Combinatorics and Graph Theory

Description

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.

Availability

Callaghan Campus

  • Semester 1 - 2015

Learning Outcomes

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.

Content

  • 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.

Assumed Knowledge

MATH1510

Assessment Items

In Term Test: Examination - Class

Written Assignment: Assignments

Tutorial / Laboratory Exercises: Group/tutorial participation & contribution: Lab exercises and group case study

Formal Examination: Final examination

Contact Hours

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term