Structured PhD (Arts, Humanities, and Social Sciences) (Mathematics)

College of Arts, Social Sciences, & Celtic Studies,

Course overview

Download Structured PhD guidelines (PDF file) here.


The research activity in Mathematics at NUI Galway covers a broad range of  topics spanning Algebra, Analysis, Geometry and Topology. There is a particular strength in Computational Algebra, which has led to the establishment of de Brún Centre, whose mission is to support research in broad areas of algebra and its applications.

The various research groups within the discipline of Mathematics host a wide range of workshops, seminars and graduate courses, resulting in a unique and thriving graduate research programme with a strong international dimension.

Recent graduates are working as (a) lecturers and postdoctoral researcher at third-level institutes, (b) in industry, including banking and finance, and (c) in   the Meteorological Service.

As part of the doctoral training available on the Structured PhD programme, students avail themselves of a range of taught modules.  The wide menu of available options include:

  • graduate-level courses in Mathematics covering topics such as Advanced Algebra and Analysis, Geometry, Topology/Set Theory and Computational Mathematics;

  • modules in Statistics, Bioinformatics and Applied Mathematics available from the cognate disciplines within the School of Maths;

  • a wide range of interdisciplinary modules from other schools in the College of Arts, Humanities and Social Sciences;

  • modules on core skills such as research methods, computing, communications, and languages;

  • modules acknowledging a student’s professional development, including presentation of posters and paper at an International Conference

  • modules to enhance a student’s employability through generic training e.g. Careers' Workshops, computing skills, etc.

Each student will be assigned a primary Supervisor(s) and a Graduate Research Committee made up of experienced researchers to plan their programme of study and to provide on-going support to their research.

Programmes available

Structured PhD (Mathematics)—full-time
Structured PhD (Mathematics)—part-time

Entry requirements

Candidates for the degree of PhD or MSc by research must have reached a high honours standard (minimum H2.2 [or equivalent international qualification] for an MSc) at the examination for the primary degree, or presented such other evidence as will satisfy the Head of School and the College of his/her fitness.

Areas of interest

Group theory including group varieties, representation theory of finite groups, associative and non-associative rings, and group rings, coding theory and cryptography.
Computational algebra including computational homological algebra, computational group theory, computational representation theory.


Linear and Multilinear Algebra


Finite Field Theory


Analysis and Numerical Analysis:
Functional analysis, in particular tensor products, multilinear forms, polynomials and holomorphic functions on Banach spaces.
Non-linear analysis, including differential and integral equations, and fixed point theory.
Numerical analysis and computational differential equations.


Geometry and Topology:
Differential geometry and the geometry and topology of Lie groups and homogeneous spaces
Analytic topology and order.


Mathematics Education

Find out more

Ms Mary Kelly
School of Mathematics, Statistics, and Applied Mathematics

PAC code

GYG23 full-time
GYG55 part-time

Current project

Topological data analysis, with applications to medical imaging.

The mathematics of finite fields, with applications to combinatorics and communications.

An exploration of the experiences and approaches of students as they engage with the themes of abstract and theoretical mathematics at university, in particular mathematical proof.

Fees for this course

EU: €4,275 p.a. 2016/17

Non-EU: €13,250 p.a. 2016/17

What Our Students Say


Pádraig Ó Catháin |   Computational Algebra

I love being a PhD student in Maths. It's given me the skills to analyse complex problems and uncover unexpected links between different topics. I also know that I am being prepared for either a career in academia or industry.