This is the webpage of an older Algebra I course. You may want to visit the HS18 Algebra I course webpage
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 classes on Monday/Wednesday.
You are warmly encouraged to hand in your solutions by the following Friday at 12:00 in your assistant's box in HG J 68. Your solutions will be corrected and returned in the following exercise class or, if not collected, returned to the box in HG J 68.
| week | material covered (page numbers: see main reference) | assignment | due by | solutions |
|---|---|---|---|---|
| 1 | General information on the course, arithmetic with the integers, Zorn's lemma. (pages 9-13, 313-314, 319-320) | A1 | Sept 29 | S1 |
| 2 | Category Theory, first definitions on Rings (pages 441-445, 461, 29-37) | A2 | Oct 6 | S2 |
| 3 | Fraction field, Polynomial Rings (pages 36-38, 41-45, 48-49) | A3 | Oct 13 | S3 |
| 4 | Ideals, First Isomorphism Theorem (pages 50-51, 55-60, 61: Ex A-3.52, 21: A-2.25, 74-75) | A4 | Oct 20 | S4 |
| 5 | Prime ideals and maximal ideals, Existence of maximal ideals, Arithmetic of Polynomials with coefficients in a field, Chinese Remainder Theorem, definition of UFD (pages 74-75, 315, 62-64, 104) | A5 | Oct 27 | S5 |
| 6 | UFDs (pages 104-111) | A6 | Nov 3 | S6 |
| 7 | First definitions on Groups, Group homomorphisms, Subgroups, Conjugacy (pages 127-134, 150-155, 143-145) | A7 | Nov 10 | S7 |
| 8 | Normal subgroups, quotient groups, Isomorphism theorems for groups (pages ...) | A8 | Nov 17 | S8 |
| 9 | Group action (see notes), Sylow theorems | A9 | Nov 24 | S9 |
| 10 | Sylow theorems (continuation, see notes from last week), the symmetric group (pages 116-126, 174-176) | A10 | Dec 1 | S10 |
| 11 | Field extensions, algebraic elements | A11 | Dec 8 | S11 |
| 12 | Algebraic closure, splitting field, finite fields | A12 | Dec 15 | S12 |
| 13 | Finite fields, modules over a ring | A13 | No hand-in. | S13 |
| 14 | Elementary divisors, Finitely generated modules over a PID | A14 | No hand-in. | S14 |
All exercise classes are held in English. Please enroll in one exercise group through this link.
| time | room | assistant |
|---|---|---|
| Mo 14-16 | LFW C 4 | Patricia Dietzsch |
| Mo 14-16 | ML F 39 | Carlos De la Cruz Mengual |
| Mo 14-16 | ML J 37.1 | Angela Maennel |
| We 15-17 | HG G 19.2 | Riccardo Ferrario |
| We 15-17 | LEE C 114 | Alexey Pokrovskiy |