Prof Julia Boettcher

This course is available on the MSc in Applicable Mathematics and MSc in Operations Research & Analytics. This course is available with permission as an outside option to students on other programmes where regulations permit.

Students should have experience with proofs and proof techniques used in pure mathematics.

This course will cover the basics of graph theory and discrete probability, with an emphasis on how these subjects are used in modern technology.

In the first half of the course, we will introduce the necessary background including discrete random variables and expectations; moments and deviations; Chernoff bounds and concentration inequalities; Markov chains. In the second half we will cover practical applications. The emphasis will be on a rigorous analysis of the mathematics in a model situation, but we will explain briefly the connection to the real world usage. Possible topics include:

randomised routing;

discrete Fourier transform;

Monte Carlo sampling;

compressive sensing;

infection models on networks.

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

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

Weekly exercises are set and solved in the seminar. Feedback will be provided on selected exercises.

Diestel, Graph Theory, Springer.

Mitzenmacher and Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis, Cambridge University Press.

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 summer exam period.
Coursework (10%) in the MT.
Coursework (15%) in the LT.