Lectures related to Non-associative algebra

Representation Theory: Algebras and Homomorphisms

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

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Elliptic Curves: Group Structure and Isomorphism

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

Associative Operations: Fundamentals

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

Density Theorem: Endomorphisms of Simple Modules

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Simple Modules: Schur's Lemma

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

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.

Lie Algebra: Group Theory

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Natural Transformations Composition

Covers the theory of categories, emphasizing the importance of naturalness in the composition of transformations.

Fold Reduce Operations

Explores fold (reduce) operations in parallel programming using Scala, covering associative operations, expression trees, parallel reduction, and array reduction.

Associative Operations: Tuples and Sets

Explores associative operations on tuples and sets, demonstrating their properties through various examples and proofs.

Rings and Modules: Color Codes and Homological Algebra

Covers rings and modules, emphasizing color codes and homological algebra concepts.

Introduction to Category Theory: Natural Transformations

Covers the concept of natural transformations between functors and their associativity.

Intersection: Set Operations

Introduces set intersection, its properties, and its relation to arithmetic operations.

Group Theory: Definitions and Properties

Introduces group theory concepts, including definitions and properties of groups, rings, and fields.

Auxiliary Assertions in Stainless

Showcases the use of assertions in Stainless to prove properties of fractions.

Groups & Subgroups: Definitions, Theorems, and Morphisms

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