Bachelor Seminar on Algebra (Summer 2018)

with Dr. Heer Zhao

We will study a series of topics which naturally continues those discussed in the lecture course Algebra 1 – Trace and Norm, Hilbert’s Theorem 90, Solvability of equations by radicals, infinite Galois theory, cyclotomic fields, the quadratic reciprocity law, simple cases of Fermat’s Last Theorem.

Prerequisites: Algebra 1 (Groups, Rings, Fields, Galois theory) and of course the basics (Linear Algebra 1 + 2, and maybe a bit of analysis).

Time and place: Tue, 14-16, S-U-3.03, First talk: April, 10.

Contact: ulrich.goertz@uni-due.de

ECTS points: 6 credit points for a successful seminar talk (in German or in English upon the choice of the speaker)

Program: pdf

Organisational meeting: February 15, 2:15pm, S-3.14. If you are interested in giving a talk in the seminar but cannot come to the organisational meeting, please send me an email.

Talks

1 The main theorem of Galois theory U. Görtz
2 Symmetric functions H. Zhao
3 The class equation and applications O. Girnth
4 The Sylow theorems L. Meurs
5 The fundamental theorem of algebra D. Tambaro
6 The Galois group of a polynomial I H. Zhao
7 The Galois group of a polynomial II U. Görtz
8 Norm and trace, Hilbert’s Theorem 90 H. Zhao
9 Cyclic extensions I. Tselepidis
10 Cyclotomic fields and solvable extensions A. Salarzai
11 The quadratic reciprocity law F. Siethoff
12 The first case of Fermat’s Last Theorem for regular primes N. N.
13 Topological groups N. N.
14 Infinite Galois theory N. N.