MTH5153 Combinatorics
Faculty of Science
MTH5153 Combinatorics is a level 5, 6-credit-point, postgraduate unit from the Faculty of Science, offered in 2026 in Semester 1 at Clayton. It has no prerequisites.
- Credit points
- 6
- Offered in 2026
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
This is the 2026 handbook entry. See the 2027 entry.
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Requisites
Before MTH5153
No prerequisites or corequisites besides the enrolment rules below.
After MTH5153
No unit lists MTH5153 as a prerequisite in the 2026 handbook.
Equivalent units
The same content under another code. Only one of them counts.
Overview
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.
Offerings in 2026
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should 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.
Workload and teaching
- Applied sessions12 hours
- Seminars36 hours
- Teaching approachActive learning
- Teaching approachProblem-based learning
- Teaching approachPeer assisted learning
- 3 hours of lectures;
- 1-hour tutorial and
- 10 hours of independent study per week.
Primary content is delivered through traditional lectures (which will be recorded, and available for review via the Moodle page). Applied classes will be active learning. Small groups of students will work together around a whiteboard to solve problems. A key aspect is that this component involves writing your solutions on the board and critiquing the solutions of others, meaning that both written and spoken communication of mathematical ideas are developed (with input from your teaching staff). You also develop strategies for solving the questions together, meaning this is peer-assisted learning. Assignments will be problem-based learning. The questions will involve techniques from recent lectures and applied classes, but sometimes in settings or formats that are not immediately familiar. Thus part of the challenge is adapting what you previously knew or have just learnt to a new setting.
Learning resources
Recommended resources
A Course in Combinatorics, by van Lint and Wilson.
Generatingfunctionology, by Herb Wilf.
Available for free from https://www.math.upenn.edu/~wilf/DownldGF.html <https://www.math.upenn.edu/~wilf/DownldGF.html>
Contacts
- Chief Examiners
- Professor Ian Wanless
- Unit Coordinators
- Professor Ian Wanless
Common questions
What are the prerequisites for MTH5153?
MTH5153 has no prerequisites, but enrolment rules apply.
When is MTH5153 offered?
In 2026, MTH5153 runs in Semester 1 at Clayton.
Does MTH5153 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.