MAU34107 Combinatorics
| Module Code | MAU34107 |
|---|---|
| Module Title | Combinatorics |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Ruth Britto |
| Module Prerequisites | MAU11101 Linear algebra I |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Continuous assessment contributes 25% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Describe and employ several techniques of combinatorial proofs and calculations.
- Demonstrate the existence or non-existence of combinatorial objects.
- Count permutations, combinations, multisets, and partitions of finite sets.
- Use ordinary and exponential generating functions, as well as their products and compositions.
- Define and analyze basic concepts of graphs, directed graphs, and weighted graphs.
- Define posets and their algebraic properties, and give examples.
Module Content
- Principles of enumeration: permutations, partitions, sieve methods, generating functions.
- Graph theory: paths, cycles, spanning trees, coloring, matching.
- Partially ordered sets, lattices, hyperplane arrangements.
Recommended Reading
- A walk through combinatorics by M. Bóna.
- Enumerative combinatorics by R. Stanley.
- Combinatorics by N. Loehr.