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Fractions of Rings

Explores the concept of fractions of rings and their uniqueness in ideals and quotients.

Group Theory Fundamentals

Introduces group theory basics and group action concepts with associated subsets.

Cohomology Groups: Hopf Formula

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.

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Group Homomorphisms: Kernels, Images, and Normal Subgroups

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

Group Theory: Introduction

Covers group theory fundamentals, motivations for studying group actions, equivalent definitions, and subsets associated with group actions.

Powers and Multiples: Subgroups and Stabilizers

Covers powers, multiples, subgroups, and stabilizers in group theory.

Symmetries in Physics

Explores symmetries in physics through group theory, emphasizing how symmetries keep equations of motion unchanged.

Groups & Subgroups: Definitions, Theorems, and Morphisms

Covers the fundamental concepts of groups and subgroups, including definitions, theorems, and morphisms.

McKay Correspondence and Coxeter Groups

Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.