406-2004-AAL Algebra II
|Spring Semester 2021
|every semester recurring course
|Language of instruction
|Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.
Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
|Galois theory and related topics.
The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
|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
|Algebra I, in Rotman's book this corresponds to the topics treated in the Chapters A3 and A4.