Polynomial Equations: Solutions and Elimination

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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.