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Algebraic Topology

Algebraic Topology

  • Author: N.A
  • Publisher: 清华大学出版社有限公司
  • ISBN: 9787302105886
  • Category: Algebraic topology
  • Page: 544
  • View: 4848
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An Introduction to Algebraic Topology

An Introduction to Algebraic Topology

  • Author: Andrew H. Wallace
  • Publisher: Courier Corporation
  • ISBN: 0486152952
  • Category: Mathematics
  • Page: 208
  • View: 3026
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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.

A Combinatorial Introduction to Topology

A Combinatorial Introduction to Topology

  • Author: Michael Henle
  • Publisher: Courier Corporation
  • ISBN: 9780486679662
  • Category: Mathematics
  • Page: 310
  • View: 4842
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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.

Algebraic Topology

Algebraic Topology

Homology and Cohomology

  • Author: Andrew H. Wallace
  • Publisher: Courier Corporation
  • ISBN: 0486462390
  • Category: Mathematics
  • Page: 272
  • View: 737
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Surveys several algebraic invariants, including the fundamental group, singular and Cech homology groups, and a variety of cohomology groups.

Algebraic Topology

Algebraic Topology

  • Author: C. R. F. Maunder
  • Publisher: Courier Corporation
  • ISBN: 9780486691312
  • Category: Mathematics
  • Page: 375
  • View: 8727
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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.

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: 7767
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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.

Topology

Topology

  • Author: John G. Hocking,Gail S. Young
  • Publisher: Courier Corporation
  • ISBN: 0486141098
  • Category: Mathematics
  • Page: 384
  • View: 4696
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Superb one-year course in classical topology. Topological spaces and functions, point-set topology, much more. Examples and problems. Bibliography. Index.

Combinatorial Topology

Combinatorial Topology

  • Author: Pavel S. Aleksandrov
  • Publisher: Courier Corporation
  • ISBN: 9780486401799
  • Category: Mathematics
  • Page: 148
  • View: 9955
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Clearly written, well-organized, 3-part text begins by dealing with certain classic problems without using the formal techniques of homology theory and advances to the central concept, the Betti groups. Numerous detailed examples.

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: 5363
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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.

Counterexamples in Topology

Counterexamples in Topology

  • Author: Lynn Arthur Steen,J. Arthur Seebach
  • Publisher: Courier Corporation
  • ISBN: 0486319296
  • Category: Mathematics
  • Page: 272
  • View: 8897
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Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.

Topology

Topology

An Introduction with Application to Topological Groups

  • Author: George McCarty
  • Publisher: Courier Corporation
  • ISBN: 0486450821
  • Category: Mathematics
  • Page: 288
  • View: 4060
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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.

Basic Concepts of Algebraic Topology

Basic Concepts of Algebraic Topology

  • Author: F.H. Croom
  • Publisher: Springer Science & Business Media
  • ISBN: 1468494759
  • Category: Mathematics
  • Page: 180
  • View: 4665
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This text is intended as a one semester introduction to algebraic topology at the undergraduate and beginning graduate levels. Basically, it covers simplicial homology theory, the fundamental group, covering spaces, the higher homotopy groups and introductory singular homology theory. The text follows a broad historical outline and uses the proofs of the discoverers of the important theorems when this is consistent with the elementary level of the course. This method of presentation is intended to reduce the abstract nature of algebraic topology to a level that is palatable for the beginning student and to provide motivation and cohesion that are often lacking in abstact treatments. The text emphasizes the geometric approach to algebraic topology and attempts to show the importance of topological concepts by applying them to problems of geometry and analysis. The prerequisites for this course are calculus at the sophomore level, a one semester introduction to the theory of groups, a one semester introduc tion to point-set topology and some familiarity with vector spaces. Outlines of the prerequisite material can be found in the appendices at the end of the text. It is suggested that the reader not spend time initially working on the appendices, but rather that he read from the beginning of the text, referring to the appendices as his memory needs refreshing. The text is designed for use by college juniors of normal intelligence and does not require "mathematical maturity" beyond the junior level.

Elementary Concepts of Topology

Elementary Concepts of Topology

  • Author: Paul Alexandroff
  • Publisher: Courier Corporation
  • ISBN: 0486155064
  • Category: Mathematics
  • Page: 64
  • View: 4587
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Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

Elements of Point Set Topology

Elements of Point Set Topology

  • Author: John D. Baum
  • Publisher: Courier Corporation
  • ISBN: 0486668266
  • Category: Mathematics
  • Page: 150
  • View: 7506
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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.

Principles of Topology

Principles of Topology

  • Author: Fred H. Croom
  • Publisher: Courier Dover Publications
  • ISBN: 0486801543
  • Category: Mathematics
  • Page: 336
  • View: 7624
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Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.

Algebraic Geometry

Algebraic Geometry

  • Author: Solomon Lefschetz
  • Publisher: Courier Corporation
  • ISBN: 0486154726
  • Category: Mathematics
  • Page: 256
  • View: 4378
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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: 1660
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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.

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: 2807
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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.

Lectures on Algebraic Topology

Lectures on Algebraic Topology

  • Author: Sergeĭ Vladimirovich Matveev
  • Publisher: European Mathematical Society
  • ISBN: 9783037190234
  • Category: Algebraic topology
  • Page: 99
  • View: 2040
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Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.

Topology and Geometry for Physicists

Topology and Geometry for Physicists

  • Author: Charles Nash,Siddhartha Sen
  • Publisher: Courier Corporation
  • ISBN: 0486318362
  • Category: Mathematics
  • Page: 320
  • View: 7687
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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.