Algebra II Spring 2019

Prof. Dr. Rahul Pandharipande
Fri 8-10 HG G 5
Jennifer-Jayne Jakob
Exercise classes
Wed 10-12
Tue 15-17 (for students attending the electrodynamics course)
rooms: see below

The exam question lists are now available here (Algebra I) and here (Algebra II).

Information about the exam question lists:

  1. If you are taking the joint Algebra I+II exam, approximately 20 minutes will be from the Algebra I list and approximately 10 minutes will be from the Algebra II list. If you are only taking the exam for one of the courses Algebra I or Algebra II, the entire exam will be from the corresponding list.
  2. The question selection will be somewhat random, but not completely — once a question is selected, questions about very similar topics will be excluded.
  3. I may ask further questions about any definitions, theorems, or arguments that you bring up in the solutions.
  4. You are not permitted to bring notes to the exam.
  5. Unless defined otherwise, S_n is the symmetric group, A_n is the alternating group, and F_q is the finite field with q elements (where q is a prime power).
  6. The Galois group of a polynomial over a field F is the Galois group of the splitting field of the polynomial over F.
  7. The lists may be revised before the beginning of the exam session to correct typos and inaccuracies, but no new problems will be added.

Students who wish to reschedule their exam for valid study-related reasons (e.g. early semester start, student visa issues, study project etc.) should contact the coordinator (jennifer.jakob at as soon as possible.

The exercise class taught by Ajith Urundolil Kumaran is now in English.

A copy of this year's midterm can be found here, the answers are here.

The voluntary midterm exam will take place on the first Friday of the spring semester, in the usual slot of the lecture.

The first lecture of the semester will be on Monday, the 18th of February 2019, 8:00-10:00 in the usual lecture hall (HG G5). Note also that the first lecture of the topology class has been moved to 10-11, see here.

The exercise classes start in the second week of the semester.

The two main references for the course are

The page references for each week of the course are from these books.

The new exercises will be posted here on Fridays. We expect you to look at the problems over the weekend and to prepare questions for the exercise class on Wednesday (or Tuesday). Please hand in your solutions by the following Friday at 12:00 in your assistant's box in HG J68. They will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J68.

week material covered (page numbers: see main reference) exercise sheet due by solutions
1 The automorphism group of a field extension, solution of the cubic (Rotman: A-1, pp 3-6, A-5.1,5.2,5.3 and other examples, pp 179-181; Artin: Ch.II, Section F, pp 34-38). A15 March 1 S15
2 Characters, fixed fields, solution of the quartic, (Rotman: A-1, pp 6-8, A-5.38,5.39,5.40, pp 203-205; Artin: Ch.II, Section F, pp 34-38). A16 March 8 S16
3 Fixed fields, Galois extensions, (Rotman: A-5.38,5.39,5.40, pp 203-205; Artin: Ch.II, Sections G-H, pp 39-49). A17 March 15 S17
4 Characterizations of Galois extensions, Normal field extensions, (Rotman: A-5.42, page 206; Artin: Ch.II, Sections G-H, pp 39-49). A18 March 22 S18
5 Fundamental Theorem of Galois theory (Rotman: A-5.44,5.45,5.51,5.54, pp 207,211-213; Artin: Ch.II, Section H, pp 41-49). A19 March 29 S19
6 Solvability by radicals (Rotman: A-5.55,5.56,5.62,5.63,5.64, pp 214,218-219; Artin: Ch.III, Section D, pp 74-76). A20 April 05 S20
7 Constructions with straightedge and compass. See notes, as well as N. Jacobson, Basic Algebra I, 2nd edition: Section 4.2. A21* April 12 S21
8 Solvable groups, solvability by radicals. (Rotman: A-5.22,5.23,5.25,5.33,5.34, pp 192-195,200-201; Artin: Ch.III, Section D, pp 74-76). A22 April 19 S22
9 Constructible polygons, cyclotomic polynomials, cyclotomic field extensions (Jacobson: Section 4.11). A23** May 10 S23
10 Constructible polygons, cyclotomic polynomials, cyclotomic field extensions (Jacobson: Section 4.11). A24 May 17 S24
11 Primitive Element Theorem, Wedderburn's Little Theorem. (Rotman: A-5.54,5.55,5.56, pp 213-215; Artin: Ch.II, Section M, pp 64-66; Jacobson: Section 7.7). A25 May 24 S25
12/13 Linear representations of finite groups. (J.-P. Serre: Linear representations of finite groups, GTM 42, Sections 1.1-1.4 (Week 12), Sections 2.1-2.4 (Week 13)). A26 No hand-in S26
* corrected typo in Exercise 1

** added a hint in Exercise 3

Lecture notes on Galois theory (Prof. Dr. M. Burger)

Please enroll in one of the exercise classes via echo.

Tue 15-17ETZ E 7Alireza Ataeien
Wed 10-12CLA E 4Ajith Urundolil Kumaranen
Wed 10-12HG E 33.1Emie Sunen
Wed 10-12HG F 26.5Tim-Henrik Buellesen
Wed 10-12LFW E 13Dominique Heynen
Wed 10-12ML F 40Yujie Wuen

For general information on the course, check the Course Catalogue.