Lectures related to Polynomials and Endomorphisms

Ring Structure: Polynomials and Coefficients

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

Polynomials: Operations and Properties

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

Vector Spaces: Properties and Examples

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Polynomials and Endomorphisms

Covers the fundamentals of polynomials, endomorphisms, division, roots, matrices, and algebraic homomorphisms.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

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.

Polynomials: Rings and Operations

Covers the basics of polynomials, focusing on rings, operations, and properties.

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Associative Operations: Fundamentals

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

Linear Algebra: Abstract Concepts

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Operations in Z

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

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.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Complex Roots and Polynomials

Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.

Polynomials on a Field: Properties and Applications

Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.

Cohomology Real Projective Space

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

Elliptic Curves: Group Structure and Isomorphism

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

Properties of Rational Multiplication

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