Books for transitional mathematics courses are becoming more common and this book falls short of most of them. The writing style is nice and dry, but the topics in the book don't flow well. The author doesn't develop foundational material in the first three chapters (no axiomatic set theory or predicate calculus). Also, there isn't enough discussion of proof techniques (existencial and universal arguments, indirect proofs, etc.). The abstract algebra and analysis chapters aren't enough to give a full treatment, but are beyond the scope of good "bridge" course.

This book deserves its three stars because it does provide a very good selection of problems and appropriate hints. A student able to complete the problems does in fact demonstrate comprehension of the subject matter.