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)

After successful completion of the course, the student should be able to
- solve diophantine equations
- solve simple equations in cyclic groups, dihedral groups, and permutation groups
- provide routine proofs of simple propositions
- define and illustrate central group theoretic concepts such as groups and subgroups, permutation groups, symmetry and dihedral groups, modular arithmetic and cyclic groups, alternating groups, cosets and normal subgroups, quotient groups, homomorphisms, the homomorphy theorem, group actions and conjugacy classes
- deduce and apply properties of the concepts above
- use mathematical terminology well and describe solutions of problems in the areas above in a correct and consistent way.

Properties of the integers and some elementary number theory, groups and subgroups, permutation groups, symmetry and dihedral groups, modular arithmetic and cyclic groups, alternating groups, cosets and normal subgroups, quotient groups, homomorphisms, the homomorphy theorem, group actions and conjugacy classes, orbit-stabilizer theorem, Pólya enumeration.

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).

The course grading is translated to the ECTS grading scale.

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

Linear 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).

When a course has been discontinued or been the subject of major changes there are specific rules regarding examination /completion of compulsory components.

Required Reading

See this Course Syllabus as PDF