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MA1510: COMBINATORICS (2022-2023)

Last modified: 20 Jan 2023 16:02


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
Co-ordinators
  • 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?

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 * 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 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

Summative Assessments

Exam

Assessment Type Summative Weighting 50
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
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Homework

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
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Homework

Assessment Type Summative Weighting 25
Assessment Weeks Feedback Weeks

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Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Formative Assessment

There are no assessments for this course.

Resit Assessments

Exam

Assessment Type Summative Weighting 100
Assessment Weeks Feedback Weeks

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Best of (resit exam mark) or (resit exam mark combined with CA marks).

Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

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

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