Week 1
4, 6, 8 Aug 08

Combinatorics: Basic counting, sets, multisets,
Suggested reading: pages 120 of [S].
Set Theory: Basic axioms. Suggested reading
pages 111 of [H]
Algebra: Matrices, rowechelon form.
Suggested reading: pages 135 of [A]; try the
exercises.


Week 2
11, 13 Aug 08

Combinatorics: Permutations, cycle structure, standard
form, the Stirling numbers of the first kind.
Homework (due 25 Aug 08): [PDF].
Set Theory: Unions, intersections, ordered pairs.
Suggested reading: pages 1225 of [H].
Homework (due 3 Sep 08):
attempt the exercises on page 10,
page 16, page 25 and the
`nontrivial' exercise on
page 23 of [H].


Week 3
18, 20, 22 Aug 08

Combinatorics: Cycle structure, inversions.
Set Theory: Cartesian products, relations, functions.
Suggested reading: pages 1633 of [H].
Algebra: Determinants. Homework (due 12 Sep 08):
[PDF].


Week 4
25, 27, 29 Aug 08

Combinatorics: permutations and trees,
counting functions.
Set Theory: families, inverses, compositions, natural numbers.
Suggested reading: pages 3445 of [H].
Algebra: Permutation matrices, Cramer's rule, Groups.
Suggested reading Chapter 2 of [A].


Week 5
1, 5 Sep 08

Combinatorics: Inclusionexclusion.
Set Theory: Holiday
Suggested reading: pages 3445 of [H].
Algebra: Subgroups, homomorphisms, isomorphism,
kernel, image.


Week 6
8, 10, 12 Sep 08

Combinatorics: Inclusionexclusion formula,
graph reconstruction, derangements.
Homework (due 25 Sep 08):
[PDF].
Set Theory: Natural Numbers, Peano's axioms.
Suggested reading: pages 4649 of [H].
Algebra: Modular arithmetic,
cosets, quotient groups, normal subgroups.


Week 7
17, 19 Sep 08

Combinatorics: Mobius inversion (Amitava Bhattacharya
was the guest lecturer while Jaikumar was away).


Week 8
22, 24, 26 Sep 08

Set theory: Recursion theorem. Suggested reading:
Homework (due 22 Oct 08): Bottom of page 49,
bottom of 53 of [H]. Suggested reading:
pages 5153 of [H].
Algebra: Products of groups,
Quotient groups, first isomorphism theorem.


Week 9
29 Sep 08 1, 3 Oct 08

Combinatorics: Hall's theorem.
Homework (due 3 November 08):
[PDF]
Set Theory: Arithmetic, order in natural
numbers. Suggested reading: 5457 of
[H].
Algebra: Chinese remainder theorem. Homework
(assigned 1 Nov 08, due 14 Nov 08):
problem 11 on page 70, problems 12 and 14 on
page 71, problem 8 on page 75, problem 6 page
76, problem 4 on page 77 (all from [A]).


Week 10
6, 8, 10 Oct 08

Combinatorics: Homework, Linear codes.
Set Theory: Axiom of choice.
Suggested reading: 5961 of [H].
Algebra: Vector Spaces. Suggested
reading: pages 78103 of [A].


Week 11
13 Sep 08

Combinatorics: Group actions, orbits, the orbit
counting lemma.


Week 12
20, 22 Oct 08

Combinatorics: Counting objects under symmetry, cycle
index polynomial.
Set theory: Zorn's lemma. Suggested reading pages
6265 of [H].


Week 13
3, 5, 7 Nov 08

Combinatorics:
Set theory:
Algebra

