Teaching in winter semester 2025/26:
Algebra
The fundamental algebraic structures, groups, rings, and fields, will be introduced (again) and studied in details. We will introduce and study operations of groups on sets and their basic properties. We will deduce among other things the Sylow theorems for finite groups. In commutative rings theory, polynomial rings, Euclidean rings, principal ideal domain, factorial and noetherian rings will be introduced and studied. Basic examples will be given. The lecture will end with fields theory; algebraic or transcendental extensions, Galois extensions and the Galois correspondence will be covered, and many examples will be explained and treated on the way. One of the aim being to understand how the fact that the Galois group of a polynomial be "solvable" is equivalent to the fact that the roots of the polynomial are expressable by "iterated radicals".
Lectures: Tuesday 10:00-12:00 (B047) and Wednesday 10:00-12:00 (B134) . Exercise class: Thursday 10:00-12:00 (B134).
New: From the week 10-14 November on:
Lectures: Tuesday 10:00-12:00 (B047) and Friday 10:00-12:00 (B251). Exercise class Wednesday 10:00-12:00 (B134).
New: Exam: on thursday 5th of February, 10:00-12:00 Room B134.
References:
S. Lang : Algebra, Springer (in english).
G. Fischer : Lehrbuch der Algebra, Vieweg (in German).
Exercise Sheets
Tutorial Sheets (Laurenz Wiesenberg)
Solutions to the Tutorial Sheets (Laurenz Wiesenberg)
Tutorial classes (with Laurenz Wiesenberg): Monday 16-18 Room B039, Tuesday 12-14 Room B134, Thursday 14-16 Room B040.
14 Previous semesters