MA408      Half Unit
Contemporary Discrete Mathematics

This information is for the 2022/23 session.

Teacher responsible

Prof Julia Boettcher

Availability

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.

Pre-requisites

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

Course content

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.

Teaching

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

Formative coursework

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.

Indicative reading

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.

Assessment

Exam (75%, duration: 2 hours) in the summer exam period.
Coursework (10%) in the MT.
Coursework (15%) in the LT.

Key facts

Department: Mathematics

Total students 2021/22: 9

Average class size 2021/22: 9

Controlled access 2021/22: No

Lecture capture used 2021/22: Yes (MT)

Value: Half Unit

Guidelines for interpreting course guide information

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Communication
  • Application of numeracy skills
  • Specialist skills