Mathematical Modelling & Self-Learning Systems

Self-learning systems are an important and newly emerging technique in many areas of applied science such as Applied Mathematics, Engineering, Computer Science and Statistics. In particular, self-learning systems are a disruptive approach to mathematical modelling which use differential equations at their foundation. A particular strength of this approach is that it combines numerical learning algorithms such as dynamic machine learning with differential equations to design applications that can adapt to a changing environment. This approach is new and unique because it explicitly takes into account the dynamic aspects of data and allows for fast and accurate modelling of self-learning systems. This is a new and rapidly developing area at the interface between applied mathematics and machine-learning (for example see here).

The primary aim of this course is to provide training in the use and development of modern numerical methods and self-learning software. Graduates will develop and apply new skills to real-world problems using mathematical ideas and techniques together with software tailored for complex networks and self-learning systems. While there is a strong focus on modern applications, graduates will gain in-demand skills in mathematical modelling, problem-solving, scientific computing, dynamic machine learning, complex networks and communication of mathematical ideas to a non-technical audience.

More general hands-on skills include mathematical typesetting, mathematical writing, desktop and web-based mathematical software development, and the use of computer languages and packages such as C#, R, Python and TensorFlow.

Why choose this course?
This MSc reflects a philosophy of cutting edge teaching methods and pragmatism. As well as providing you with a host of abilities which are in demand in industry, this MSc provides skills which are complementary to most scientific and engineering undergraduate courses. The MSc not only opens up new possibilities, you also gain a set of skills that sets you apart from the crowd in your original field of study. The final project is an excellent opportunity for you to showcase your abilities to future employers or to undertake a detailed study in a new area of interest. The course is extremely flexible in helping you realise your ambitions.

Entry requirements


Candidates must have obtained at least a 2.2 honours degree or equivalent in a numerate discipline (i.e., commensurate with science or engineering programmes).

Candidates are expected to have taken courses in mathematics, applied mathematics or statistics at university level, and be familiar with calculus, vectors, matrices and elementary statistics. They are expected to have sufficient background in university-level mathematics as assessed by the course coordinator. In the case of competition for places selection will be made on the basis of primary degree results and/or interview. For online modules, students are advised to have access to a laptop/home computer with internet connection, modern browser, word processing and spreadsheet software.

Candidates from Grandes Écoles Colleges are also eligible to apply if they are studying a cognate discipline in an ENSEA or EFREI Graduate School and are eligible to enter the final year (M2) of their programme.

All candidates must ultimately be approved by the director of the MSc (Mathematical Modelling and Self-Learning Systems) programme.

If you are applying with Qualifications obtained outside Ireland and you wish to verify if you meet the minimum academic and English language requirements for this programme please view the grades comparison table by country and for details of recognised English language tests.

Non-EU Candidates

Non-EU candidates are expected to have educational qualifications of a standard equivalent to Irish university primary degree level. In addition, where such candidates are non-native speakers of the English language they must satisfy the university of their competency in the English language. To verify if you meet the minimum academic requirements for this programme please visit our qualification comparison pages.

For more detailed entry requirement information please refer to the International website .

Subjects taught

Part 1
AM6004 Numerical Methods and Applications (5 credits)
AM6005 Nonlinear Dynamics (5 credits)
AM6007 Scientific Computing with Numerical Examples (10 credits)
AM6013 Statistical, Dynamical and Computational Modelling (10 credits)
AM6015 Computational Techniques with Networks (5 credits)
AM6016 Dynamic Machine Learning with Applications (5 credits)
AM6017 Complex and Neural Networks (5 credits)
AM6020 Open Source Infrastructure for Mathematical Modelling and Big Data Applications (5 credits)
ST4060 Statistical Methods for Machine Learning I (5 credits)**
ST4061 Statistical Methods for Machine Learning II (5 credits)**

**Students who have taken ST4060 or ST4061 in a previous degree must select alternative modules (subject to availability and timetabling) from list A and list B of fourth year of the BSc (Mathematical Sciences) in consultation with the Programme Coordinator.

Part 2
AM6018 Dissertation in Mathematical Modelling and Self-Learning Systems (30 credits)

Further details on the modules listed above can be found in our book of modules. Any modules listed above are indicative of the current set of modules for this course but are subject to change from year to year.


1 year full-time

Enrolment dates

Start Date 7 September 2020

Post Course Info

Skills and Careers Information
Graduates with quantitative skills and expertise in self-learning algorithms are in high demand in industry according to the Governments Expert Group on Future Skills Needs. Demand for these skills is projected to rise over the coming years not just in Ireland but in the EU and globally. Graduates from a similar MSc have secured jobs in the following areas: banking, financial trading, consultancy, online gambling firms, software development, logistics, data analysis and with companies such as AIB, McAfee, Fexco, DeCare Systems, MpStor, the Tyndall Institute,, First Derivatives and KPMG.

More details
  • Qualification letters


  • Qualifications

    Degree - Masters (Level 9 NFQ)

  • Attendance type


  • Apply to