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Understanding Topology

A Practical Introduction

By (author) Shaun V. Ault
Format: Hardback
Publisher: Johns Hopkins University Press, Baltimore, MD, United States
Published: 27th Mar 2018
Dimensions: w 178mm h 254mm d 30mm
Weight: 998g
ISBN-10: 142142407X
ISBN-13: 9781421424071
Barcode No: 9781421424071
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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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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