Discrete Mathematics and Graph Theory
| Code | School | Level | Credits | Semesters |
| MATH3054 | School of Mathematical Sciences | 3 | 10 | Spring China |
- Code
- MATH3054
- School
- School of Mathematical Sciences
- Level
- 3
- Credits
- 10
- Semesters
- Spring China
Summary
The aim of Discrete Mathematics is the study of discrete and finite rather than continuous quantities. This includes counting problems, graphs and other quantities parametrised by integers. As such Discrete Mathematics is of great importance for various branches of Pure Mathematics, Mathematical Physics, Statistics and Computer Sciences. The course will cover a range of Discrete Mathematics topics, including an introduction to advanced aspects of combinations and permutations, ordinary and exponential generating functions, recurrence relations and applications to counting problems, graphs, digraphs, Eulerian and Hamiltonian trails, planar graphs, graph colouring, trees and minimum spanning tree algorithms.
Target Students
Single Honours students from the School of Mathematical Sciences who have successfully completed Part I. Requisites: MATH1028Analytical and Computational Foundations.
Classes
- One 2-hour lecture each week for 12 weeks
Assessment
- 100% Exam 1 (2-hour): 2 hour written examination
- 100% Exam 1 (2-hour): 2 hour written examination
Assessed by end of spring semester
Educational Aims
This course provides a self-contained account of the basic ideas of Discrete Mathematics (e.g. combinatronics, generating functions, graph theory) which will enable those attending to acquire the necessary knowledge and skills to solve problems in the topic and to establish the grounding for further study in this area.Learning Outcomes
A student who completes this course successfully will be able to:
L1 - solve counting problems involving permutations and combinations;
L2 - use generating functions to address enumerating questions;
L3 - solve recurrence equations with a view to applications to counting problems;
L4 - prove statements about graphs, including paths, trees, graph colouring, planarity and minimum spanning trees;
L5 - apply results of graph theory to problems in other subjetcs.