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Curricular information is subject to change
Upon successful completion of this module a student should have the following skills:
1. Solid understanding of the main concepts and results indicated within the contents of this module.
2. The ability to apply counting arguments involving Lagrange's theorem and the class equation to deduce statements on the structure of groups.
3. The ability to compare group (via homomorphisms between them).
4. The ability to use the isomorphism theorems to identify groups.
5. The ability to build combinatorial and arithmetic arguments relying on fundamentals of group theory.
Basics of groups, subgroups, cyclic groups, cosets, Lagrange's theorem, normal subgroups and quotient groups, the centre of a group, homomorphisms, the isomorphism theorems, the subgroup correspondence theorem, group actions, orbits, Cayley's theorem, inner automorphisms, conjugacy, the class equation, Cauchy's theorem and p-groups.
|Student Effort Type||Hours|
|Specified Learning Activities||
|Autonomous Student Learning||
Students should have completed a course in abstract algebra prior to taking this module (for example, MST20010). This course should contain at least an introduction to groups, subgroups, cosets, and permutation groups.
All questions about eligibility (in particular if you think the meet the requirements but have not passed MST20010) should be addressed to the module coordinator.
|Description||Timing||Component Scale||% of Final Grade|
|Examination: Final Exam||2 hour End of Trimester Exam||No||Standard conversion grade scale 40%||No||
|Assignment: 4 homework assignments||Varies over the Trimester||n/a||Standard conversion grade scale 40%||No||
|Examination: Midterm Exam (on Week 8, tentative)||Unspecified||No||Standard conversion grade scale 40%||No||
|Resit In||Terminal Exam|
|Spring||Yes - 2 Hour|
• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
• Self-assessment activities
Self-assessment activities are tentative and will be based on the following model: Students will be asked to grade their own responses to select assignments, based on a detailed solution sheet. They will prepare a detailed report on their weaknesses on key aspects of the module. Based on the accuracy of this report, their homework grades will be positively updated. The other two feedback strategies to employed (Feedback individually to students, post-assessment and Group/class feedback, post-assessment) are self-explanatory.
|Lecture||Offering 1||Week(s) - Autumn: All Weeks||Mon 13:00 - 13:50|
|Tutorial||Offering 1||Week(s) - Autumn: Weeks 2-12||Mon 15:00 - 15:50|
|Lecture||Offering 1||Week(s) - Autumn: All Weeks||Wed 13:00 - 13:50|