MATMC1 Algebraic Structures , 7.5 credits, is an alternative-compulsory course at upper-basic level for a Bachelor or Master of Science degree in mathematics. The course is given jointly by the departments of mathematics at the Faculty of Science and at the Faculty of Engineering. Also, an extended version of the course can be taken of Ph.D students from both faculties. The course can be taken as an stand-alone course. The language of instruction in English.

The course is given at half-study pace during one half the spring semester. In the upcoming spring semester of 2024 the course is planned to be given in the second half of the semester.

Course Content
The course treats:

Number theory: the fundamental theorem of arithmetic, modular artithmetic.
Groups: definition, basic examples of groups, subgroups, normal subgroups, factor groups, isomorphisms and homomorphisms, Lagrange's theorem, permutation groups, symmetric and alternating groups, finitely generated Abelian groups.
Rings: definition, basic examples of rings, isomorphisms and homomorphisms, ideals, factor rings, polynomial rings, factorisation of polynomials as products of irreducible poynomials.
Fields: characteristic, simple field extensions, finite fields.

Teaching
The teaching consists of lectures and seminars. A compulsory written assignment is part of the course.

Assessment
The examination consists of a written examination followed by an oral examination at the end of the course, as well as a written presentation of a problem assignment during the course.

The oral examination may only be taken by those students who pass the written examination.

Grades
The grading scale for all examination parts is Pass, Fail. To pass the course it is required to pass the written examination, the oral examination and the written problem assignment. In addition, the grade Pass with distinction requires that the total number of points obtained in the written and the oral examination is at least 75% of the total maximal number of points. The maximal
number of points that can be obtained in the written and the oral examination are weighted three to one.

Course Literature

T.W. Hungerford, Abstract Algebra, An Introduction, 3rd edition, International Edition, 2012, ISBN: 978-1-111-57333-1.

Official Course Description

Course Evaluation
Link to course evaluations on the department's website:

Course Evaluations, Mathematics at Faculty of Science