The Course Notes are going to appear here as the lectures are given; problem sheets and solutions will appear as the course progresses. Here is your picture - with apologies to Steven on the front right.

Remember 15% of the course mark will come from solutions to homework. The homework will consist of 6 hand-ins (each worth 10 points), and the best 5 will count toward your 15%. I will indicate on this webpage whenever there is a homework problem to hand in, and when its due date is.

**Lecture 1 (7/1/08):** Revision on groups
and linear algebra.

Here are some exercises: make sure you can do 4-6 and 9-10.

**Hand in Question 4 (the D_4 and D_5 part only) and Question 2.
Both are worth 5 marks. Due on 14/1/08.**

**Lecture 2 (10/1/08):** Representations of groups.

Here are some exercises for this lecture and the next: try at least 1,2, 3, 4, 5, 7, 9, 11, 13, 14 (but it is best to do them all).

**Hand in Question 3 and Question 14.
The first is worth 3 marks; the second 7. Due on 21/1/08.**

**Lecture 3 (14/1/08):** Subrepresentations and irreducibility
.

**Lecture 4 (17/1/08):** Complete reducibility

**Lecture 5 (24/1/08)**: Complete Reducibility,
G-homomorphisms and Schur’s
lemma

Here are some exercises on complete reducibility: try 3 and 4 and the stuff on unitary representations. Solutions

**Lecture 6 (28/1/08)**: Abelian groups, isotypic components

Here are some exercises.

**Hand in Question 2 and Question 7(a),(b).
The first is worth 6 marks; the second 4. Due on 11/2/08.**

**Lecture 7 (31/1/08)**: Isotypic components

**Lecture 8 (4/2/08)**: Characters

**Lecture 9 (7/2/08)**: Orthogonality of characters

Here are some exercises to flex your mathematical muscles on. Solutions

**Lecture 10 (11/2/08)**: Proof of orthogonality

Here are some exercises that are the start to all types of character calculations. Make sure you can do them!.

**Hand in Questions 2,3 and 4.
The first is worth 6 marks; the last two both 2. Due on 21/2/08.**

**Lecture 11 (18/2/08)**: Class functions

**Lecture 12 (21/2/08)**: Character tables and lifting representations

**Lecture 13 (28/2/08)**: Lifting representations and A_5 character table

Here are some exercises. They are all good!

**Hand in Questions (3),(4),(5) (assuming (1) and (2)) and (8). .
The first three are worth 5 marks; the last 5. Due on 10/3/08.**

**Lecture 14 (3/3/08)**: A_5 character table and induced representations

**Lecture 15 (6/3/08)**: Induced representations

Here are some exercises. Solutions

**Lecture 16 (13/3/08)**: Nilpotent groups

Here are some exercises. Solutions

**Hand in Question (3) from the sheet attached to Lecture 15 and Question (2) from the sheet for this lecture.
The first is worth 3 marks; the second 7. Due no later than on 20/3/08 in the folder on my door.**

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