Julia Sets and Polynomial Roots

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Polynomials on a Field: Basics and Operations

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

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Stone-Weierstrass Theorem

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

Interlacing Polynomials

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

Polynomials: Definitions and Operations

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

Complex Numbers: Roots and Polynomials

Covers the properties of complex numbers, including finding roots and factorizing polynomials.

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.

Limits in Function Analysis

Introduces the concept of limits in function analysis and demonstrates their application through various examples.