Lectures related to Complex Numbers: Gauss-Wantzel Theorem

Complex Roots and Polynomials

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

Complex Roots: Conjugate Pairs and Quadratic Equations

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

Polynomials with Real Coefficients

Explores polynomials with real coefficients, complex roots, and sequences' properties.

Complex Numbers: Roots and Polynomials

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

Linear Combinations and Vector Spaces

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

Square Roots and Complex Numbers

Explores square roots in quadratic equations, complex numbers, Fermat prime numbers, and the Gauss-Wantzel theorem.

Linear Algebra: Abstract Concepts

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

The Fundamental Theorem of Algebra

Covers the fundamental theorem of algebra, explaining how every polynomial has complex roots.

Vector Spaces: Properties and Examples

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Vector Spaces: Examples and Subspaces

Covers examples of vector spaces and the concept of subspaces, emphasizing key properties and verification methods.

Factorisation: Polynomials and Theorem

Covers irreducible polynomials, fundamental theorem of algebra, and factorization in complex and real polynomials.

Interlacing Polynomials

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

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.

Eigenvalues and Matrix Equations: A Comprehensive Analysis

Examines conditions for the existence of invertible matrices satisfying specific matrix equations involving eigenvalues.

Complex Numbers: Equations and Constructibility

Explores polynomial equations in complex numbers, constructibility conditions, roots of unity, and Fermat primes.

Polynomials: Operations and Properties

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

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Complex Numbers: Operations and Applications

Explores complex number properties, roots, and polynomial equations in the complex plane.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Limits in Function Analysis

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