The course covers the basic theory of groups rings and field, including concepts like residue classes, ideals, and isomorphisms. Applications of the underlying theory is given in combinatorics, cryptology, coding theory, and geometric constructions.
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 three classical geometric problems; trisection of an angle, doubling the cube, and squaring a circle, and why these are unsolvable.
The course requires 60 ECTS in mathematics or at least two years university studies and in both cases courses in Discrete Mathematics and Linear Algebra or equivalent. Proficiency in English equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
Applicants in some programs at Umeå University have guaranteed admission to this course. The number of places for a single course may therefore be limited.
Application deadline was
16 October 2017.
Please note: This second application round is intended only for EU/EEA/Swiss citizens.