MAT5001

Week	Topics	Prerequisite Skills	Student Learning Outcomes
Week 1	Propositional logic: Axioms and Rules of Inference. Boolean Algebras. Limitations of propositional logic: Informal introduction to quantifiers and syllogisms.
Week 2	Predicate Logic: Existential and universal quantification, free variables and substitutions. Discussion of the various axiomatic systems for first-order logic (including axioms and rules of inference). The power and the limitations of axiomatic systems for logic: Informal discussion of the completeness and incompleteness theorems.
Week 2	Sets: Operations on sets. Correspondence between finitary set operations and propositional logic. Correspondence between infinitary operations and quantifiers. The power and limitations of the language of set theory: Informal discussion of the set-theoretic paradoxes and the need for axiomatic systems for set theory.
Week 3	(4) Relations: Properties of relations. Special relations: Equivalence relations, partially ordered sets, totally ordered sets.
Week 3	(5) Functions: Operations of functions, direct image and inverse image.
Week 4	(6) Well-ordered sets: Correspondence between well-ordering relations and induction. Correspondence between well-ordering relations and choice functions. (6) Introduction to computability. Classical models of computation (recursive functions, and Turing models).
Week 4	(7) Limitations of computation. Contemporary models of computation: Digital vs analog vs quantum computing.