MT5861 Advanced Combinatorics

Academic year

2025 to 2026 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Module runs in odd years only (2023/24, 2025/26, 2027/28, etc)

Planned timetable

12 noon Mon (weeks 1, 3, 5, 7, 9, 12), Wed & Fri

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr T D H Coleman

Dr T D H Coleman
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Tom Coleman; Prof Nik Ruskuc

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

Combinatorics underlies and interacts many topics in discrete mathematics including group theory, statistical design, and statistical mechanics, as well as being a lively subject in its own right. The module will give students a good grounding in the techniques and will engage students with research-level problems. It is designed to make a wide area of combinatorics available to students.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT4514 OR PASS MT4516

Anti-requisites

YOU CANNOT TAKE THIS MODULE IF YOU TAKE MT5821

Assessment pattern

2-hour written examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x10 weeks), 1 tutorial (x10 weeks)

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

117

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Use standard counting techniques and work with coefficients including the Stirling numbers and their generating functions.
  • Apply techniques of formal power series to obtain combinatorial information.
  • Prove results about strongly regular graphs, and recognise various families of such graphs.
  • Prove results in Ramsey theory using a variety of techniques, including induction and probabilistic approaches.
  • Understand advanced material, such as extremal combinatorics; enumeration under group action; further algebraic combinatorics; or an advanced topic in coding theory.