401-2004-00L  Algebra II

SemesterSpring Semester 2019
LecturersR. Pandharipande
Periodicityyearly recurring course
Language of instructionEnglish

AbstractThe main topics are field extensions and Galois theory.
ObjectiveIntroduction to fundamentals of field extensions, Galois theory, and related topics.
ContentThe 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.
LiteratureJoseph 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 / NoticePrerequisites is Rahul Pandharipande's course "Algebra I" or similar, in Rotman's book ideally Chapter A3 and A4.