Enumerative Combinatorics (MAST90031)

Graduate courseworkPoints: 12.5Not available in 2025

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Overview

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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;
  • Studied the solution of recurrence relations; methods of asymptotic enumeration;
  • Considered some applications in statistical mechanics; and
  • 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: 4 March 2025

Eligibility and requirements

Prerequisites

Code Name Teaching period Credit Points
MAST30021 Complex Analysis
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
 12.5

Or equivalent

Corequisites

None

Non-allowed subjects

None

Recommended background knowledge

Use of mathematical symbolic computation packages such as Mathematica and Maple is encouraged.

Inherent requirements (core participation requirements)

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

Last updated: 4 March 2025

Assessment

DescriptionTimingPercentage

Up to 40 hours of assignments (two assignments worth 20% each, due mid and late in semester)

  • 40 hours
Throughout the teaching period40%

A written examination

  • 3 hours
During the examination period60%

Last updated: 4 March 2025

Dates & times

Not available in 2025

What do these dates mean

Visit this webpage to find out about these key dates, including how they impact on:

  • Your tuition fees, academic transcript and statements.
  • And for Commonwealth Supported students, your:
       -  Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
     

    Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.

Last updated: 4 March 2025

Further information

  • Texts

    Prescribed texts

    "Analytic Combinatorics" by Philippe Flajolet and Robert Sedgewick, Cambridge University Press, 2009

    Recommended texts and other resources

    None

  • Related Handbook entries

    This subject contributes to the following:

    TypeName
    CoursePh.D.- Engineering
    CourseMaster of Science (Mathematics and Statistics)
    CourseDoctor of Philosophy - Engineering
    CourseMaster of Philosophy - Engineering
    Informal specialisationMathematics and Statistics
  • Available through the Community Access Program

    About the Community Access Program (CAP)

    This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.

    Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants

    Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.

  • Available to Study Abroad and/or Study Exchange Students

    This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.

Last updated: 4 March 2025