Mathematics 410 - Galois Theory
Fall
2018
01
4.00
David Cox
MWF 01:00PM-01:50PM; TH 01:00PM-01:50PM
Amherst College
MATH-410-01-1819F
SCCE A331; SMUD 207
dacox@amherst.edu
The quadratic formula shows us that the roots of a quadratic polynomial possess a certain symmetry. Galois Theory is the study of the corresponding symmetry for higher degree polynomials. We will develop this theory starting from a basic knowledge of groups, rings, and fields. One of our main goals will be to prove that there is no general version of the quadratic formula for a polynomial of degree five or more. Along the way, we will also show that a circular cake can be divided into 17 (but not 7) equal slices using only a straight-edged knife.
Requisite: MATH 350 or consent of the instructor. Fall semester. Professor Cox.