MA1510: COMBINATORICS (2021-2022)

Last modified: 31 May 2022 13:05

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
Term	Second Term	Credit Points	15 credits (7.5 ECTS credits)
Campus	Aberdeen	Sustained Study	No
Co-ordinators	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?

None.

What courses cannot be taken with this course?

None.

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

Syllabus

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.

Contact Teaching Time

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

Teaching Breakdown

More Information about Week Numbers

Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

Alternative Assessment

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 Level	Thinking Skill	Outcome
Factual	Remember	ILO’s for this course are available in the course guide.