Mathematics (4 years) at Durham University - UCAS

Course options

Course summary

This course is ideal if you are considering postgraduate study or a career involving high-level mathematical skills or research. When you choose maths you’ll be taught by a team of mathematicians with a passion for sharing the beauty of mathematics and a wealth of experience in research across the spectrum of pure and applied mathematics and statistics. And with many of the teaching team actively involved at the forefront of research, the degree is designed to link learning to research in distinctive and creative ways. The first year of the course begins with a broad-based introduction to pure and applied mathematics, statistics and probability and provides a sound foundation for in-depth study in subsequent years. In the second and third years the structure offers more flexibility, enabling you to shape your degree around one specific area or continue developing your skills across a wide range of subjects. During the final year the range of optional modules expands further, introducing more advanced concepts and theories. The degree culminates in a double-module project that gives you the opportunity to investigate a mathematical topic of interest in depth. You can also apply to add a placement year or a year abroad to your degree, increasing the course from four years to five. Year 1 The first year consists of 100 compulsory Mathematics credits:

  • Analysis (20)
  • Linear Algebra (20)
  • Calculus (20)
  • Programming (10)
  • Dynamics (10)
  • Probability (10)
  • Statistics (10)
Together with a further 20 credits which can be chosen from:
  • Discrete Mathematics (20)
  • Any other available Sciences, Arts and Social Sciences modules (subject to prerequisites and timetabling)
In the Mathematics modules, topics that may be familiar from A level (or equivalent) are expanded and developed to help you adjust to university life, provide a sound foundation for your Mathematics degree and enable you to make informed choices when picking modules from second year onwards. Year 2 In the second year, you will choose six Maths modules. You will take two compulsory modules:
  • Complex Analysis
  • Analysis in Many Variables
Together with modules from a range which includes:
  • Numerical Analysis
  • Statistical Concepts
  • Mathematical Physics
  • Algebra
  • A combination of two shorter courses on a wide range of mathematical topics – Elementary Number Theory, Probability, Mathematical Modelling, Geometric Topology, Monte Carlo, Actuarial Mathematics, and Special Relativity and Electromagnetism.
At this stage, you can begin to specialise in areas of pure mathematics, applied mathematics, statistics and probability although you can also maintain a wide range of options for the third year. Year 3 In the third year you choose six from a wide choice of around 20 modules covering a variety of topics in areas such as algebra, geometry, topology, applied mathematics, mathematical physics, statistics and probability, together with options including Mathematical Finance, Mathematical Biology and Mathematics Teaching. Many of these topics are closely linked to and informed by current research. Year 4 In the fourth year, you take a double module project, giving you the opportunity to investigate a mathematical topic of interest. You will produce a written report and poster and give a short presentation. This develops your research and communication skills which are very important for future employment or postgraduate studies. You also choose four taught modules from a wide variety of topics as in Year 3. Some but not all of these modules follow on from options in Year 3, allowing you to both advance and broaden your mathematical expertise approaching research level. Placement Year You may be able to take a work placement. Find out more:


Year 1 Core modules: Calculus builds on ideas of differentiation and integration in A level mathematics, beginning with functions of a single variable and moving on to functions of several variables. Topics include methods of solving ordinary and partial differential equations, and an introduction to Fourier Series and Fourier transforms. Linear Algebra presents mathematical ideas, techniques in linear algebra and develops the geometric intuition and familiarity with vector methods in preparation for more challenging material later in the course. Analysis aims to provide an understanding of real and complex number systems, and to rigorously develop the calculus of functions of a single variable from basic principles. Programming is taught via lectures and practical sessions that introduce basic principles and basic competence in computer programming. You will also study control structures; floating point arithmetic; and lists, strings and introduction to objects. Dynamics develops an understanding of elementary classical Newtonian dynamics as well as an ability to formulate and solve basic problems in dynamics. Probability introduces mathematics ideas on probability in preparation for more demanding material later in the course. The module presents a mathematical subject of key importance to the real-world (applied) that is based on rigorous mathematical foundations (pure). Statistics introduces frequentist and Bayesian statistics and demonstrates the relevance of these principles and procedures to real problems. This module lays the foundations for all subsequent study of statistics. Year 2 Core modules: Complex Analysis introduces the theory of complex analysis through the study of complex differentiation; conformal mappings; metric spaces; series and uniform convergence; contour integrals and calculus of residues; and applications. Analysis in Many Variables provides an understanding of calculus in more than one dimension, together with an understanding of, and facility with, the methods of vector calculus. It also explores the application of these ideas to a range of forms of integration and to solutions of a range of classical partial differential equations. Examples of optional modules: Algebra Mathematical Physics Numerical Analysis Statistical Inference Data Science and Statistical Computing Elementary Number Theory Geometric Topology Markov Chains Mathematical Modelling Probability Special Relativity and Electromagnetism Statistical Modelling. Year 3 Examples of optional modules: Advanced Statistical Modelling Bayesian Computation and Modelling Decision Theory Dynamical Systems Galois Theory Geometry of Mathematical Physics Mathematical Biology Mathematics into Schools Operations Research Quantum Computing Solitons Topology. Year 4 Core module: In the final-year Project you will investigate a mathematical topic of interest and then produce a written report and give a short presentation. The project develops your research and communication skills which are important for future employment or postgraduate studies. Examples of optional modules: Advanced Quantum Theory Algebraic Topology Ergodic Theory Functional Analysis and Applications Topics in Algebra and Geometry General Relativity Representation Theory Riemannian Geometry Statistical Mechanics Topics in Applied Mathematics Topics in Combinatorics.

Assessment method

Most of your modules are assessed by end-of-year examinations. In your final year you also complete a project which is worth one-third of your final-year marks, it includes a written project report, a poster and a short presentation on your chosen topic.

How to apply

Application codes

Course code:
Institution code:
Campus name:
Durham City
Campus code:

Points of entry

The following entry points are available for this course:

  • Year 1

Entry requirements

Qualification requirements

Contextual Offers: Our contextual offer for this programme is A level A*AB including A*A in Mathematics and Further Mathematics in any order or A*A*C including A*A* in Mathematics and Further Mathematics (or equivalent). To find out if you’re eligible, please visit: Maths Tests: We strongly encourage applicants to sit the University’s Admissions Test if it is available to them, as we give a high weighting in our selection process to evidence of ability in Mathematics. TMUA: MAT: STEP:

Please click the following link to find out more about qualification requirements for this course

English language requirements

Durham University welcomes applications from all students irrespective of background. We encourage the recruitment of academically well-qualified and highly motivated students, who are non-native speakers of English, whose full potential can be realised with a limited amount of English Language training either prior to entry or through pre-sessional and/or in-sessional courses. It is the normal expectation that candidates for admission should be able to demonstrate satisfactory English proficiency before the start of a programme of study, whether via the submission of an appropriate English language qualification or by attendance on an appropriate pre-sessional course. Acceptable evidence and levels required can be viewed by following the link provided.

English language requirements

Student Outcomes

Operated by the Office for Students
Employment after 15 months (Most common jobs)
Go onto work and study

The number of student respondents and response rates can be important in interpreting the data – it is important to note your experience may be different from theirs. This data will be based on the subject area rather than the specific course. Read more about this data on the Discover Uni website.

Fees and funding

Tuition fees

Republic of Ireland £9250 Year 1
Channel Islands £9250 Year 1
EU £27000 Year 1
England £9250 Year 1
Northern Ireland £9250 Year 1
Scotland £9250 Year 1
Wales £9250 Year 1
International £27000 Year 1

Additional fee information

There may also be additional course costs for things like books (if you want to purchase them), field trips etc.
Mathematics (4 years) at Durham University - UCAS