Last modified: 18 Nov 2025 14:46
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 |
|---|---|---|---|
| Term | Second Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Aberdeen | Sustained Study | No |
| Co-ordinators |
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* Induction * Growth rates * Subsets and binomial coefficients (subsets of fixed size, properties of binomial coefficients, the binomial theorem) * Partitions and Bell numbers * Counting with symmetry * Recurrences * Generating functions * Derangements * Principle of inclusion-exclusion * Extremal problems * The Pigeonhole Principle * Ramsey theory * Graph theory
Syllabus
Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Problem-solving homework |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Create | Apply generating functions |
| Conceptual | Understand | Understand prinicple of inclusion and exclusion |
| Procedural | Apply | Apply Ramsey theory and colouring problems |
| Procedural | Understand | To be able to count partitions |
| Procedural | Understand | Understand generating functions and formal power series |
| Assessment Type | Summative | Weighting | 70 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
2-hour Exam (on campus) |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Apply | To be able to use binomial coefficients |
| Conceptual | Create | Apply generating functions |
| Conceptual | Understand | Understand graphs and trees |
| Conceptual | Understand | Understand prinicple of inclusion and exclusion |
| Procedural | Apply | Apply Ramsey theory and colouring problems |
| Procedural | Apply | To be able to apply Euler's theorem to polyhedra |
| Procedural | Apply | To be able to recognise and count different types of selections |
| Procedural | Remember | To be able to operate with elementary counting functions and magnitudes |
| Procedural | Understand | To be able to count partitions |
| Procedural | Understand | Understand generating functions and formal power series |
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Problem-solving homework |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Apply | To be able to use binomial coefficients |
| Procedural | Apply | To be able to recognise and count different types of selections |
| Procedural | Remember | To be able to operate with elementary counting functions and magnitudes |
| Procedural | Understand | To be able to count partitions |
There are no assessments for this course.
| Assessment Type | Summative | Weighting | 100 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Best of (resit exam mark) or (resit exam mark combined with CA marks). |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
|
|
||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Procedural | Understand | To be able to count partitions |
| Conceptual | Create | Apply generating functions |
| Procedural | Remember | To be able to operate with elementary counting functions and magnitudes |
| Procedural | Apply | To be able to recognise and count different types of selections |
| Procedural | Apply | Apply Ramsey theory and colouring problems |
| Conceptual | Understand | Understand prinicple of inclusion and exclusion |
| Conceptual | Understand | Understand graphs and trees |
| Procedural | Understand | Understand generating functions and formal power series |
| Conceptual | Apply | To be able to use binomial coefficients |
| Procedural | Apply | To be able to apply Euler's theorem to polyhedra |
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