Lectures related to Gaussian Lemma III: Irreducibility and Primitive Polynomials

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 Equations: Solving Methods

Covers various methods for solving polynomial equations through examples.

Polynomial Roots: Finding Solutions and Division

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

Factorisation: The Fundamental Theorem of Algebra

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

Algebraic Geometry

Covers the fundamentals of algebraic geometry, including algebraic numbers and irreducible polynomials.

Polynomials: Roots and Factorization

Explores polynomial roots, factorization, and the Euclidean algorithm in depth.

Tests of Invariance in Polynomial Equations

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

Complex Numbers: Operations, Polar Form, and Solutions

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

Polynomials: Theory and Operations

Covers the theory and operations related to polynomials, including ideals, minimal polynomials, irreducibility, and factorization.

Built-In Self-Test (BIST): Techniques and Implementations

Explores Built-In Self-Test (BIST) techniques in VLSI systems, covering benefits, drawbacks, implementation details, and the use of Linear Feedback Shift Registers (LFSRs) for test pattern generation.

Polynomial Equations: Determining Coefficients

Covers the process of determining coefficients in polynomial equations.

Complex Roots and Polynomials

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

Complex Polynomials and Factorization

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

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.

Complex Numbers: Operations and Applications

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

Complex Numbers: Equations and Constructibility

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

Complex Numbers: Definitions and Applications

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

Polynomial Equations

Covers the topic of polynomial equations and methods to solve them.