Quality has a quantity of its own, according to Stephen Barr’s accessible account of topology and related mathematical concepts.
This book is excellent for an intelligent adult looking to return to mathematical investigation, without building on a recent “core study” of algebra, geometry, and differential calculus. The issues of exotic topological surfaces, networks, continuity and discreteness, and set theory are all approached in a candid manner with efficient examples. Despite the informality of the prose, anyone reading this like a novel will get very little out of it. This is really a math book, and it often requires the reader to take considerable time to assimilate new ideas.
Part of Barr’s approach to the abstractions of topology is to encourage the reader to construct paper models to approximate some of the surfaces introduced. These exercises are quite worthwhile. Although there is no “test,” the book does include a number of interesting puzzles applying the concepts discussed. [via]