See our review of the first edition. Dineen is a professor at University College, Dublin, where he teaches serious mathematics to students in Economics and Finance. His experience has led him to write unique textbooks such as this one. After the publication of the first edition, Dineen had the opportunity to teach a preliminary real analysis course to the same group of students. The resulting book, Analysis: A Gateway to Understanding Mathematics was reviewed here as well.
In addition to the usual improvements in response to comments and suggestions, the new edition reflects the experience of teaching real analysis. In particular, this edition includes a construction of Lebesgue measure using dyadic rationals, an approach that fits well with the construction of the real numbers presented in the analysis text.
Dineen is doing something valuable by trying to find ways to communicate mathematics in a serious way to an audience that often gets little more than recipes and rules. It's a project definitely worth supporting.
Fernando Q. Gouvêa is the editor of MAA Reviews.