Lectures related to Separable polynomial

Purely Inseparable Decompositions

Explores purely inseparable decompositions, Galois property, and algebraic closures.

Algebraic Extensions and Decomposition of Fok [x]

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

Dedekind Rings: Factorisation and Ideal Class Group

Explores Dedekind rings, factorisation, ideal class group, heredity, separable extensions, and matrix properties.

Sobolev Spaces in Higher Dimensions

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Separable Extensions: Dedekind Rings

Explores separable extensions and Dedekind rings, focusing on coefficients and prime ideals.

Algebraic Decomposition: Understanding Simple Algebraic Structures

Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Decomposition and Separability

Covers the concepts of separable imperfect functions and equine conditions.

Finite Degree Extensions

Covers the concept of finite degree extensions in Galois theory, focusing on separable extensions.

Galois Theory: Extensions and Residual Fields

Explores Galois theory, unramified primes, roots of polynomials, and finite residual extensions.

Linear Binary Classification: Perceptron, SGD, Fisher's LDA

Covers the Perceptron model, SGD, and Fisher's Linear Discriminant in binary classification.

Galois Theory Fundamentals

Explores Galois theory fundamentals, including separable elements, decomposition fields, and Galois groups, emphasizing the importance of finite degree extensions and the structure of Galois extensions.

Preimages in a Gluing Construction

Delves into preimages of closed sets in a disjoint union.

Ramification Theory: Residual Fields and Discriminant Ideal

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

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Finite Fields: Properties and Applications

Explores the properties and applications of finite fields, including isomorphism and cyclic properties.

Galois Theory: Recap and Transitivity

Covers the recap of Galois theory and emphasizes the transitivity of Galois groups.

Cell Attachment: Gluing and Application

Covers cell attachment, gluing cells, and separability in a compact space.

Linear Classification: Logistic Regression

Covers linear classification using logistic regression, regularization, and multiclass classification.

Functional Analysis: Banach and Hilbert Spaces

Covers Banach and Hilbert spaces, separability, norm, continuity, and functional analysis.