Lecturer Prof. Dr. Rahul Pandharipande	Lectures Fri 8-10 HG G 5
Coordinator 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 math.ethz.ch) 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

• J. Rotman, Advanced modern algebra, 3rd edition, part 1 (link only works from ETH computers and via vpn),
• E. Artin, Galois Theory: Lectures Delivered at the University of Notre Dame, 2nd edition.

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)

• I. Introduction
• II. Galois group of an extension - Part 1
• II. Galois group of an extension - Part 2
• II. Galois group of an extension - Part 3
• II. Galois group of an extension - Part 4
• III. Solvability by radicals and solvable groups - Part 1
• III. Solvability by radicals and solvable groups - Part 2
• III. Solvability by radicals and solvable groups - Part 3
• IV. The Galois correspondence - Part 1
• IV. The Galois correspondence - Part 2
• IV. The Galois correspondence - Part 3
• IV. The Galois correspondence - Part 4
• IV. The Galois correspondence - Part 5

Please enroll in one of the exercise classes via echo.

time	room	assistant	language
Tue 15-17	ETZ E 7	Alireza Ataei	en
Wed 10-12	CLA E 4	Ajith Urundolil Kumaran	en
Wed 10-12	HG E 33.1	Emie Sun	en
Wed 10-12	HG F 26.5	Tim-Henrik Buelles	en
Wed 10-12	LFW E 13	Dominique Heyn	en
Wed 10-12	ML F 40	Yujie Wu	en

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