In the course, classical abstract algebra is studied, where concepts such as groups, rings, integral domains and fields, as well as residue classes, ideals, and isomorphisms are central. Applications of the fundamental theory of these structures is given in combinatorics, cryptology and coding theory.
Further, polynomials with coefficients in a field are studied, and how zeros of a polynomial can be found in a larger field. The general theory for such field extensions is then connected to the three classical geometric problems; trisection of an angle, doubling the cube, and squaring a circle, and why these are unsolvable.
