The course content is divided into three broad themes.
- Describing Sets: Logic & Proofs -- Introduction to Logic. Propositional Logic, Truth tables, Deduction, Resolution, Predicates and Quantifiers, Mathematical Proofs. Infinite sets, well-ordering. Cardinality of finite sets, Cartesian Product, countable and Uncountable sets, Cantor's diagonalization. Mathematical Induction - weak and strong induction.
- Sizes of Sets: Counting & Combinatorics -- Counting, Sum and product rule, Principle of Inclusion Exclusion. Pigeon Hole Principle, Counting by Bijections. Double Counting. Linear Recurrence relations - methods of solutions. Generating Functions. Permutations and counting.
- Structured Sets: Algebraic & Relational Structures -- Relations, Equivalence Relations. Functions, Bijections. Binary relations and Graphs. Trees (Basics). Posets and Lattices, Hasse Diagrams. Boolean Algebra. Structured sets with respect to binary operations.