Looking for a Great book on Proving, on Mathematical Logic in general

Question

I'm looking for a good/great book on Mathematics. More specifically one that focuses on how I should go about to prove various things, e.g. given equations what are the methods I can use in order to solve them. Generally, I mostly want a book about logic, a book that organizes one's ability to reason and not fall into traps of logical fallacies. I have found this book by David Hilbert to be more or less what I want (I think). What are your thoughts and suggestions? Thanks in advance.

Answer 1

"A book that organizes one's ability to reason and not fall into traps of logical fallacies."

Daniel Velleman's much admired, much recommended, How to Prove It (CUP) is probably just what you are looking for. It aims, precisely, to teach techniques for writing and reading proofs.

Answer 2

Kenneth Rosen's Discrete Math and its Applications

A Concise Introduction to Logic by Patrick J. Hurley

The former is an intro to proof text and the latter is not a math text but it has considerable examples of logical fallacies.