Understanding Topology: A Practical Introduction

by Shaun V Ault

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
• 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.

Genres: Mathematics

584 pages, Kindle Edition

Published January 17, 2018

Reviews

[Katelyn Jenkins]

Again, this is one of those books that I am so sure is very important, I just did not understand the major concepts.

Topology, the study of surfaces and depicting them in 2D and 3D interfaces. This book is organized well for the topics of topological surfaces, vectors fields, graphs (both algebraic and eluidan), knots, group theory, and much, much more content. There are also two proficiency problems to solve with each chapter, answers in the back to check them, and appendices to solidify prerequisite understandings for the mathematics of the calculations.

A very good book, I plan to read this again when I am ready!