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Combinatorics (MAST30036)

Undergraduate level 3Points: 12.5Not available in 2026

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Overview

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This subject provides a comprehensive overview of three key areas of modern combinatorial theory: enumerative, algebraic and extremal combinatorics. The emphasis will be on building theoretical tools that can be applied to wide variety of problems.

The topics to be covered include generating functions (ordinary and exponential), asymptotic analysis of counting sequences, partition theory, symmetric functions, lattice paths, graphs and Ramsey theory.

This subject is relevant to those pursuing further study in pure mathematics, particularly algebra or representation theory, but also maintains important links with mathematical physics, computer science and operations research.

Intended learning outcomes

On completion of this subject, students should be able to:

  • Apply the method of generating functions to solve complex problems in enumeration and to conduct asymptotic analysis of combinatorial structures.
  • Analyse and manipulate central objects in algebraic combinatorics, including symmetric functions and tableaux, demonstrating advanced ability to describe their properties and relationships.
  • Evaluate and apply key results of extremal combinatorics, including Sperner's Theorem and Ramsey's Theorem, to solve combinatorial problems relevant in research and industry.
  • Construct rigorous combinatorial arguments and proofs, demonstrating logical reasoning and mathematical sophistication appropriate for further mathematical studies

Generic skills

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time-management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 8 December 2025