Abstract Algebra, 7.5 credits

Learning outcomes

Knowledge and understanding
After the end of the course the student shall be able to

• choose and apply suitable methods to solve problems in Abstract Algebra.

Skills and caapabilities
After the end of the course the student shall be able to

• define, exemplify, and apply central notions in Abstract Algebra,
• state and apply the most important Theorems in Absstract Algebra and give routine proofs of minor propositions, and
• describe solutions of problems in Abstract Algebra in a logically sound and mathematically correct way.

Evaluation ability and approach
After the end of the course the student shall to be able to

• evaluate the plausibility of the solutions obtained.

Content

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.

Examinations and grades

Examination, 7.5 credits (Code: A001)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

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 determine which grading system is to be used. The grade must be determined by a teacher specifically nominated by the university (the examiner).

In accordance with university regulations on grading systems for first and second-cycle courses and study programmes (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades is to be used: fail (U), pass (G) or pass with distinction (VG). For courses included in an international master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the A to F grading scale is to be used. The vice-chancellor, or a person appointed by them, may decide on exceptions from this provision for a specific course, if there are special grounds for doing so.

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

Modes of assessment

• Examination (code A001): Written examination

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

For further information, see the university's local examination regulations.

Specific entry requirements

Linear Algebra, 7.5 Credits.

For further information, see the university's admission regulations.

Other provisions

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

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.

Reading list and other learning resources

Required Reading

Schellwat, Holger (Latest edition)
Introduction to Abstract Algebra, Part I, Groups
Institutionen för naturvetenskap och teknik, Örebro universitet

Additional Reading

Hillman, Abraham, P. and Alexanderson, Gerald, L. (Latest edition)
Abstract Algebra
Waveland Press, Inc.

Svensson, Per-Anders (Latest edition)
Abstrakt algebra
Studentlitteratur