Unit name | Linear Algebra 2 |
---|---|
Unit code | MATH21100 |
Credit points | 20 |
Level of study | I/5 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Professor. Rickard |
Open unit status | Not open |
Pre-requisites |
MATH10015 Linear Algebra |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Unit Aims
This unit further develops the theory of vector spaces over arbitrary fields and linear maps between them. Topics include quotient spaces, dual spaces, determinants, and canonical forms of linear maps. The unit also introduces bilinear and quadratic forms, and touches on linear algebra over the ring of integers.
Unit Description
Lecturers: Jeremy Rickard and Charles Cox
This unit continues the study of vector spaces over arbitrary fields begun in level C/4. Emphasis is on building insight into the concepts and reasoning clearly from basic definitions. Much of the unit is devoted to formulation and proof of the key results. The tools developed are essential in a variety of areas, both pure and applied, such as geometry, differential equations, group theory and functional analysis.
A major goal is to show that any linear operator on a vector space, even if it is not diagonalisable, has a certain canonical form, the "Jordan normal form". Another aim is to generalise inner products by defining and investigating bilinear and quadratic "forms" on vector spaces. There is also an introduction to linear algebra over the ring of integers, including the classification of finitely-generated abelian groups.
Relation to Other Units
This unit develops the linear algebra material from first year Linear Algebra and Geometry, giving a general and abstract treatment, using central algebraic structures, such as groups, rings, and fields. This material is an essential part of Pure Mathematics; it is a prerequisite for Representation Theory, and is relevant to other Pure Mathematics units at levels 3 and 4, particularly Functional Analysis.
Learning Objectives
Students will deepen their understanding of vector spaces and the natural maps between them. They will be able to state, use and prove fundamental results in linear algebra.
Transferable Skills
Assimilation of abstract ideas. Reasoning in an abstract context. Setting out a sustained argument in a form comprehensible to others.
The unit will be taught through a combination of
90% Timed, open-book examination 10% Coursework
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATH21100).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the Faculty workload statement relating to this unit for more information.
Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an
assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.