MTH4151 · Advanced graph theory

Overview

Networks are ubiquitous and fundamental in the modern world, whether they are computer networks, transport networks, food webs, polymer chains, social networks and so on. Graph theory is the mathematics of networks. Familiarity with the basic notions and terminology will be assumed and built on to give an advanced understanding of a number of topics chosen from the following list: random graph theory, probabilistic method, extremal graph theory, Ramsey theory, advanced algorithms, combinatorial optimisation, geometric graph theory, topological graph theory, structural graph theory, algebraic graph theory, graph colouring, matroid theory.

Areas of study: Master of Mathematics

Offerings

The Handbook publishes no offerings for this unit.

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Formulate complex problems using appropriate graph-theoretic terminology.
2. Appreciate the role of graph theory in other areas of mathematics.
3. Apply sophisticated mathematical methods in the setting of graph theory.
4. Apply sophisticated graph-theoretic arguments in a variety of settings.
5. Communicate complex information about graphs.
6. Apply critical thinking in the field of graph theory.
7. Read, understand and verify expert mathematical proofs about graphs.
8. Develop and write mathematical proofs about graphs.
9. Understand several real-world applications of graph theory.

Workload

• 3 hours of seminars; • 1 hour applied sessions and • 8 hours independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.