MSc Advanced Computational Mathematics
ApplyKey facts
- Start date: September
- Application deadline: September
- Study mode and duration: on campus, 12 months full-time
Study with us
- designed for students with a strong background in mathematics, computational science, or numerical methods
- develop expertise in computational methods, algorithm development, machine learning theory and numerical methods
- gain computational skills that are highly sought after in finance, engineering and data-driven industries
Why this course?
Our MSc Advanced Computational Mathematics is an advanced course, offering the opportunity to develop understanding of computational mathematics and numerical analysis, enabling students to model complex real-world problems. The course combines theoretical foundations with practical computing skills, making students highly employable in finance, technology and scientific computing.
You will have the opportunity to gain skills in:
- computation and algorithmic techniques
- machine learning
- development and implementation of numerical methods
- working in an interdisciplinary framework
- problem solving
- effective communication
What you’ll study
In addition to compulsory modules, there are a range of elective modules, meaning you can tailor the course in line with your career interests.
Semester 1
In Semester 1, modules will focus on a strong foundation in computational techniques, including finite element methods for boundary value problems and machine learning mathematics. These modules will equip you with the theoretical and practical skills needed for advanced numerical computing.
Semester 2
In Semester 2, the focus shifts to numerical methods and deep learning for partial differential equations, expanding your understanding of algorithmic approaches to complex mathematical problems.
Throughout both of these semesters, you will also have the opportunity to choose from a selection of optional modules, allowing you to tailor the course to your interests in areas such as optimisation, big data, and financial mathematics.
Semester 3
Semester 3 is dedicated to a research project, where you will apply your computational mathematics skills to tackle a real-world problem. This project is an excellent opportunity to develop your independent research abilities and engage with industrial or academic applications.
Learning & teaching
Classes are delivered by a number of teaching methods:
- lectures (using a variety of media including electronic presentations and computer demonstrations)
- tutorials
- computer laboratories
- coursework
- projects
Teaching is student-focused, with students encouraged to take responsibility for their own learning and development. Classes are supported by web-based materials.
Assessment
The form of assessment varies from class to class. For most classes the assessment involves both coursework and practical computer-based or written examinations.
- The assessment will ask you to demonstrate your computational and mathematical knowledge to model and analyse a suitable situation and to interpret the results in the context of the research question
- Projects will involve writing code, interpreting outputs, and producing a report, interactive visualisation or presentation outlining the findings from your analysis
- Group work may be undertaken in some classes
- There is also a graded research dissertation
Facilities
The Department of Mathematics & Statistics has teaching rooms which provide you with access to modern teaching equipment and University computing laboratories, with all necessary software available.
You'll also have access to a common room facility which gives you a modern and flexible area for individual and group study work and is also a relaxing social space.
The Department of Mathematics & Statistics
At the heart of the Department of Mathematics & Statistics is the University’s aim of developing useful learning. We're an applied department with many links to industry and government. Most of the academic staff teaching on this course hold joint-appointments with, or are funded by, other organisations, including APHA, Public Health and Intelligence (Health Protection Scotland), NHS Greater Glasgow and Clyde and the Marine Alliance for Science and Technology Scotland (MASTS). We bridge the gap between academia and real-life. Our research has societal impact.
Though the programme involves all staff in the Mathematics and Statistics department, it is primarily led by three level-2 Research Groups, namely Numerical Analysis, Continuum Mechanics & Industrial Mathematics, and Data Science & Learning Algorithms.
Course content
Throughout your studies, you will take 60 credits of compulsory taught modules, 60 credits of elective taught modules, and in the third (summer) term you'll also undertake your MSc Project (60 credits)
Compulsory modules
Finite Element Methods for Boundary Value Problems & Approximation
20 credits
This module introduces the mathematical foundations of approximation, interpolation, and the finite element method (FEM) for solving boundary value problems. You will explore:
- approximation in normed vector spaces, orthogonal bases, and best approximation
- interpolation techniques, including Lagrange polynomials and finite element interpolation
- error analysis for approximation, interpolation, and finite elements
- quadrature formulas for numerical integration
- the Galerkin finite element method, weak formulation, and convergence analysis
- extension to two-dimensional problems, including triangulations and basis functions
Elective modules
Modelling & Simulation with Applications to Financial Derivatives
20 credits
This module introduces mathematical modelling and computational techniques used in financial derivatives pricing and risk assessment. You will explore:
- fundamental tools for discrete and continuous-time modelling, including ODEs, PDEs, and stability analysis
- finite difference methods for solving PDEs, including Crank-Nicolson schemes
- probability theory and stochastic processes, including birth-death processes and Monte Carlo methods
- introduction to financial derivatives, including European and exotic options
- stochastic calculus, Brownian motion, and the Black-Scholes model
- computational methods for pricing options, including Monte Carlo simulation and binomial trees
Applicable Analysis 3
20 credits
This module explores advanced topics in functional analysis, focusing on operator theory and its applications to integral and differential equations. You will study:
- continuous linear operators on normed vector spaces, including operator norms and eigenvalue-type equations
- key theorems in functional analysis, such as the Open Mapping Theorem and Uniform Boundedness Principle
- dual spaces, the Hahn–Banach Theorem, and weak convergence in Banach spaces
- linear operators on Hilbert spaces, including adjoint, self-adjoint, and normal operators
- spectral theory and compact operators, including the Fredholm Alternative
- applications to integral equations, differential operators, and Green’s functions
Optimisation: Theory
10 credits
This module provides a rigorous foundation in the mathematical theory of optimisation, covering key theoretical results and techniques for constrained and unconstrained problems. You'll explore:
- fundamentals of variational calculus and optimisation principles
- necessary and sufficient conditions for extrema, including Euler-Lagrange equations
- constrained optimisation using Lagrange multipliers
- analytical methods for solving optimisation problems
Big Data Fundamentals
10 credits
This module will introduce the challenges of analysing big data with specific focus on the algorithms and techniques which are embodied in data analytics solutions.
At the end of the module, you'll understand:
- the fundamentals of Python for use in big data technologies
- how classical statistical techniques are applied in modern data analysis
- the limitations of various data analysis tools in a variety of contexts
Big Data Tools & Techniques
10 credits
This module will enhance your understanding of the challenges posed by the advent of Big Data and will introduce you to scalable solutions for data storage and usage.
You can expect to learn about:
- the design and implementation of cloud NoSQL systems
- addressing design trade-offs and their impact
- the Map-Reduce programming paradigm
Legal, Ethical and Professional Issues for the Information Society
10 credits
This module examines the legal, ethical, and professional responsibilities of IT professionals in modern society. You will explore:
- professional competence, codes of practice, and ethical responsibilities
- the role of professional bodies and continuing professional development
- the impact of ICT on society, including cybercrime and digital evidence
- key legal frameworks, including intellectual property law, data protection, and computer misuse legislation
- business practices, change management, and professional duties to clients, employers, and the public
Data Analytics in R
20 credits
This module will introduce the R computing environment and enable you to import data and perform statistical tests. The module will then focus on the understanding of the least squares multiple regression model, general linear model, transformations and variable selection procedures.
You can expect to cover concepts such as:
- use of functions and packages in R
- use of the tidyverse for data manipulation
- data visualisation using both base R and ggplot2
- multiple linear regression
- using variable selection techniques to cope with large data sets
- more general model comparison
Foundations of Statistics
10 credits
This module will provide the basic tools in statistical data analysis and the underlying theory. The module will enable you to:
- understand fundamentals of probability and distributions
- learn appropriate visualisations and summaries for different data types
- undertake appropriate statistical tests for different types of data, including producing confidence intervals
Compulsory modules
Numerical Methods & Deep Learning Algorithms for Partial Differential Equation
20 credits
This module provides advanced numerical techniques for solving differential equations, including stochastic, partial, and ordinary differential equations, with applications in finance, biology, and electromagnetism. You'll explore:
- simulating stochastic differential equations (SDEs), including Monte Carlo methods and stability analysis
- finite difference methods for PDEs, focusing on parabolic and hyperbolic equations
- computational methods for electromagnetic wave propagation, including Maxwell’s equations and finite difference schemes
- optimisation techniques, including steepest descent and Newton’s method
- subspace methods in numerical linear algebra, including Krylov methods and eigenvalue computations
- advanced numerical analysis of ordinary differential equations (ODEs), including Runge-Kutta methods and stability considerations
Elective modules
Mathematical Introduction to Networks
20 credits
This module demonstrates the central role network theory plays in mathematical modelling.
Topics include:
- the connection between linear algebra and graph theory
- the use of theory as a tool for revealing structure in networks
- application of algorithms on a network using programming
Optimisation for Analytics
10 credits
This module introduces key mathematical techniques for optimisation, with applications in analytics and decision-making. You'll explore:
- the distinction between local and global optimisation problems
- methods for unconstrained optimisation, including gradient-based and Newton-type methods
- techniques for constrained optimisation, including penalty methods and relaxation techniques
- theoretical foundations of constrained optimisation, including Kuhn-Tucker conditions and Lagrangian methods
- introduction to variational principles and functional differentiation, with applications to optimisation problems
Medical Statistics
20 credits
This module will cover the fundamental statistical methods necessary for the application of classical statistical methods to data collected for healthcare research. There will be an emphasis on the use of real data and the interpretation of statistical analyses in the context of the research hypothesis under investigation.
Topics covered include:
- survival analysis
- analysing categorical data using hypothesis tests
- experimental Design and sampling
- clinical measurement
Quantitative Risk Analysis
10 credits
This module will cover the theory of assessing risks under uncertainty. It will focus on the practical assessment of risk using simulation methods such as Monte Carlo simulation. You'll develop skills in communicating risk to risk managers as well as formulating practical risk questions that can influence policy decisions.
You can expect to learn about:
- uncertainty and variability
- bootstrapping
- Monte Carlo Simulation
- selecting appropriate probability distributions based on given scenarios
Bayesian Spatial Statistics
10 credits
This module will introduce you to Bayesian statistics and the modern Bayesian methods that are used in a variety of applications. Like with other modules, the focus is on real-life data and using statistical software packages for analysis.
You will gain experience in working with the following:
- visualising spatial data
- geospatial data, including methods for prediction
- bayesian modelling using software to implement Markov Chain Monte Carlo
- areal unit modelling
Statistical Machine Learning
10 credits
This module provides you with the basic theories of machine learning and how to construct a machine model for a real dataset using R. You will also understand the ethical issues regarding data processing and management.
On completion of this module, you will be able to:
- clean data using RStudio and the tidyverse
- understand missing data and the role it plays
- understand ethical issues regarding data processing and management
- carry out single-value imputation
- carry out multiple imputed chained equations in R
- understand and implement artificial neural networks
- understand and implement support vector machines
- understand and implement tree-based classification and regression techniques
- understand and implement ensemble methods
Data dashboards with RShiny
10 credits
This module will develop your skills in data presentation and statistical communication. You will learn to develop data dashboards, which are increasingly used to allow key stakeholders (and the public) to gain key insights into data via interactive visualisation.
Topics covered will include:
- Creating a data dashboard in RStudio
- User interface design with respect to accessibility
- Creating interactive data visualisations which reflect a specific aim
- Reactive programming in RStudio
- Static programming in R
Deep Learning
10 credits
This module introduces deep Learning prediction algorithms covering background theory and practical application in Python.
Topics covered include:
- activation functions
- gradient descent, backpropagation and optimisation
- convolutional Neural Networks
- recurrent Neural Networks
- generative Adversarial Networks
Compulsory module
Mathematics of Machine Learning
20 credits
This module will enable you to develop a more fundamental understanding of the mathematics of machine learning and of the ideas underpinning some classical algorithms in the field.
Following this module you'll be able to:
- critically interpret new algorithms in machine learning
- understand convergence and properties of the computed solution
- work on real world problems using machine learning techniques
Compulsory module
Research project
60 credits
You will undertake a research project, applying computational mathematics to a real-world challenge. You may work on many different areas including numerical simulations, deep learning applications, or optimisation problems. Working with academic or industry partners is possible.
Entry requirements
| Academic requirements/experience | Minimum second-class (2:2) Honours degree or overseas equivalent* in mathematics, computer science or a closely related discipline Prospective students with relevant experience or appropriate professional qualifications are also welcome to apply. *For Australia and Canada, normal degrees are accepted. |
|---|---|
| English language requirements | You must have an English language minimum score of IELTS 6.0 (with no component below 5.5). We offer comprehensive English language courses for students whose IELTS scores are below 6.0. Please see ELTD for full details. As a university, we now accept many more English language tests in addition to IELTS for overseas applicants, for example, TOEFL and PTE Cambridge. View the full list of accepted English language tests here. |
Pre-Masters preparation course
The Pre-Masters Programme is a preparation course held at the University of Strathclyde International Study Centre, for international students (non-UK/Ireland) who do not meet the academic entry requirements for a Masters degree at University of Strathclyde.
Upon successful completion, you'll be able to progress to this degree course at the University of Strathclyde.
International students
We've a thriving international community with students coming here to study from over 140 countries across the world. Find out all you need to know about studying in Glasgow at Strathclyde and hear from students about their experiences.
Fees & funding
Fees may be subject to updates to maintain accuracy. Tuition fees will be notified in your offer letter.
All fees are in £ sterling, unless otherwise stated, and may be subject to revision.
Annual revision of fees
Students on programmes of study of more than one year (or studying standalone modules) should be aware that the majority of fees will increase annually. The University will take a range of factors into account, including, but not limited to, UK inflation, changes in delivery costs and changes in Scottish and/or UK Government funding. Changes in fees will be published on the University website in October each year for the following year of study and any annual increase will be capped at a maximum of 10% per year.
| Scotland | £11,900 |
|---|---|
| England, Wales & Northern Ireland | £11,900 |
| Republic of Ireland |
If you are an Irish citizen and have been ordinary resident in the Republic of Ireland for the three years prior to the relevant date, and will be coming to Scotland for Educational purposes only, you will meet the criteria of England, Wales & Northern Ireland fee status. For more information and advice on tuition fee status, you can visit the UKCISA - International student advice and guidance - Scotland: fee status webpage. Find out more about the University of Strathclyde's fee assessments process. |
| International | £25,500 |
| Additional costs | If you are an international student, you may have associated visa and immigration costs. For more information, please see student visa guidance. |
| Available scholarships | Take a look at our scholarships search for funding opportunities. |
Please note: the fees shown are annual and may be subject to an increase each year. Find out more about fees.
How can I fund my course?
Scottish postgraduate students
Scottish postgraduate students may be able to apply for support from the Student Awards Agency Scotland (SAAS). The support is in the form of a tuition fee loan and for eligible students, a living cost loan. Find out more about the support and how to apply.
Don’t forget to check our scholarship search for more help with fees and funding.
Students coming from England
Students ordinarily resident in England may be to apply for postgraduate support from Student Finance England. The support is a loan of up to £10,280 which can be used for both tuition fees and living costs. Find out more about the support and how to apply.
Don’t forget to check our scholarship search for more help with fees and funding.
Students coming from Wales
Students ordinarily resident in Wales may be to apply for postgraduate support from Student Finance Wales. The support is a loan of up to £10,280 which can be used for both tuition fees and living costs. Find out more about the support and how to apply.
Don’t forget to check our scholarship search for more help with fees and funding.
Students coming from Northern Ireland
Postgraduate students who are ordinarily resident in Northern Ireland may be able to apply for support from Student Finance Northern Ireland. The support is a tuition fee loan of up to £5,500. Find out more about the support and how to apply.
Don’t forget to check our scholarship search for more help with fees and funding.
International students
We've a large range of scholarships available to help you fund your studies. Check our scholarship search for more help with fees and funding.
Careers
Studying a postgraduate programme in maths and computing helps you further develop skills in logical thinking and statistical or strategic knowledge, which are valued by employers across many job sectors. Our mathematics graduates enter industries such as aerospace and software engineering, manufacturing, the actuarial, accountancy and banking professions, commerce and government, consultancy and education.
Many go on to work as financial analysts, software developers, accountants, operations analysts, treasury analysts, auditors and management trainees.
A masters degree in mathematics and computing is desirable to a wide range of employers who recruit from any degree subject. It is also useful for those considering a more general business career.
Glasgow is Scotland's biggest & most cosmopolitan city
Our campus is based right in the very heart of Glasgow. We're in the city centre, next to the Merchant City, both of which are great locations for sightseeing, shopping and socialising alongside your studies.
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Start date: Sep 2025
Advanced Computational Mathematics
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