MAU34107 Combinatorics

This module is examined in a 2-hour examination at the end of Semester 1.
Continuous assessment contributes 20% towards the overall mark.
The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows:
1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session;
2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam;
3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.
Capping of reassessments applies to Theoretical Physics (TR035) students enrolled in this module. See full text at https://www.tcd.ie/teaching-learning/academic-affairs/ug-prog-award-regs/derogations/by-school.php Select the year and scroll to the School of Physics.

11 weeks of teaching with 3 lectures per week.

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.

Principles of enumeration: permutations, partitions, sieve methods, generating functions.
Graph theory: paths, cycles, spanning trees, coloring, matching.
Partially ordered sets, lattices.