Information about the exam question lists:
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.
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 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|
** added a hint in Exercise 3
Please enroll in one of the exercise classes via echo.
|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.