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Understanding Topology
A Practical Introduction
Synopsis
A fresh approach to topology makes this complex topic easier for students to master.
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 projects
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.
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What Reviewers Are Saying
A 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 textbook's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles, and might reasonably be expected to become a standard reference for teaching backgrounds of topology in the years to come.
-Marek Golasinski (Olsztyn), Zentralblatt Math A useful book for undergraduates, with the initial introduction to concepts being at the level of intuition and analogy, followed by mathematical rigour.
-John Bartlett CMath MIMA, Mathematics Today