100% Mathematical Proof vs Vellmen's How to Prove it

[abelgalois]

"100% Mathematical Proof" vs Vellmen's "How to Prove it"

Hello, I'm looking for books that teach proof methods and techniques. I know Vellemen's book is a popular choice but a few dissenting reviews among unanimous praise, on its amazon page, caught my attention. Like this one:

I found that this book utilized a little too much set theory for beginning students. If the author could have given more concrete examples, perhaps from group theory or simpler ones from analysis or number theory, it would have been much better. For students wanting a more lucid exposition of proof techniques, I highly recommend, "100% Mathematical Proof" by Rowan Garnier and someone else,whos name escapes me at the moment. "100% Mathematical Proof" is far superior to this book, and it has answers to the exercises which is crucial to the beginning student learning on his/her own. Velleman needs to bring the abstract nearer to the concrete for the beginning student.

And here are a coupe of positive reviews under "100% Mathematical Proofs" page:

This sentence exactly describes the books content. You'll find a lucid explanation without any shortcoming. This is the math that masters keep as secret of their kingdom. This book reveals all secrets and you'll see, masters are also humans like you.

You'll understand what the real power of mathematical proofs (without mythes). Further you'll have a good idea about the structure of mathematical theories, and their axiomatic base.

I first came across this book while searching for similar titles in a university library. Of all of the books on mathematical logic/proofs, this one stands as the definitive source for proof techniques of all skill levels. This book is easy to read, while at the same time, presents the methods in a systematic way to help the reader's conceptual understanding and develop their full potential. I am a mathematics major and this book has helped me tremendously and I am sure it will do the same for others!

So has anyone else used this book to learn how to write proofs? How does it compare to Vellemen's book?

 

[DivisionByZro]

I own Velleman's book, it's quite nice. I couldn't possibly imagine someone working through it and not being able to work through proofs.

As for 100% Mathematical Proof, just the fact that it says "This is the math that masters keep as secret of their kingdom. This book reveals all secrets and you'll see, masters are also humans like you. " is a turn off for me. Seriously, mathematics is not some mystical kung-fu, there are no super-secrets that only "masters" know; that's absolute nonsense.

Other opinions are welcome.

 

[micromass]

mathematics is not some mystical kung-fu

I guess you haven't been initiated yet.

No, seriously, I also like Vellemans book more. It's true that it has more emphasis on set theory, but this is in fact a very good thing. Many people find mathematics difficult because they don't understand set theory well, so the faster you'll be introduced to set theory and the likes, the better for you.

Also, I found "100% mathematical proof" too chaotic. And a lot of the book is concerned with stuff you'll never need again...

 

[Sankaku]

I have Velleman and I like it. However, I actually learned proofs (properly) from the first half this book:

Discrete Mathematics with Graph Theory
by Goodaire & Parmenter
http://www.abebooks.com/products/isbn/9780131679955/4747967302

... which I thought was good. It has more worked out solutions than Velleman.

To learn proof, you need something worthwhile to do proofs on. Basic set theory, discrete math and simple number theory are often the easiest places to start.

Edit: The reviews on Amazon for it are misleading. Discrete math is often required in CS programs and many students come to Proof courses totally unprepared. Most of the reviews are from people who are totally clueless.