Lectures related to Polynomial Equations

Complex Numbers: Operations and Applications

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

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Polynomial Roots: Finding Solutions and Division

Explains how to find solutions for polynomial equations and perform polynomial division.

Tests of Invariance in Polynomial Equations

Explores testing invariance in polynomial equations, emphasizing solution identification and variable changes.

Linear Algebra: Abstract Concepts

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

Complex Polynomials and Factorization

Explores complex polynomials, factorization, roots of equations, equilateral triangles, and infinite sums in sequences.

Polynomial Equations: Determining Coefficients

Covers the process of determining coefficients in polynomial equations.

Gaussian Lemma III: Irreducibility and Primitive Polynomials

Explains irreducibility in polynomial equations and the properties of primitive polynomials.

Local Zeta Functions

Covers the classification of comport p-adic fields using integration and Igusa's local zeta functions.

Galois Theory: Solvability and Radical Extensions

Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.

Complex Numbers: Equations and Constructibility

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

Complex Roots and Polynomials

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

Differentiable Functions and Lagrange Multipliers

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

Complex Numbers: Operations and Applications

Covers the properties and operations of complex numbers and their applications.

Polynomial Equations: Solving Methods

Covers various methods for solving polynomial equations through examples.

Complex Numbers: Definitions and Applications

Explores complex numbers, arguments, modules, and polynomial equations with complex coefficients.

Factorisation: The Fundamental Theorem of Algebra

Covers the Fundamental Theorem of Algebra, polynomial division, and complete factorization of complex polynomials.

Polynomial Equations: Solutions and Elimination

Covers the solutions of polynomial equations and the concept of logarithms.

Polynomials: Operations and Properties

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

Complex Numbers: Introduction and Properties

Covers the introduction to complex numbers and their properties, including historical background and norm calculation.