Last modified: 22 Jul 2026 13:41
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 * Subsets and binomial coefficients (subsets of fixed size, properties of binomial coefficients, the binomial theorem) * Partitions * The Pigeonhole Principle * Graph theory
Syllabus
• Counting, induction.
• Permutations, subsets, selections, the Binomial Theorem, partitions.
• Graphs, paths, trees, topological graph theory, Euler’s Theorem, the Platonic solids.
Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 70 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
2-hour Exam (on campus) |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Apply | To be able to use binomial coefficients |
| Conceptual | Create | Apply generating functions |
| Conceptual | Understand | Understand prinicple of inclusion and exclusion |
| Conceptual | Understand | Understand graphs and trees |
| Procedural | Apply | Apply Ramsey theory and colouring problems |
| Procedural | Apply | To be able to recognise and count different types of selections |
| 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 |
| Procedural | Understand | Understand generating functions and formal power series |
| Procedural | Understand | To be able to count partitions |
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Problem-solving homework |
|||
| 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 | Understand generating functions and formal power series |
| Procedural | Understand | To be able to count partitions |
| 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 | 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 |
| Conceptual | Create | Apply generating functions |
| Procedural | Understand | Understand generating functions and formal power series |
| Procedural | Apply | To be able to apply Euler's theorem to polyhedra |
| Procedural | Apply | Apply Ramsey theory and colouring problems |
| Procedural | Understand | To be able to count partitions |
| Conceptual | Understand | Understand prinicple of inclusion and exclusion |
| Conceptual | Understand | Understand graphs and trees |
| Conceptual | Apply | To be able to use binomial coefficients |
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