This book is awesome.  I went to school for engineering, and I have never understood what it took to make a complete proof.  Any time I needed to "prove" something, I just tried to find counterexamples. If I couldn't, I figured it was probably true.  This is obviously not particularly rigorous.<br><br>I figured it was time I learn (for no reason, really), and this helped a great deal.  This book also has some topics I would have never thought to look up, such as how to analyze a proof, how to analyze a theorem, surjection, etc.  I had no idea how important implications are in mathematical proofs.  I had never heard of a contrapositive.  I feel like I now have some insight into how pure math is done.<br><br>My only complaints: no solutions in the book (a few are online) and the binding is a little weak.