MA398-15 Matrix Analysis & Algorithms
Introductory description
Many large scale problems arising in data analysis and scientific computing require efficient solutions to systems of
linear equations, least-squares problems, and eigenvalue problems. The module is based around understanding the
mathematical principles underlying the design and the analysis of effective methods and algorithms to solve these
types of challenges. It involves an interplay between mathematical analysis and computing, including programming
aspects, validation and result analysis.
Module aims
Understanding how to construct algorithms for solving problems central in numerical linear algebra and how to
analyse them with respect to accuracy and computational cost. Selecting, evaluating and characterising findings when
applying both analytical and numerical methods to practical problems of interest.
Outline syllabus
This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.
Many large scale problems arising in data analysis and scientific computing require efficient solutions to systems of
linear equations, least-squares problems, and eigenvalue problems. The module is based around understanding the
mathematical principles underlying the design and the analysis of effective methods and algorithms to solve these
types of challenges. Key concepts include matrix decompositions, factorisations, direct and iterative system solvers.
They are supported by fundamental aspects related to floating point arithmetic, computational cost analysis, stability
and convergence, with examples such as image compression and operating in data-rich environments. Incursions into
ideas from high performance computing will also feed into the material in order to inform about modern software
engineering practices in academia and beyond. This module is suitable for students in joint degrees with Mathematics, as well as associated departments such as (but not limited to) Computer Science, Physics and Statistics.
Learning outcomes
By the end of the module, students should be able to:
- explain concepts and ideas related to matrix factorisations as the theoretical basis for algorithms,
- assess algorithms with respect to computational cost, conditioning of problems and stability of algorithms,
- demonstrate theoretical concepts using numerical software tools,
- compare different (competing) numerical methodologies and critically evaluate bottlenecks in algorithmic design for real-world applications.
Indicative reading list
Reading lists can be found in Talis
Interdisciplinary
The module sits naturally between mathematics, computer science and elements from related disciplines such as
physics, biology or image processing.
Subject specific skills
Discrete mathematical analysis, algorithmic construction, cost and error analysis, concepts in numerical methods for a
range of applied problems in mathematical sciences.
Transferable skills
Informed problem solving, software development, creative solution analysis, project management, critical thinking, application-oriented solution strategy design, programming language expertise.
Study time
| Type | Required |
|---|---|
| Lectures | 30 sessions of 1 hour (20%) |
| Tutorials | 9 sessions of 1 hour (6%) |
| Private study | 111 hours (74%) |
| Total | 150 hours |
Private study description
Weekly problem sheets comprise both short questions as well as longer assignment-style questions. Feedback on the model answers for both will be provided during the support classes as well as by the lecturer during the delivered material.
Costs
No further costs have been identified for this module.
You must pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group B1
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| Centrally-timetabled examination (On-campus) | 100% | No | |
|
Pen and paper work only, with a combination of theoretical content (theorem proving,
|
|||
Assessment group R1
| Weighting | Study time | Eligible for self-certification | |
|---|---|---|---|
| In-person Examination - Resit | 100% | No | |
|
Pen and paper work only, with a combination of theoretical content (theorem proving,
|
|||
Feedback on assessment
The only assessment is via the final exam; however, the weekly problem sheets can comprise both short questions as well as longer assignment-style questions. Feedback on the model answers for both will be provided during the support classes as well as by the lecturer during the delivered material. There will also be lectures where previous exam questions are worked through with feedback given.
Pre-requisites
MA106 Linear Algebra and (to a lesser extent) MA259 Multivariable Calculus are sufficient in terms of core 1st and
2nd year modules within Mathematics. Helpful but not mandatory is some knowledge of numerical concepts such as
accuracy, iteration processes, and stability as provided in MA228 Numerical Analysis or MA261 Differential Equations:
Modelling and Numerics.
To take this module, you must have passed:
Courses
This module is Optional for:
-
UMAA-G100 Undergraduate Mathematics (BSc)
- Year 3 of G100 Mathematics
- Year 3 of G100 Mathematics
- Year 3 of G100 Mathematics