| 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 |
| Units you must take before you take this one (pre-requisite units) |
MATH10015 Linear Algebra MATH10010 Introduction to Proofs and Group Theory is helpful (students will benefit from some familiarity with groups and functions) but not required |
| Units you must take alongside this one (co-requisite units) |
None |
| Units you may not take alongside this one |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Lecturers: Jeremy Rickard and Charles Cox
Unit Aims
Algebra encompasses a wide range of topics and areas of research. This course focuses on Linear Algebra, which mostly concerns itself with vector spaces and the (linear) maps between them.
Unit Description
We begin by recapping the key notions from Linear Algebra 1, by using the example of the vector space of real polynomial functions. This example is used throughout the course to introduce various topics, including the dual of a vector space and the notion of a quotient space. The space of polynomial functions is an infinite dimensional vector space, meaning that we cannot find a finite basis for it. Linear Algebra 1 looked at when a linear operator on a finite dimensional vector space (such as R^3, i.e. 3 dimensional real space) was diagonalisable. In Linear Algebra 2 we complete this theory, by showing that linear maps that are not diagonalisable still fit into a general form, called "Jordan normal form". This form can always be computed, but we will cover some shortcuts for doing this. We will also see how to compute the Smith normal form of an integer matrix, and will use this to obtaing the classification of finitely-generated abelian groups. We will apply this theory in various ways: e.g., to decide how many abelian groups there are of a given order.
Relation to Other Units
This unit fits well with other pure mathematics units, covering fundamental objects, interesting examples, and some key theorems.
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 plus 10% Coursework (10x 1% individually marked courseworks)
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.
