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Lecture
Polynomials with Real Coefficients
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Related lectures (27)
Complex Roots: Conjugate Pairs and Quadratic Equations
Explores complex roots, conjugate pairs, and quadratic equations solving strategies.
The Fundamental Theorem of Algebra
MOOC: Analysis I
MOOC: Analysis I (part 2) : Introduction to complex numbers
Covers the fundamental theorem of algebra, explaining how every polynomial has complex roots.
Complex Polynomials and Factorization
Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.
Complex Numbers: Roots and Polynomials
Covers the properties of complex numbers, including finding roots and factorizing polynomials.
Complex Numbers: Operations and Applications
Explores complex number properties, roots, and polynomial equations in the complex plane.
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.
Factorisation: Polynomials and Theorem
Covers irreducible polynomials, fundamental theorem of algebra, and factorization in complex and real polynomials.
Correlations of the Liouville function
Explores correlations of the Liouville function along deterministic and independent sequences, covering key concepts and theorems.
Untitled
General case of degree two polynomials
MOOC: Analysis I
MOOC: Analysis I (part 2) : Introduction to complex numbers
Explores Viète's formula for finding roots of degree two polynomials and their significance.
Differential Equations: Coefficients and Methods
Discusses methods for solving differential equations, focusing on undetermined coefficients and variation of constants.
Second Degree Trinomial: Roots and Formulas
Covers second degree trinomials, discriminants, Viète's formulas, and root calculations.
Algebraic Identities and Trigonometry
Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.
Limits in Function Analysis
Introduces the concept of limits in function analysis and demonstrates their application through various examples.
Julia Sets and Polynomial Roots
Explores Julia Sets, polynomial roots, Newton's method, and critical points in complex functions.
Quadratic Forms: Definitions, Examples
MOOC: Linear Algebra (Part 3)
Covers the definition of quadratic forms in R^n with examples in R^2 and R^3.
Complex Factorization Examples
Explores complex polynomial factorization examples, demonstrating the process and implications of complex roots in real polynomials.
Attack on RSA using LLL
Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.
Complex Roots and Polynomials
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Explores complex roots, polynomials, and factorizations, including roots of unity and the fundamental theorem of algebra.
Sequences: Definitions and Examples
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Covers solving equations over complex numbers, sequences, induction, and properties of complex numbers.
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