Algebra 1977/78, 1978/79, 1986/87, 1987/88, 1988/89, 1989/90, 1996/97.

For 1st year mathematics students. Official name: Algebra.
Program 1996/97.
PRELIMINARIES

The Greek alphabet
Sets
Axioms of Peano and the induction principle
Some logics
Set operations with an infinite number of operands
The cartesian product
Binomial numbers

THE INTEGERS

The euclidean algorithm
Continued fractions
Fundamental relations for continued fractions
Linear diophantine equations in two variables
Prime numbers

RELATIONS AND FUNCTIONS

Functions
Relations
Equivalence relations

GROUP THEORY

Groupoids and semigroups
Groups
Rings and modules
Congruences in a semigroup
Isomorphisms and homomorphisms
Congruences in a group and normal subgroups
All cyclic groups
Theorems of Lagrange and Fermat
Theorems of isomorphy
Direct products of groups
The Chinese remainder theorem
Number theoretic congruences

COMMUTATIVE RINGS

Polynomial rings
Symmetric polynomials
Divisibility in a commutative ring
Congruences in a commutative ring
Prime ideals and maximal ideals
Factorial rings
If A is integer, every finite subgroup of A* is cyclic
Roots of unity
The quotient field of an integral domain

FIELD THEORY

The minimal subfield of a field and the characteristic
Algebraic and transcendent elements
Adjunction of roots
Algebraic extensions
Existence of an algebraic closure
Separable extensions
Simple algebraic extensions
Normal extensions
The fundamental theorem of Galois theory
Extension of homomorphisms
Finite fields
The field with 4 elements
The field with 8 elements