN: 0486810445
Category: Mathematics
Page: 336
View: 6561

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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.

Introduction to Topology

Third Edition
Author: Bert Mendelson
Publisher: Courier Corporation
ISBN: 0486135098
Category: Mathematics
Page: 224
View: 5858

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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 Lebesgue Integration and Fourier Series


Author: Howard J. Wilcox,David L. Myers
Publisher: Courier Corporation
ISBN: 9780486682938
Category: Mathematics
Page: 159
View: 3471

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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.

Elementary Topology


Author: Michael C. Gemignani
Publisher: Courier Corporation
ISBN: 9780486665221
Category: Mathematics
Page: 270
View: 7889

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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.

A First Course in Partial Differential Equations with Complex Variables and Transform Methods


Author: Hans F. Weinberger
Publisher: Courier Corporation
ISBN: 9780486686400
Category: Mathematics
Page: 446
View: 2670

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Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Topics include one-dimensional wave equation, properties of elliptic and parabolic equations, separation of variables and Fourier series, nonhomogeneous problems, and analytic functions of a complex variable. Solutions. 1965 edition.

Introduction to Topology

Second Edition
Author: Theodore W. Gamelin,Robert Everist Greene
Publisher: Courier Corporation
ISBN: 0486320189
Category: Mathematics
Page: 256
View: 6573

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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.

Topology

An Introduction with Application to Topological Groups
Author: George McCarty
Publisher: Courier Corporation
ISBN: 9780486656335
Category: Mathematics
Page: 270
View: 1781

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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.

Conformal Mapping

Methods and Applications
Author: Roland Schinzinger,Patricio A. A. Laura
Publisher: Courier Corporation
ISBN: 9780486432366
Category: Mathematics
Page: 583
View: 7139

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This volume introduces the basic mathematical tools behind conformal mapping, describes advances in technique, and illustrates a broad range of applications. 1991 edition. Includes 247 figures and 38 tables.

Algebraic Topology


Author: C. R. F. Maunder
Publisher: Courier Corporation
ISBN: 9780486691312
Category: Mathematics
Page: 375
View: 4021

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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.

General Investigations of Curved Surfaces


Author: Karl Friedrich Gauss,Peter Pesic
Publisher: Courier Corporation
ISBN: 048644645X
Category: Mathematics
Page: 144
View: 8348

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Originally published: General investigations of curved surfaces of 1827 and 1825. [Princeton]: Princeton University Library, 1902.

Graphs, Surfaces and Homology


Author: Peter Giblin
Publisher: Cambridge University Press
ISBN: 1139491172
Category: Mathematics
Page: N.A
View: 387

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Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.

Invitation to Combinatorial Topology


Author: Maurice Fréchet,Ky Fan
Publisher: Courier Corporation
ISBN: 0486147886
Category: Mathematics
Page: 136
View: 4077

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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.

Topology and Geometry for Physicists


Author: Charles Nash,Siddhartha Sen
Publisher: Courier Corporation
ISBN: 0486318362
Category: Mathematics
Page: 320
View: 848

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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.

Algebraic Geometry


Author: Solomon Lefschetz
Publisher: Courier Corporation
ISBN: 0486154726
Category: Mathematics
Page: 256
View: 3183

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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.

Einführung in die Geometrie und Topologie


Author: Werner Ballmann
Publisher: Springer-Verlag
ISBN: 3034809018
Category: Mathematics
Page: 162
View: 5907

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Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.

General Topology


Author: Stephen Willard
Publisher: Courier Corporation
ISBN: 9780486434797
Category: Mathematics
Page: 369
View: 8334

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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.

Eichfeldtheorie

Eine Einführung in die Differentialgeometrie auf Faserbündeln
Author: Helga Baum
Publisher: Springer-Verlag
ISBN: 3642385397
Category: Mathematics
Page: 380
View: 8571

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Dieses Lehrbuch bietet eine Einführung in die Differentialgeometrie auf Faserbündeln. Nach einem Kapitel über Lie-Gruppen und homogene Räume werden lokal-triviale Faserungen, insbesondere die Hauptfaserbündel und zu ihnen assoziierte Vektorbündel, besprochen. Es folgen die grundlegenden Begriffe der Differentialrechnung auf Faserbündeln: Zusammenhang, Krümmung, Parallelverschiebung und kovariante Ableitung. Anschließend werden die Holonomiegruppen vorgestellt, die zentrale Bedeutung in der Differentialgeometrie haben. Als Anwendungen werden charakteristische Klassen und die Yang-Mills-Gleichung behandelt. Zahlreiche Aufgaben mit Lösungshinweisen helfen, das Gelernte zu vertiefen. Das Buch richtet sich vor allem an Studenten der Mathematik und Physik im Masterstudium. Es stellt mathematische Grundlagen bereit, die in Vorlesungen zur Eichfeldtheorie in der theoretischen und mathematischen Physik Anwendung finden.