As of May 4 2007 the scripts will autodetect your timezone settings. Nothing here has to be changed, but there are a few things

Please follow this blog

Search this blog

Wednesday, November 4, 2009

Galois Theory

Galois Theory is a topic which is, at least in the algebra books I have, covered in the last chapter as the most beautiful result of algebra. I know that Galois introduced group theory and proved that it was impossible to solve an equation of type f(x)=0, where f(x) has a term of x in the 5th degree or higher, by means of  a formula. ( Solving the quintic by radicals is how it is described. ) What bothers me is that I still can't follow the proof, or worse: I simply don't get it.

I found a hint though. The Galois Group of x^2-1=0 is C2 and of x^4-2=0 the Galois Group is the Dihedral Group of order 8 ( symmetry group of the square ). Will play a bit with these examples, I hope it will break some ice.

Update: the field we work in is Q.

No comments:

Post a Comment

Popular Posts

Welcome to The Bridge

Mathematics: is it the fabric of MEST?
This is my voyage
My continuous mission
To uncover hidden structures
To create new theorems and proofs
To boldly go where no man has gone before




(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)