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March 21st, 2010, 05:05 AM  #1 
Member Joined: Jun 2009 Posts: 82 Thanks: 1  (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 
March 21st, 2010, 12:20 PM  #2 
Senior Member Joined: Nov 2008 Posts: 199 Thanks: 0  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.

March 22nd, 2010, 12:47 PM  #3  
Member Joined: Jun 2009 Posts: 82 Thanks: 1  Re: (Un)solvable equations (by radicals) Quote:
Where can I get information about topics you mention? I prefer some edocuments. Thank you.  
March 23rd, 2010, 08:22 AM  #4 
Senior Member Joined: Apr 2008 Posts: 435 Thanks: 0  Re: (Un)solvable equations (by radicals)
Ian Stewart has a book on Galois Theory which is very accessible for someone who is relatively mathliterate. Presuming you don't need to construct such proofs yourself, you don't even need to know abstract algebra.

March 24th, 2010, 04:15 AM  #5  
Senior Member Joined: Nov 2008 Posts: 199 Thanks: 0  Re: (Un)solvable equations (by radicals) Quote:
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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equations, radicals, unsolvable 
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