Group Theory: Definitions and Properties

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Related lectures (32)

Group Theory: Direct Sum of Abelian Groups Log in to Mediaspace to watch this video

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

Elliptic Curves: Group Structure and Isomorphism Log in to Mediaspace to watch this video

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

Group Theory: Definition and Examples Log in to Mediaspace to watch this video

Covers the definition of a group, properties of symmetries, and group operations.

Groups and Numbers: Mathematical Elements on Groups Log in to Mediaspace to watch this video

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

Injectivity and Surjectivity Log in to Mediaspace to watch this video

Covers injectivity, surjectivity, and bijectivity in mathematical functions, explaining unique mappings and pre-image existence.

Polynomials and Endomorphisms Log in to Mediaspace to watch this video

Covers the properties of rings, examples of rings, and polynomials.

Representation Theory: Algebras and Homomorphisms Log in to Mediaspace to watch this video

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

Proofs and Sets: Applications Log in to Mediaspace to watch this video

Covers the basics of proofs, defining sets, and applications between sets.

Cartesian Products and Equivalence Relations Log in to Mediaspace to watch this video

Introduces Cartesian products, equivalence relations, and functions, emphasizing the importance of order and discussing injective, surjective, and bijective functions.

Mathematics: Sets and Functions Log in to Mediaspace to watch this video

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Category Theory: Introduction Log in to Mediaspace to watch this video

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

Active Learning Session: Group Theory Log in to Mediaspace to watch this video

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

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