1) Prerequisites
Basic knowledge of graph theory, linear algebra (properties of real symmetric matrices) and algebra (in particular, permutation groups, group actions). Any bachelor level courses on graph theory, linear algebra, and group theory should be sufficient.
2) Aim of the course
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) Rules about Homework/Exam
The course will have a midterm exam (30%) and a final exam (70%). The resit exam replaces 100% of the grade. The course will have four homework assignments with problems corresponding to each week's lecture. These problems will not be handed in, but discussion about their solution and feedback will be given during the tutorial portion of lectures. The midterm will consist entirely of problems appearing on the homework, or very similar variants thereof. At least half of the final exam will consist entirely of problems appearing on the homework (and very similar variants thereof) from the second half of the course.
4) Lecture notes/Literature
Lecture notes will be provided at the beginning of the course on elo.
- Docent: Krystal Guo