# MTH5153 - Combinatorics - 2019

## Postgraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Chief examiner(s)

To be advised

Coordinator(s)

Not offered in 2019

Prerequisites

Enrolment in the Master of Mathematics

Prohibitions

MTH4153Not offered in 2019

Notes

This unit is offered in alternate years commencing Semester 1, 2020

## Synopsis

Combinatorics is the study of arrangements and combinations of

discrete objects. Combinatorial problems arise in many areas of pure mathematics, (e.g. algebra, probability, topology, and geometry), and in many applied areas as well (e.g. communications, operations research, experiment design, genetics, statistical physics etc). This unit will cover a selection of topics from the following list: combinatorial enumeration, ordinary and exponential generating functions, asymptotic enumeration, counting via matrix functions or group actions, the principle of inclusion-exclusion, Mobius inversion, permutations, partitions, compositions, combinatorial designs, Latin squares, Steiner triple systems, block designs, Hadamard matrices, finite geometries, algebraic combinatorics, strongly regular graphs, symmetric functions, Young tableaux, additive combinatorics and combinatorial geometry.

## Outcomes

On completion of this unit students will be able to:

1. Formulate complex problems using appropriate combinatorial terminology.
2. Demonstrate a profound understanding of the benefits and challenges unique to working with discrete mathematical objects.
3. Recognise certain features of combinatorial problems which indicate their level of difficulty.
4. Apply sophisticated combinatorial arguments in a variety of settings.
5. Appreciate the role of combinatorics in other areas of mathematics.
6. Understand several real-world applications of combinatorics.

## Assessment

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5153 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4153Not offered in 2019. The assignments and exam in this unit will use some common items from the MTH4153Not offered in 2019 assessment tasks, in combination with several higher level questions and tasks.

## Workload requirements

3 hours of lectures

1-hour tutorial and

10 hours of independent study per week

See also Unit timetable information

## This unit applies to the following area(s) of study

Master of Mathematics