Fields and codes 1987/88.

For 4th year mathematics students. Official name: Algebra superiore.
EXTENSIONOS OF FIELDS

The minimal subfield in a field
Algebraic and transcendental elements
Adjunction of roots
Algebraic extensions

GALOIS THEORY

Recalling some results in group theory
Groups of permutations
Splittings fields and normal extensions
The Galois group
Symmetric polynomials
Fundamental theorem of Galois theory
Extension of homomorphisms
Normality theorems

FINITE FIELDS

The group of invertible elements of a field
Finite extensions of a finite field
The field with 16 elements
Existence and unicity of finite fields

INTRODUCTION TO THE THEORY OF CODES

Fundamental concepts
Linear algebra
Linear codes
Cyclic codes
Polynomial division