Lectures related to Factorization

Elementary Algebra: Numeric Sets

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Weierstrass Preparation Theorem

Explores the Weierstrass Preparation Theorem for entire functions and the construction of root sequences.

Complex Numbers: Operations and Applications

Explores complex number properties, roots, and polynomial equations in the complex plane.

RST Regulator: Theory and Implementation

Covers the theory and implementation of RST regulators, focusing on factorization of zeros and matrix writing.

Complex Eigenvalues Appendix

Covers the factorization of polynomials with complex coefficients and diagonalizability of matrices.

Polynomial Factorization over a Field: Eigenvalues

Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.

Complex Roots and Polynomials

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

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Compression: Prediction

Covers the concepts of compression and prediction using prefix-free codes and distributions.

Polynomial Regulator Design

Covers the design of polynomial regulators using the RST method.

Completing the Square in Quadratic Polynomials

Demonstrates completing the square in quadratic polynomials for factorization simplification.

Examples: Polynomial Factorization

Covers polynomial factorization examples and polynomial division in complex numbers.

Linear Systems: Diagonal and Triangular Matrices, LU Factorization

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

Polynomial Factorization: Field Approach

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

Understanding Chaos in Quantum Field Theories

Explores chaos in quantum field theories, focusing on conformal symmetry, OPE coefficients, and random matrix universality.

Factorisation: Real Coefficients Examples

Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.

Model Categories: Properties and Structures

Covers the properties and structures of model categories, focusing on factorizations, model structures, and homotopy of continuous maps.

Integration on H_pxH and Arithme

Covers integration on H_pxH and arithmetic topics, focusing on the Hensel Lemma and the process of finding R and S such that R.S-P=0.

Groups and Numbers: Hidden Subgroup Problem

Explores groups and numbers, emphasizing the hidden subgroup problem and its complexities in classic and quantum algorithms.