Lectures related to Local field

Explores the Galois theory of Qp, covering algebraic extensions, inertia groups, and cyclic properties.

Explores local rings, Noetherian rings, and minimal primes in the context of integral domains.

Covers local Noetherian rings, integrally closed domains, discrete valuations, and fraction fields.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers the completion of a field, focusing on algebraic closure and function convergence.

Covers the basics of linear block codes and systematic codes over a field F.

Covers the Lipschitz gradient theorem and its applications in function optimization.