Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.
Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.
Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.
Delves into symmetries in physics, covering group theory, perturbation, and quantification.
Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.
Explores cryptography, perfect secrecy, group theory, and modern cryptographic milestones, emphasizing the trade-off between security and cost.
Covers the fundamental concepts of group theory and examples of real numbers and permutations.
