406-2004-AAL Algebra II
|Semester||Autumn Semester 2019|
|Periodicity||every semester recurring course|
|Language of instruction||English|
|Comment||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.
|Abstract||Galois theory and related topics.|
The precise content changes with the examiner. Candidates must therefore contact the examiner in person before studying the material.
|Objective||Introduction to fundamentals of field extensions, Galois theory, and related topics.|
|Content||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.|
|Literature||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.|