Understanding Topology: A Practical Introduction

By Shaun V Ault

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.

• Format: Hardcover
• Language: English
• ISBN: 142142407X
• ISBN13: 9781421424071
• Release Date: January 2018
• Publisher: Johns Hopkins University Press
• Length: 416 Pages
• Weight: 2.20 lbs.
• Dimensions: 1.1" x 7.2" x 10.2"
• Grade Range: Postsecondary