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Lately I've gotten a friend of mine interested in mathematics. He has no college-level education to speak of, but is well employed as a software engineer. So I feel he's competent to learn this stuff on his own.

He asked me recently if there was a 'mathematical' version of "The Little Schemer".

The point being, if there was an "introduction to proofs" book which took a more hand-holding approach. He's also expressed fondness for the metamath project.

However, metamath's proofs are obviously a bit too low level to learn anything serious.

At one point in our conversation, I mentioned the dependently typed programming language Agda, but I felt it's not quite as helpful until he at least gets some experience with Haskell (for which the target audience of Agda is Haskell programmers, hence the similarity in syntax).

Anyone have any good suggestions on a book?

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Somewhat tangential, but: it seems to me that your friend will greatly benefit from Zeitz's book. –  J. M. Dec 1 '11 at 4:06
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As J.M. mentioned the book Zeitz: The Art and Craft of Problem Solving, it reminded me of this question: math.stackexchange.com/questions/7743/getting-better-at-proofs Perhaps you can find something useful there. –  Martin Sleziak Dec 1 '11 at 7:54

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This isn't exactly on point, but since you mentioned the possibility that your friend might be learning Haskell, you could try "The Haskell Road to Logic, Maths, and Programming". Pretty good book, maybe a natural transition for your friend.

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May I humbly suggest my free DC Proof program. It's not a book, but a software program. Although I think you are selling Metamath short -- check out the vast library of formal proofs at the site! -- my program is somewhat higher level and, in my opinion, much easier for the beginner to learn. It comes with a ten-part tutorial to introduce the user to the program and various methods of proof.

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