MTH3170 - Network mathematics - 2018

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. Students will learn how to write proofs and analyse algorithms.

On completion of this unit students will be able to:

1. Apply the basic concepts of graph theory.
2. Demonstrate the importance and breadth of applications of graph theory in mathematics and the sciences, especially computer science.
3. Apply some of the most famous theorems of graph theory such as the max-flow-min-cut theorem, the marriage theorem, and the 4-colour theorem.
4. Construct and write mathematical proofs of theorems about graphs.
5. Execute, analyse and prove correctness of algorithms for solving various graph optimisation problems.
6. Demonstrate advanced problem solving skills, both individually and collectively with staff and fellow students.
7. Demonstrate advanced skills in the written and oral presentation of mathematical arguments.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

• Three 1-hour lectures per week
• One 2-hour support class per week
• Seven hours of independent study per week

See also Unit timetable information

Advanced computer science

Applied mathematics

Computational science

Mathematical statistics

Mathematics

Pure mathematics