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Year 1
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Build strong mathematical foundations to support future investigations in theoretical physics. Topics include probability and randomness, which are key ideas in quantum theories, and tools such as group theory, which are used to describe fundamental symmetries in nature. Calculus and analysis plus linear algebra, essential for studying higher dimensional theories are also introduced along with an introduction to programming.
Core modules
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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.
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Mathematical Reasoning (MATH1601)
This module introduces the basic reasoning skills needed to develop and apply mathematical ideas. Clear logical thinking is central to the understanding of mathematics. The module explores fundamental properties of prime numbers, their random generation and use in modern cryptography.
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Linear Algebra and Complex Numbers (MATH1603)
This module explores the concepts and applications of vectors, matrices and complex numbers. The deep connection between algebra and geometry is explored. The techniques that are presented in this module are at the foundation of many areas of mathematics, statistics, physics, and several other applications.
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Probability with Applications (MATH1605)
An understanding of uncertainty and random phenomena is becoming increasingly important nowadays in daily life and for a variety of fields. The aim of this module in probability is to develop the concept of chance in a mathematical framework. Random variables are also introduced, with examples involving most of the common distributions and the concepts of expectation and variance of a random variable.
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Numerical and Computational Methods (MATH1610)
This module provides an introduction to appropriate mathematical software, computational mathematics and creating simple computer programs. Students will use mathematical software interactively and also write programs in an appropriate computer language. The elementary numerical methods which underlie industrial and scientific applications will be studied.
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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.
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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.
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Year 2
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Review the evidence for the existence of dark matter and describe Newtonian cosmology using vector calculus. Acquire the mathematical language of quantum mechanics by learning about real and complex analysis. A case studies module introduces the powerful Monte Carlo technique which lies at the heart of statistical mechanics and is used to extract precision results from the Standard Model of particle physics.
Core modules
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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.
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Advanced Calculus (MATH2601)
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 relations between integration and differentiation in higher dimensional hyperspaces. This knowledge is applied to various real world problems.
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Statistical Inference and Regression (MATH2602)
The module provides a mathematical treatment of statistical inference, including confidence intervals and hypothesis testing. Methods of estimation are explored, focusing on maximum likelihood estimation. The module also demonstrates the underlying mathematical theory of the general linear model, through a variety of applications, using professional software.
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Ordinary Differential Equations (MATH2603)
The module aims to provide an introduction to different types of ordinary differential equations and the analytical and numerical methods needed to obtain their solutions. Extensive use is made of computational mathematics packages. Applications to mechanical and chemical systems are considered as well as the chaotic behaviour seen in climate models.
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Mathematical Methods and Applications (MATH2604)
Vector calculus is extended to higher dimensions and applied to a range of important scientific problems primarily from classical mechanics and cosmology. Differential and integral calculus is applied to the solution of differential equations and the orthogonal functions bases are constructed. The crucial mathematical concepts of integral transforms (Fourier and Laplace) and Fourier series are introduced.
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Operational Research and Monte Carlo Methods (MATH2605)
This module gives students the opportunity to work on open-ended case studies in operational research (OR) and Monte Carlo methods, both of which are important methods in, for example, industry and finance. It allows students to work on their own and in teams to develop specific skills in OR and programming as well as refining their presentation and communication skills. The skills in computational simulation developed in this module have many applications.
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Real and Complex Analysis (MATH2606)
This module deepens the student’s understanding of real analysis and introduces complex analysis. The important distinction between real and complex analysis is explored and the utility of the complex framework is demonstrated. The central role of power series and their convergence properties are studied in depth. Applications include the evaluation of improper integrals and the construction of harmonic functions.
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Year 3
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An optional, but highly recommended placement provides you with valuable paid professional experience to help make your CV stand out. Typically students are paid around £17,000 and employers have included the Fujitsu, GlaxoSmithKline, Liberty Living, Vauxhall Motors, VirginCare, Visteon and Jagex Games Studio.
Core modules
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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.
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Final year
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In your final year the focus
is on modern physics and you have a choice of modules. Topics include classical
mechanics, quantum mechanics, electrodynamics and special relativity. The
mathematical language of the core partial differential equations module is
essential. You can conduct a final year theoretical physics project with a
supervisor from our theoretical physics research group. Projects have
included general relativity and black holes, the gravitational super highway,
quantum algorithms, quantum field theory and the quark model.
Core modules
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Partial Differential Equations (MATH3605)
This module introduces partial differential equations using real-life problems. It provides a variety of analytic and numerical methods for their solution. It includes a wide range of applications including heat diffusion and the Tsunami wave.
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Classical and Quantum Mechanics (MATH3606)
All of physics and a large part of applied mathematics is based on classical mechanics and its extension to quantum theory. This module introduces key ideas of these topics to students with a mathematics background. An overarching theme is the key role of symmetry, both for classical motion and quantum behaviour.
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Electrodynamics and Relativity (MATH3611)
This module introduces Maxwell's theory of electromagnetism and Einstein's theory of special relativity. It includes a wide range of applications of electromagnetism, the Lorentz transformations and some of the apparent paradoxes of relativity together with their resolution. It also explains why E = mc^2.
Optional modules
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Professional Experience in Mathematics Education (MATH3603)
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 two semesters.
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Optimisation, Networks and Graphs (MATH3609)
This module introduces the mathematics of continuous and discrete optimisation. It provides the theoretical background and practical algorithmic techniques required to model and solve a diverse range of problems.
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Medical Statistics (MATH3614)
The content includes the design and analysis of clinical trials, including crossover and sequential designs and an introduction to meta-analysis. Epidemiology is studied, including case-control and cohort studies. Survival analysis is covered in detail. Computer packages are used throughout.
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Professional Experience in Industry (MATH3616)
This module provides an opportunity for students to gain experience in applying mathematics in a commercial setting by undertaking a summer placement. Students develop their skills in written and verbal communication, listening, problem solving, time management, teamwork and leadership. Recent summer placement providers include Babcock International, BMW Group, Chess Dynamics Ltd and South West Water.
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Project (MATH3628)
Students who have identified a topic of particular interest have the opportunity to study it in a final year project. Students work individually and independently, with help and advice from a supervisor, on the chosen topic. The project is assessed through presentations and the preparation of a dissertation. This is a major piece of work and the project counts as two modules
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Fluid Dynamics (MATH3629)
Fluid flow problems are at the heart of systems ranging from weather forecasting and climate models to hydroelectricity generation and aerodynamics. They are all formulated mathematically as systems of partial differential equations. These are then solved and the results interpreted for a mixture of theoretical and practical examples of both inviscid and viscous fluid flows. Applications studied include: aeronautics, ocean waves and a variety of industrial topics.
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Mathematical Sciences Group Project (MATH3631)
Students work in small groups researching a problem in mathematics, statistics or theoretical physics. These projects can involve the solution of financial, computing, industrial or scientific problems. Students give oral presentations on their work and write up a journal style article. Some of these articles have been published. This module enhances communication and employability skills.
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 Hons Mathematics with Theoretical Physics Programme Specification 5359
The modules shown for this course are those currently being studied by our students, or are proposed new modules. Please note that programme structures and individual modules are subject to amendment from time to time as part of the University’s curriculum enrichment programme and in line with changes in the University’s policies and requirements.
In light of the Coronavirus (COVID-19) pandemic, the changeable nature of the situation and any updates to government guidance, we may need to make further, last minute adjustments to how we deliver our teaching and learning on some or all of our programmes, at any time during the academic year. We want to reassure you that even if we do have to adjust the way in which we teach our programmes, we will be working to maintain the quality of the student learning experience and learning outcomes at all times.
