Mathematics
Formal Sciences
The science of pure structure — pattern, quantity, and form reasoned from first principles, from arithmetic to category theory.
Notes
Abstract Algebra
Groups, rings, fields, and algebraic structures — the study of structure itself, abstracted from any particular domain.
Algebra
Variables, expressions, equations, and the art of manipulating abstract symbolic structures.
Arithmetic
Numbers, operations, and the fundamental processes of computation — the bedrock of mathematical reasoning.
Calculus
Limits, derivatives, integrals — the mathematics of continuous change and accumulation.
Category Theory
Objects, morphisms, and universal constructions — the mathematics of mathematical structure.
Geometry
Points, shapes, space, and spatial reasoning — from Euclid's constructions to differential manifolds.
Information Theory
Entropy, coding, and the fundamental limits of communication — the mathematics of uncertainty, compression, and reliable transmission over noisy channels.
Linear Algebra
Vectors, matrices, and linear transformations
Probability
Chance, randomness, and stochastic reasoning
Set Theory
Collections, membership, and the foundational language of mathematics.
Statistics
The science of learning from data — inference, estimation, hypothesis testing, and modeling under uncertainty, powering evidence-based reasoning across all empirical domains.
Topology
Continuity, connectedness, and topological spaces