On Thu, Jul 16, 2009 at 11:22 PM, Sal <[address removed]>
Well, there are many practical applications of group theory.��
Really?�� Then why is it whenever someone mentions the "practical uses of group theory" they *always* mention the same four topics: crystallography, the Standard Model of physics, error correction and cryptography? Based on probability alone I would expect to hear more than four topics mentioned by X mathematicians where X > 4.
Channel coding theory and�� quantum error-correcting codes are two branches of science that are based on group theory.
In order to design an error correcting code that corrects information transmitted over public noise channel, one needs to find an Abelian group with certain properities.
And another thing, while technically this is a 'practical' application and a very important one to boot, the last time I had to generate quantum error-correcting codes was, hmmm, let me see...oh that's right, NEVER!
<tangent>What's the phrase I'm looking for?�� "Practical examples" or "practical applications" to mathematicians apparently means *any* application such as "quantum error-correcting codes". To the layman, that's not "practical".�� I'm not looking for an example of late Dirichlet allocation that I can use in the woodshop but I can look around me and see practical applications of Faraday's Laws (why do some wall outlets spark when you pull the plug?) , Pasteur's Germ Theory (the importance of clean water), Computer Science (the overly complicated Turing Machine that I'm typing on) and even calculus (compound interest).�� But of group theory? </tangent>
And before that guy in the last row takes my statements too far, let me state for the record, no I don't think every statememnt in higher mathematics needs a practical, everyday application that you can point out to a four year old.
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