spring 2019

MAT-2300 Algebra 1 - 10 ECTS

Sist endret: 30.08.2019

The course is provided by

Faculty of Science and Technology


Tromsø |

Application deadline

Applicants from Nordic countries: 1 June for the autumn semester and 1 December for the spring semester. Applicants from outside the Nordic countries: 1 October for the spring semester and 15 April for the autumn semester.

Type of course

The course is included in the study program Mathematics and statistics - bachelor. It may also be taken independent of study program.

Admission requirements

Applicants from Nordic countries:
Generell studiekompetanse og følgende spesielle opptakskrav:

Matematikk R1 + R2 og i tillegg enten:

  • Fysikk 1 + 2 eller
  • Kjemi 1+ 2 eller
  • Biologi 1 + 2 eller
  • Informasjonsteknologi 1 + 2 eller
  • Geofag 1 + 2 eller
  • Teknologi og forskningslære 1 + 2

International applicants: Higher Education Entrance Qualification and certified language requirements in English. It is a requirement that students have  some prior knowledge of biology and ecology, chemistry and mathematics (Participants must have taken introductory level university courses, and achieved pass grades, in these subjects).

A list of the requirements for the Higher Education Entrance Qualification in Norway can be found on the Norwegian Agency for Quality Assurance in Education website - nokut.no

Recommended prerequisites is MAT-1004 Linear algebra or equal .

Application code is 9336.

Course content

This course is required for all masters students in pure mathematics. It is also appropriate for students who need basic knowledge of algebra for applications in computer science, physics or chemistry. Covers the theory of groups, rings and fields with applications.

Recommended prerequisites

MAT-1004 Linear algebra

Objectives of the course

The students should know, and be able to use, the following concepts in simple problems:
  • groups and subgroups
  • cyclic groups
  • normal subgroups
  • permutation groups
  • the structure theorem for finitely generated abelian groups
  • homomorphisms and isomorphisms
  • quotient groups
  • rings and subrings
  • integral domains
  • quotient fields
  • polynomials
  • ideals
  • fields and subfields
  • field extensions
  • algebraic extensions
  • unique factorization domains

Language of instruction

The language of instruction and the syllabus is English. Examination questions will be given in English, but may be answered either in English or a Scandinavian language.

Teaching methods

Lectures: 40 h Coursework: 30 h


One oral exam counting 100%.

Assessment scale: Letter grades A-F.

Coursework requirements A passing grade is required on the mandatory homework sets for permission to take the exam.


Course overlap

MA-232 Algebra i - introductory theory of groups, rings and fields 9 stp

Recommended reading/syllabus

Syllabus for MAT-2300 Algebra 1, spring 2019
UiT The Arctic University of Norway, Department of Mathematics and Statistics

Textbook: John B. Fraleigh, "A First Course In Abstract Algebra", Seventh ed, Pearson Education 2003.

Chap. 0, except Cardinality
Chap. I.2 - I.6
Chap. I.7, except Cayley Digraphs
Chap. II.8 - II.11
Chap. III.13 - III.14
Chap. III.15
Chap. IV.18 - IV.19
Chap. IV.20, except ax=b(mod m)
Chap. IV.21 - IV.22
Chap. IV.23, except 23.11 - 23.17
Chap. V.26 - V.27
Chap. VI.29 - VI.30
Chap. VI.31 (31.12-31.21; only understanding of algebraically closed fields, and some examples)
Chap. VI.33
Chap. IX.45 (45.1 - 45.18)


Cordian Riener

Telefon: +4777644090 cordian.riener@uit.no