Skip to Content

MA1510: COMBINATORICS (2022-2023)

Last modified: 19 Aug 2022 15:50

Course Overview

Combinatorics is the branch of mathematics concerned with counting. This includes counting structures of a given kind (enumerative combinatorics), deciding when certain criteria can be met, finding "largest", "smallest", or "optimal" objects (external combinatorics and combinatorial optimization), and applying algebraic techniques to combinatorial problems (algebraic combinatorics). The course is recommended to students of mathematics and computing science.

Course Details

Study Type Undergraduate Level 1
Session Second Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
  • Professor Benjamin Martin
  • Dr Irakli Patchkoria

Qualification Prerequisites

  • Either Programme Level 1 or Programme Level 2

What courses & programmes must have been taken before this course?

  • Any Undergraduate Programme (Studied)

What other courses must be taken with this course?


What courses cannot be taken with this course?


Are there a limited number of places available?


Course Description

* Induction * Growth rates * Subsets and binomial coefficients (subsets of fixed size, properties of binomial coefficients, the binomial therem) * Partitions and Bell numbers * Counting with symmetry * Recurrences * Generating functions * Derangements * Principle of inclusion-exclusion * Extermal problems * The Pigeonhole Principle * Ramsey theory * Graph theory


  • Counting and probability, induction, growth rates.
  • Permutations, subsets, selections, the Binomial Theorem, partitions, Bell numbers.
  • Generating functions, derangements, exponential generating functions.
  • Inclusion and exclusion, Stirling numbers of the second kind.
  • Extermal set theory, intersecting families, Sperner families.
  • The Pigeonhole Principle, Ramsey numbers, Ramsey’s Theorem.
  • Graphs, paths, trees, topological graph theory, Euler’s Theorem, the Platonic solids.

Details for second half-session courses, including assessments, may be subject to change until 23 December 2022.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

  • 3 Lectures during University weeks 26 - 35, 39
  • 1 Tutorial during University weeks 27 - 35, 39

More Information about Week Numbers

Details for second half-session courses, including assessments, may be subject to change until 23 December 2022.

Summative Assessments

Alternative Assessment

Course Assignment - 30%

Course Assignment - 30%

Course Assignment - 40%

Alternative Resit Assessment

Resubmission of failed elements (pass marks carried forward)


Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
ProceduralApplyTo be able to use binomial coefficients
ProceduralApplyTo be able to recognise and count different types of selections
ProceduralUnderstandTo be able to count partitions
ProceduralUnderstandUnderstand generating functions and formal power series
ConceptualCreateApply generating functions
ConceptualUnderstandUnderstand prinicple of inclusion and exclusion
ProceduralApplyApply Ramsey theory and colouring problems
ConceptualUnderstandUnderstand graphs and trees
ProceduralApplyTo be able to apply Euler's theorem to polyhedra
ProceduralRememberTo be able to operate with elementary counting functions and magnitudes

Compatibility Mode

We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.