Lectures related to Commutative property

Group Theory: Direct Sum of Abelian Groups

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Cohomology Real Projective Space

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

Composition of Applications in Mathematics

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

System Composition

Explains how systems are composed in parallel or series.

Associative Operations: Fundamentals

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

Convolution: Properties and Applications

Covers the concept of convolution and its properties in signal processing.

Natural Numbers

Covers the concept of natural numbers, including properties like commutativity and associativity.

Physics 1: Vectors and Dot Product

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Q is a Field

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

Order of Operations: Unnecessary Parentheses

Discusses the significance of moving parentheses before calculations and the rules for simplifying expressions and prioritizing operations.

Properties of Operations: Equivalence Relations and Logic Basics

Explores properties of operations, equivalence relations, and logic basics.

Properties of Rational Multiplication

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

Purely Functional Priority Queue

Covers optimal purely functional priority queues, Scala implementation, Stainless integration, operations properties, and binomial queues.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Groups and Numbers: Mathematical Elements on Groups

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

Natural Numbers: Properties and Operations

Explores natural numbers, their properties, operations, and practical applications like calculating hours in a year.

Matrix Multiplication

Covers matrix multiplication, properties, and the identity matrix in algebraic operations.

Integer Operations: Parentheses and Simplification

Explains the importance of parentheses in integer operations and how to simplify calculations using properties.

Intersection: Set Operations

Introduces set intersection, its properties, and its relation to arithmetic operations.

Auxiliary Assertions in Stainless

Showcases the use of assertions in Stainless to prove properties of fractions.