# Abstract Algebra (MAT250)

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

Course description for study year 2023-2024. Please note that changes may occur.

Facts

MAT250

1

10

Spring

1

Spring

## Language of instruction

English, Norwegian

Time table

## 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.

None

## Recommended prerequisites

MAT120 Discrete Mathematics

Eirik Eik Svanes

## Method of work

4 hours lectures, 2 hours tutorials and home work.

## Open for

Control Engineering and Circuit Design, Vocational Path - Bachelor in Engineering Mathematics and Physics - Bachelor's Degree Programme Admission to Single Courses at the Faculty of Science and Technology Mathematics and Physics - Five Year Integrated Master's Degree Programme

## Course assessment

There must be an early dialogue between the course coordinator, the student representative and the students. The purpose is feedback from the students for changes and adjustments in the course for the current semester.In addition, a digital course evaluation must be carried out at least every three years. Its purpose is to gather the students experiences with the course.

## Literature

Search for literature in Leganto