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MX3020: GROUP THEORY (2022-2023)

Last modified: 21 Oct 2022 16:20


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. 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
Session First Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
Co-ordinators
  • Dr Assaf Libman

Qualification Prerequisites

  • Either Programme Level 3 or Programme Level 4

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.

Syllabus

  • Lagrange’s theorem
  • Symmetric groups and alternating groups.
  • Cyclic groups and their subgroups.
  • Homomorphisms and isomorphisms.
  • Normal subgroups and their quotient groups.
  • The three isomorphism theorems.
  • Simple groups and composition series. The Jordan-Holder theorem.
  • Group actions. The orbit-stabiliser theorem.
  • Sylow's theorems.
  • The classification of finite abelian groups

Details for second half-session courses, including assessments, may be subject to change until 23 December 2022.

Contact Teaching Time

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

Teaching Breakdown

  • 2 Lectures during University week s 8 - 18
  • 1 Tutorial during University week s 9 - 18

More Information about Week Numbers


Details for second half-session courses, including assessments, may be subject to change until 23 December 2022.

Summative Assessments

Exam

Assessment Type Summative Weighting 50
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

Students will be invited to contact Course Coordinators for feedback on the final examination.

Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

2x Homework (25% each)

Assessment Type Summative Weighting 50
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials.

Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Formative Assessment

There are no assessments for this course.

Resit Assessments

Exam

Assessment Type Summative Weighting 100
Assessment Weeks Feedback Weeks

Look up Week Numbers

Feedback

Best of (resit exam mark) or (resit exam mark with carried forward CA marks)

Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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