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Enumerative Combinatorics (MAST90031)

Graduate courseworkPoints: 12.5On Campus (Parkville)

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Overview

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Semester 1
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The subject is about the use of generating functions for enumeration of combinatorial structures, including partitions of numbers, partitions of sets, permutations with restricted cycle structure, connected graphs, and other types of graph. The subject covers the solution of recurrence relations, methods of asymptotic enumeration, and some applications in statistical mechanics. The methods covered have widespread applicability, including in areas of pure and applied mathematics and computer science.

Intended learning outcomes

After completing this subject, students should



  • have learned about the use of generating functions for enumeration of combinatorial structures, including partitions of numbers and of sets, permutations with restricted cycle structure, connected graphs and other types of graph;
  • have studied the solution of recurrence relations; methods of asymptotic enumeration;
  • have considered some applications in statistical mechanics;
  • gain the ability to pursue further studies in this and related areas.

Generic skills

Upon completion of this subject, students should gain the following generic skills:

  • Problem-solving skills including the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • Analytical skills through the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis; and
  • Time management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 3 November 2022