Future students

We live in an increasingly data-driven world with the volume of data generated annually following a roughly exponential trend. Data scientists find themselves in high demand because of their skills to derive valuable insights from data. But what exac...

An introduction to the range of mathematical techniques employed by engineers, including functions, calculus, linear algebra, vector geometry, set theory, logic and probability. This course emphasises engineering applications and modelling.

Further mathematical techniques employed by electrical and electronic engineers, with a focus on methods of calculus, differential equations, and linear algebra. There is an emphasis on engineering applications and use of software.

Mathematical techniques employed by cybersecurity and software engineers, including combinatorics, logic, probability distributions, model fitting and estimation. The course emphasises engineering applications.

This course provides an introduction to, or review of, fundamental skills and ideas in mathematics. The course is designed for students who require some mathematics in their degree, but who may not have a lot of mathematical experience. Topics includ...

Determining the rate of change of a function as its dependent variable changes is a key question in many sciences. It is also the basis for differential calculus, which is the first part of mathematical analysis. This course provides a thorough devel...

Integration looks at summing continuous variables, providing a way to define and compute areas and volumes, which are essential for many applications. This course develops integral calculus, including the view of integration as anti-differentiation, ...

Linear algebra is central to mathematics, and essential in science and engineering. This course introduces linear algebra, motivated by some of these applications, and maintaining a practical approach using fundamental mathematical objects such as ma...

Logic underlies all of mathematics. This course introduces the basic notions of logic and discusses what makes some arguments good or valid, and others invalid. This leads to a definition of a mathematical proof, whereby the truth of mathematical sta...

Heads or tails? That's fair, right? Is the coin fair though - and how could you check? How might you choose in a more complicated situation? This course gives you an introduction to probability models in Statistics and their use in good decision maki...

Discover the essential computational techniques at the heart of data science, encompassing the realms of data integration and encryption. Dive into the mathematical concepts and techniques that underpin the entire data lifecycle, from generation and ...

Explore the practical side of data management in this course designed for those working with data sources. You will get hands-on experience in programming and data management using a high-level language and SQL. You will build confidence in skills su...

The theoretical underpinnings of calculus took many years to develop rigorously. This course provides insight into the basic techniques of real analysis in the familiar context of single-variable differential calculus. There is a focus on the proof t...

In order to apply calculus to many physical systems, its concepts have to be extended to higher dimensions. The course introduces vector-valued functions of one variable (curves in the plane and in space), real-valued functions of several variables, ...

Ordinary Differential Equations (ODEs) have motivated a lot of mathematics, both for themselves and for their applications, particularly in the wider sciences. This course introduces ODEs, covering their classification, and various solution methods f...

Combining mathematics with computational techniques allows us to study a wide variety of applications in science, for example, solving physics problems by approximating integrals and derivatives, and compressing digital images using singular-value de...

Linear algebra is a fundamental part of mathematics. This is a second course in linear algebra, focusing on more abstract representations and giving an axiomatic treatment of vector spaces. The course introduces the underlying concepts of linear alge...

This course explores two fundamental mathematical structures: groups and graphs. Both have wide applications in mathematics, as well as in fields such as computer science, cryptography, physics, and chemistry. The course starts with basic group theor...

Topics covered: a review of basic probability theory; discrete and continuous random variables; joint distributions of random variables; expectation, variance, covariance and moment generating functions; correlation and linear combinations of random ...

Take your data science skills to the next level with our capstone course. Dive into interactive displays, infographics, and dashboards equipped with mathematical modelling tools and coding skills. Sharpen your communication and reporting abilities th...

This course is an introduction to Partial Differential Equations (PDEs), including those of importance for the natural sciences. The course covers solution methods for linear PDEs, including the use of boundary values and initial values. The course d...

This course introduces a range of machine learning techniques of importance in Data Science, and gives students experience in using modern software libraries for implementing machine learning pipelines. Topics will include machine learning techniques...

In this course we uncover the role that Statistics plays in Data Science. With a focus on understanding relevant statistical methods and their practical applications, this course will help you consolidate key data science skills. Topics covered inclu...

Simulation and modelling of stochastic systems, covering examples from Operations Research and Computer Science, including queues, networks and computer systems. Design, analysis and validation of simulation experiments. Previous experience with comp...

Complex analysis extends real analysis to functions of complex variables. This course covers the fundamentals of complex analysis, including the Cauchy-Riemann equations, holomorphic functions, harmonic functions, the Cauchy integral formula, power s...

Data Science uses machine learning methods to fit data and make predictions. In this course you will learn how to explore data in order to identify the appropriate ethical and cultural considerations and select the appropriate tools to analyse the da...

This course examines symbolic languages, which are a foundational pillar of mathematics as well as the basis of computer science. Their semantics and proof theory are studied, explaining the role of logic in describing mathematical structures and for...

The abstraction of algebra to sets with extra structure has led to many important mathematical developments. The basic algebraic structures, groups, rings and fields, are the focus of this course, together with some of their applications, such as sol...

This course is an introduction to spaces with a generalised length function called a metric. Metric spaces are fundamental objects in modern analysis, featuring notions of convergence of sequences and continuity of functions in a very general framewo...