Dr Peter Allen

This course is available on the MSc in Applicable Mathematics. This course is available as an outside option to students on other programmes where regulations permit.

Students should be taking the course MA407 Algorithms and Computation or have taken an equivalent course to provide a basic knowledge of algorithms, and should have experience with proofs and proof techniques used in pure mathematics.

This course provides an introduction to discrete mathematics, particularly graph theory.  Emphasis will be placed on the algorithmic aspects of the area.

Topics to be covered include: Brief Introduction to discrete mathematics and graph theoretic terminology; Ramsey's Theorem; matchings and Hall's Theorem; graph search algorithms; stable marriages and the Gale-Shapley Theorem; network flows and the Ford-Fulkerson Theorem; connectivity and Menger's Theorems; graph colouring and Brooks' Theorem; an introduction to the probabilistic method; spectral graph theory and random walks.

20 hours of lectures and 10 hours of seminars in the LT. 1 hour of seminars in the ST.

Students will be expected to produce 10 exercises in the LT.

Weekly exercises are set and marked.

Norman L. Biggs, Discrete Mathematics, Oxford University Press; T H Cormen, C E Leiserson & R Rivest and C Stein, Introduction to Algorithms, Cambridge University Press; R Diestel, Graph Theory, Springer; H S Wilf, Algorithms and Complexity, Prentice Hall.

Several of these texts are available online.  More information, plus additional notes, will be provided during the course.

Exam (75%, duration: 2 hours) in the main exam period.
Coursework (25%) in the LT.