Distilling Ideas: An Introduction to Mathematical Thinking by Brian P. Katz and Michael Starbird as part of MAA Reviews.
The authors of this book, as they explain in their first chapter, are taking readers/students on a journey — one that will “add new, powerful inquiry skills” to a student’s repertoire: abstraction, exploration, conjecture, justification, application, and extension. The book is clearly intended for inquiry-based mathematics courses. It is replete with explorations to undertake, definitions to explore, and theorems to prove, but there are no sample proofs or answers.
The book has five chapters, with the middle three chapters on graphs, groups, and ε-δ calculus constituting the bulk of the book. To me, it is clear that any one of these middle chapters by itself has the potential to be used for an entire one-semester course. There is really enough material in the ε-δ calculus chapter for an introductory junior level real analysis course. Similarly, the group theory chapter gets to Sylow’s Theorem and has more in it than most students could cover in one-semester when doing all the work themselves.
Read the full review here.
Annie Selden is Adjunct Professor of Mathematics at New Mexico State University and Professor Emerita of Mathematics from Tennessee Technological University. She regularly teaches graduate courses in mathematics and mathematics education.