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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.

Groups
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
12.3: 13*
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


6.4: 5, 11, 12, 14, 15, 20*
6 theorems of Euler and Fermat, isomorphisms 6.3, 9

6.4: 7, 8
9.1: 1, 2, 4, 5, 8, 9, 12, 16, 23*, 38, 50
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

Rings
Lecture Subject Section in Judson Recommended exercises
15 introduction to rings: rings, fields and integral domains 16.1-16.2 16.6: 1,2,3,7,9,12,17,18,28*
16 ring homomorphisms, ideals, quotient rings and isomorphism theorems 16.3

16.6: 4,5,6,7,20,21,25,27,37
17 maximal and prime ideals; polynomials 16.4-17.1 17.4: 1,2,3,4,5,12,13,15,16
18 irreducible polynomials 17.2-17.3

17:4: 8,10,24,25,28 17.5:1,2,7*
19 integral domains and fraction fields 18.1 18.3: 2,3,7,9
20 faktorization in integral domains: UFD, PID, ED, quadratic integers 18.2

18.3: 11,12,15,16,18
21 field extensions (and a bit on quadratic integers) 21.1

21.4:1,2,3,4
22 algebraic extensions and algebraic closure 21.1 21.4: 9,17, 12,13,16,22
23

splitting fields and geometric constructions

 21.2-21.3 21.4: 20, 21, 25, 26
24 finite fields  22.1 22.3:3,4,5,6,14,16
25 Galois theory 23.1-23.2 free, not on the exam
26 repetition: groups
27 repetition: rings and fields

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