Lectures related to Fermat's factorization method

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

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

Understanding Chaos in Quantum Field Theories

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

Integer Factorization: Quadratic Sieve

Covers the Quadratic Sieve method for integer factorization, emphasizing the importance of choosing the right parameters for efficient factorization.

Completing the Square in Quadratic Polynomials

Demonstrates completing the square in quadratic polynomials for factorization simplification.

Integer Factorization: Methods and Algorithms

Explores methods and algorithms for integer factorization, including testing for B smoothness and computing small primes.

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.

Factoring Polynomials: Complexity and Algorithms

Delves into the complexity of factoring polynomials and the implications for security.

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.

Möbius Transformations: Properties and Applications

By the instructor Malo Jézéquel explores Möbius transformations and bounded distortion in SL(2, R).

Complex Numbers: Operations and Applications

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

Groups and Numbers: Hidden Subgroup Problem

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

Integers: Well Ordering and Induction

Explores well ordering, induction, Euclidean division, and prime factorization in integers.

Polynomial Regulator Design

Covers the design of polynomial regulators using the RST method.

Quantum and nanocomputing

Covers the basics of number theory, RSA encryption, and Shor's period finding algorithm.

Matrix Determinant: Factorization and Linear Equations

Covers the determinant of a matrix, factorization, and linear equations with infinite solutions.

Algebraic Structures: Groups and Rings

Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.

Viète Relations: Polynomial Roots and Coefficients

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

Polymer Modeling: Interactions and Scaling Behavior

Explores polymer modeling, interactions, and scaling behavior of real polymers.

RST Regulator: Theory and Implementation

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