VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.

401-2004-00L 5 Credits BSC D-PHYS , D-MATH
You're viewing possible stale or outdated data. Please check the latest semester for more up-to-date information.

Algebra II

Lecturers & Examiners: Prof. Dr. Lorenz Halbeisen
VVZ CR n/a

Last Updated: 2026-02-05 16:06:50

Abstract

The main topics are field extensions and Galois theory.

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.

Resources

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.

Learning Materials (Links)

General Information

Language
German
Levels
BSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 150 minutes
Aids
keine
Während des Semesters wird eine Zwischenprüfung angeboten. Die genaue Berechnung des sich daraus ergebenden Bonus von maximal 0.25 Notenpunkten wird auf der Vorlesungshomepage veröffentlicht. Dieser Bonus wird ungerundet zu der vorläufigen Note aus der Prüfung addiert; das Resultat wird zur Endnote gerundet.Geplanter Termin für die Zwischenprüfung: Donnerstag, 3. März 2022, 18:15-19:15.

Course Components

Type Title Time & Place Hours
lecture Algebra II
  • Fri 08:15-10:00 (HG G 5)
  • 25.02 Date 08:15-10:00 (HG E 5)
2 h weekly
exercise Algebra II
Groups are selected in myStudies.
  • Tue 16:15-18:00 (CHN D 44)
  • Tue 16:15-18:00 (ETZ E 7)
  • Tue 16:15-18:00 (HG E 33.5)
  • Tue 16:15-18:00 (HG G 26.3)
  • Tue 16:15-18:00 (NO D 11)
2 h weekly

Offered In