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MA1510: COMBINATORICS (2018-2019)

Last modified: 22 May 2019 17:07


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 None. 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?

No

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 * External 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.
  • External 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.

Further Information & Notes

Course Aims

The course will develop a collection of techniques to solve existence and counting problems in discrete mathematics. It will touch on applications to other parts of mathematics and computer science.

 

Learning Objectives
By the conclusion of the course the student should have gained an understanding of basic combinatorial concepts and techniques including induction, permutations, partitions, binomial coefficients, generating functions and graphs. The course will also develop students’ skills of logical reasoning and proofs. Many of the methods encountered will be applicable in later mathematics courses.

Contact Teaching Time

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

Teaching Breakdown

  • 3 Lectures during University weeks 25 - 35
  • 1 Tutorial during University weeks 26 - 35

More Information about Week Numbers


In light of Covid-19 and the move to blended learning delivery the assessment information advertised for courses may be subject to change. All updates for first-half session courses will be actioned no later than 1700 (GMT) on 18 September 2020. All updates for second half-session courses will be actioned in advance of second half-session teaching starting. Please check back regularly for updates.

Summative Assessments

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%). Resit: 1 two-hour written examination paper (maximum of (100%) resit and (80%) resit with (20%) in-course assessment).

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials.

Course Learning Outcomes

None.

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