The math of countable things.
Nine units. The toolkit computer science, combinatorics, and proofs are built from.
Logic & propositions
Statements, connectives, truth tables, tautologies, logical equivalence.
Unit 2 · InferenceProofs
Direct, contrapositive, contradiction, induction, the structure of an argument.
Unit 3 · CollectionsSets & functions
Set operations, cardinality, injective / surjective / bijective functions.
Unit 4 · CountingCombinatorics
Permutations, combinations, the binomial theorem, inclusion–exclusion.
Unit 5 · Discrete structuresRelations
Reflexive, symmetric, transitive, equivalence relations, partial orders.
Unit 6 · RecurrenceSequences & recursion
Recurrence relations, linear recurrences, generating functions, the master theorem.
Unit 7 · NetworksGraph theory
Vertices, edges, paths, trees, bipartite graphs, planar graphs, Euler and Hamilton.
Unit 8 · AlgebraModular arithmetic
Congruence, the Euclidean algorithm, Fermat's little theorem, RSA in spirit.
Unit 9 · Counting spacesFinite state machines
DFA, NFA, regular expressions, what computability looks like at the smallest scale.