9781421424071

142142407X

"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.

"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.