BSc (Hons) Mathematics

• Year 1

• Learn the underlying mathematics that underpins the rest of your degree and master coding in the industrial software Python, right from the start. You’ll begin by building on the mathematical skills and topics you learnt at school, studying six core modules including calculus, linear algebra, numerical methods, pure mathematics, and probability. We’ve structured the curriculum so that all of our students acquire a common mathematical expertise, so you’ll also have the flexibility to move between courses as you progress.

  Core modules

  • Stage 1 Mathematics Placement Preparation (BPIE113)

    The route to graduate-level employment is found easier with experience. These sessions are designed to assist students in their search for a year-long placement and in their preparation for the placement itself. Such placements are optional but strongly recommended.

  • Calculus (MATH1702)

    Calculus underpins mathematical modelling in science, finance and industry. This module gives students the ability to calculate accurately and efficiently. Key results are proven and calculus is extended to higher dimensions through partial differentiation and multiple integration. The methods covered in this module will be used by students throughout the rest of their degree.

  • Analysis and Group Theory (MATH1704)

    In this module we explore two fundamental areas of pure mathematics. Analysis provides a rigorous foundation of calculus, while group theory introduces important algebraic structures that are used in many branches of pure mathematics and their applications. A rigorous approach will be taken in both topics, with emphasis on proof. Python will be used to illustrate and investigate cutting edge applications.

  • Mathematical Reasoning (MATH1701)

    This module will introduce the basic reasoning skills needed for the development and applications of modern mathematics. It also introduces Python as a new tool for exploring and applying mathematics to real world problems. The importance of logical thinking will be investigated in various mathematical topics. This will include fundamental properties of prime numbers, their random generation and use in cryptography.

  • Linear Algebra (MATH1703)

    Vectors and matrices are fundamental in mathematics, and central to its applications in statistics, physics, data science, and engineering. This module develops practical skills in handling vectors and matrices, explores the mathematical structure of linear spaces, and elucidates their deep connections with analytic geometry.

  • Probability (MATH1705)

    An understanding of uncertainty and random phenomena is becoming increasingly important in daily life and in the modern workplace. The aim of this module is to develop the concept of chance in a mathematical framework. Random variables are introduced, with examples involving some common distributions, and the concepts of expectation, variance and correlation are investigated using mathematical tools.

  • Numerical Methods (MATH1706)

    In mathematics, solving most real world problems requires the use of computers. This module introduces computational mathematics and algorithms . Students will use mathematical software interactively and write programs in Python. The numerical methods which underlie industrial, scientific and financial applications will be studied.

• Year 2

• In Year 2 you'll expand your knowledge with topics including vector calculus, complex analysis, differential equations, transform theory, algebra and mathematical statistics. You will also have a case study-based introduction to operational research, the branch of mathematics developed for better management and decision making, and powerful Monte Carlo methods for simulating complex problems.

  Core modules

  • Stage 2 Mathematics Placement Preparation (BPIE213)

    These sessions are designed to help students obtain a year-long placement in the third year of their programme. Students are assisted both in their search for a placement and in their preparation for the placement itself.

  • Advanced Calculus (MATH2701)

    In this module the geometrical and dynamical concepts needed to describe higher-dimensional objects are introduced. This includes vector calculus techniques and new forms of integration, such as line integration. Students also explore the relationships between integration and differentiation in higher dimensions. We apply advanced calculus to problems from areas such as mechanics and electromagnetism.

  • Statistical Inference and Regression (MATH2702)

    This module provides a mathematical treatment of statistical methods for learning from the data abounding in the modern world. Confidence intervals and hypothesis testing are studied. Methods of estimation are explored, focusing on the maximum likelihood method. The module demonstrates the underlying theory of the general linear model. Applications are implemented using the professional statistical software, R.

  • Differential Equations (MATH2704)

    Differential equations are used to describe changes in nature. This module introduces methods to find exact solutions to ordinary differential equations, and numerical solutions to ordinary and partial differential equations. Extensive use will be made of computational tools. The behaviour of higher dimensional systems will be analysed using the theory of continuous dynamical systems.

  • Operational Research (MATH2705)

    This module gives students the opportunity to work on open-ended case studies in Operational Research (OR) and Monte Carlo methods, both of which play an important role in many areas of industry and finance. Students work both on their own and in teams to develop expertise in Operational Research and programming. They will refine their presentation and communication skills, so enhancing their employability.

  Optional modules

  • Algebra and Transforms (MATH2703)

    This module introduces mathematical structures called rings and fields, which capture properties of objects such as integers, real numbers or polynomials. These structures are used to explore error-correcting codes for data transmission. Calculus is used to introduce Laplace and Fourier transforms, and Fourier series. They are applied to solve differential equations and uncover identities involving irrational numbers.

  • Complex Analysis and Vector Calculus (MATH2706)

    This module explores fundamental relationships between dimensionality and integration. Vector integration theorems for circulation, vorticity and divergence are introduced and vector calculus is applied to real-world examples, such as classical mechanics and orbital dynamics. The mathematics of complex numbers and functions are studied, revealing deep results with applications throughout mathematics.

  • Financial Institutions and Markets (ACF5002)

    This module deals with financial markets, instruments, and institutions. You will examine the bond market, the stock market and the foreign exchange market and explore investment banking and mutual funds.

  • Learning Matters (EDST518)

    A module that builds students’ capacity to recognise and evaluate learning as it occurs in educational, work and recreational settings. It draws upon established, current and critical theory on learning and human development, and focuses on applying these theories to examples of educational practice from existing research and the students’ experiences.

• Optional placement year

• You'll have the opportunity to participate in an optional but highly recommended placement year, providing valuable paid professional experience and helping make your CV stand out. Typically students are paid around £17,000 and placement providers have included the Department for Communities and Local Government, Fujitsu, GSK, Vauxhall Motors, VirginCare, Visteon and Jagex Games Studio.

  Optional modules

  • Mathematics and Statistics Placement (BPIE331)

    A 48-week period of professional training is spent as the third year of a sandwich programme while undertaking an approved placement with a suitable company. This provides an opportunity for the student to gain experience of how mathematics is used in a working environment, to consolidate their previous study and to prepare for the final year and employment after graduation. Recent placement providers include GSK, the Office for National Statistics, NATS (air traffic control) and VW Group.

• Final year

• Choose from a wide range of modules covering pure and applied mathematics, and operational research, as well as theoretical physics and statistics. A choice of small group case studies and the additional option of an individual project offer you the chance to study an interest in depth. You may opt to study a school-based placement module.

  Optional modules

  • Machine Learning (COMP3003)

    This module introduces machine learning, covering unsupervised, supervised and reinforcement learning from a Bayesian perspective. This includes theory behind a range of learning techniques and how to apply these representations of data in systems that make decisions and predictions.

  • Big Data Analytics (COMP3008)

    The key objective of this module is to familiarise the students with the most important information technologies used in manipulating, storing and analysing big data. Students will work with semi-structured datasets and choose appropriate storage structures for them. A representative of recent non-relational trends is presented—namely, graph-oriented databases.

  • Partial Differential Equations (MATH3701)

    This module deepens students’ understanding of partial differential equations and applies them to real world problems. It provides a variety of analytic and numerical methods for their solution. It includes a wide range of applications such as transport, heat diffusion, wave propagation and nonlinear phenomena.

  • Statistical Data Modelling (MATH3702)

    We study statistical models, including regression and the general and generalised linear models. We estimate model parameters in the classical and Bayesian inference frameworks, using R and Stan software. We describe related computer techniques, including computational matrix algebra and Markov chain Monte Carlo algorithms. We work with multiple data sources using state-of-the art data handling tools.

  • Financial Statistics (MATH3703)

    This module introduces students to financial time series analysis and modelling, illustrated using a variety of applications from the finance industry. We study univariate and multivariate time series models, as well as inferential techniques. Model selection, forecasting and 'curse of dimensionality' problems are treated from both a methodological and a computational point of view.

  • Fluid Dynamics (MATH3704)

    In this module, students will learn how to use mathematics to model a variety of fluid flows. Fluid flow problems are described mathematically as ordinary or partial differential equations. These equations are then solved and the results interpreted for a mixture of theoretical and practical examples of both inviscid and viscous fluid flows. Applications from environmental and industrial modelling will be studied.

  • Quantum Computing (MATH3705)

    Quantum mechanics describes physical systems at the atomic and molecular scale. This allows properties of matter and its interactions with light to be modelled, and these models underpin the rapid development of quantum technologies. This module introduces the principles of quantum mechanics and applies them to quantum computing. Students will study quantum algorithms and techniques to program quantum computers.

  • Industrial Placement (MATH3706)

    This module provides an opportunity for final year students to gain experience of applying mathematics in a professional environment. Students can carry out a placement in a wide variety of areas, including data science, finance, management, research, and software development. As part of this, they develop a range of skills that considerably increase future employment opportunities.

  • Relativity and Cosmology (MATH3707)

    This module introduces the basic concepts of special and general relativity, such as the Lorentz transformations, time dilation, and the curvature of space-time. These ideas help students to understand the basic concepts of modern cosmology, including the standard model of the expanding universe (FLRW model) and its extensions using dark matter and dark energy.

  • Modelling and Numerical Simulation (MATH3708)

    Simulations and modelling are crucial tools that support industrial research and innovation. Students will learn to analyse mathematical models and develop programs to solve them. They will investigate algorithms and discuss their performance. Students will code and run numerical programs on a high performance computer. These forward-looking skills are highly sought after by many employers.

  • Optimisation, Networks and Graphs (MATH3709)

    Optimisation and graph theory are related branches of mathematics with applications in areas as diverse as computer science and logistics. Graphs are used to capture relationships between objects, while optimisation studies algorithms that search for optimal solutions. This module provides both the theory and modern algorithms, including those used in artificial intelligence, required to solve a broad range of problems.

  • Medical Statistics (MATH3710)

    This module equips students with the skills to plan and analyse clinical trials, including crossover and sequential designs, and to perform sample size calculations. The principles of meta-analysis are introduced. Epidemiology is studied, including case-control and cohort studies. Survival analysis is covered in detail. Students gain experience with computer packages that are used in health and medicine.

  • Mathematics of Planet Earth (MATH3712)

    Students work in small groups to research problems directly related to sustainability and the protection of the environment, so addressing some of the most serious problems faced by humanity. This can involve the solution of mathematical, statistical, computational, industrial or economic problems, or challenges in renewable energy engineering. Students present their conclusions orally and in a professional report.

  • Project (MATH3713)

    In this module, students perform individual independent research into a topic in Mathematical Sciences, or Mathematics Education. Students choose a subject to explore in depth, which they are particularly interested in, and receive regular advice and feedback from an expert supervisor. The outputs of the project are a dissertation and a presentation. This module is an ideal preparation for progressing to further study.

  • School Placement (MATH3714)

    This module provides an opportunity for final year students to gain experience in teaching and to develop their key educational skills by working in a school environment for one morning a week over both semesters. Students typically progress from assisting in the classroom to teaching a starter activity over the academic year.

  • Algebraic Geometry and Cryptography (MATH3711)

    Algebraic geometry is a cutting-edge branch of mathematics that links the study of geometric objects to the solution of polynomial equations. This module introduces basic concepts of algebraic geometry and algebraic curves. It applies these ideas to elliptic curve cryptography, an encryption method widely used in today’s world. The encryption techniques that we explore are implemented using Python.

Every undergraduate taught course has a detailed programme specification document describing the course aims, the course structure, the teaching and learning methods, the learning outcomes and the rules of assessment.

The following programme specification represents the latest course structure and may be subject to change:

BSc Mathematics Programme Specification September 2024 0153