Lecture

Group Theory: Basics

Related lectures (27)

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.

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.

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

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

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 symmetries in Newtonian mechanics and wave equations, highlighting their significance in understanding physical laws.

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.

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

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

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