Discrete Mathematics and Graph Theory
| Code | School | Level | Credits | Semesters |
| MATH3002 | Mathematical Sciences | 3 | 10 | Spring UK |
- Code
- MATH3002
- School
- Mathematical Sciences
- Level
- 3
- Credits
- 10
- Semesters
- Spring UK
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 and Joint Honours students from the School of Mathematical Sciences and Liberal Arts who have successfully completed Part I.
Classes
- Two 1-hour lectures each week for 10 weeks
Assessment
- 100% Exam 1 (2-hour): Written examination
Assessed by end of spring semester
Educational Aims
Thiscourse provides a self-contained account of the basic ideas of Discrete Mathematics (e.g. Combinatorics, 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 subjects