401-2004-00L Algebra II
|Spring Semester 2019
|yearly recurring course
|Language of instruction
|The main topics are field extensions and Galois theory.
|Introduction to fundamentals of field extensions, Galois theory, and related topics.
|The main topic is Galois Theory. Starting point is the problem of solvability of algebraic equations by radicals. Galois theory solves this problem by making a connection between field extensions and group theory. Galois theory will enable us to prove the theorem of Abel-Ruffini, that there are polynomials of degree 5 that are not solvable by radicals, as well as Galois' theorem characterizing those polynomials which are solvable by radicals.
|Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1,
Graduate Studies in Mathematics,Volume 165
American Mathematical Society
Galois Theory is the topic treated in Chapter A5.
|Prerequisites / Notice
|Prerequisites is Rahul Pandharipande's course "Algebra I" or similar, in Rotman's book ideally Chapter A3 and A4.