Progress plan

Expected course progression and suggested exercises.

Week ofSectionsTopicsSuggested problemsNotes
19 Jan2,3,4Binary operations, isomorphisms, groups2: 8, 10, 23, 34
3: 4, 8, 16, 27
4: 3, 9, 17, 29, 33, 35, 38, 41
?
26 Jan5,6,8Subgroups, cyclic groups, permutation groups5: 8, 12, 43, 45, 57
6: 12, 15, 23, 34, 44
8: 6, 7, 18, 49, 53
?
1 Feb9,10Cycles & orbits. Cosets and Lagrange's theorem9.1, 9.2, 9.3, 9.7, 9.9, 9.29, 9.33
10.4, 10.6, 10.15, 10.30, 10.37, 10.38
?
8 Feb11, 13Direct products, homomorphisms11.3, 11.6, 11.14e, 11.16, 11.47, 11.52
13.4,13.5, 13.46, 13.49
Assignment 1 posted
16 Feb14, 15Quotient groups, simple groups14.3, 14.6, 14.34, 14.35
15.3, 15.4, 15.5, 15.34, 15.35, 15.36
?
23 Feb16, 17Group actions, Burnside's formula16.1, 16.11, 16.14, 16.15 , 16.16
17.1, 17.2, 17.4, 17.6
Assignment 1 due 26 Feb
1 Mar18Rings and fields18.3, 18.5, 18.11, 18.20, 18.37, 18.46, 18.47, 18.52No lecture 5 Mar
8 Mar19, 20Integral domains. Fermat's and Euler's theorems19.1, 19.2, 19.3, 19.11, 19.23, 19.29
20.1, 20.5, 20.12, 20.15, 20.27
?
15 Mar21, 22Quotient fields, polynomial rings21.1, 21.2, 21.6. 21.12, 21.14.
22.2, 22.5, 22.12, 22.13, 22.27
?
22 Mar23, 26Factorisation of polynomials, homomorphisms of rings23.2, 23.5, 23.9, 23.12, 23.14, 23.18, 23.19, 23.34, 23.35
26.1, 26.12, 26.13, 26.14, 26.25, 26.26, 26.30, 26.34, 26.35
Assignment 2 posted
30 MarEaster, no lectures
6 Apr27, 29Prime/maximal ideals, extension fields27.4, 27.5, 27.15, 27.16, 27.17, 27.18, 27.19, 27.28, 27.30
29.1, 29.3, 29.4, 29.17, 29.18, 29.25
Assignment 2 due 9 Apr
13 Apr30, 31Vector spaces, algebraic field extensions30.4, 30.5, 30.6, 30.9, 30.10, 30.21
31.3, 31.5, 31.7, 31.11, 31.13, 31.23, 31.24, 31.29, 31.30
?
20 Apr33, 48Finite fields, automorphisms of fields33.4, 33.9, 33.10, 33.11, 33.12
48.9-14, 48.33, 48.34, 48.36
?
27 Apr49, 50Isomorphism extension theorem, splitting fields49.1, 49.2, 49.3, 49.4, 49.5, 49.6, 49.10, 49.13
50.2, 50.3, 50.6, 50.7, 50.22, 50.23
?
4 May51, 53Separable extensions, Galois theory53.1-53.5, 53.11, 53.17, 53.18?
11 May?Revision/exam practice??
18 May?Revision/exam practice??
Published Jan. 16, 2026 3:37 PM - Last modified Jan. 16, 2026 3:37 PM