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.
The course requires 60 ECTS in mathematics and mathematical statistics 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
15 October 2019.
Please note: This second application round is intended only for EU/EEA/Swiss citizens.