MTH4170 · Network mathematics

Overview

This unit provides an introduction to graph theory, which is the mathematics of networks. Topics covered include trees, Eulerian tours, Hamiltonian cycles, shortest path problem, bipartite graphs, matchings, graph colouring, max-flow problem, graph connectivity, independent sets, planarity, random graphs. Applications to a variety of the sciences will be presented. You will learn how to write proofs and analyse algorithms.

Areas of study: Advanced computer science Applied mathematics Computational science Mathematical statistics Mathematics Pure mathematics

Offerings

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

Learning outcomes

1. Critically analyse and synthesise concepts in graph theory.
2. Evaluate and illustrate the extensive applications and significance of graph theory across diverse fields, particularly in mathematics and computer science
3. Apply some of the most famous theorems in graph theory, such as the max-flow-min-cut theorem, the marriage theorem, and the 4-colour theorem, to solve complex problems.
4. Construct mathematical proofs of theorems about graphs, demonstrating creativity and depth of understanding
5. Design, implement, and critically evaluate algorithms for solving various graph optimisation problems.
6. Exhibit mastery in advanced problem-solving techniques, working both independently and collaboratively with staff and fellow students.
7. Communicate complex mathematical arguments and concepts related to graph theory with clarity and precision, both in written and oral forms, suitable for academic and professional contexts

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

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