| Unit name | Matrix Algebra and Linear Models |
|---|---|
| Unit code | MATH10016 |
| Credit points | 20 |
| Level of study | C/4 |
| Teaching block(s) |
Teaching Block 4 (weeks 1-24) |
| Unit director | Dr. Donald |
| Open unit status | Not open |
| Units you must take before you take this one (pre-requisite units) |
None |
| 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 |
Why is the unit important?
The tools of matrix and linear algebra are vitally important throughout mathematics. Many complex problems may be expressed or approximated using linear models and the methods developed in this course can be used to solve them. By building a rigorous understanding of how to manipulate matrices and their properties, students will also develop intuition about the shapes of solutions. Many of the techniques in matrix algebra have a geometric interpretation in small dimensions but much of the power of these techniques comes from their scalability. Methods in this unit extend naturally to much more complicated and higher-dimensional versions of these problems. As a result, the unit will also include implementing these techniques numerically on computers, formulating practical problems in ways that are amenable to these techniques and discuss the numerical and computation considerations needed to make informed choices about such implementations.
How does this unit fit into your programme of study?
This methods for solving linear problems will be useful throughout the programme. In parallel units, students will see techniques from calculus to approximate non-linear problems by linear ones, which can be approached using the methods from this unit. Subsequent courses will build on the fundamental techniques introduced in this one. In the Data Science programme, more advanced linear models will draw on this framework to analyse datasets. In joint honours programmes, students will see applications of material in this unit whenever modelling problems require consideration of many variables.
An overview of content
In this unit, students will learn about manipulation of matrices and their properties (multiplication, determinants, inverses); how to link matrices to linear mapping; multiple ways to solve systems of linear equations; how to work with, calculate and interpret eigenvalues and eigenvectors; using inner products and orthogonality; how to select appropriate methods based on consideration of numerical complexity; algorithms to implement many of the above techniques in a standard programming language (such as Python); how to formulate practical problems in terms of these methods and how to interpret the result.
How will students, personally, be different as a result of the unit
Students will have gained geometric insights into small-dimensional matrix problems and have seen how (and where) to extend these to more complicated and higher-dimensional settings. They will gain fluency in working with matrices and, through this, begin to develop insight into the use of algorithms for calculations and how to use knowledge about numerical complexity to inform choices of appropriate methods for practical problems.
Learning Outcomes
The unit will be taught through a combination of face-to-face lectures, asynchronous independent activities such as problem sheets and other exercises (where students will practice and consolidate their understanding), synchronous weekly group tutorials (where students will receive feedback on formative and summative coursework), interactive computer-based labs (where students will be guided through computational parts of the course) and weekly office hours.
Tasks which help you learn and prepare you for summative tasks (formative)
There will be regular problem sheets (approx.. fortnightly) and students will hand in formative work to be marked by tutors for feedback on their understanding and presentation of material. These tasks will have a similar form to assessed coursework and examination questions, allowing students to act upon this feedback for summative tasks.
Task which count towards your unit mark (summative)
When assessment does not go to plan
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. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.
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. MATH10016).
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 University Workload statement relating to this unit for more information.
Assessment
The assessment methods listed in this unit specification are designed to enable students to demonstrate the named learning outcomes (LOs). Where a disability prevents a student from undertaking a specific method of assessment, schools will make reasonable adjustments to support a student to demonstrate the LO by an alternative method or with additional resources.
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. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
