The Nuts and Bolts of Proofs by Antonella Cupillari

     In my quest to better understand bioinformatics, I have found myself on the topic of algorithms.  After thumbing through Cormen's classic text, and a couple other resources online, I decided that a better grasp of mathematical proofs would give me the tools needed to tackle algorithms.  I picked up The Nuts and Bolts of Proofs by Antonella Cupillari, and worked my way through in about a month.  The topics covered were: Direct proof, proof by contrapositive, equivalence theorems, use of counterexamples, mathematical induction, uniqueness/existence theorems, and equality of sets/numbers.
      Cupillari does an excellent job explaining the how to construct proofs, and leaves the reader with plenty of exercises after each chapter, as well as an hefty section of exercises without solutions and a collection proofs.  I felt he did a good job covering the concepts of proofs, using no math beyond high school algebra to place the emphasis on constructing arguments using mathematical logic.  The allowed me to start thinking in proofs sooner, without being bogged down by mathematical theory.  Having completed the chapter exercises, and with no other training on mathematical proofs, I feel very comfortable constructing proofs which make up a large portion of the exercises in many algorithm text books.  If you are interested in learning proofs and aren't afraid to put a little work in, I would definitely recommend this book!