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  6. MX3020: GROUP THEORY

MX3020: GROUP THEORY (2015-2016)

Last modified: 25 Mar 2016 11:35


Course Overview

Group theory concerns the study of symmetry. The course begins with the group axioms, which provide an abstract setting for the study of symmetry. We proceed to study subgroups, normal subgroups, and group actions in various guises. Group homomorphisms are introduced and the related isomorphism theorems are proved. Composition series are introduced and the Jordan-Holder theorem is proved. Sylow p-subgroups are introduced and the three Sylow theorems are proved. Throughout symmetric groups are consulted as a source of examples.




Course Details

Study Type Undergraduate Level 3
Term First Term Credit Points 15 credits (7.5 ECTS credits)
Campus None. Sustained Study No
Co-ordinators
  • Dr William Turner

Qualification Prerequisites

None.

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

  • Group axioms, subgroups, examples of groups.
  • Cosets of a subgroup
  • Lagrange's Theorem.
  • Homomorphisms, isomorphisms, normal subgroups, quotient groups.
  • Calculations in symmetric and alternating groups.
  • Group actions.
  • Sylow's Theorems.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%). Resit: 1 two-hour examination (maximum of 100% resit and 80% resit with 20% in-course assessment). Only the marks obtained on first sitting can be used for Honours classification.

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinators for feedback on the final examination.

Course Learning Outcomes

None.
 

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