Lectures:

• Monday 3pm in D110 
• Tuesday 12 in CG93 
• Problems Class Thursday 9:00 in D110 weeks 12,14,16,18 

Contents (only material covered in the course is examinable [some bits in course booklet syllabus have been left out]):

Lecture 1 (Mo 16.1.): Factor groups, the isomorphism theorem for groups and some applications.

Lecture 2 (Tu 17.1.): Conjugacy classes.

Lecture 3 (Mo 23.1.): More on conjugacy; the centre of a group.

Lecture 4 (Tu 24.1.): Permutations, symmetric groups, cycle notation.

Lecture 5 (Mo 30.1.): Odd/even permutations, the alternating groups.

Lecture 6 (Tu 31.1.): Distinguishing and identifying groups; direct product, isomorphisms.

Lecture 7 (Mo 6.2.): Cayley's Theorem; rotations of the cube as permutation groups.

Lecture 8 (Tu 7.2.): Group actions.

Lecture 9 (Mo 13.2.): Group actions, orbits and stabilisers.

Lecture 10 (Tu 14.2.): Conjugacy as a group action, Orbit-Stabiliser Theorem.

Lecture 11 (Mo 20.2.): Orbit-Stabiliser Theorem, Cauchy's Theorem.

Lecture 12 (Tu 21.2.): Cauchy's Theorem, groups of order 2p (p prime).

Lecture 13 (Mo 27.2.): Conjugacy classes in S_n.

Lecture 14 (Tu 28.2.): Conjugacy classes in A_n.

Lecture 15 (Mo 5.3.): Normal subgroups of S_4 and A_4.

Lecture 16 (Tu 6.3.): Classification of groups of order p^2 (p prime); a Sylow Theorem.

Lecture 17 (Mo 12.3.): Towards classification of finitely generated abelian groups.

Lecture 18 (Tu 13.3.): Fundamental Theorem of finitely generated abelian groups; how many elements of a given order?

Lecture notes:

Update (21.2.12): Here are notes for the lectures so far (starting in week 12). There is also a songified version (Safari plays it directly, Firefox opens iTunes to play it, only Google Chrome doesn't seem to work) of the latest poem from the lectures.

Pure Maths joy: A wonderful a cappella treatment of the finite simple group of order 2, performed by The Klein Four.

Assignments:  Set and collected each Tuesday.

• Hand in on 24 January:  Week 11; Q1, 5, 6. 
• Hand in on 31 January:  Week 12; Q1, 10. Try also Q3 for extra points. 
• Hand in on 7 February:  Week 13; Q4, 6, 11. 
• Hand in on 14 February:  Week 14; Q4, 5. Try also Q6 for extra points. 
• Hand in on 28(!) February:  Week 15; Q1, 2 and Week 16; Q2, 3.  
• Hand in on 6 March:  Week 16; Q10, 11. 
Hand in on 9th February:  29, 31. 
• Hand in on 16th February:  36, 37.   Try also before then 25, 26 (equiv rel), 32, 33 (Cayley), 35 (group action).
• Hand in on 23th February:  45 (alternatively, Q50) and 44.  
• Hand in on 2nd March:  46 (for extra marks try Q52).  
• Hand in on 9th March:  55, 56.  
• Hand in on 16th March:  61, 64.  

Problems:

(Almost) every week a new sheet will be added, and eventually solutions will be given to most of the problems.

Here is a summary of most of Michaelmas term's material.

Here is a summary of Epiphany term's material.

NEW: In case you have missed any of the lectures, here and here (Michaelmas term) as well as here and here (Epiphany term) is a complete set of notes, taken by Steven Charlton.

Each of the following references covers most of the material in the lectures (in rather different form). Examples and motivation are taken from various sources.