Lectures related to System Composition

Convolution: Properties and Applications

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

Natural Numbers: Properties and Operations

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

Multiplication: Properties and Definitions

Explains the definition and properties of integer multiplication in various scenarios.

Boolean Algebra: Properties and Optimization

Covers Boolean algebra properties, optimization techniques, and the importance of valid groups in Karnaugh maps.

Polynomials and Endomorphisms

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

Composition of Applications in Mathematics

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

Associative Operations: Fundamentals

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

Matrix Multiplication

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

Cohomology Real Projective Space

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

Ring Structure: Polynomials and Coefficients

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

Q is a Field

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

Matrix Algebra: Addition, Scalar Multiplication, Transpose

Introduces matrix algebra operations and their properties, including commutativity and distributivity.

Elliptic Curves: Group Structure and Isomorphism

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

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.

Auxiliary Assertions in Stainless

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

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.

Module Theory: Definitions and Examples

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Intersection: Set Operations

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