Lectures related to Polynomial Equations: Determining Coefficients

Polynomial Roots: Finding Solutions and Division

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

Complex Numbers: Operations and Applications

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

Polynomial Equations: Solving Methods

Covers various methods for solving polynomial equations through examples.

Differentiable Functions and Lagrange Multipliers

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

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 Equations: Solutions and Elimination

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

Tests of Invariance in Polynomial Equations

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

Mathematics: Basics and Applications

Covers the basics of mathematics and its applications in architecture.

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.

Complex Numbers: Definitions and Applications

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

Complex Numbers: Equations and Constructibility

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

Complex Polynomials and Factorization

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

Roots of n-th Degree

Covers the concept of roots of n-th degree in complex numbers and their exact solutions.

Equations: Degree and Solutions

Explores polynomial equations, their degree, solutions, and domain definition.

Gaussian Lemma III: Irreducibility and Primitive Polynomials

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

Galois Theory: Solvability and Radical Extensions

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

Local Zeta Functions

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

Developing Cosine Composition

Explores the composition of Taylor expansions through an example, simplifying complex compositions to identify essential terms.

Taylor Series: Basics

Covers Taylor series, polynomial approximations for function behavior, coefficient finding, and error estimation.

Complex Numbers: Operations and Applications

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