Group Theory: Definitions and Properties

Related lectures (30)

Page 2 of 3

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

Covers the properties of rings, examples of rings, and polynomials.

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

Covers the properties of rational multiplication through fractions and simple calculations, leading to the resolution of division problems.

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

Covers the ring structure, focusing on polynomials and coefficients, including associativity, distributivity, and the product of rings.

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

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

Covers the properties and definitions of subtraction using addition and multiplication as a basis.

Explores polynomial operations, properties, and subspaces in vector spaces.