p. 050 573 5734
| Algebra II on Department's wiki | Course index | Suomeksi |
Department of Mathematics and Statistics, spring 2010, scope 10 cr
This course is a sequel to Algebra I. The student is supposed to learn new algebraic structures, and become better acquainted with the ones they already know. Particular themes are e.g. group theory, rings and modules, polynomial algebras and field extensions.
The course has ended. In the spring term of 2011 the course will be given by Åsa Hirvonen, and the new course page can be accessed here.
During periods III and IV
Easter vacation is 1–7 April.
Problem classes are held on Thursdays at 12-14 in room C322. The classes start on the second lecturing week (week 4). Sessions are supervised by Johanna Rämö.
| Sheet 1 | PS, PDF |
| Sheet 2 | PS, PDF |
| Sheet 3 | PS, PDF |
| Sheet 4 | PS, PDF |
| Sheet 5 | PS, PDF |
| Sheet 6 | PS, PDF |
| Sheet 7 | PS, PDF |
| Sheet 8 | PS, PDF |
| Sheet 9 | PS, PDF |
| Sheet 10 | PS, PDF |
| Sheet 11 | PS, PDF |
| Sheet 12 | PS, PDF |
| Sheet 13 | PS, PDF |
Participating in the problem classes is not compulsory. However, extra points are granted for solving the questions. These points are added to the exam result (see Requirements).
| Problems solved | Points |
| 25 % | 1 |
| 50 % | 2 |
| 75 % | 3 |
The course exam can be taken on the Department's general examination dates, e.g. 11th May. The maximum score available in the exam is 30 points.
To pass the course, students must also compose a short essay. The essay will be marked on the scale 0–3, and the student must score at least 1 point to be able to pass the course. The essay can be written during either the first or the latter half of the course. The topics and some instructions can be found on this page.
The exam may also be taken on the general examination day in June. If someone can neither take the exam in May nor in June, they should contact the lecturer immediately.
The extra points coming from solved problems will add to the points from the exam and essay. However, the maximum score will always be 33 points. These extra points will stay in effect until the end of the summer.
| revision | PS | ||
| week 3 | PS | (1. Tekijärakenteet — 'Quotient structures') | |
| week 4 | PS | (2. Ryhmän toiminta — 'Group actions') | |
| week 5 | PS | (3. Symmetriaryhmiä — 'Some symmetry groups') | |
| week 6 | PS | (3.5. Sisäiset symmetriat — 'Inner symmetries' – 4.3. Isomorfialauseet — 'The isomorphism theorems') | |
| week 7 | PS | (5. Ryhmän kompositiotekijät — 'The composition factors of a group') | |
| week 8–9 | PS | (6. Ideaalit — 'Ideals') | |
| week 8–9 | PS | (7. Modulit — 'Modules') | |
| week 11 | PS | (8. Modulikonstruktioita — 'Module constructions') | |
| viikko 12 | PS | (9. Algebrat — 'Algebras') | |
| viikko 13 (Wed) | PS | (9.5. Lien algebrat — 'Lie algebras') | |
| viikko 14 (Fri) | PS | (10. Esimerkki: Äärelliset kunnat — 'Example: Finite fields') | |
| viikko 15 (Wed) | PS | (11. Jaollisuudesta — 'On divisibility') | |
| viikko 15 (Fri) | PS | (12. Yleiset laajennokset — 'General extensions') | |
| viikko 16 | PS | (13. Algebralliset laajennokset — 'Algebraic extensions') | |
| viikko 17 (Wed) | PS | (13.3. Transkendenttisuudesta — 'On transcendentality' – 14.2 Algebrallinen sulkeuma — 'The algebraic closure') | |
| viikko 17 (Fri) | PS | (15. Laajennosten väliset homomorfismit — 'Homomorphisms between extensions') | |
| viikko 18 | PS | (16. Valikoituja aiheita — 'Selected topics') |
In addition to lecture notes, there are many good books available in the Campus Library under "Algebran oppikirjat" (section 51.08, last time I checked). Below is an arbitrary selection of some books that might be suitable (in alphabetical ordering).
For additional reference, there are also the lecture notes written by Kalevi Suominen (in Finnish). These can be found e.g. from the last year's course page.
Problem sets and solutions can be found under Problem classes.
| Jokke Häsä p. 050 573 5734 | Johanna Rämö |
You can give the lecturer anonymous feedback via the following form. Only the IP address of the sender will show on the received message. If you want to ask a question, it is preferred to send email directly to the above address. (More information about the service — in Finnish.)
| Algebra II on Department's wiki | Course index |
Modified 5.1.2011.
