Course

Abstract Algebra (MAT250)

Facts

Course code MAT250

Credits (ECTS) 10

Semester tuition start Spring

Language of instruction English, Norwegian

Number of semesters 1

Exam semester Spring

Time table View course schedule

Literature Search for literature in Leganto

Introduction

Introduction to the axiomatic approach to algebraic objects, such as groups, rings and fields, with applications to modular arithmetic and symmetries of geometric shapes.

Content

Groups, rings and fields; subgroups and ideals; factor groups and factor rings, homomorphisms. Examples and applications.

Learning outcome

After completion of the course, the student is be able to:

  • Reproduce and exemplify the axioms and elementary properties of an abstract group, ring and field
  • Reproduce and exemplify definitions of central algebraic notions such as subgroup, factor group, ideal, factor ring and homomorphism.
  • Explain and apply the notions of finite and finitely generated group.
  • Identify subgroups, residue classes and factor groups in manageable examples.
  • Identify ideals and quotient rings in manageable examples.
  • Carry out and convey reasoning with abstract algebraic objects.

Required prerequisite knowledge

None

Recommended prerequisites

Discrete Mathematics (MAT120)

Exam

Written exam

Weight 1/1

Duration 4 Hours

Marks Letter grades

Aid Basic calculator

Exam system Paper Based

Written exam is with pen and paper. The examination may be submitted in English in addition to the language of instruction.

Method of work

4 hours lectures, 2 hours tutorials and home work.

Using AI to support learning and study activities

AI tools may be used in MAT250 as a learning aid, but must never substitute for the abstract-algebra understanding the course builds — working with groups, rings and fields and constructing proofs yourself is precisely what you must master yourself, and the exam is written by hand. Productive uses include asking AI to explain a concept (e.g., what the axioms of a group are, what an ideal is, or how a homomorphism works), to check the setup of a problem you have solved yourself, or to generate practice problems for self-testing before the exam. You remain responsible for critically evaluating whatever the AI produces, and any use of AI in assessed work must follow the course's guidelines.

Overlapping courses

Course Reduction (SP)
Groups and Symmetry (MAT230_1) , Abstract Algebra (MAT250_1) , Groups and symmetry (ÅMA230_1) 16
Abstract Algebra (MAT250_1) , Groups and symmetry (ÅMA230_1) 6
Groups and Symmetry (MAT230_1) , Abstract Algebra (MAT250_1) 6

Open for

Open course for all who meet the requirements for general university admissions certification (GSK) and mathematics and science requirement.

Admission requirements

General university admissions certification (GSK) and mathematics and science requirement.

Course assessment

The faculty decides whether early dialogue will be held in all courses or in selected groups of courses. The aim is to collect student feedback for improvements during the semester. In addition, a digital course evaluation must be conducted at least every three years to gather students’ experiences.

Contact

Head of Department:
Bjørn Henrik Auestad
Head of Department:
Bjørn Henrik Auestad
Course coordinator:
Eirik Eik Svanes
Course coordinator:
Martin Gunnar Gulbrandsen

Offered by

Faculty of Science and Technology

Department of Mathematics and Physics

The course description is retrieved from FS (Felles studentsystem). Version 1