Lectures related to Polynomial Equations: Solutions and Elimination

Complex Numbers: Operations and Applications

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

Polynomial Equations: Determining Coefficients

Covers the process of determining coefficients in polynomial equations.

Polynomial Roots: Finding Solutions and Division

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

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.

Algebraic Identities and Trigonometry

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

Polynomial Equations: Solving Methods

Covers various methods for solving polynomial equations through examples.

Differential Calculation: Trigonometric Derivatives

Explores trigonometric derivatives, composition of functions, and inflection points in differential calculation.

Tests of Invariance in Polynomial Equations

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

Complex Numbers: Introduction and Properties

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

Taylor Polynomials: Approximating Functions with Taylor Polynomials

Delves into Taylor polynomials, showcasing how higher orders improve function approximations and how they can be used to calculate limits.

Differentiable Functions and Lagrange Multipliers

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

Complex Numbers: Definitions and Applications

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

Sequences: Definitions and Examples

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

Complex Numbers: Operations and Applications

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

Roots of n-th Degree

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

Power Series Functions: Logarithm and Exponential

Explores power series functions, particularly the logarithm and exponential functions, discussing convergence, extension, and roots of entire functions.

Complex Numbers: Operations, Polar Form, and Solutions

Covers operations on complex numbers, polar coordinates, and polynomial solutions.

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.