Lectures related to Modular Arithmetic: Foundations and Applications

Covers commutative groups and their significance in cryptography.

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Explores modular arithmetic, emphasizing inverses and equations in Z/mZ, with practical examples and exercises.

Explores modular arithmetic and its role in the RSA cryptosystem for error detection.

Introduces number theory and its essential applications in cryptography.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Explores the proof of the Prime Number Theorem and its implications in number theory.

Explores the Euclidean algorithm, Bézout's identity, extended Euclid algorithm, and commutative groups in mathematics.

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Introduces Cartesian product and induction for proofs using integers and sets.

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

Explores the composition of applications in mathematics and the importance of understanding their properties.

Covers the basics of group theory, including elements, associativity, identity, inverses, and closure.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Explores prime numbers and Euclid's Theorem through a proof by contradiction.

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

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Explores the history and concepts of Number Theory, including divisibility and congruence relations.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.