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Lecture
Polynomials on a Field
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Related lectures (29)
Polynomials: Roots and Factorization
Explores polynomial roots, factorization, and the Euclidean algorithm in depth.
Reed Solomon Codes: Basics and Applications
Introduces Reed Solomon Codes, their applications, polynomial definitions, interpolation, roots, and the Fundamental Theorem of Algebra.
Complex Polynomials and Factorization
Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.
Polynomials: Definition and Operations
Covers polynomials, their operations, division theorem, and provides illustrative examples.
Euclidean Algorithm
Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.
Correlations of the Liouville function
Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.
Analyse 2: Division euclidienne
Explores the process of division euclidienne in polynomials, emphasizing the importance of polynomial degrees during operations.
Complex Factorization Examples
Explores complex polynomial factorization examples, demonstrating the process and implications of complex roots in real polynomials.
Stein Algorithm: Polynomial Identity Testing
Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.
Ideals: Polynomials and Definitions
Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.
Division Euclidienne: Exemples
Explains the Euclidean division of polynomials and demonstrates its application through examples and root-based divisibility.
Complex Roots: Conjugate Pairs and Quadratic Equations
Explores complex roots, conjugate pairs, and quadratic equations solving strategies.
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.
Polynomials: Theory and Operations
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Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.
Complex Roots and Polynomials
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Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.
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.
Linear Algebra: Abstract Concepts
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Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.
Jordan Normal Form
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Covers the Jordan Normal Form theorem and invariance of kernels under transformations.
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.
Polynomials on a Field: Properties and Applications
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Explores the properties and applications of polynomials on a field, including formal derivation and uniqueness.
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