School of Science and Technology

Course Syllabus

General aims for first cycle education

First-cycle courses and study programmes shall develop:
- the ability of students to make independent and critical assessments
- the ability of students to identify, formulate and solve problems autonomously, and
- the preparedness of students to deal with changes in working life.

In addition to knowledge and skills in their field of study, students shall develop the ability to:
- gather and interpret information at a scholarly level
- stay abreast of the development of knowledge, and
- communicate their knowledge to others, including those who lack specialist knowledge in the field.

(Higher Education Act, Chapter 1, Section 8)

Knowledge and understanding:
After completed studies, the student shall
- be able to explain basic concepts in linear functional analysis and how they are related, and
-be able to formulate and prove basic theorems in linear functional analysis.

Competence and skills:
After completed studies, the student shall
- be able to apply definitions, theorems and methods in linear functional analysis in order to solve problems in linear functional analysis, and
-be able to present well-structured solutions both in oral and written form for problems in functional analysis.

Metric spaces. Convergence and completeness. Linear och bounded maps on Banach spaces and Hilbert spaces. Banach fixed point theorem and applications. Linear functionals and Reisz representation theorem. Othogonal projection and othonormal systems in Hilbert spaces. Spectral theorem for compact and self adjoint operators on Hilbert spaces. Unbounded operators. Applications on integral and differential equations.

Lectures and seminars.
The teaching methods may be altered, should only a few students take the course.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

For further information, see the university's local examination regulations (in Swedish).

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may prescribe which grading system shall apply. The grade is to be determined by a teacher specifically appointed by the university (an examiner).

According to regulations on grading systems for first- and second-cycle education (vice-chancellor's decision 2010-10-19, reg. no. CF 12-540/2010), one of the following grades is to be used: fail, pass, or pass with distinction. The vice-chancellor or a person appointed by the vice-chancellor may decide on exceptions from this provision for a specific course, if there are special reasons.

Grades used on course are Fail (U), Pass (G) or Pass with Distinction (VG).

For further information, see the university's local examination regulations (in Swedish).

Computational Mathematics I, 9 Credits, Foundations of Analysis, 7,5 Credits, Abstract Algebra, 7,5 Credits.

For further information, see the university's admission regulations (in Swedish).

Students who have previously completed higher education or other activities are, in accordance with the Higher Education Ordinance, entitled to have these credited towards the current programme, providing that the previous studies or activities meet certain criteria.

For further information, see the university's local credit transfer regulations (in Swedish).

All or part of the course may be given in English.


Reading List and Other Teaching Materials

Required Reading

See this Course Syllabus as PDF