عنوان

Understanding topology :

142142407X

1421424088

9781421424071

9781421424088

Understanding topology :

[Book]

a practical introduction /

Shaun V. Ault.

Baltimore :

Johns Hopkins University Press,

2018.

©2018

x, 399 pages :

illustrations ;

26 cm

Includes bibliographical references (pages 391-394) and index.

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.

0

"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.

"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.

Topology.

Topology.

Ault, Shaun V.,1979-

20200822182401.0

rda

[Book]

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