Lectures related to Number Theory: Congruence

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Covers matrix operations, Fourier transformations, Gaussian models, and signal representations using algebraic methods.

Explores magnetic fields from moving charges and the properties of complex numbers.

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Number Theory: Fundamental Concepts

Covers binary addition, prime numbers, and the sieve of Eratosthenes in number theory.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Example: 1D steady diffusion

Explores the numerical simulation of steady convection-diffusion problems, discretization, boundary conditions, and algebraic system assembly.

Integers: Well Ordering and Induction

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