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