Machine Learning Technology to Improve Symbolic Integration and Simplification in a Leading Computer Algebra System

Machine Learning Technology to Improve Symbolic Integration and Simplification in a Leading Computer Algebra System

Eligibility: UK/EU/International graduates with the required entry requirements

Funding details: Bursary plus tuition fees (UK/EU/International)

Duration: Full-time – between three and three and a half years fixed term

Application deadline: 26th April 2021

Interview dates: Interviews will take place via video call in the middle of May.  Details will be confirmed to shortlisted candidates at least one week before.

Start date: September 2021 

For queries please contact Dr Matthew England


Coventry University is inviting applications from suitably qualified graduates for a fully funded PhD studentship. 

Sponsored by the software company Maplesoft, the successful candidate will work on a new project to embed machine learning technology within some of the core symbolic routines of Maplesoft’s flagship product, the Maple computer algebra system.  The aim is to optimise the performance of the system without any risk to the exact symbolic correctness which is central to computer algebra. 

About the project

Machine Learning (ML) refers to artificial intelligence techniques that employ a combination of statistics and big data to solve problems.  A Computer Algebra Systems (CAS) is a piece of software that performs symbolic mathematical computations with exact precision, as a human mathematician would by hand. 

This project seeks to improve the performance of routines in Maple, a leading CAS, using ML technology.  It may seem that the probabilistic nature of ML would invalidate the exact results prized by a CAS.  However, many CAS algorithms come with choices which have no effect on the mathematical correctness of the output, but greatly affect its presentation and the resources required to find it.  Such choices are prime candidates for ML. 

The particular focuses of the project are the symbolic integration and symbolic simplification routines in Maple: two commands widely used by both users and other parts of Maple.  Successful application here would in-turn impact on the wide range of engineering and scientific applications which users tackle with Maple every day. 

The project is hosted by the Coventry University Research Centre for Data Science, which is the university’s hub for cutting edge research in the areas of Artificial Intelligence, Data Science and Future Computing Technologies. The project is co-sponsored by the software company Maplesoft who develop Maple.  The successful candidate will interact not only with academics, but also the company’s engineers to ensure the speedy impact of their research in a product used globally in both academia and industry.


Fully funded single studentship, which includes tuition fees and living expenses for a doctoral candidate over 3.5 years.

Stipend rates will be equivalent to those set by UKRI and will rise annually with a projected average increase of 1.25% per year. Coventry University fees are adjusted yearly in line with the rates set by UKRI.


The successful candidate will receive comprehensive research training including technical, personal and professional skills. All researchers at Coventry University (from PhD to Professor) are part of the Doctoral College and Centre for Research Capability and Development, which provides support with high-quality training and career development activities. 

Students have access to training on data science and computational intelligence techniques from the Research Centre for Data Science.  In particular, PhD candidates can undertake relevant postgraduate modules from the university portfolio at no extra cost.  The successful candidate will also receive training from Maplesoft employees on the professional coding standards of their products.  The project has funding to facilitate travel between Coventry and Maplesoft’s sites.

Candidate specification

  • A minimum of a 2:1 first degree in a relevant discipline/subject area with a minimum 60% mark in the project element or equivalent with a minimum 60% overall module average. 
    the potential to engage in innovative research and to complete the PhD within a 3.5 years
  • a minimum of English language proficiency (IELTS overall minimum score of 7.0 with a minimum of 6.5 in each component)
In addition

We expect candidates for this position to have previously studied at degree level either Computer Science / Data Science or Mathematics.

  • If Computer Science then applicants should take care to emphasise their prior mathematical education in their supporting statement.
  • If Mathematics then applications should take to emphasise their prior programming and software development skills in their supporting statement.

How to apply

All applications require full supporting documentation, and a supporting statement.  The supporting statement should be a maximum of 2000 words and should address the following three topics:

  • The applicant’s understanding of the project topic.
  • How it compares to any similar research projects found in the literature.
  • How their personal expertise and interests are relevant to the project. In particular, include details of prior mathematics education, programming skills, and data science experience.
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