Concept

Associative property

Related lectures (30)

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

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

Lie Algebra: Group Theory

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Elliptic Curves: Group Structure and Isomorphism

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

Group Theory Basics

Introduces the basics of group theory, including operations, properties, and Lie groups.

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.

Fold Reduce Operations

Explores fold (reduce) operations in parallel programming using Scala, covering associative operations, expression trees, parallel reduction, and array reduction.

System Composition

Explains how systems are composed in parallel or series.

Convolution: Properties and Applications

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

Associative Operations: Tuples and Sets

Explores associative operations on tuples and sets, demonstrating their properties through various examples and proofs.

Order of Operations: Unnecessary Parentheses

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

Modular Arithmetic: Introducing Z/mZ

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

Properties of Rational Multiplication

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

Q is a Field

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

Polynomials: Operations and Properties

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

Purely Functional Priority Queue

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

Natural Numbers

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

Set Union: Properties and Operations

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

Abstract Concepts: Semi-Ring

Explores the concept of a commutative semi-ring based on set theory properties.

Natural Numbers: Properties and Operations

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