Lectures related to Decomposition and Separability

Algebraic Extensions and Decomposition of Fok [x]

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

Finite Degree Extensions

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

QR Factorization: Least Squares System Resolution

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

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Linear Systems: Diagonal and Triangular Matrices, LU Factorization

Covers linear systems, diagonal and triangular matrices, and LU factorization.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Volume Calculations: Decomposition and Composition

Covers advanced topics in volume calculations, focusing on decomposing and composing domains.

Algebraic Decomposition: Understanding Simple Algebraic Structures

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

Complete and Orthonormal Families

Covers complete and orthonormal families in a Hilbert space, discussing unique projections and vector decomposition.

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Generalized Integrals: Elementary Cases

Explores elementary cases of generalized integrals, convergence criteria, and the interpretation of integrals of type i and ii.

Eisenstein Series: Decomposition and Unitarizability

Covers the decomposition of Eisenstein series into orthogonal components and the unitarizability of certain representations.

Numerical Analysis: Solving Linear Systems in Higher Dimensions

Covers numerical analysis and optimization, focusing on solving linear systems in higher dimensions using finite difference methods.

Markov Chains Decomposition

Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.

Decomposition of a Vector

Covers the decomposition of a vector in a base and its applications in speed and distance calculations.

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

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.

Geometric Primary Decomposition

Covers radical ideals, Nullstellensatz, primary ideals, and algebraic sets.

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Normed Spaces

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