Fachbereich Mathematik 
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Algebra II


Dates for the oral final Exam (3rd round)

Tue 27.08. 10:15 - 11:00 6034032
Tue 27.08. 11:00 - 11:45 6251092
Tue 27.08. 14:00 - 14:45 6041985
Tue 27.08. 14:45 - 15:30 6478305

Material

Lecture

Here is a short summary of the topics discussed in the lecture.

Exercises

Solutions

Literature

I will follow these lecture notes by Christoph Schweigert for a large part of the lecture. In addition to the literature that is mentioned there I can also recommend the book "Algebra" by S. Lang.

Content

The lecture will be about the theory of modules over rings and the associated homological algebra. Modules over rings are generalizations of vector spaces that have many more invariants than only the dimension in the case of vector spaces. Particular ones are the so-called derived functors, which are the main objective in homological algebra.
A particularly interesting example will be modules over group rings. The resulting derived functors yield the group cohomology, which can be used to solve problems that we already encountered in the introductory course last term. If time permits we will in the end turn to sheaves and their cohomology, which yields one of the most important interaction points between algebra and geometry.

Exercises

There will be homework exercises that I will put here above each Friday. We then discuss them in the exercise class in the following week.

 
  Seitenanfang  Impress 2013-08-22, Christoph Wockel