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What are the best introduction books to mathematical proofs in undergraduate mathematics? I know of "Proofs from the Book" by M. Aigner and G. Ziegler, but also need one that shoots to analysis kind of proofs.

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The "proofs from the book" are wonderful, but not ideal as a first introduction, I think. –  Goldstern Oct 22 '13 at 22:23
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Analysis is not good as introduction to the proofs. Euclidean geometry is way better. –  Anton Petrunin Oct 22 '13 at 22:37
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You might try Kevin Houston's 'How To Think Like a Mathematician', a gentle introduction to proof and to reading and understanding mathematics. –  Marius Kempe Oct 23 '13 at 0:09

2 Answers 2

The William Lowell Putnam Competition is an excellent example of undergraduate proofs which are fun to solve. You can buy their book or find their problems online. I'm 14 years old but I like it since it gives me a nice look at a variety of elegant proofs which helps high school proof-writing as well. I highly recommend it!

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Not a book, but a nice and (very) brief intro is provided by Joel Feinstein's camcasts (these and these) and the accompanying materials. On the same site, he has also posted an introductory course on real analysis (course materials and recordings of the lectures included) where you can find further "analysis kind of proofs".

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