I am teaching a course in proof technique to undergraduate students. One of the things they can do for their project is read an involved proof and explain it, for example Gödel's Incompleteness Theorem. Does anyone have any good proofs? They can come from any field accessible to a student with a month to work on it and with knowledge of multivariable calculus and abstract algebra.
Proofs for Undergraduates
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8Gödel's Incompleteness Theorem seems pretty ambitious. I'd guess that less onerous proofs are best for the occasion. – 2012-09-20
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1I agree that you should be less ambitious. I would start with proofs in elementary number theory and combinatorics (graph theory, enumeration, etc.). Some of them can be involved too, but the technical prerequisites are at a minimum and I think this makes it easier to concentrate on the proof itself. – 2012-09-20
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0@MichaelHardy I've taught them the propositional calculus. I would have them read Newman and Nagel's "Godel's Proof" or some other less rigorous explanation. – 2012-09-20
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0@QiaochuYuan My projects are in two flavors. One is what my question addresses. The other is what you are saying. I want to offer different degrees of difficulty. – 2012-09-20
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0@JoeJohnson126 There are some problems with this book, as explained in the [AMS Notices Review](http://www.ams.org/notices/200403/rev-mccarthy.pdf). – 2012-09-20
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2Maybe proofs from the book "[Proofs from THE BOOK](http://www.amazon.com/Proofs-BOOK-Martin-Aigner/dp/3642008550)" would be suitable? – 2012-09-20