Kursöversikt
See the course memo for information on literature, homework and exam. Also see the formal course syllabus.
Lecture plan
Recommended exercises marked with an asterisk (*) are more difficult and those in bold are more important.
Lecture | Subject | Section in Judson | Recommended exercises |
---|---|---|---|
1 | introduction to groups: symmetry groups och axioms of groups | 3.1-3.2 | 3.4: 2,4,7,14,17*,25,31*,33* |
2 | dihedral groups, subgroups, generators, matrix groups | 3.3, 12.1 |
3.4: 37,41,47,53,54 |
3 | cyclic groups | 4 | 4.4: 1, 2, 5, 13, 14, 22, 23, 25, 34 |
4 | permutation groups | 5.1 |
5.3: 1, 2, 3, 6, 7, 18, 21, 23, 25 |
5 | cosets and Lagrange's theorem | 6.1-6.2 |
|
6 | theorems of Euler and Fermat, isomorphisms | 6.3, 9 |
6.4: 7, 8 |
7 | normal subgroups and quotient groups | 10 | 10.3: 1, 4, 7, 13 |
8 |
A5 is simple; repetition |
||
9 | homomorphisms and isomorphism theorems | 11 | 11.3: 2, 5, 8, 11, 14, 15, 16 |
10 | abelian groups | 13.1 | 13.3: 1, 2, 3, 6, 7 |
11 | group actions | 14.1 | 14.4: 2, 4, 5, 6, 20, 24* |
12 | Sylow theorems I | 15.1-15.2 | 15.3: 1, 2, 4, 6, 7, 8, 9, 12, 16*, 22, 25* |
13 | Sylow theorems II | 15.1-15.2 | see above |
14 | repetition |
Kurssammanfattning:
Datum | Information | Sista inlämningsdatum |
---|---|---|
Tor den 30 jan 2020 | Uppgift Homework 1 | ska lämnas in senast 12:00 |
Tor den 13 feb 2020 | Uppgift Homework 2 | ska lämnas in senast 12:00 |
Tis den 3 mar 2020 | Uppgift Homework 3 | ska lämnas in senast 12:00 |
Fre den 17 apr 2020 | Uppgift Homework 4 | ska lämnas in senast 12:00 |
Tis den 5 maj 2020 | Uppgift Homework 5 | ska lämnas in senast 12:00 |
Tis den 19 maj 2020 | Uppgift Homework 6 | ska lämnas in senast 12:00 |