Foundations of mathematics

Propositional logic

Preterite logic

Set theory

Number theory

Arithmetic

Sequences

Elementary algebra

Prime numbers

Real numbers

Complex numbers

Abstract algebra

Group theory

Rings

Fields

Univariate real analysis

Real functions

Univariate calculus

Trigonometry

Taylor and Fourier analysis

Important functions of real numbers

Ordinary Differential Equations (ODEs)

Linear algebra

Vector spaces

Linear endomorphisms

Linear forms

Linear maps

Algebra over a field, and Lie algebra

Exterior algebra

Tensors

Infinite-dimensional vector spaces

Multivariate real analysis

Multivariate calculus

Partial Differential Equations (PDEs)

Exterior calculus

Calculus of variations

Optimisation

Complex analysis

Complex calculus

Riemann surfaces

Topology

Metric space

Topology of finite sets

Measure space

Topological manifolds

Differentiable manifolds

Riemann manifolds

Euclidian geometry

Graph theory