Lectures related to Generalities (conclusion)

Division Polynomials: Theorems and Applications

Explores division polynomials, theorems, spectral values, and minimal polynomials in endomorphisms and vector spaces.

Development Limit: Order 1 and 2

Covers limited order 1 and 2 development, focusing on linearity and polynomial approximation.

Quadratic Approximation: Example

Covers finding the best quadratic approximation for a given function in a continuous space.

Error Analysis and Interpolation

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Linear Recurrence Relations

Explores linear recurrence relations, including examples like the Fibonacci numbers and the proof of related theorems.

Minimal Polynomials: Uniqueness and Division

Explores the uniqueness of minimal polynomials and the division algorithm for polynomials.

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, cyclic unit groups, and field construction.

Eigenvalues and Minimal Polynomial

Explores eigenvalues and minimal polynomial, emphasizing their importance in linear algebra.

Taylor Polynomials: Correction Term

Explores the correction term in Taylor polynomials, showcasing its role in refining function approximations.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, and the construction of unique finite fields from irreducible polynomials.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Decomposition of Linear Operators

Covers the decomposition of linear operators and properties of eigenspaces.

Properties of Euclidean Domains

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Viète Relations: Polynomial Roots and Coefficients

Explores Viète's identities, relating polynomial roots and coefficients to solve equations.

Mechanics of Rotational Motion

Covers the mechanics of rotational motion, including moments of inertia and energy conservation.

Interpolation de degré 2 par intervalles

Explores constructing a piecewise continuous function using degree 2 interpolation by intervals.

Ordinary Differential Equations: Definitions and Solutions

Explores Ordinary Differential Equations definitions, solutions, polynomial degrees, autonomous solutions, maximal solutions, and Cauchy's problem.

Algebra Review: Rings, Fields, and Groups

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.