Expected course progression and suggested exercises.
| Week of | Sections | Topics | Suggested problems | Notes |
| 19 Jan | 2,3,4 | Binary operations, isomorphisms, groups | 2: 8, 10, 23, 34 3: 4, 8, 16, 27 4: 3, 9, 17, 29, 33, 35, 38, 41 | ? |
| 26 Jan | 5,6,8 | Subgroups, cyclic groups, permutation groups | 5: 8, 12, 43, 45, 57 6: 12, 15, 23, 34, 44 8: 6, 7, 18, 49, 53 | ? |
| 1 Feb | 9,10 | Cycles & orbits. Cosets and Lagrange's theorem | 9.1, 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 Feb | 11, 13 | Direct products, homomorphisms | 11.3, 11.6, 11.14e, 11.16, 11.47, 11.52 13.4,13.5, 13.46, 13.49 | Assignment 1 posted |
| 16 Feb | 14, 15 | Quotient groups, simple groups | 14.3, 14.6, 14.34, 14.35 15.3, 15.4, 15.5, 15.34, 15.35, 15.36 | ? |
| 23 Feb | 16, 17 | Group actions, Burnside's formula | 16.1, 16.11, 16.14, 16.15 , 16.16 17.1, 17.2, 17.4, 17.6 | Assignment 1 due 26 Feb |
| 1 Mar | 18 | Rings and fields | 18.3, 18.5, 18.11, 18.20, 18.37, 18.46, 18.47, 18.52 | No lecture 5 Mar |
| 8 Mar | 19, 20 | Integral domains. Fermat's and Euler's theorems | 19.1, 19.2, 19.3, 19.11, 19.23, 19.29 20.1, 20.5, 20.12, 20.15, 20.27 | ? |
| 15 Mar | 21, 22 | Quotient fields, polynomial rings | 21.1, 21.2, 21.6. 21.12, 21.14. 22.2, 22.5, 22.12, 22.13, 22.27 | ? |
| 22 Mar | 23, 26 | Factorisation of polynomials, homomorphisms of rings | 23.2, 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 Mar | Easter, no lectures | |||
| 6 Apr | 27, 29 | Prime/maximal ideals, extension fields | 27.4, 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 Apr | 30, 31 | Vector spaces, algebraic field extensions | 30.4, 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 Apr | 33, 48 | Finite fields, automorphisms of fields | 33.4, 33.9, 33.10, 33.11, 33.12 48.9-14, 48.33, 48.34, 48.36 | ? |
| 27 Apr | 49, 50 | Isomorphism extension theorem, splitting fields | 49.1, 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 May | 51, 53 | Separable extensions, Galois theory | 53.1-53.5, 53.11, 53.17, 53.18 | ? |
| 11 May | ? | Revision/exam practice | ? | ? |
| 18 May | ? | Revision/exam practice | ? | ? |