Lectures related to Group Theory: Basics

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

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Introduces Cartesian product and induction for proofs using integers and sets.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Explores associativity, Lie algebra, Lie groups, relativity, and symmetry preservation in quantum field theory.

Delves into symmetries in physics, covering group theory, perturbation, and quantification.

Covers Lie groups, focusing on SU(2) and SO(3), discussing group structure and representations.

Explores bijections in linear algebra and the concept of cardinality between sets.

Explores totally discontinuous group actions on sets and their mathematical implications.

Covers Lie algebra, group representations, symmetry groups, and Schur's lemma in the context of symmetry and group operations.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Introduces the basics of group theory, including operations, properties, and Lie groups.

Explores the modern definition of symmetry and its practical applications.

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Explores the symmetries of Navier-Stokes equations in periodic boxes, including translations, transformations, rotations, and scaling.

Explores symmetries in physics through group theory, emphasizing how symmetries keep equations of motion unchanged.

Covers simplicial and cosimplicial objects in category theory with practical examples.

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Introduces group theory concepts, properties, and examples, including injective functions and group properties like associativity and inverses.

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