How to Prove It: A Structured Approach, 2nd Edition

Author: Daniel J. Velleman
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by maroonblazer   2018-08-15
To clarify:

Velleman wrote "How to Prove It":

Polya wrote "How to Solve It":

by defen   2018-03-27
On the topic of newcomers to proof-based math - "How to Prove It" is a great resource:
by nickpsecurity   2018-03-14
The last time people asked, I collected the responses so I could do the same thing as you. Note that I'm wanting to learn it in a way where I can do proofs. So, I have general-purpose books and stuff for that. I just ordered the three books I've seen pop up the most. Although 2 are in the mail, Concepts of Modern Mathematics by Stewart just got here yesterday. It had an awesome opening that made me wish the math I was taught in school was done like this back when I went. Makes newer stuff make a lot more sense, too. I included a link to Dover that has a Google Preview button on it where you can read full, first chapter for free to see if it's what you like. Other two are more about exploring and proving things which may or may not interest you. I added them in case anyone is reading your question to learn that stuff.

Concepts of Modern Mathematics by Stewart

Dover Version with Google Preview Button

How to Prove It by Velleman

by frostirosti   2018-01-07
This is a jump straight into the deep end. I can't recommend starting here. "How to prove it" would be a much more appropriate start
by 1331   2017-08-19
As for studying proofs, _How To Prove It_ [1] is indeed a good book. You may also be interested in _Book of Proof_ [2], which is available under a Creative Commons license. (You can download the PDF for free, and you can order it from Amazon [3] if you want a hard copy.)




by jfarmer   2017-08-19
Polya's How to Solve It was recommended below. I also like How to Prove it by Daniel Velleman ().
by corey   2017-08-19
Velleman's "How to Prove It" is a great book to learn how to do mathematics.

by ice109   2017-08-19

>Never done any proofs, but I will ask my math teacher if he can recommend any books or resources that will help me learn.

by kyp44   2017-08-19

If you are interested in getting started with "real" math, i.e. moving from solving computational problems to writing proofs, I highly recommend picking up a copy of How to Prove It . The author assumes basically no knowledge of higher level math and teaches various techniques in reading and writing proofs, learning quite a bit of basic set theory along to way to practice your proof writing.

EDIT: wanted to also mention that set theory is the "core" of modern math, or rather its foundation.

by kyp44   2017-08-19

I've always enjoyed all types of math but all throughout (engineering) undergrad and grad school all I ever got to do was computational-based math, i.e. solving problems. This was enjoyable but it wasn't until I learned how to read and write proofs (by self-studying How to Prove It ) that I really fell in love with it. Proofs are much more interesting because each one is like a logic puzzle, which I have always greatly enjoyed. I also love the duality of intuition and rigorous reasoning, both of which are often necessary to create a solid proof. Right now I'm going back and self-studying Control Theory (need it for my EE PhD candidacy but never took it because I was a CEG undergrad) and working those problems is just so mechanical and uninteresting relative to the real analysis I study for fun.

EDIT: I also love how math is like a giant logical structure resting on a small number of axioms and you can study various parts of it at various levels. I liken it to how a computer works, which levels with each higher level resting on those below it. There's the transistor level (loosely analogous to the axioms), the logic gate level, (loosely analogous set theory), and finally the high level programming language level (loosely analogous to pretty much everything else in math like analysis or algebra).