Recap of Group Theory

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Related lectures (31)

Page 3 of 4

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Categorical Perspective: Abelian Groups

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

The Role of Symmetries

Delves into symmetries in physics, covering group theory, perturbation, and quantification.

Push-out and Quotients

Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.

Group Theory: Direct Sum of Abelian Groups

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

Quotient Groups: Homomorphisms and Isomorphisms

Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.

Functors and Homomorphisms in Group Theory

Explores functors F_{Ab} and Hom (-,-) in group theory, including presentations and homomorphisms.

Categorical Perspective: Group Quotients

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Cryptography and Information Theory

Explores cryptography, perfect secrecy, group theory, and modern cryptographic milestones, emphasizing the trade-off between security and cost.

Quotient Groups and Homomorphisms

Covers explicit calculations of push-outs in Ens and the study of induced homomorphisms between quotient groups.