Objective:
The course objective is to introduce cryptomathematicians to enumeration, generating functions and recursions, random mappings, permutations, and Mobius inversion in partially ordered sets with applications. Selected topics in graph theory block designs, and combinatorial algorithms will also be introduced.
Learning Outcomes:
- apply the basic concepts of graph theory
- design and apply various algorithmic approaches for combinatorial optimization
- construct optimal algorithms for various well-known problems
- formulate and validate various methods of enumeration
- analyze and apply generating functions and recurrence relations
- test application of appropriate inversion techniques
- research, formulate and defend presented research on synthesized combinatorial topic
General Course Topics:
- Enumeration
- Recurrence
- Generating functions
- Inversion
- Graph theory
- Combinatorial optimization
- Designs