Logic, set theory, and mathematical induction play essential roles in modern mathematics and computer science. This book is intended to fill the gap between rigorous, advanced mathematical logic texts and "discrete mathematics" texts that do not treat logic with the depth and rigor required in modern computer science. It will prepare students for advanced courses in mathematics, computer science, logic and its applications.
Holy crap this was one of the hardest courses I took in college and only many all nighters and copious caffeine saw me through. It was also one of the biggest ah-ha moments of my life when I started to see the patterns down there beneath the maths. I have been thinking of picking up a copy and just sitting down to sharpen up my mind--it has become a little dulled with use.
I had trouble appreciating this book for the longest, but after some studies in the Foundations of Mathematics, experience with other logic books, and application of greater attention to the books details, I've grown to like it.