Group Theory: Definitions and Properties

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Related lectures (30)

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Groups and Numbers: Mathematical Elements on Groups

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Introduction to Category Theory: Functors

Covers the concept of functors in category theory, including composition, identity functors, and forgotten functors.

Natural Numbers

Covers the concept of natural numbers, including properties like commutativity and associativity.

Higher Homotopy Groups: Generalization and Structure

Explores the generalization and structure of higher homotopy groups, including their abelianness, historical context, and properties of H spaces.

Group Theory Basics

Covers the fundamental concepts of group theory and examples of real numbers and permutations.

Category Theory: Introduction

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

Subgroups Criteria: Propositions and Examples

Covers the criteria for subgroups and provides examples and proofs.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Vector Spaces: Properties and Examples

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Associative Operations: Fundamentals

Covers associative and commutative operations in parallel programming, using mathematical examples and discussing challenges in preserving associativity.