Customer Reviews

The Nuts and Bolts of Proofs

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I own the second edition of this book and find it incredibly well done. I am a math major, and this book was recommended to me by a caring professor to help aid my transition between computational mathematics and the more abstract area of Mathematical Proofs.

It is a complete and easy to follow introduction to proofs. It quickly goes over the basic properties of numbers and symbols, then goes into direct proofs. It then explains the logic of using the contrapositive instead of using direct proof by showing truth trees of the statements. After that she goes over special types of theorems.

Everything is well documented and there are tons of examples. In her examples Antonella first explains the peculiarities of the proof she is about to attempt, and then she does the proof. That discussion is enlightening and her proofs are easy to follow.

I found going through this book was invaluable to my mathematics career. The level of difficulty of this book is very EASY, so it is perfect for going though on ones own. You will likely have much more difficult proofs in class, but by going through this book will become familiar with the techniques and ideas of Proofs, which is where most students have difficulty!

The book is small and does not feel like a textbook. It has about 80 pages of text and the rest of the book is solutions to exercises. The new edition is larger, but still relatively small, and so hopefully it has this same feel, and if nothing else is light enough to carry around!

When I was going through this book, I would carry it around in my purse with me--that is how small and portable and useful this treasure is.

This book is like no other. Its short and to the point which means that the busy math major can actually sit down and read it! We all know how hard it is to try and read a wordy book on how to write proofs while at the same time trying to study abstract algebra! We dont need a full 100 pages on informal logic! Antonella Cupillari seems to understand this and sums up everything we need to know concerning logic in under 12 pages! Excellent book! Well worth the $32.95!

Learning to do proofs is a difficult task. I found this out in a course on abstract algebra: Solving a problem is one thing, doing a proof is another, and proofs require methods that are logically sound. Somehow I did get through the class, then ran across this book and snapped it up. It helped extremely much. Working through the book took a long time, partly because it is a lot to learn and partly because I had to supplement it with addtional resources. I also used Schaum's outline on Logic, to learn how to accurately build truth tables, and this worked out well. I also went through The Teaching Company course The Art and Craft of Mathematical Problem Solving by Paul Zeitz, and this was a huge help.

I really wanted to learn about cryptography, but my math background is weak and I would always feel intimidated when confronted with a proof. Going through this book, doing the well-written exercises, and reading the solutions really helped me understand proofs better. Now I am not afraid to tackle an introductory cryptography book. I wish I read this book before college.

I purchased this book to prepare for the CSET Subtest 1 since I've had no preparation that I can recall in formal proof writing. I loved this book and it really made me wonder why I've never had to write proofs! In this book, you can go as deep as you would like, however, covering the first 2-3 chapters would be plenty for the CSET. I did in fact pass, and I attribute what I learned in this book as helping my score push me over to the "pass" side!

Lots of examples and then the real works is when you try to do the proof yourself - which the author suggests will be worth it! I'm so excited to have found this book!