Not offered 2007-2008
MATH 414 Galois Theory (Q)
The relation of high school algebra to the abstraction of Mathematics 312 is not apparent, but Galois Theory shows the link. One goal of high school algebra is to solve (find roots of) linear equations (ax + b = 0) and quadratic equations. By the sixteenth century, methods were found to solve third and fourth degree equations. Here progress stopped until the early nineteenth century, when Abel and Galois showed that no such general method for finding roots of equations of degree higher than four can exist. They needed totally new tools, which led to the mathematics of abstract algebra. The goal of Mathematics 414 is to develop through linear algebra, the deep connection between roots of polynomials and finite groups.
Format: lecture/discussion. Evaluation will be based on homework and exams.
Prerequisites: Mathematics 312 or 315 or 317 and permission of the instructor. No enrollment limit (expected: 15).

GARRITY