Combinatorics and Graph Theory
Combinatorics and Graph Theory is a blend of the mathematical techniques applicable to Computer Science, Information Technology and Statistics. This is 'discrete' mathematics as distinct from the continuous mathematics of calculus. It is a major growth area in modern mathematics, largely because of emerging applications in areas such as biotechnology and communication security.
Much of the subject matter is a continuation of topics studied in MATH1510 such as graphs, trees, and enumeration, and additional topics such as experimental design and finite geometry are introduced. Some use is made of basic techniques from calculus and abstract algebra.
- Semester 1 - 2015
1. An in-depth knowledge of one specific area of mathematics.
2. An improved ability to communicate mathematical ideas.
3. Some experience with applications of mathematics to the Information Sciences.
- Enumeration: generating functions, recurrence relations, Polya's Theorem, inclusion-exclusion.
- Graph theory: paths and cycles, connectivity, factorisations, colouring, planarity applications.
- Combinatorial Designs: finite fields, Latin squares, Steiner triple systems, finite geometries.
In Term Test: Examination - Class
Written Assignment: Assignments
Tutorial / Laboratory Exercises: Group/tutorial participation and contribution: Lab exercises and group case study
Formal Examination: Final examination
Face to Face On Campus 3 hour(s) per Week for Full Term