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Polynomial Averaging: Root Pairing
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Related lectures (29)
Second Degree Trinomial: Roots and Formulas
Covers second degree trinomials, discriminants, Viète's formulas, and root calculations.
Polynomials with Real Coefficients
Explores polynomials with real coefficients, complex roots, and sequences' properties.
Complex Roots: Conjugate Pairs and Quadratic Equations
Explores complex roots, conjugate pairs, and quadratic equations solving strategies.
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.
General case of degree two polynomials
MOOC: Analysis I
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Explores Viète's formula for finding roots of degree two polynomials and their significance.
Complex Polynomials and Factorization
Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.
Factorisation: Real Coefficients Examples
Covers the factorization of polynomials with real coefficients in the complex domain, demonstrating how to find complex roots and obtain irreducible factors.
Coppersmith's Method: Small Roots of Polynomials Mod N
Covers Coppersmith's method for finding small roots of polynomials modulo N efficiently.
Correlations of the Liouville function
Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.
Polynomials: Roots and Factorization
Explores polynomial roots, factorization, and the Euclidean algorithm in depth.
Polynomial Identity Testing
Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.
Interlacing Polynomials
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Explores interlacing polynomials, real rooted theorems, and pseudo-probabilistic methods in polynomial analysis.
Complex Roots and Polynomials
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Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.
Linear Algebra: Abstract Concepts
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Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.
Building Ramanujan Graphs
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Explores the construction of Ramanujan graphs using polynomials and addresses challenges with the probabilistic method.
Interlacing Families and Ramanujan Graphs
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Explores interlacing families of polynomials and 1-sided Ramanujan graphs, focusing on their properties and construction methods.
Polynomials on a Field: Basics and Operations
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Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.
Polynomials: Theory and Operations
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Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.
Polynomials: Definitions and Operations
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Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.
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