About the Project
Supervisor: Dr Andersen Ang
This PhD project uses ideas from pure mathematics to create faster and more reliable optimization algorithms for machine learning, engineering and data science. It is especially suited to mathematically trained students who want to move into computational research, even with little programming experience.
The PhD project explores how ideas from pure mathematics can be drawn upon to improve the design, analysis, abstraction and computational efficiency of mathematical optimization algorithms arising in applied mathematics, machine learning and engineering.
The specific mathematical direction is flexible and will be shaped by the student's background and interests. Possible directions include variational analysis and nonsmooth optimization; functional analysis and monotone operator methods; stochastic analysis for uncertainty-aware optimization; PDE techniques for constrained optimization; harmonic analysis for signal and inverse problems; convex and algebraic geometry for optimization and control; discrete topology for graph-based information retrieval; and persistent homology or topological data analysis.
The central emphasis is computational rather than purely theoretical. Pure mathematics is used as a source of structure, abstraction and analytical tools that can lead to faster algorithms, stronger convergence guarantees, improved numerical stability, dimensional reduction, or more efficient representations of optimization problems. The aim is to translate mathematical structure into concrete computational advantage.
This project is suited to students with training in pure mathematics who wish to transition towards applied or computational mathematics related to optimization or machine learning. Prior programming experience is not essential; limited coding experience is acceptable. A strong mathematical background, mathematical maturity, and willingness to engage with computational problems are more important.
Entry requirements
You must have a UK 2:1 honours degree, or its international equivalent, pure mathematics is strongly preferred.
You must have:
- a strong mathematical background
- mathematical maturity
- willingness to engage with computational problems
Prior programming experience is not essential.
Limited coding experience is acceptable.
Fees and funding
We offer a range of funding opportunities for both UK and international students. Horizon Europe fee waivers automatically cover the difference between overseas and UK fees for qualifying students.
Competition-based Presidential Bursaries from the University cover the difference between overseas and UK fees for top-ranked applicants.
Competition-based studentships offered by our schools typically cover UK-level tuition fees and a stipend for living costs for top-ranked applicants.
Funding will be awarded on a rolling basis, so apply early for the best opportunity to be considered.
For more information, please visit our postgraduate research funding pages.
How to apply
You need to:
- choose programme type (Research), 2027/28, Faculty of Engineering and Physical Sciences
- select Full time or Part time
- search for programme PhD Computer Science (7089)
- add name of the supervisor in section 2 of the application
Applications should include:
- your CV (resumé)
- 2 academic references
- degree transcripts and certificates to date
- English language qualification (if applicable)
Contact us
Faculty of Engineering and Physical Sciences
For questions about applying, doctoralcollege-admissions@soton.ac.uk.
Project leader
For an initial conversation, andersen.ang@soton.ac.uk.