Pinch and Fold: Fundamentals of Group Theory

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Monster Group Construction

Explores the construction of the Fischer-Greiss monster group, emphasizing its key properties and the process involved.

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

Group Theory in Physics

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

Topology: Fundamental Groups and Applications

Provides an overview of fundamental groups in topology and their applications, focusing on the Seifert-van Kampen theorem and its implications for computing fundamental groups.

Subsets and subgroups associated with an action

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

Group Theory: Basics

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Motivations for Studying Actions: Universal Action of Bijections

Explores the motivations for studying actions through the universal action of bijections.

Rheology of Suspensions

Explores the rheology of suspensions, covering viscosity, particle interactions, and dynamic effects.

Two Definitions of Group Action

Explores two definitions of group action on a set, focusing on properties and applications.

Classification of Extensions

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