Understanding topology : a practical introduction
- Shaun V. Ault.
- Baltimore : Johns Hopkins University Press, 2018.
- Copyright notice
- Physical description
- x, 399 pages : illustrations ; 26 cm
Science Library (Li and Ma)
|QA611 .A86 2018||Unknown|
- Ault, Shaun V., author.
- Includes bibliographical references and index.
- PrefaceI Euclidean Topology1. Introduction to Topology1.1 Deformations1.2 Topological Spaces2. Metric Topology in Euclidean Space2.1 Distance2.2 Continuity and Homeomorphism2.3 Compactness and Limits2.4 Connectedness2.5 Metric Spaces in General3. Vector Fields in the Plane3.1 Trajectories and Phase Portraits3.2 Index of a Critical Point3.3 *Nullclines and Trapping RegionsII Abstract Topology with Applications4. Abstract Point-Set Topology4.1 The Definition of a Topology4.2 Continuity and Limits4.3 Subspace Topology and Quotient Topology4.4 Compactness and Connectedness4.5 Product and Function Spaces4.6 *The Infinitude of the Primes5. Surfaces5.1 Surfaces and Surfaces-with-Boundary5.2 Plane Models and Words5.3 Orientability5.4 Euler Characteristic6. Applications in Graphs and Knots6.1 Graphs and Embeddings6.2 Graphs, Maps, and Coloring Problems6.3 Knots and Links6.4 Knot ClassificationIII Basic Algebraic Topology7. The Fundamental Group7.1 Algebra of Loops7.2 Fundamental Group as Topological Invariant7.3 Covering Spaces and the Circle7.4 Compact Surfaces and Knot Complements7.5 *Higher Homotopy Groups8. Introduction to Homology8.1 Rational Homology8.2 Integral HomologyAppendixesA. Review of Set Theory and FunctionsA.1 Sets and Operations on SetsA.2 Relations and FunctionsB. Group Theory and Linear AlgebraB.1 GroupsB.2 Linear AlgebraC. Selected SolutionsD. NotationsBibliographyIndex.
- (source: Nielsen Book Data)9781421424071 20180226
- Publisher's Summary
- Topology-the branch of mathematics that studies the properties of spaces that remain unaffected by stretching and other distortions-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 mapping DNA to determining the shape of the universe, will engage students in a way traditional topology textbooks do not.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 projectsFollowing 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.
(source: Nielsen Book Data)9781421424071 20180226
- Publication date
- Copyright date
- 9781421424071 hardback alk. paper
- 142142407X hardback alk. paper
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