Lectures related to System of polynomial equations

Complex Numbers: Operations and Applications

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

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

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.

Roots of n-th Degree

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

Polynomial Equations: Solving Methods

Covers various methods for solving polynomial equations through examples.

Complex Numbers: Equations and Constructibility

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

Polynomial Equations: Determining Coefficients

Covers the process of determining coefficients in polynomial equations.

Complex Numbers: Definitions and Applications

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

Galois Theory: Solvability and Radical Extensions

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

Tests of Invariance in Polynomial Equations

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

Gaussian Lemma III: Irreducibility and Primitive Polynomials

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

Polynomial Roots: Finding Solutions and Division

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

Local Zeta Functions

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

Linear Algebra: Cramer's Rule

Covers Cramer's Rule for solving linear equations using determinants.

Linear Algebra: Systems of Equations

Explores solving systems of equations using matrices and determinants.

Reflection and Rotation Composition

Explores reflection and rotation composition in analytical geometry, including finding centers and solving fixed point systems.

Complex Numbers: Operations and Applications

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

Linear Algebra: Systems of Equations and Vector Operations

Explores systems of equations, vector operations, and geometric interpretations in linear algebra.

Linear Algebra: Operations and Applications

Explores operations and applications of linear algebra in solving equations and transformations.

Eigenspaces: Definitions and Examples

Introduces eigenspaces in linear algebra through definitions and practical examples of determining eigenspaces for matrices.