Where Can I Find a Good Introductory Book for Writing Mathematical Proofs?

[hawaiifiver]

Hello

Could anyone recommend a good introductory book for learning how to write mathematical proofs.

Thank you.

 

[SolomonX]

How to Prove It by Daniel Velleman

I'd post a link to Amazon but I have less than 10 posts. It's cheap but well written.

 

[Voivode]

Here's the link.

https://www.amazon.com/gp/product/0521675995/?tag=pfamazon01-20

 

[Dr Transport]

how to solve it by polya

https://www.amazon.com/dp/4871878309/?tag=pfamazon01-20

 

[mateomy]

I'm using this right now...https://www.amazon.com/dp/0321390539/?tag=pfamazon01-20I've also read through...https://www.amazon.com/dp/0471406473/?tag=pfamazon01-20

which was decent. The formerly mentioned was/is much more structured though.

Have fun.

 

[20Tauri]

Are those appropriate for first proofs or for people who have some proof experience already? I've done proofs in linear algebra, number theory, etc. but I've never taken a discrete math or mathematical logic class. I know induction, contradiction, contraposition, and such, but I'd like to have some more experience before I take more rigorous courses like algebra and analysis this fall. (It's a long story, but I'm doing transitional coursework in grad school, and my university teaches proofs in the advanced sequences rather than in a separate logic class.)

 

[Headacheguy]

I liked the free Book of Proof, by Richard Hammack http://www.people.vcu.edu/~rhammack/BookOfProof/index.html

The book will really ease you into the concepts behind the techniques of proof. Moreover, the exercises are great. You'll like it a lot if you're a complete beginner.

 

[Cod]

How to Prove It by Daniel Velleman

I'd post a link to Amazon but I have less than 10 posts. It's cheap but well written.

I second this book. I went from a novice to decent proof writer after reading Velleman's book.

 

[theorem4.5.9]

My proof writing class used Doing Mathematics: an introduction to proofs and problem solving by Steven Galovich.

However, I didn't particularly like the class or the book (though there are a lot of fun problems at the back of the book), not because either one was bad, but I didn't like learning how to prove things for its own sake. I got a better experience with proofs from abstract algebra and topology classes.

 

[TheShrike]

I don't know how helpful this is but I found it awhile back:

http://www.math.vt.edu/people/day/ProofsBook/

I'm not totally sure what level of mathematics is expected for it either, but someone might find it useful.

 

[EulersFormula]

Elementary Analysis: The Theory of Calculus, by Kenneth A. Ross

 

[mathwonk]

"If yer going to be stoopid, you got to be tough"

I heard this as "life is hard; if you're stupid, it's really hard!"

oh yeah, proofs: i agree it is best to learn actual proofs of interesting things, but a tiny basic amount of logic (propositional calculus) helped me, from Principles of mathematics, chapter one I think.

 

[hawaiifiver]

Hello to all,

Wow this thread has really taken off. Thanks for all the suggestions. I actually bought Velleman's book. I just finished the first three chapters. It's really well written.

Good luck.