Lectures related to Polynomials with Real Coefficients

Complex Roots: Conjugate Pairs and Quadratic Equations

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

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

The Fundamental Theorem of Algebra

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.

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Sequences: Definitions and Examples

Covers solving equations over complex numbers, sequences, induction, and properties of complex numbers.

General case of degree two polynomials

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.

Linear Algebra: Abstract Concepts

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

Complex Numbers: Gauss-Wantzel Theorem

Covers the Gauss-Wantzel Theorem and Fermat prime numbers.

Second Degree Trinomial: Roots and Formulas

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

Linear Combinations and Vector Spaces

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

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Polynomials: Operations and Properties

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

Limits in Function Analysis

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