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Mathematical Sciences Institute · ANU College of Systems and Society
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.
Regular assignments
Learning outcomes 1, 2, 3, 4, 5, 6, 7
Mid-semester examination
Learning outcomes 1, 3, 4, 5, 6
Final examination
Learning outcomes 1, 3, 4, 5, 6
Workshop participation
Learning outcomes 1, 2, 3, 4, 5, 6, 7
The expected workload will consist of approximately 130 hours throughout the semester including: - Face-to face component which may consist of 3 x 1 hour lecturer per week (36 hours) as well as 16.5 hours of workshop time. - Approximately 77.5 hours of self directed study per semester which will include preparation for lectures and assessment tasks.
Prescribed texts are not required. Course notes will be available through Wattle.