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March 21st, 2010, 05:05 AM   #1
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(Un)solvable equations (by radicals)

Hi,
I am searching for an article explaining (im)possibility of sovlving polynomial equations by radicals. It probably concerns Galois group but I cannot find any comprehensive (understandable) material about it. Do you know about some material where this is discussed and also clearly explained?

Thank you
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March 21st, 2010, 12:20 PM   #2
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Re: (Un)solvable equations (by radicals)

What is your current level of knowledge? The problem you are interested in does indeed involve Galois theory, which is an intermediate/advanced level course on most maths undergraduate degrees. I seem to recall that to get a reasonable grasp of what's going on (using a modern approach) you need some group theory, some theory of field extensions and knowledge of symmetric polynomials.
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March 22nd, 2010, 12:47 PM   #3
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Re: (Un)solvable equations (by radicals)

Quote:
Originally Posted by pseudonym
What is your current level of knowledge? ... you need some group theory, some theory of field extensions and knowledge of symmetric polynomials.
I have graduated about 10 years ago (informatics) but forget some knowledge, I must admit...
Where can I get information about topics you mention? I prefer some e-documents. Thank you.
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March 23rd, 2010, 08:22 AM   #4
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Re: (Un)solvable equations (by radicals)

Ian Stewart has a book on Galois Theory which is very accessible for someone who is relatively math-literate. Presuming you don't need to construct such proofs yourself, you don't even need to know abstract algebra.
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March 24th, 2010, 04:15 AM   #5
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Re: (Un)solvable equations (by radicals)

Quote:
Originally Posted by honzik
I have graduated about 10 years ago (informatics) but forget some knowledge, I must admit...
Where can I get information about topics you mention? I prefer some e-documents. Thank you.
I don't know of anything specific. If you search for things like 'group theory lecture notes' you should find some things of around undergraduate standard. It may take a while to build up to an understanding of galois theory in this way because, as I said earlier, galois theory is a relatively advanced undergrad course. I don't know if the effort is avoidable though as, in my experience at least, in order to even roughly understand something in abstract maths you have to have a solid understanding of the background material. Maybe that's just me though.

Edit:
A general introductory lecture course on abstract algebra (groups, rings and fields) can be found here
A more detailed course on field extensions is here
A first course on galois theory (the course I did a few years ago) is here. This also has some reminder material on groups and fields. The apporach is quite abstract and may be confusing but hopefully you'll be able to get something out of it.
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