Swansea University

What you'll study

The BSc Pure Mathematics degree emphasises rigorous foundations in core areas of mathematics and the development of proof and abstraction skills. In early years you study core subjects such as calculus, linear algebra, introductory real analysis, differential equations and basic discrete mathematics. As you progress, modules typically include:

• Real Analysis – rigorous treatment of limits, continuity, sequences and series, and metric spaces.
• Complex Analysis – theory of complex functions, contour integration and applications.
• Abstract Algebra – group theory, ring theory and fields, including structure theorems and homomorphisms.
• Topology – basic point-set topology and introductory algebraic topology topics.
• Differential Equations and Dynamical Systems – ordinary differential equations, qualitative behaviour and stability.
• Mathematical Logic and Set Theory – foundations of mathematics, proofs and formal systems (often optional).
• Numerical Methods and Scientific Computing – numerical linear algebra and solution techniques implemented in appropriate software.
• Optional modules – probability and statistics, mathematical modelling, number theory, geometry and special topics that reflect staff research interests.

In the final year you normally complete advanced option modules and an individual project or dissertation, which gives hands-on experience of formulating and presenting original mathematical work under academic supervision.

Entry requirements

Typical entry is on the basis of strong performance in A-levels, International Baccalaureate or equivalent qualifications. Applicants are normally expected to have a high grade in A-level Mathematics; Further Mathematics is strongly recommended where available. As a guideline, typical offers are in the upper range of school leaver qualifications; international applicants should hold equivalent qualifications with a strong emphasis on mathematics. Mature applicants and those with non-standard backgrounds are considered on an individual basis; relevant evidence of mathematical ability may be required such as graded certificates, prior study, or an interview.

Career prospects

Graduates with a degree in pure mathematics have versatile skills valued across many sectors. Common career paths include:

• Further study and research (MSc, PhD) leading to careers in academia or research institutes.
• Actuarial roles and financial services where strong mathematical and analytical skills are essential.
• Data science, analytics and machine learning positions in technology and industry.
• Software development, quantitative analysis and modelling roles.
• Secondary school mathematics teaching (usually following a teacher-training qualification such as a PGCE).
• Roles in government, engineering, cryptography and operations research.

The degree emphasises logical thinking, problem solving and communication of complex ideas — competencies that employers in diverse fields seek.

Why study at Swansea University

Swansea University's School of Mathematics offers a balance of small-group teaching and research-led modules, allowing students to work closely with academic staff. The department has active research groups across pure areas such as algebra, analysis and topology, which informs advanced teaching and provides opportunities for dissertation supervision. Students benefit from access to computing facilities, seminar programmes, and a supportive learning environment on a compact campus by the coast. The university also provides careers support and opportunities to undertake placements, internships or collaborations that connect mathematical study with industry and applied projects.