# 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.

## Year 1

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 compulsory 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. The remainder of your time will be spent taking **optional mathematics **courses or outside courses.

There are 2 optional mathematics courses:

**Fundamentals of Algebra and Calculus**(Semester 1)

This is an introductory online course in University Mathematics which provides extra preparation in key topics from advanced mathematics. The course introduces and develops a range of topics that incoming undergraduates may not have previously studied, or may benefit from studying in more depth.

**Introduction to Data Science**(Semester 1)

This is an introductory course in data science and statistical thinking. You will learn to explore, visualise, and analyse data to understand natural phenomena, investigate patterns, model outcomes, make predictions and do so in a reproducible and shareable manner. You will work on problems and case studies inspired by and based on real-world questions and data, and will also gain experience in R, a statistical computing language.

Alternatively, **outside courses** can be chosen from across the University, provided the timetable fits. Popular choices include Physics, Informatics (Computer Science), Economics, Business, Philosophy and Languages

## Year 2

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.

As part of most programmes, you will also study **Probability, Statistics** and **Computing and Numerics**.

You can also choose to study **Facets of Mathematics**, a project-based course showcasing modern applications of mathematics. You will continue studying outside subjects.

## Year 3

In **Year 3**, there are a range of core 'Honours' courses which develop your knowledge of important topics in Algebra, Analysis, Differential Equations and Complex Variables. These core courses will also enhance your skills in programming, mathematical writing and presentations. From this point of the degree, you can begin to tailor the degree to your interests and ambitions by choosing from a wide range of options.

## Year 4

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 take a project-based course like Mathematical Education.

## Year 5

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.