University of Lancaster

What you'll study

The programme integrates core undergraduate mathematics with systematic philosophical study. In the mathematics component you will cover foundational and applied topics such as calculus and analysis, linear algebra, probability and statistics, differential equations, mathematical modelling, numerical methods and an introduction to abstract algebra. The philosophy component focuses on areas that connect closely with formal and conceptual thinking: logic (including formal and symbolic logic), philosophy of mathematics, epistemology, and selected modules in metaphysics or philosophy of science.

Early years introduce essential techniques and theorems that underpin later work. In the middle years you will choose from optional modules to tailor the balance between pure, applied and computational mathematics and between history, ethics or more technical philosophy. The placement year is taken after the second year and enables a full-time work placement or internship in industry, government, charities or research settings. The final year typically includes a substantial project or dissertation — either a mathematics project, a philosophy dissertation, or an interdisciplinary project combining both subjects — together with advanced options such as real analysis, measure and probability theory, model theory, modal logic or advanced topics in mathematical modelling.

Typical modules and themes

• Foundations of Analysis and Calculus
• Linear Algebra and Matrix Methods
• Introductory and Advanced Logic
• Probability and Statistical Inference
• Numerical Methods and Scientific Computing
• Philosophy of Mathematics and Concepts of Proof
• Mathematical Modelling and Differential Equations
• Independent Project / Dissertation

Entry requirements

Applicants should demonstrate a strong background in mathematics. Typically this means an advanced level qualification in mathematics (A‑level Mathematics or equivalent); Further Mathematics is advantageous but not always required. Admissions consider a range of UK and international qualifications and contextual information, and alternative qualifications such as Access to HE diplomas, international baccalaureates or recognised international equivalents are accepted where appropriate.

The programme assesses applicants on quantitative ability and logical thinking; those without formal maths qualifications but with strong quantitative experience may be considered. International applicants are expected to meet Lancaster's standard English language requirements. The university provides advice and pre-sessional English where necessary.

Career prospects

Graduates leave with a combination of technical mathematical skills and rigorous philosophical reasoning. Career paths commonly pursued include data science and analytics, actuarial work, finance and risk analysis, software development, quantitative roles in industry, policy and consultancy, and research or doctoral study. The placement year increases employability by providing industry experience, workplace skills and professional networks. Some graduates also move into teaching or careers that value strong logical and problem-solving abilities, such as public sector strategy roles and legal or regulatory positions where analytical precision is important.

Why study at University of Lancaster

Lancaster offers close-knit teaching within departments that emphasise both research-led content and student support. The structure of the degree encourages interdisciplinary study while maintaining depth in both mathematics and philosophy. Students benefit from dedicated computing and mathematics facilities, small-group tutorials, and access to the Careers Service and placement support to secure a meaningful year in industry. The university’s campus environment and departmental seminar programmes provide opportunities to engage with researchers and visiting speakers across mathematics, logic and philosophy.