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Algebra (Winter Semester 2011/12)

  • Lecturer: PD Dr. Stefan Kühnlein
  • Classes: Lecture (0102200), Problem class (0102300)
  • Weekly hours: 4+2
  • Audience: mathematics (5.-9. semester)

We will continue the course "Einführung in Algebra und Zahlentheorie" started in summer 2011, thereby preparing more advanced topics such as algebraic number theory and algebraic geometry.

There will be a tutorial by Jonathan Zachhuber on mondays, 09:45-11:15, in 1C-01.

The results of the evaluations are to be found here: lectures,problem sessions.

Schedule
Lecture: Thursday 9:45-11:15 Chemie-Hörsaal II Begin: 20.10.2011, End: 10.2.2012
Friday 11:30-13:00 AOC 201
Problem class: Wednesday 8:00-9:30 HS 9 Begin: 19.10.2011, End: 8.2.2012
Lecturers
Lecturer PD Dr. Stefan Kühnlein
Office hours:
Room 1.032 Kollegiengebäude Mathematik (20.30)
Email: stefan.kuehnlein@kit.edu
Problem classes Jochen Schröder
Office hours: Das machen wir am besten per E-Mail aus.
Room Allianz-Gebäude (05.20)
Email: jochen.schroeder@kit.edu

Jonathan will give an additional tutorial for your questions on Monday, 5th of March, 11.30 in the room 1C-01. You may hand in your questions in advance by sending him (or your teaching assistant) an e-mail.



We will first discuss some group theoretic notions and afterwards turn to Galois theory and its most important applications. We will also discuss valuations of fields and Dedekind domains.

problem class
You can download the problem sheets (and the solutions) here. You may hand in your solutions either in English or in German.
problem sheet 1 and the problem_sheet_1_solution.pdf|solution
problem sheet 2 and the problem_sheet_2_solution.pdf|solution
problem sheet 3 and the problem_sheet_3_solution.pdf|solution
problem sheet 4 and the problem_sheet_4_solution.pdf|solution
problem sheet 5 and the problem_sheet_5_solution.pdf|solution
problem sheet 6 and the problem_sheet_6_solution.pdf|solution
problem sheet 7 and the problem_sheet_7_solution.pdf|solution
problem sheet 8 and the problem_sheet_8_solution.pdf|solution
problem sheet 9 and the problem_sheet_9_solution.pdf|solution
the christmas sheet and the christmas_sheet_solution.pdf|solution
problem sheet 11 and the problem_sheet_11_solution.pdf|solution
problem sheet 12 and the problem_sheet_12_solution.pdf|solution
problem sheet 13 and the problem_sheet_13_solution.pdf|solution
problem sheet 14 and the problem_sheet_14_solution.pdf|solution


If there are mistakes in any sheet or solution please contact me.

Corrected sheets are returned in the tutorial or in problem class. Afterwards I will put them in the box next to room 4A-05 (Allianzgebäude). The box is labeled 'Einführung in Algebra und Zahlentheorie'.

Examination

As announced in the lectures, there will be oral examinations.

References

There exist lecture notes in german: algebraws2012.pdf We occsionally refer to the lecture notes einfalgzahl.pdf covering the course "Introduction to Algebra and Number Theory" from summer 2011.

Here are my slides on the construction of the regular 17-gon.

The following books are also recommended:

  • Bosch, S.: Algebra, Springer (in German)
  • Cohn, P.M.: Basic Algebra, Springer
  • Hungerford, T.W.: Algebra, Springer Graduate Texts
  • Jacobson, N.: Basic Algebra II, WH Freeman
  • Jantzen / Schwermer, Algebra, Springer (in German)
  • Lang, S.: Algebra, Springer
  • Leutbecher, A.: Zahlentheorie, Springer (in German)