Knots and Surfaces: A Guide to Discovering Mathematics

by David W. Farmer

In most mathematics textbooks, the most exciting part of mathematics--the process of invention and discovery--is completely hidden from the reader. The aim of Knots and Surfaces is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequisites for understanding the text. Any college student interested in discovering the beauty of mathematics will enjoy a course taught from this book. The book has also been used successfully with nonscience students who want to fulfill a science requirement.

Genres: Mathematics, Nonfiction

101 pages, Paperback

First published November 1, 1995

Reviews

[Rachel Johnson · Rating 4 out of 5]

Honestly didn't need to read either of the textbooks that much but from what I did read, this book seemed like a nice and gentle introduction to topology.

[Gordon · Rating 5 out of 5]

I picked this up from the LA central library as a reference guide in a self-led study on knot theory. It's fantastic. Farmer and Stanford write superbly, introducing a number of truly innovative analogies that are as effective as they are daring. It's not easy to propose considering the perspective of an insect or large connected chain of people holding hands in a formal mathematics context. The style encourages the reader to "discover" mathematics and I got the most out of it when I put the book down and worked on the suggested tasks on my own for a length of time -- sometimes for a week or more. The reward of feeling like I figured out the next step before I had to read on was worth more than any amount of knowledge that I might ever parrot from someone else.

The particular bonus for me was the introduction to topology (segued into effortlessly from easy examples of nontrivial surfaces) and the connection between knots, graphs, and the four-coloring theory.