Course Syllabus for

Mathematical Structures
Matematiska strukturer

FMAN65F, 6 credits

Valid from: Spring 2023
Decided by: Maria Sandsten
Date of establishment: 2023-01-14

General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMAN65
Teaching language: Swedish


Besides mere knowledge imparting, the course aims to give training in theorem proving, and to bring out the possibilities of a more abstract representation of mathematical concepts and the connections between them. The intention is to give an overall view elucidating the foundations of the mathematical theories in the basic courses.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Course Contents

Sets. Real numbers. Metric spaces. Algebra (groups and linear spaces). Banach spaces and Hilbert spaces with applications.

Course Literature

Kaplansky, I.: Set Theory and Metric Spaces. American Mathematical Society. 2001. ISBN 9780821826942.

Instruction Details

Types of instruction: Lectures, seminars

Examination Details

Examination formats: Written exam, oral exam. The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: FMAF01 Analytic functions and FMAF05 Systems and Transforms, or equivalent.

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page:

Complete view