Masters/Higher Diploma in Mathematics

The masters in mathematics is a flexible 12-month programme comprising a selection from a breadth of advanced taught courses and a research project. The higher diploma in mathematics is a flexible 9-month programme without a research project. Graduates pursue careers in business, finance, public service, teaching and related fields, and some go on to PhD studies in the mathematical sciences.

The programme content is dynamic and research-led. Each year, a diverse range of courses are given, designed to offer an insight into new and emerging areas of mathematical research.

Mathematics at NUI Galway

The School of Mathematics, Statistics and Applied Mathematics offers a great environment for any student wishing to pursue advanced study in mathematics. We have approximately 30 faculty members across four disciplines: Mathematics, Statistics, Applied Mathematics and Bioinformatics.

We are well recognised within NUI Galway as a very student-friendly School. Several of our members have been formally recognised for their teaching excellence by both NUI Galway and national awards.

Faculty members are internationally recognised researchers. We hold regular seminars in which local and visiting researchers present their latest work and we typically host 2 or 3 international conferences in various mathematical disciplines each year.

Programme Overview

The masters (GYS09) is a 12-month programme comprising 90 ECTS credits. Students take 60 credits of taught modules, with at least 30 credits of M-modules and at most 30 credits of H-modules (see Tables 1&2). Modules are examined in December and April. A 30-credit research project is completed under the guidance of a faculty member and submitted in August. The project is an opportunity to explore a particular topic of interest in greater depth.

The higher diploma (GYS15) is a 9-month programme comprising 60 credits of taught U-modules, H-modules or M-modules (see Tables 1&2).

The modules on offer vary from year to year, but the typical range is indicated in the tables.

  Mathematics   Statistics Applied Mathematics Financial Mathematics Computing ECTS
M Advanced linear
algebra
(MA500-II)
    Mathematics of
finance
(MA500-I)
  10
H Rings (MA416) Applied regression models (ST313) Modelling 1 (MP305) Annuities & life
assurance
(MA311)
Object-oriented
and internet
programming
(CS424)
5
H Measure theory
(MA490)
Applied Statistics 1 (ST311) Electromagnetism (MP366) Actuarial
mathematics &
life contingencies
II (MA495)
Numerical
analysis
(MA385)
5
H Euclidean and
non Euclidean
geometry
(MA3101)
Probability theory and applications (ST415) Partial differential equations (MP494)   Logic (CS3304) 5
H Groups
(MA3343)
        5
H Metric spaces
(MA341)
        5
U Discrete
mathematics
(MA284)
Probability (ST235)     Mathematical
molecular biology
(MA215)
5

Table 1: Typical Semester I modules offered subject to timetable contraints.

  Mathematics   Statistics Applied Mathematics Financial Mathematics Computing ECTS
M Topology
(MA535)
 Topological data
analysis
(MA500-III)
    Advanced
operating
systems (CS428)
5
H Advanced group
theory (MA4344)
Applied Statistics
II (ST312)
Modelling II (MP307) Differential
equations with
financial
derivatives
(MA418)
Numerical
analysis II
(MA378)
5
H Functional
analysis
(MA482)
Statistical
modelling
(ST413)
Fluid mechanics
(MP365)
Networks
(CS4423)
Cryptography
(CS402)
5
H Fields &
applications
(MA3491)
Introduction to
Bayesian
modelling
(ST417)
Cosmology &
general relativity
(MP403)
Actuarial
mathematics
(MA310)
Scientific
computing
(CS319)
5
H     Nonlinear
systems
(MP491)
 

5
U Complex analysis
(MA2287)
Statistical
inference
(ST236)
    Mathematical
molecular biology II
(MA216)
5

Table 2: Typical Semester II modules offered subject to timetable contraints

Why study this programme?

The programmes offer students the opportunity to further their mathematical knowledge to a very advanced level in areas ranging from pure mathematics to financial mathematics and computing.

Employers in all sectors are increasingly seeking out graduates with advanced problem solving and analytical skills. The masters in mathematics affords students the opportunity to hone these skills to an extremely high level. It is also an ideal preparation for a research career in several disciplines.

The higher diploma in mathematics is often used to partially fulfill the entry requirements for the teaching and other professions. There are three reasons for choosing the higher diploma rather than the masters programme: (i) it is more flexible as it includes U-module options and does not require 30 credits of M-modules; (ii) it is of 9-months duration; iii) it does not incorporate project work.

Entry Requirements

Higher diploma students should hold a bachelor's degree involving at least 35 ECTS of appropriate mathematics or applied mathematics modules or equivalent.

Masters students should hold a BA or BSc in a mathematical discipline at upper
second-class honours level or equivalent.

Contact information/Enquiries to:

Professor Graham Ellis
graham.ellis@nuigalway.ie

Some typical module choices

Incoming degreeTypical ChoicesAward
BA Mathematics Semester I: Advanced linear algebra
Mathematics of finance
Measure theory
Rings
Semester II: Topology
Topological data analysis
Differential equations with financial derivatives
Functional analysis
Advanced group theory
Networks
Semester I+II+III: Project
MSc
BA Mathematical Studies Semester I: Advanced linear algebra
Mathematics of finance
Metric spaces
Numerical Analysis
Semester II: Topology
Topological data analysis
Fields & applications
Actuarial mathematics
Cryptography
Networks
Semester I+II+III: Project
MSc
BSc Mathematics Semester I: Advanced linear algebra
Mathematics of finance
Actuarial mathematics & life contingencies
Object-oriented & internet programming
Semester II: Topological data analysis
Advanced operating systems
Differential equations with financial derivatives
Statistical modelling
Introduction to Bayesian modelling
Actuarial mathematics
Semester I+II+III: Project
MSc
BSc CS&IT
or
BEng
(with at least 45
ECTS of
appropriate
maths modules)
Semester I: Advanced linear algebra
Mathematics of finance
Measure theory
Object-oriented & internet programming
Semester II: Topology
Topological data analysis
Advanced operating systems
Differential equations with financial derivatives
Statistical modelling
Scientific computing
Semester I+II+III: Project
MSc
BSc Physics
or
BSc Chemistry
or
BEng
(with at least 35
ECTS of
appropriate
maths modules)
Semester I: Geometry
Groups
Probability
Metric spaces
Numerical analysis I
Logic
Semester II: Topology
Fields & applications
Statistical inference
Complex analysis
Cryptography
Numerical analysis II
HDip
Timetable clashes between modules
modulesincompatible modules
CS402
CS4423
MA215
MA216
MA2287
MA284
MA310
MA3101
MA3491
MA378
MA416
MA4344
MA490
MA495
MA500-1
MA500-2
MA500-3
MP305
MP365
MP366
MP403
MP491
MP494
ST235
ST236
ST311
ST312
ST415
ST417
MA216, ST312
MA495
MP366
CS402, MA3491
MA3491, MA500-3, MP365, MP491
MA490, MA500-2, MP494
MA378
MA500-1
MA216, MA2287, MA500-3, MP491
MA310
MA500-1, MP366
MA500-3
MA284
CS4423
MA3101, MA416, MP366
MA284, MP305, MP494, ST235, ST311
MA2287, MA3491, MA4344, MP491
MA500-2
MA2287
MA215, MA416, MA500-1
ST236, ST312, ST417
MA2287, MA3491, MA500-3
MA284, MA500-2, ST235, ST311, ST415
MA500-2, MP494, ST311, ST415
MP403, ST312
MA500-2, MP494, ST235, ST415
CS402, MP403, ST236
MP494, ST235, ST311
MP403