This course is designed to introduce students to abstraction and its role in modeling problems mathematically. It focuses on discrete mathematics with elements of computer science, and is designed for students with a broad range of backgrounds.

Topics to be covered include:

• Foundations: Relations on sets, including equivalence and partial order relations, properties of functions, arithmetic of integers modulo n.
• Topics in graph theory: Applications of the adjacency matrix, graph colouring and the chromatic polynomial.
• Partially ordered sets: Incidence algebras and the relationship to the inclusion-exclusion principle.
• Automata and languages: Finite state automata and the equivalence with regular languages, the pumping lemma.
• Game Theory: Game graphs, impartial combinatorial games, matrix games.