Abstract Algebra, 7.5 credits

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 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 is expected to 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,
• describe solutions of problems in Abstract Algebra in a logically sound and mathematically correct way, and
• implement simpel models in MATLAB.

Evaluation ability and approach
After the end of the course the student is

• expected to be able to evaluate the plausibility of the solutions obtained.

Main content of the course

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.

Teaching methods

Teaching is done in the form of lectures and calculation exercises.
The teaching methods may be altered, should only a few students take the course.

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

Examination, 7.5 credits (Code: A001)
Written exam. Re-exam will take place within eleven weeks after the regular exam.

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).

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

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

Specific entry requirements

Linear 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 can be given in English.

Reading list and other teaching materials

Required Reading

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