## Teaching

In Semester 2, 2017 I am teaching (one stream of) the Algebra half of MATH1241 Higher Mathematics 1B.

In Semester 1, 2017 I taught MATH5425 Graph Theory. For more detail on this course, see below.

I also taught half of MATH1081 Discrete Mathematics in Semester 1, 2017.

### MATH5425 Graph Theory

MATH5425 Graph Theory is a 6 UOC level V course which I put together, covering classical graph theory as well as results proved using the probabilistic method. This course has run in 2006, 2008, 2010, 2012, 2015 and 2017. I hope that it will also run in 2019 though this is not known yet. (That will be under the trimester system!)

Graphs are fundamental objects in combinatorics, which can be used to model the relationships between the members of a network or system. They have many applications in areas such as computer science, statistical physics and computational biology. Specifically, a graph is a set of vertices and a set of edges, where (generally) an edge is an unordered pair of distinct vertices. The course covers various combinatorial aspects of graph theory and introduces some of the tools used to tackle graph theoretical questions. A particular focus will be on the use of probability to answer questions in graph theory. This is known as the "Probabilistic Method", initiated by Erdős.

Topics include:

- matchings, coverings and packings,
- connectivity,
- graph colourings: vertex colourings and edge colourings,
- planar graphs,
- Ramsey theory,
- the probabilistic method,
- random graphs.

The main textbook is R. Diestel, *Graph Theory* 5th edn. (Springer, 2017),
which is also available online
at
diestel-graph-theory.com.

Some material is also drawn from

- B. Bollobás,
*Modern Graph Theory*(Cambridge University Press, 1998), - N. Alon and J. Spencer,
*The Probabilistic Method*(Wiley 2000).

### Honours

Here is a list of past Honours students, as well as some possible topics for an Honours project.