Mathematics
MA284: Discrete Mathematics (5 ECTS)
This course covers topics in combinatorics, graph theory, and their applications. Section titles are as follows. Addition and multiplication principles; Permutations and combinations; Ordered and unordered selections with repetition; Inclusion and Exclusion; Graph isomorphism, subgraphs, connectedness; Traveling around a graph; Vertex coloring; Planarity; Trees.
Taught in Semester(s) 1. Examined in Semester(s) 1.
Workload: 111 hours (24 Lecture hours, 12 Tutorial hours, 75 Self study hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Use the addition and multiplication principles correctly and appropriately.
- Construct a combinatorial proof from first principles.
- Distinguish between different combinatorial situations and use suitable techniques to solve the problems involved.
- Identify inherent properties of graphs (planarity, Eulerian and Hamiltonian properties) from pictorial representations.
- Apply graph-theoretic ideas to solve scheduling and optimisation problems.
- Model relevant real-life problems using trees and solve them.
Indicative Content
This course covers topics in combinatorics, graph theory, and their applications. Section titles are as follows. Addition and multiplication principles; Permutations and combinations; Ordered and unordered selections with repetition; Inclusion and Exclusion; Graph isomorphism, subgraphs, connectedness; Traveling around a graph; Vertex coloring; Planarity; Trees.
Module Resources
- Alan Tucker, Applied Combinatorics, 4th edition, Wiley.
- Norman Biggs, Discrete Mathematics, 2nd edition, Oxford University Press.
- Susanna S. Epps, Discrete Mathematics with Applications, 4th edition, Brooks Cole.
Back