Chapter Zero: Fundamental Notions of Abstract Mathematics (2nd Edition)

Rating:
Summary: Good intro to advanced mathematics
Review: The aim of this textbook is to teach students methods of proof, logic, and basic set theory in a small group/seminar setting. It begins rather slowly, introducing logical implications etc. As it gains speed, it presents most theorems without proof (indicated by a hollow square). The author suggests that the student try to complete these proofs his or herself, possibly for presentation and critique in class. Thus the book progresses and as the subject matter becomes more complicated, the student has the confidence of knowing that he/she proved 95% of the underlying material his/herself.

I used this book in my "Intro to Advanced Mathematics" course at a small liberal arts college. It worked well for that purpose - since then I've taken higher level courses and had no trouble at all with proof techniques. It wouldn't work as a set theory or an abstract algebra text on its own, though if it would certainly help in either of those courses if you don't have much grounding in rigorous proof.

Anyway, you can get the exact same book from Amazon Canada (www.amazon.ca) for like $75US, so do that instead of buying it from Amazon US.