Lectures related to Group Theory: Definitions and Properties

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Q is a Field

Covers the properties of rational numbers and introduces the concept of an ordered field in Q.

Operations in Z

Covers addition properties and operations in the set of integers Z.

Representation Theory: Algebras and Homomorphisms

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

Proofs and Sets: Applications

Covers the basics of proofs, defining sets, and applications between sets.

Cartesian Products and Equivalence Relations

Introduces Cartesian products, equivalence relations, and functions, emphasizing the importance of order and discussing injective, surjective, and bijective functions.

Recap of Group Theory

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Associative Operations: Fundamentals

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