Last modified: 19 Aug 2022 15:50
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.
Study Type  Undergraduate  Level  1 

Session  Second Sub Session  Credit Points  15 credits (7.5 ECTS credits) 
Campus  Aberdeen  Sustained Study  No 
Coordinators 

* 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 inclusionexclusion * Extermal problems * The Pigeonhole Principle * Ramsey theory * Graph theory
Syllabus
Information on contact teaching time is available from the course guide.
Alternative Assessment
Course Assignment  30%
Course Assignment  30%
Course Assignment  40%
Alternative Resit Assessment
Resubmission of failed elements (pass marks carried forward)
There are no assessments for this course.
Knowledge Level  Thinking Skill  Outcome 

Procedural  Apply  To be able to use binomial coefficients 
Procedural  Apply  To be able to recognise and count different types of selections 
Procedural  Understand  To be able to count partitions 
Procedural  Understand  Understand generating functions and formal power series 
Conceptual  Create  Apply generating functions 
Conceptual  Understand  Understand prinicple of inclusion and exclusion 
Procedural  Apply  Apply Ramsey theory and colouring problems 
Conceptual  Understand  Understand graphs and trees 
Procedural  Apply  To be able to apply Euler's theorem to polyhedra 
Procedural  Remember  To be able to operate with elementary counting functions and magnitudes 
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