1. Prerequisites

Basic knowledge of graph theory, linear algebra (properties of real symmetric matrices) and algebra (in particular, permutation groups, group actions, group characters). Any bachelor level courses on graph theory, linear algebra, and group theory should be sufficient. No prior knowledge of quantum computing is required.

2. Course Description

In the first part of the course, we will cover symmetries of graph and eigenvalue techniques in graph theory. Topics will include vertex-transitivity, Cayley graphs, automorphism groups, eigenvalue interlacing and strongly regular graphs. In the second part of the course, we will study combinatorial designs, including (complete imbalanced) block designs, symmetric designs, Hadamard Matrices, projective geometries, Latin squares and t-designs. We will study their constructions and point graphs, which will give some examples of strongly regular graphs, allowing us to applying techniques from the first half of the course.

3. Assessments

There will be 4 assignments and one final exams (and a resit). The assignments will be 30% and the final exam will be 70%. Assignments will still count towards the grade after the resit.

3.1 Final exam

The final exam will be in an open book format; students will be allowed to use their own notes, course notes provided by the instructor and their own assignment solutions. As with other Mastermath courses, the grade on the final exam must be at least a 5.0 in order to pass the course.

4. References

The course will largely follow lecture notes will be provided online (in elo).

Supplementary texts

Algebraic Graph Theory, C. Godsil & G. Royle.
A Course in Combinatoric, J. H. van Lint & R. M. Wilson

These books are recommended for use as a resource and supplementary reading material. They are not required reading and material for assignments and exams will come from lectures.

5. Instructor: Krystal Guo