Lectures related to Discriminant

Explores the Gaussian Discriminant Rule for classification using Gaussian Mixture Models and discusses drawing boundaries and model complexity.

Demonstrates completing the square in quadratic polynomials for factorization simplification.

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Explores examples of algebraic quotients using invariance maps and discriminant.

Explores the Class Number Formula in number theory, focusing on Lemmas, Proofs, and a significant theorem.

Covers the manipulation of algebraic laws on complex numbers.

Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.

Explores the discriminant in matrices, ideal class groups, and optimal embeddings in mathematics.

Explores residue fields, quadratic forms, discriminants, and Dedekind recipes in algebraic number theory.

Covers the solutions of homogeneous linear differential equations and how to find linearly independent solutions.

Covers the Class Number Formula and a counting problem related to the lattice and Lipschitz principle.

Explores integral representations, quadratic lattices, and the Hasse Principle.

Covers Simpson's rule for numerical integration and its accuracy for polynomial functions.

Covers second degree trinomials, discriminants, Viète's formulas, and root calculations.

Covers the LLL algorithm for lattice reduction and discusses Hermite's constant and Minkowski's theorem.

Explores ramification theory, residual fields, and discriminant ideals in algebraic number theory.

Covers polynomial factorization examples and polynomial division in complex numbers.

Covers solving complex number equations with discriminants and exploring roots.

Covers spherical coordinates and the determinant of Jacobi in linear algebra.

Explores quadratic spaces, norms, and quaternion algebra over fields.