SF1678 Groups and Rings 7.5 credits

Grupper och ringar

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Offering and execution

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Course information

Content and learning outcomes

Course contents *

Group theory: groups, permutations, homomorphisms, group actions, Lagrange's theorem, Sylow's theorems, structure of abelian groups.

Ring theory: rings, ideals, fields and field extensions, factorization, principal ideal domains, polynomial rings, rings of integers.

Intended learning outcomes *

After completing the course a student should be able to:

  • use concepts, theorems and methods to solve, and present the solution of, problems in those parts of group and ring theory described by the main contents of the course,
  • read and understand mathematical text,

in order to

  • be able to carry out abstract reasoning about algebraic structures
  • be trained in logical thinking and in constructions of mathematical proofs
  • be able to recognize and use algebraic structures in engineering and science subjects and in his or her forthcoming work.

Course Disposition

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Literature and preparations

Specific prerequisites *

Completed basic course SF1672 Linear Algebra or SF1624 Algebra and Geometry.

Recommended prerequisites

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Equipment

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Literature

Announced no later than 4 weeks before the start of the course on the course web page.

Examination and completion

Grading scale *

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

Examination *

  • TEN1 - Exam, 7.5 credits, Grading scale: 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.

The examiner decides, in consultation with KTHs Coordinator of students with disabilities (Funka), about any customized examination for students with documented, lasting disability. The examiner may allow another form of examination for re-examination of individual students.

Opportunity to complete the requirements via supplementary examination

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Opportunity to raise an approved grade via renewed examination

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Examiner

David Rydh

Johan Håstad

Further information

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.

Course web SF1678

Offered by

SCI/Mathematics

Main field of study *

Technology

Education cycle *

First cycle

Add-on studies

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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.