Ideas behind proofs.
Intermediate steps where needed.
Foundations
Natural numbers, induction, structure, basic logic.
Algebra
Groups, rings, fields, linear algebra.
Analysis
Limits, continuity, integration, complex analysis.
Geometry
Euclidean, affine/projective, transformations.
Combinatorics
Counting, designs, discrete structures.
Number Theory
Primes, congruences, arithmetic structures.
Topology
Continuity, spaces, invariants.
Probability
Randomness, expectation, stochastic ideas.
Dynamics
Iteration, stability, bifurcations.