Galois Theory: Solvability and Radical Extensions

Related lectures (30)

Page 3 of 3

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

Covers the solution of a practice exam in Algebra, focusing on finding greatest common divisors of polynomials and exploring group properties.

Introduces Galois fields, elliptic curves, factorization algorithms, and the discrete logarithm problem in cryptography.

Discusses the classification of finite extensions of Qp and introduces Krassner's Lemma on root continuity.

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

Explores purely inseparable decompositions, Galois property, and algebraic closures.

Covers the process of determining coefficients in polynomial equations.

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

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

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