Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition)

This is one of the most well-written textbooks that I have ever had the pleasure to read. I come from a mechanical engineering background, but have a strong interest in mathematics and regularly tutor undergraduates. I picked up this book not for a course, but for self-study. From this book alone I was about to learn the material, teach it to one of my tutoring students, and get her an 'A'! I can't say that about most textbooks I suffered through in college. The only downside, as some reviewers have mentioned, is the hefty price tag. C'est la vie. I actually like the presentation of this book so much that I'm now looking into other works that the authors have.

As a math major who wants to continue on to an advanced math degree, I could not have made it this far without this book. The authors do a wonderful job of making the aspects of writing an effective proof easy to learn and, more importantly, understand. Specifically, the way they teach both Proof by Contradiction and Proof by Mathematical Induction, two techniques that are vital to any upper level analysis/algebra/geometry class, is phenomenal. Vellman's "How to Prove It" is also a great one, but it lacks the completeness of this book. Highly recommended!!!

This is such an amazing book! It's a reference book that should be mandatory on a math bookcase. I graduated already from math, but it is so rewarding to look at this book, and I even find myself doing these problems again! Covers from the very beginning about sets, logic, direct proof by contrapositive, proof by contradiction, mathematical induction, about functions, proofs on number theory, calculus, and group theory. Excellent book!

A good book for an introduction to mathematical proofs. It gives the different types of proofs and how to go about each one. It's easy to read and most of the time doesn't feel like you're reading a textbook at all. The book assumes you are unfamiliar with proofs so it's a great jumping off point for someone a the beginning. While I don't think I would recommend it as casual reading, if you are interested in learning more about mathematical proofs and plan to start studying computer science or high level math, I strongly recommend it.

It's an all around great book. Some people might complain about it holding the reader's hand too much, but that's what makes the book so great. It assumes you never seen a proof before, and it helps guide you towards writing and analyzing proofs. The examples provided are clear. The section problems for the most part mirror the examples provided, so usually you have a model solution to work with. All in all, it's a great book for self study. If you have to purchase it for a class your instructor made an excellent choice.

It is an excellent book to get started with mathematical proofs.

If you plan to take any seconed year math courses such as linear algebra, calculus or real analysis I strongly suggest you read this book. I found that some seconed year books assume that you have some knowledge of how proofs are constructed. This book assumes that you know nothing about proofs.It cleared up a lot of confusion for me. I am pleased with book and it was well worth the price.

The approach this book takes is very simple to start and then it become more complicated towards the end. Concepts are mostly from set, and number theory in the first five chapters. Most instructors will not likely get to the more interesting sections towards the end (group theory, calculus proofs) as was the case in my class. But a good start for early math undergrads.

I love it and it's one of best proof book I have, it's as described.

Very Good, Fast,