# Undergraduate mathematics in mathlib

This gives pointers to undergraduate maths topics that are currently covered in mathlib. The list is gathered from the French curriculum. There is also a page listing undergraduate maths topics that are not yet in mathlib.

To update this list, please submit a PR modifying docs/undergrad.yaml in the mathlib repository.

#### Linear algebra

Finite-dimensional vector spaces finite-dimensionality, isomorphism with $K^n$, rank of a linear map, isomorphism with bidual.

Multilinearity multilinear map, determinant of vectors, determinant of endomorphisms.

Endomorphism polynomials minimal polynomial, characteristic polynomial, Cayley-Hamilton theorem.

Structure theory of endomorphisms eigenvalue, eigenvector, generalized eigenspaces.

#### Group Theory

Classical automorphism groups general linear group, special linear group, orthogonal group, unitary group.

#### Ring Theory

Fundamentals ring, subrings, ring morphisms, ring structure $\Z$, product of rings.

Ideals and Quotients ideal of a commutative ring, quotient rings, prime ideals, maximal ideals, Chinese remainder theorem.

#### Affine and Euclidean Geometry

General definitions affine space, affine function, affine subspace, barycenter, affine span.

#### Single Variable Real Analysis

Real numbers definition of $\R$, field structure, order.

Sequences of real numbers convergence, limit point, recurrent sequences, limit infimum and supremum, Cauchy sequences.

Numerical series Geometric series, convergence of $p$-series for $p>1$.

Real-valued functions defined on a subset of $\R$ continuity, limits, intermediate value theorem, image of a segment, continuity of monotone functions, continuity of inverse functions.

Elementary functions (trigonometric, rational, $\exp$, $\log$, etc) polynomial functions, logarithms, exponential, power functions, trigonometric functions, hyperbolic trigonometric functions, inverse trigonometric functions, inverse hyperbolic trigonometric functions.

Sequences and series of functions uniform convergence, continuity of the limit, Weierstrass polynomial approximation theorem, Weierstrass trigonometric approximation theorem.

#### Multivariable calculus

Differential equations Grönwall lemma.

#### Probability Theory

Definitions of a probability space probability measure, independent events, sigma-algebra, independent sigma-algebra, Borel-Cantelli lemma (easy direction).

Random variables and their laws discrete law, independence of random variables, Bernoulli law.

Convergence of series of random variables almost surely convergence.