Lectures related to Quotients of Groups by Relations of Equivalence

Covers commutative groups and their significance in cryptography.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Introduces the concept of a group and its properties through illustrative examples.

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Provides a recap of group theory, defining a group as a set with a multiplication operation.

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

Explores Lagrange's theorem in commutative groups and the concept of equivalence relations, demonstrating their practical applications.

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

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.

Covers simplicial and cosimplicial objects in category theory with practical examples.

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Covers the fundamentals of group theory in physics, focusing on symmetries and transformations leaving physical equations unchanged.

Explores character representations in group repetition theory, discussing irreducibility, equivalence, and associated values.

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

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

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

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.