Course syllabus

Linear Algebra II, 7.5 credits

Course code: MA162G Credits: 7.5
Main field of study: Mathematics Progression: G1F
    Last revised: 11/09/2020
Education cycle: First cycle Approved by: Head of school
Established: 02/12/2019 Reading list approved: 11/09/2020
Valid from: Spring semester 2021 Revision: 1

Aims and objectives

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)

Course objectives

Knowledge and Understanding
After completed studies the student shall be able to

  • use central concepts from abstract algebra on vector spaces and linear maps.

Competence and Skills
After completed studies the student shall be able to

  • using algebraic proof methods to prove statements in linear algebra,
  • formulate and use the most important theorems in linear algebra,
  • describe solutions to problems in linear algebra in a logically coherent and mathematically correct way, and
  • solve problems in linear algebra using computer tools.

Evaluation Ability and Approach
After completed studies the student shall be able to

  • choose a suitable method for solving problems in linear algebra as well as be able to argue for the choice of method.

Main content of the course

Complex vector spaces, inner product spaces, QR factorization and the method of least squares, diagonalization and quadratic forms, linear transformations, canonical forms, singular value decomposition, LU factorization, quotient spaces and the isomorphism theorem, direct sum, linear forms and the algebraic dual, the tensor product.

Teaching methods

The teaching consists of lectures and computer labs.

If the course has only a few registered participants, the above-described teaching methods can be completely or partially replaced by supervision and self-study.

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.

Examination methods

Theory and Problem Solving, 6 credits (Code: A001)
Written examination.
The re-exam will take place within eleven weeks after the regular exam.

Computer-Aided Calculations, 1.5 credits (Code: A002)
Oral presentation.


For students with a documented disability, the university may approve applications for adapted or other forms of examinations.

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

Grades

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).

In accordance with university regulations regarding grading systems for first and second-cycle courses (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades shall be used: Fail (U), Pass (G) or Pass with Distinction (VG). For courses that are included in an international Master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the grading scale of A-F shall be used. 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 grounds.

Grades used on course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Theory and Problem Solving
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Computer-Aided Calculations
Grades used are Fail (U) or Pass (G).

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

Comments on grades

The final course grade is given as the grade for the examination component Theory and problem solving, provided that the grade for the examination component Computer-aided calculations is Passed.

Specific entry requirements

Multivariate Calculus, 9 credits and Abstract Algebra, 7.5 credits.

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

Transfer of credits for previous studies

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).

Other provisions

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

Reading list and other teaching materials

Material handed out by the Department of Mathematics.