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I'm on the last semester of my bachelor's degree (undergrad degree) and I will be writing my thesis next semester. I have talked to a professor at my university and one of the topics he suggested was Galois theory. I am interested in doing 'my own' research, if you catch my drift. That is, I would like to apply the Galois theory I will be studying to something, and do some research. My professor mentioned some possible applications within coding-theory and cryptography. Do you have any specifics in mind? I would be happy to hear your insights.

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    $\begingroup$ If you don't know Galois theory, that in itself sounds like a semester-long topic, worthy of understanding well whether or not you do any "research". You'll probably have more than enough on your plate learning Galois theory without trying to do something original (doubtful). $\endgroup$ – KCd Jan 15 '14 at 18:55
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    $\begingroup$ @KCd: To learn Galois theory and apply it meaningfully in some way that no one has done before: yes, that sounds like a tall order. But maybe the OP means that he wants to spend some time applying Galois theory himself rather than just reading about it, whether or not what he does has been done previously. (And if he doesn't mean this, perhaps he should...) $\endgroup$ – Pete L. Clark Jan 15 '14 at 19:05
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    $\begingroup$ I think it is easy to come up with polynomials whose Galois group hasn't been computed by hand so far - and it is very nice to see explicit radical expressions of the roots in the solvable case (for degree $8$, say). Of course this won't be any original research, but I would count this as research. $\endgroup$ – Martin Brandenburg Jan 15 '14 at 19:09
  • $\begingroup$ @PeteL.Clark That is what I mean! I realize I won't be able to do original research at this point.. :-) $\endgroup$ – Numbersandsoon Jan 15 '14 at 19:12
  • $\begingroup$ And it's very unlikely someone will expect you to, @BoSchmidt . I think Martin's idea is a very good one. Think of it. $\endgroup$ – DonAntonio Jan 15 '14 at 20:40

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