I'm taking an intro to proof's class this semester. What are your thoughts on Velleman's How to prove it book? Are the exercises easy or hard to do?
Answers and Replies
The book has great examples (though some haves errors). The proofs can be really easy or take 30-60 minutes to do. The key point of the book is to use logic to carry out a proof the right way. It helps you decide to prove directly, by exhaustion, or by contradiction. The book goes into proof by induction much later but I haven't gone over it in class.
Tip: If you get stuck on proving a theorem, try to translate it to symbolic logic and keep trying to finish the proof. If an hour has gone by, you can go get help. This helps you try out more approaches to the problem.
Finally, one way to self check a proof is to read it and be convinced.