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What is Mathematics?

Mathematics has a rich and varied history stretching back many millennia. In ancient Babylon and Egypt, people developed practical mathematical skills for solving problems related to surveying and accountancy. Great mathematicians such as Archimedes, Eudoxus, Euclid and Apollonius in ancient Greece and its colonies developed mathematics as a deductive science founded on logic, delving deeply into the basic principles of geometry and the theory of numbers. Mathematicians of the seventeenth and eighteenth centuries developed the basic principles of calculus that are fundamental to the applications of mathematics in areas of science and engineering. Mathematicians of the nineteenth and twentieth centuries developed the subject in a myriad of directions, discovering and classifying algebraic structures that, though initially considered part of pure mathematics with no obvious practical application, found surprising applications in areas such as cryptography, the automatic correction of errors in data transmission and computer graphics.

Much of contemporary mathematics is concerned with the theory and applications of infinite-dimensional spaces, and novel mathematical methods were developed to develop basic understanding and solve practical problems arising in the physical and biological sciences, engineering, management science, economics and finance. In recent decades deep and surprising connections were made between modern theoretical physics and theories developed by pure mathematicians over many decades concerning geometrical and topological properties of curved spaces in many dimensions that, at the time they were developed, were not perceived as having particular relevance to physics.

Is this the right course for you?

Mathematics is an excellent choice for anyone hoping to meet the demand for mathematics graduates in the job market, which values numeracy, ability in abstract reasoning and the skill to turn ideas into methods.

If you have a natural ability in mathematics and are genuinely interested in applying mathematical solutions to problem solving, then this course will suit you well. It is also a great start for a career in actuarial work, finance or accounting, although these will require further training. The course has been successful over a long period in providing diverse career opportunities for many students.

Why study Mathematics at Trinity?

Trinity is justly proud of its long tradition of excellence in mathematics. Research interest in the School of Mathematics is enormously varied; ranging from the abstract ideas of differential geometry and analysis to practical ideas of numerical analysis, modelling and computer algorithms; the nature of fundamental particles and general relativity; non-linear systems and fluid mechanics. This departmental diversity is reflected in the specialist degree-level courses available to students. With an academic staff that brings expertise and experience from many parts of the world, the course aims to be world class, while also catering for those with talents in different mathematical areas.

What will you study?

These programmes are designed to provide you with a broad mathematical training that will, in turn, allow you to work in any environment that requires strong numerical and logical skills.

The modules offered can be grouped into four areas:

  • Pure mathematics which explores basic concepts and abstract theories
  • Applied and computational mathematics to solve practical problems
  • The mathematics of theoretical physics
  • Statistical models and methodology

All students take common modules in their first year developing skills and understanding in Calculus and Linear algebra. Single honour students also take introductory modules in group theory, mechanics statistics and computing in the first year. In the second year much of the programme consists of compulsory modules in the areas of real and complex analysis, algebra, topology, and mathematical methods together with a choice of optional modules in areas such as probability, statistics and mechanics. In the third and fourth years of the programme, you will be able to specialise in the areas that appeal most to you.

Further details are to be found on the School of Mathematics website at the following location:

Study abroad

You may choose to spend the third year at a European university as part of the Erasmus exchange programme. In particular, there are agreements in place that allow study at the University of Durham (UK) and Université Lille 1 (France). Also, in recent years some students have spent the third year at universities in the United States of America and in Australia under exchange programmes.


A degree in mathematics opens up the possibility of a career in a variety of industries and sectors. Graduates have found employment in computing, where mathematics skills have immediate and practical application. The financial services and internet security sectors are also common first destinations for graduates. Other options include statistics, teaching, accountancy, actuarial work, finance, and all areas of pure and applied mathematics. Many of these involve further study or intensive research.

Further information


Tel: +353 1 896 1949

Specific Entry Requirements

Leaving CertificateHB3 Mathematics
Advanced GCE (A-Level)Grade B Mathematics
Other EU examination systemsSee

Graduate Profile

Aoibheann Brady

The maths degree at Trinity allowed me to explore a wide range of topics, and the research programmes for undergraduates guided my decision to pursue a PhD at the University of Bath. I also worked in finance during summers and after graduating, the possibilities open to me have been incredibly broad.

The course had great social aspects: I have made friends for life through the Mathematical Society and was a founding member of the “Ireland for CERN” campaign – an experience not available elsewhere.

The standard of courses, the opportunities, and the level of support and engagement of academic staff make choosing the degree a fantastic decision.