- Extremal Combinatorics (Dr I.B. Leader, Mich. 2004)
- Topics in Combinatorics (Prof. W.T. Gowers, F.R.S., Lent 2004)
- Ramsey Theory (Dr I.B. Leader, Mich. 2000)
- Groups, Rings and Fields (Dr J.M.E. Hyland, Lent 1998)

Notes from a course lectured for Part III of the Mathematical Tripos by Dr I.B. Leader in the Michaelmas Term 2004: DVI (115k), PS (323k), PDF (229K).

Last Updated: 17th May 2006

Notes from a course lectured for Part III of the Mathematical Tripos by Prof. W.T. Gowers, F.R.S. in the Lent Term 2004: DVI (172k), PS (444k), PDF (310k).

Course contents: random walks on graphs, quasirandom graphs, Szemerédi's regularity lemma, crossing numbers and combinatorial geometry, monotone circuit complexity, algebraic methods, topological methods.

Last Updated: 13th November 2004

Notes from a course lectured for Part III of the Mathematical Tripos by Dr I.B. Leader in the Michaelmas Term 2000: DVI (106k), PS (311k), PDF (231k).

Course contents:

**Monochromatic Systems:**Ramsey's theorem (finite and infinite). Canonical Ramsey theorems. Colourings of the natural numbers; focussing and van der Waerden's theorem. Combinatorial lines and the Hales-Jewett theorem. Applications, including Gallai's theorem.**Partition Regular Equations:**Definitions and examples. The columns property; Rado's theorem. Applications. (m,p,c)-sets and Deuber's theorem. Ultrafilters; the Stone-Cech compactification. Idempotent ultrafilters and Hindman's theorem.**Infinite Ramsey Theory:**Basic definitions. Not all sets are Ramsey. Open sets and the Galvin-Prikry lemma. Borel sets are Ramsey. Applications.

Last Updated: 8th December 2005

Notes on a few topics from this course, related to the current IB Groups, Rings and Modules course. These notes are based on lectures given by Dr J.M.E. Hyland in the Lent Term 1998.

- Principal Ideal Domains: DVI (7k), PS (107k), PDF (62k).
- Unique Factorization Domains: DVI (11k), PS (126k), PDF (73k).
- Euclidean Domains: DVI (7k), PS (101k), PDF (59k).
- Eisenstein's Irreducibility Criterion: DVI (7k), PS (113k), PDF (65k).

For the structure of finitely generated modules over Euclidean domains, I recommend the relevant section of Peter Cameron's "Introduction to Algebra".

Last Updated: 24th March 2009