Last modified: 23 Jul 2024 11:03
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 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
Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
1-hour in-class test |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
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| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
1-hour in-class test |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
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| Assessment Type | Summative | Weighting | 70 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
2-hour Exam (on campus) |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
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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). |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Procedural | Remember | To be able to operate with elementary counting functions and magnitudes |
| Conceptual | Create | Apply generating functions |
| Procedural | Apply | To be able to recognise and count different types of selections |
| Conceptual | Understand | Understand graphs and trees |
| Procedural | Apply | To be able to use binomial coefficients |
| Conceptual | Understand | Understand prinicple of inclusion and exclusion |
| Procedural | Apply | To be able to apply Euler's theorem to polyhedra |
| Procedural | Understand | Understand generating functions and formal power series |
| Procedural | Understand | To be able to count partitions |
| Procedural | Apply | Apply Ramsey theory and colouring problems |
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