School of Mathematics

What will I study?

All of our programmes start with a common core of mathematics courses, with increasing options for specialisation in later years depending on your interests.

First Year

Students working on a problem in an Introduction to Linear Algebra workshop.
Students working on a problem in an Introduction to Linear Algebra workshop.

Our first year courses are designed to introduce you to studying mathematics at university level.

You may be familiar with some of the concepts from school (e.g. vectors, matrices, differentiation and integration), but these courses will look at them in a different way as well as going much more deeply into the theory.

There are 3 core mathematics courses:

  • Introduction to Linear Algebra (Semester 1)

    You will learn more about vectors, matrices and systems of linear equations. You may have met some of the early ideas at school but throughout the course you will learn about new abstract concepts. You will use the mathematical ideas encountered in practical contexts but also lay the foundations for your study of pure mathematics in subsequent years.

  • Calculus and its Applications (Semester 2)

    Calculus is the most fundamental tool in the study of mathematics and is vital for many of its applications. This course will revise some of the calculus you studied at school and develop it further but will treat it with the rigour required at university level.

  • Proofs and Problem Solving (Semester 2)

    This course introduces the fundamental skills needed for advanced study in pure mathematics. You will develop the skill of reading, understanding and using the precise language of professional mathematicians and learn to construct your own rigorous proofs. During the course you will also engage with many problems, obtaining the practice required to become an effective problem-solver.

Together these courses will take up half your time, with the other half being spent on outside courses. These can be chosen from across the University, provided the timetable fits. Popular choices include:

  • Physics
  • Informatics (Computer Science)
  • Economics
  • Business Studies
  • Logic
  • Astrobiology
  • Languages, e.g. French, Spanish

Year 2

Students constructing a dodecahedron in a workshop about symmetry
Students constructing a dodecahedron in a workshop about symmetry

There are 2 core mathematics courses:

  • Several Variable Calculus and Differential Equations (Semester 1)

    This course builds on the calculus from Year 1, by extending the ideas to functions of more than one variable. You will learn about partial derivatives and multiple integrals, as well as methods for solving first and second order differential equations.

  • Fundamentals of Pure Mathematics (Semester 2)

    You will learn about real analysis – including a rigorous treatment of limits, continuity, differentiability and infinite series – as well as being introduced to group theory and the mathematics of symmetry.

In most programmes you will also study Probability and Computing and Numerics.

You will continue studying an outside subject, and you can also choose to study Statistics and Facets of Mathematics, a project-based course showcasing modern applications of mathematics.

Later Years

Final-year students working together in the Maths Hub
Final-year students working together in the Maths Hub

In Year 3, there are a range of core courses which develop your knowledge of important topics in Algebra, Analysis, Differential Equations and Complex Variables, while also enhancing your skills in programming, mathematical writing and presentations. You will begin to tailor the degree to your interests and ambitions by choosing from a wide range of options.

The range of courses on offer by Year 4 is such that two mathematics students could be following entirely different programmes. You can choose from a wide range of options reflecting the diversity of research interests in the School. There are options in all the major branches of pure mathematics such as analysis, algebra and geometry, as well as in applied mathematics, theoretical physics, statistics, operational research and financial mathematics. You will also complete a project or a project-based course such as Data Analysis or Mathematical Education.

For the MMath degree, you would continue into Year 5, studying advanced topics at masters level and working on a substantial dissertation with an academic member of staff.

Explore in detail

You can browse full details of all our courses on the Path website which was developed by some of our students. Note that if you do not have an EASE password, you can set up an EASE Friend account to obtain access.