Discrete Mathematics and Proof
How mathematics is actually argued.
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Logic and Proof Techniques
Propositional/predicate logic, direct proof, contrapositive, and contradiction.
Mathematical Induction
Weak and strong induction, and inductive constructions.
Sets, Relations and Functions
Set algebra, equivalence relations, and injections/surjections/bijections.
Combinatorics
Advanced counting, pigeonhole, inclusion-exclusion, and recurrences.
Introduction to Graph Theory
Graphs, trees, connectivity, Eulerian/Hamiltonian paths, and colouring.
Elementary Number Theory
Divisibility, primes, gcd, and modular arithmetic.