Selected topics concerning rings, groups, fields, including Galois theory. The official Course Catalogue page can be found here.
| date | content | notes |
|---|---|---|
| Mo 19.02. | Review - Rings and fields, Isomorphism theorems for rings | Lecture 0 |
| We 21.02. | Quotient field of an integral domain, Euclidean domains, Principal ideal domains | Lecture 1 |
| Mo 26.02. | Prime and irreducible elements, Principal ideal domains, Unique factorisation domains | Lecture 2 |
| We 28.02. | Prime and irreducible elements, Principal ideal domains, Unique factorisation domains | Lecture 3 |
| Mo 04.03. | Principal ideal domains, Unique factorisation domains, Gauss lemma | Lecture 4 |
| We 06.03. | Irreducibility criteria, Fields and field extentions | Lecture 5 |
| Mo 11.03. | Field extentions, Kronecker's theorem | Lecture 6 |
| We 13.03. | Field extentions, Algebraic extentions | Lecture 7 |
| Mo 18.03. | Algebraic extentions | Lecture 8 |
| We 20.03. | Transcendental numbers, Splitting fields | Lecture 9 |
| Mo 25.03. | Algebraic closures | Lecture 10 |
| We 27.03. | Normal extentions, Separable extentions | Lecture 11 |
| Mo 08.04. | Separable extentions, Simple extentions | Lecture 12 |
| We 10.04. | Finite fields, Basic definitions of Galois theory | Lecture 13 |
| We 17.04. | Galois theory | Lecture 14 |
| Mo 22.04. | Galois theory | Lecture 15 |
| We 24.04. | Galois theory | Lecture 16 |
| Mo 29.04. | Galois correspondence | Lecture 17 |
| Mo 06.05. | Galois correspondence | Lecture 18 |
| We 08.05. | Galois correspondence, Galois groups of polynomials, Cyclotomic extentions | Lecture 19 |
| Mo 13.05. | Cyclotomic extentions, Solvability by radicals and solvable groups | Lecture 20 |
| We 15.05. | Solvability by radicals and solvable groups, Fundamental theorem of algebra | Lecture 21 |
| We 22.05. | Modules | Lecture 22 |
| Mo 27.05. | Modules | Lecture 23 |
| We 29.05. | Abelian groups, Torsion modules, Modules over PID's | Lecture 24 |
The lecture continues the Algebra I lecture from HS2023.
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 Tuesday.
Please hand in your solutions by the following Friday at 12:00 in your assistant's box in HG J68 or per email. Your solutions will usually be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J68.
Office hours will take place in the weeks after a new exercise sheet is posted, on Wednesdays at 16:15-18:00 (the first one being on the 28th of February) in HG F 5. There will be no office hours on 06.03., 17.04., 01.05. and 29.05.
The learning elements offered during the semester measure active participation in the exercises. From the second week of the semester onwards, 5 single-choice exercises are completed individually at the beginning of each lesson. Each correctly answered task is worth 1 point. The number of points n achieved in the semester is converted into a grade bonus of a maximum of 0.25 grade points using the formula max(0,min(1,(n-20)/25)) times 0.25. This bonus is added to the provisional grade from the examination without rounding; the result is rounded to the final grade.
The solutions provided for the exercises below are suggested answers and may contain errors.
| time | room | assistant | language |
|---|---|---|---|
| Tu 16-18 | ETZ E 7 | Raphael Angst | english |
| Tu 16-18 | HG E 33.5 | Samuel Huber | english |
| Tu 16-18 | HG G 26.3 | Janine Roshardt | english |
| Tu 16-18 | CHN D 44 | Joel Sommer | english |