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" Understanding topology : "
Shaun V. Ault.
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BL
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| Record Number
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845477
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| Main Entry
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Ault, Shaun V.,1979-
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| Title & Author
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Understanding topology : : a practical introduction /\ Shaun V. Ault.
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| Publication Statement
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Baltimore :: Johns Hopkins University Press,, 2018.
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, ©2018
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| Page. NO
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x, 399 pages :: illustrations ;; 26 cm
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| ISBN
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142142407X
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: 1421424088
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: 9781421424071
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: 9781421424088
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| Bibliographies/Indexes
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Includes bibliographical references (pages 391-394) and index.
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| Contents
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1. Euclidean topology. Introduction to topology -- Metric topology in Euclidean space -- Vector field in the plane. 2. Abstract topology with applications. Abstract point-set topology -- Surfaces -- Applications in graphs and knots. 3. Basic algebraic topology. The fundamental group -- Introduction to homology. Appendixes. Review of set theory and functions -- Group theory and linear algebra -- Selected solutions -- Notations.
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| Abstract
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"This groundbreaking new text: presents Euclidean, abstract, and basic algebraic topology; explains metric topology, vector spaces and dynamics, point-set topology, surfaces, knot theory, graphs and map coloring, the fundamental group, and homology; includes worked example problems, solutions, and optional advanced sections for independent projects; [and] provides a brief review of set theory and functions and a summation of essential topics in group theory and linear algebra. Following a path that will work with any standard syllabus, the book is arranged to help students reach that 'Aha!' moment, encouraging readers to use their intuition through local-to-global analysis and emphasizing topological invariants to lay the groundwork for algebraic topology"--Back cover.
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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"--Back cover.
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| Subject
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Topology.
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Topology.
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| Dewey Classification
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514
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| LC Classification
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QA611.A86 2018
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