Pure Mathematics

UCAS code: G110

Here's what Swansea University says about its Pure Mathematics course.

Mathematics underpins all contemporary science, business and technology, creatively applying the ideas of pure mathematics.

Our three-year BSc degree in Pure Mathematics covers the fundamental mathematical concepts of real and complex analysis, geometry, and linear, abstract and categorical algebra. It allows you to focus your studies on pure aspects of the subject.

Your learning will be shaped by inspirational and internationally-renowned academics including Prof Tomasz Brzezinski, Professor of Mathematics and expert in algebra and non-commutative geometry, and Prof Elaine Crooks, Professor of Mathematics, expert in analysis and partial differential equations.

Why Pure Mathematics at Swansea?

• 3rd in the UK for Student Satisfaction (Complete University Guide 2025)

• 7th in the UK (Guardian University 2025)

• 13th in the UK for Teaching Quality (Guardian University 2025)

• Top 201-250 in the world (QS World University Rankings 2025)

Your Pure Mathematics Experience

• Our staff are experts in their areas of mathematics with the majority being recognized by the Higher Education Academy with a Fellowship or Senior Fellowship.

• You will master the ideas and logic of mathematics and their applications and acquire a highly desirable set of transferable skills that will set you apart in the employment marketplace.

• You will receive high-quality personalised support through small-group tutorials.

• Elected student representatives make sure that every student voice is heard.

• The Swansea University Mathematics student society sponsors frequent social and academic events to bring students and staff together.

• Our Mathematics Department is right next to the beautiful Swansea Bay beachfront, with numerous social and sport opportunities.

• Our peer mentoring scheme helps new students settle into university and make new friends.

• The new £32.5M Computational Foundry building at our Bay Campus gives students access to bespoke study and teaching spaces designed by and for mathematicians.

• Our Mathematics Reading Room provides a quiet study space for mathematics students, as well as housing a departmental library of resources for study and research.

In Year 1, you will typically study areas including: Geometry: Mathematics, Logic and Communication; Introduction to Modelling and Simulation; Introduction to Analysis; Foundations of Algebra; Introductory Linear Algebra; Mechanics and Dynamics; Introduction to Biomathematics; and Probability and Statistics.

In Year 2, you will typically study areas including: Differential Equations; Probability Theory; Multi-variable analysis; Metric spaces and measure theory; Vector Spaces; Groups and Rings; Professional Development and Career Planning; Mathematical Modelling: Theory and Practice; Credibility, Liability and Ruin; Game Theory and Optimization; and Statistical Data Analysis.

In Year 3, you will typically study areas including: Applied Algebra: Coding Theory; Higher Algebra; Differential Geometry; Complex Analysis; Partial Differential Equations; Cashflows and Interest Rates; Financial Mathematics in Discrete Time; Markov Processes and Applications; Machine Learning; Assurance and annuity; Financial Mathematics in Continuous Time; Risk and Survival Models; Biomathematics; and Teaching Mathematics via a School Placement. You will also undertake a project.

We are proud to provide an outstanding educational experience, using the most effective learning and teaching approaches, carefully tailored to suit the specific needs of your course. Apart from a small number of online-only courses, most of our courses consist of in-person, on-campus teaching, enabling full engagement with your lecturers and fellow students.

Practical skills sessions, lab work seminars, and workshops predominantly take place in person, allowing for group working and demonstrations. We also operate virtual labs and Simulated Learning Environments which will facilitate greater access to training opportunities in the future. However, our approach also includes the use of some online learning to support and enhance traditional face-to-face teaching.

Online learning may take place ‘live’ using software such as Zoom, allowing you to interact with the lecturer and other students and to ask questions. Lecture recordings also allow for more flexibility to revisit material, to revise for assessments and to enhance learning outside of the classroom. Some modules have extra resources in Canvas, such as videos, slides and quizzes enabling further flexible study.

This course may offer some modules taught through the medium of Welsh or bilingually for students who consider themselves to be fluent Welsh speakers. For more details on the provision available see the Welsh Provision expander below.