Understanding Topology: A Practical Introduction

China Internet Development Report 2018: Blue Book of World Internet Conference 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.\n\nUnderstanding 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.Understanding Topology: A Practical Introduction is written by Shaun V. Ault and published by JHUP. ISBNs for Understanding Topology are 9781421424088, 1421424088 and the print ISBNs are 9781421424071, 142142407X.