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Curricular information is subject to change
On completion of this module, the student is expected to:- demonstrate an understanding of the theoretical aspects covered in this module;- be able to carry out any computations involving the objects described in this module (such as finding the orbits of a group action, finding the Smith normal form of a matrix, decomposing a module into invariant factors, reducing a matrix to Jordan canonical form, for example).
Indicative Module Content:Review of the first, second and third isomorphism theorems for groups and rings. Subgroups generated by a subset, generators and relations. Group actions, orbit-stabilizer theorem, Burnside’s lemma. Sylow theorems, other examples and applications. Linear groups.
Ideals and subrings generated by subsets, review of principal ideal domains, unique factorization domains, Euclidean domains. The Chinese Remainder Theorem. Matrices over EDs and PIDs, the Smith normal form. Modules, free modules and torsion modules. Finitely generated modules over a PID, and the structure theorem. Applications including the classification of finite abelian groups, Jordan canonical form, rational canonical form.
| Student Effort Type | Hours |
|---|---|
| Lectures | 24 |
| Tutorial | 6 |
| Specified Learning Activities | 36 |
| Autonomous Student Learning | 34 |
| Total | 100 |
Not applicable to this module.
| Description | Timing | Component Scale | % of Final Grade | ||
|---|---|---|---|---|---|
| Examination: Take-home exam (6-hours-long), to be scheduled on Week 13 | Coursework (End of Trimester) | Yes | Standard conversion grade scale 40% | No | 60 |
| Assignment: Each assignment submission will receive 0.7 marks towards final grade. | Throughout the Trimester | n/a | Standard conversion grade scale 40% | No | 5 |
| Examination: Midterm Exam 1 | Week 6 | Yes | Standard conversion grade scale 40% | No | 20 |
| Examination: Midterm Exam 2 | Week 10 | Yes | Standard conversion grade scale 40% | No | 15 |
| Resit In | Terminal Exam |
|---|---|
| Autumn | Yes - 2 Hour |
• Group/class feedback, post-assessment
Not yet recorded.
| Name | Role |
|---|---|
| Firtina Kucuk | Tutor |
| Mr Peter Neamti | Tutor |
| Lecture | Offering 1 | Week(s) - 20, 21, 22, 23, 24, 25, 26, 30, 31, 32, 33 | Thurs 11:00 - 11:50 |
| Lecture | Offering 1 | Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 | Tues 11:00 - 11:50 |
| Lecture | Offering 1 | Week(s) - 29 | Tues 14:00 - 14:50 |
| Lecture | Offering 1 | Week(s) - 30 | Tues 14:00 - 14:50 |
| Lecture | Offering 1 | Week(s) - 32 | Tues 14:00 - 14:50 |
| Tutorial | Offering 1 | Week(s) - 29 | Thurs 11:00 - 11:50 |
| Tutorial | Offering 1 | Week(s) - 22, 24, 26, 31, 33 | Tues 14:00 - 14:50 |