MATA23 Foundations of Algebra, 7.5 credits, is a compulsory course for a Bachelor of Science degree in mathematics. The course can be taken as an stand-alone course. The course is given at half-study pace during the second half of each semester. The course has been given in Swedish during the autumn semester and in English during the spring semester.

The course isn't scheduled for the autumn semester 2023 but will be given in English in the spring semester both 2023 and 2024.

Course Content
The course treats

Elementary logic and set theory.
The structure of the number systems from an axiomatic perspective.
Basic properties of the integers: Induction, divisibility, prime numbers, Euclid's algorithm, modular arithmetic, representation of numbers in different bases, Diophantine equations.
Rational and irrational numbers.
Enumerability.
Complex numbers.
Functions and relations. Equivalence relations.
Elementary combinatorics.
Polynomials and algebraic equations: Factorisation, Euclid's algorithm, relationship between zeros and coefficients.

Teaching
The teaching consists of lectures, seminars and exercise classes. An essential element of the seminars and exercise classes is training in problem solving and oral mathematical communication. A project, or a series of smaller written assignments, is included in the course requirements. The project and the assignment series concern theoretical aspects and applications of the course content but can also have a didactic specialisation. The project and the written assignments also aim at providing the students with training in mathematical communication in speech and writing.

Assessment
The examination consists of

a presentation of the project or the written assignments (1.5 credits)
a written examination, possibly together with an oral examination (6 credits)

More information regarding the examination and a selection of past examination papers is available on the following link:

Regarding examination

Course Literature

Kjell Elfström, Foundations of Algebra, 2019.

Official Course Description

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

Course Evaluations, Mathematics at Faculty of Science