Lectures related to Cyclic Groups: Structure and Applications

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Covers the concept of morphism of groups, actions on sets, and automorphisms.

Explores isomorphic groups, bijective morphisms, and their applications in group theory.

Covers Barrett reduction, Montgomery form of integers, and efficient Montgomery product computation.

Introduces number theory and its essential applications in cryptography.

Covers the main concepts behind RSA encryption and examples of homomorphisms between cyclic groups.

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.