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Lecture
Proof of Existence
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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.
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Subgroups and Generators
Covers subgroups, generators, cyclic groups, and group morphisms in group theory.
Associative Operations: Fundamentals
Covers associative and commutative operations in parallel programming, using mathematical examples and discussing challenges in preserving associativity.
Proof of Sylow Subgroup Properties
Explores the properties of p-subgroups of Sylow in a group.
The Lemma of the Five: Abelian Groups
Presents the Lemma of the Five, a fundamental result in group theory.
Introduction to Category Theory: Examples
Introduces the theory of categories through examples and discusses the product of categories.
Finitely Generated Abelian Groups
Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.
Lie Algebra: Group Theory
Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.
Existence of Direct Sums: Abelian Groups
Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.