Lectures related to Properties of Operations: Equivalence Relations and Logic Basics

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Cartesian Product and Equivalence Classes

Covers the Cartesian product of sets and binary relations with detailed examples and graphical representations.

Explores binary relations, Cartesian products, and applications between sets, emphasizing their properties and significance.

Cohomology Real Projective Space

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

Cartesian Product and Induction

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

Logical Expressions and Equivalence Relations

Covers logical expressions, sets, elements, and equivalence relations.

Groups and Numbers: Mathematical Elements on Groups

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Commutation Groups: Euler's Totient Function

Explores commutative groups, Euler's Totient Function, and Cartesian products in group theory.

Cartesian Product in Linear Algebra

Explores the Cartesian product in linear algebra and the method of induction for proving propositions.

Equivalence Relations: Classes, Partitions

Covers equivalence relations, classes, and partitions of a set.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Set Union: Properties and Operations

Explains the union of sets, its properties, operations, and intersection.

Sets and Functions

Introduces binary relations, functions, and various types of relations in sets.

Cartesian Product: Sets and Recurrence

Explores the Cartesian product of sets, subsets, and recurrence in mathematics with examples and exercises.

Associative Operations: Fundamentals

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

Elliptic Curves: Group Structure and Isomorphism

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

Mathematics: Sets and Functions

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Sets and Relations

Introduces sets, Cartesian product, order importance, and relations on sets.

Equivalence Relations and Functions

Covers equivalence relations, functions, injectivity, surjectivity, and bijectivity with illustrative examples.

Tensor Products and Symmetric Power

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.