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, rank of a set of vectors, isomorphism with bidual.

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

Structure theory of endomorphisms eigenvalue, eigenvector, generalized eigenspaces.

Linear representations Schur's lemma.

Exponential matrix exponential.

#### Group Theory

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

Representation theory of finite groups Maschke theorem, orthogonality of irreducible characters, characters of a finite dimensional representation.

#### 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.

#### Bilinear and Quadratic Forms Over a Vector Space

Low dimensions cross product, triple product.

#### Affine and Euclidean Geometry

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

#### 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 $p>1$, alternating series.

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.

Taylor-like theorems Taylor's theorem with Lagrange form for remainder.

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

#### Single Variable Complex Analysis

Complex Valued series radius of convergence, continuity, differentiability with respect to the complex variable, complex exponential, extension of trigonometric functions to the complex plane(cos, sin), power series expansion of elementary functions(cos, sin).

#### Multivariable calculus

Differential equations Cauchy-Lipschitz Theorem, Grönwall lemma.

#### Probability Theory

Convergence of a sequence of random variables convergence in probability, $\mathrm{L}^p$ convergence, almost surely convergence, Markov inequality, Chebychev inequality, strong law of large numbers.

#### Distribution calculus

Spaces $\mathcal{S}(\R^d)$ Schwartz space of rapidly decreasing functions, stability by derivation.

#### Numerical Analysis

Approximation of numerical functions Lagrange interpolation, Lagrange polynomial of a function at (n + 1) points.