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5.2 parsecs

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| | mattbaker.blog

I'm teaching Graduate Algebra this semester, and I wanted to record here the proof I gave in class of the (existence part of the) structure theorem for finitely generated modules over a PID. It's a standard argument, based on the existence of the Smith Normal Form for a matrix with entries in a PID, but...
4.1 parsecs

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| | qchu.wordpress.com

As an undergraduate the proofs I saw of the Sylow theorems seemed very complicated and I was totally unable to remember them. The goal of this post is to explain proofs of the Sylow theorems which I am actually able to remember, several of which use our old friend The $latex p$-group fixed point theorem...
4.8 parsecs

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| | wavewatching.net

Recently Scott Aaronson offered a bounty of $100,000 to anybody who can prove that universal quantum computing is not possible in the real world. This was countered by a $200,000 bet, put forward b...
20.7 parsecs

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