Lecture

Polynomial Averaging: Root Pairing

Related lectures (28)

Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.

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

Linear Algebra: Abstract Concepts

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

Second Degree Trinomial: Roots and Formulas

Covers second degree trinomials, discriminants, Viète's formulas, and root calculations.

Building Ramanujan Graphs

Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.

Polynomials with Real Coefficients

Explores polynomials with real coefficients, complex roots, and sequences' properties.

Interlacing Families and Ramanujan Graphs

Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.

Polynomials on a Field: Basics and Operations

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

Complex Roots: Conjugate Pairs and Quadratic Equations

Explores complex roots, conjugate pairs, and quadratic equations solving strategies.

Polynomials: Theory and Operations

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Attack on RSA using LLL

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

Reed Solomon Codes: Basics and Applications

Introduces Reed Solomon Codes, their applications, polynomial definitions, interpolation, roots, and the Fundamental Theorem of Algebra.

Polynomials: Definitions and Operations

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

Linear Combinations and Vector Spaces

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

General case of degree two polynomials

Explores Viète's formula for finding roots of degree two polynomials and their significance.

Polynomials: Operations and Properties

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

Polynomials on a Field

Covers the construction of polynomials on a field and the concept of minimal polynomials.

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Polynomials on a Field: Properties and Applications

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

Jordan Normal Form

Covers the Jordan Normal Form theorem and invariance of kernels under transformations.