*Instructor:* Dr. Csaba SZABÓ

*Prerequisite*: some experience of algebra (rings) is necessary.
Also, some knowledge about permutation groups is needed (this can be substituted
by taking the AAL course.)

*Text*: Ian Stewart, Galois Theory (Second edition), Chapman and
Hall and handouts about the classical approach.

*Optional topics *(depending on the background of the students)

**Ring theory: ** factor rings, Euclidean
domains, polynomials over fields and over the integers, maximal
ideals in rings, quotient fields.

*Topics*

**Field extensions:** simple extensions, algebraic and transcendental
numbers, the degree of an extension, normality and separability,
finite fields.

**The Galois group:** Normal closure, the Galois correspondence,
soluble and simple groups, ruler and compass constructions, solution
of equations by radicals.

**Examples:** the general polynomial equation, the general Galois
group, calculating the Galois group, the regular *n-*gon, quadratic
and cyclotomic felds.

**Ordered fields**: the fundamental theorem of algebra.

*Optional topics *(depending on the background of the students):

**Coding theory**: Linear codes, syndrome decoding, cyclic codes,
BCH-codes.