Lectures related to Abstract algebra

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores algebraic structures, classes of examples, and properties of cyclic groups.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Explores the direct sum of abelian groups, emphasizing bijections and uniqueness.

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.

Covers monads as data structures with specific laws and examples like List and Option.

Explores algebraic decomposition, simple structures, irreducibility, and separability in finite degrees.

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Explores convolution, uniform continuity, Hilbert structure, and Lebesgue measure in analysis.

Covers abstract algebra concepts using type classes in Scala, including defining monoids, generalizing reduce functions, and typeclass laws.

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

Explores area determination, linear applications, matrix operations, and vector spaces.

Covers polynomial rings, irreducibility criteria, and algebraic structures in fields.

Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.

Covers the manipulation of algebraic laws on complex numbers.

Explores the importance of irreducible representations and orthogonality in group theory.