The math of countable things.

Unit 1 · Language

Logic & propositions

Statements, connectives, truth tables, tautologies, logical equivalence.

1 demo lesson · 8 cards Unit 2 · Inference

Proofs

Direct, contrapositive, contradiction, induction, the structure of an argument.

1 demo lesson · 8 cards Unit 3 · Collections

Sets & functions

Set operations, cardinality, injective / surjective / bijective functions.

1 demo lesson · 8 cards Unit 4 · Counting

Combinatorics

Permutations, combinations, the binomial theorem, inclusion–exclusion.

1 demo lesson · 8 cards Unit 5 · Discrete structures

Relations

Reflexive, symmetric, transitive, equivalence relations, partial orders.

1 demo lesson · 8 cards Unit 6 · Recurrence

Sequences & recursion

Recurrence relations, linear recurrences, generating functions, the master theorem.

1 demo lesson · 8 cards Unit 7 · Networks

Graph theory

Vertices, edges, paths, trees, bipartite graphs, planar graphs, Euler and Hamilton.

1 demo lesson · 8 cards Unit 8 · Algebra

Modular arithmetic

Congruence, the Euclidean algorithm, Fermat's little theorem, RSA in spirit.

1 demo lesson · 8 cards Unit 9 · Counting spaces

Finite state machines

DFA, NFA, regular expressions, what computability looks like at the smallest scale.

1 demo lesson · 8 cards