MTH4153 - Combinatorics - 2019

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.

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.

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.

• 3 hours of lectures
• 1-hour tutorial and
• 8 hours of independent study per week

See also Unit timetable information

Master of Mathematics