Course contents

Groups, permutations, homomorphisms, group actions, rings, ideals, modules, fields and field extensions.

Intended learning outcomes

After the course, the student shall be able to pursue abstract reasoning about algebraic structures. The student shall be trained in logical thinking and in constructions of mathematical proofs. Algebraic structures appear in many disciplines within Science and Technology. The student shall be able to recognize and use such structures in his or her forthcoming work. Concretely, this means that the student shall be able to:

• Identify and describe fundamental algebraic structures such as groups, rings and fields,
• Identify algebraic substructures such as subgroups, subrings and ideals,
• Identify and describe relations between algebraic structures, such as homomorphisms and group actions,
• Define and use bijective functions between algebraic structures, with special attention to permutations,
• Use classical results in basic group theory and ring theory, such as Lagrange's theorem or Cauchy's theorem, to describe the structure of the group or the ring,
• Explain relations using mathematical proofs and logical reasoning,
• Formulate certain practical problems by means of algebraic structures.

Course Disposition

No information inserted

Specific prerequisites

SF1604 Linear algebra or corresponding courses are required prerequisites.

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

David S. Dummit, Richard M. Foote: Abstract Algebra, 3rd Edition

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

A, B, C, D, E, FX, F

Examination

• TEN1 - Examination, 7,5 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

One written exam which can partly be replaced by homework assignments and one mid term exam.

Grade scale A, B , C, D, E, Fx, F.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Tilman Bauer

Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Offered by

SCI/Mathematics

Main field of study

Mathematics

Education cycle

Second cycle

Add-on studies

No information inserted

Contact

Tilman Bauer (tilmanb@kth.se)

Supplementary information

The course is replaced by SF1678.