Learning Outcomes:
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.
Curricular information is subject to change.
In this module we introduce and develop some of the more advanced ideas in Linear Algebra. A sample of topics covered are:
Inner product spaces, bilinear forms, dual spaces, transpose and adjoint, Gram-Schmidt process. Quotient spaces. Multilinear algebra, tensor products of vector spaces, symmetric and alternating group, determinants. Endomorphisms, minimal polynomials, Cayley-Hamilton theorem. Invariant subspaces. Companion matrices, Vandermonde matrices, circulant matrices.
Inner product spaces, bilinear forms, dual spaces, transpose and adjoint, Gram-Schmidt process. Quotient spaces. Multilinear algebra, tensor products of vector spaces, symmetric and alternating group, determinants. Endomorphisms, minimal polynomials, Cayley-Hamilton theorem. Invariant subspaces. Companion matrices, Vandermonde matrices, circulant matrices.
About this Module
Student Effort Hours:
| Student Effort Type | Hours |
|---|---|
| Lectures | 18 |
| Tutorial | 6 |
| Specified Learning Activities | 36 |
| Autonomous Student Learning | 40 |
| Total | 100 |
Approaches to Teaching and Learning:
Problem-based learning via lectures, tutorials, assignments and a final exam.Requirements, Exclusions and Recommendations
Not applicable to this module.
Module Requisites and Incompatibles
Not applicable to this module.Assessment Strategy
| Description | Timing | Component Scale | % of Final Grade | ||
|---|---|---|---|---|---|
| Participation in Learning Activities: Participation during tutorial classes. | Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11 | Graded | No | 10 |
No |
| Assignment(Including Essay): Two homework assignments. | Week 7, Week 12 | Graded | No | 30 |
No |
| Exam (In-person): Final exam | End of trimester Duration: 2 hr(s) |
Standard conversion grade scale 40% | No | 60 |
No |
| Resit In | Terminal Exam |
|---|---|
| Spring | Yes - 2 Hour |
Feedback Strategy/Strategies
• Group/class feedback, post-assessment
How will my Feedback be Delivered?
Not yet recorded.
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
| Autumn | Lecture | Offering 1 | Week(s) - Autumn: All Weeks | Tues 10:00 - 10:50 |
| Autumn | Tutorial | Offering 1 | Week(s) - Autumn: All Weeks | Tues 12:00 - 12:50 |
| Autumn | Lecture | Offering 1 | Week(s) - Autumn: All Weeks | Wed 11:00 - 11:50 |