BSc Hons Mathematics & Physics

You'll study the basic concepts and standard methods of mathematical notation and proof, polynomial equations and inequalities, sequences and series, functions, limits and continuity, differentiation and integration.

The fundamental concepts of calculus (differentiation and integration) presented in Applications of Calculus will be examined in more detail, extended to a larger class of functions by means of more sophisticated methods, including an introduction to complex numbers and variables. These will all be demonstrated in application to practical problems including solving basic first and second-order differential equations.  

This module will introduce you to vectors and matrices.

This module will introduce basic ideas and techniques of statistics.

This module is an introduction to working in a laboratory environment. You'll learn how to design and undertake simple experiments related to the taught components of the first-year physics curriculum. By the end of the course you will be able to write a formal report, perform simple uncertainty analysis, make dimensional analysis of physical systems, and perform simple data analysis with Python.

This module will provide you with an understanding of motion of simple mechanical systems, gravitation and simple harmonic motion. You'll also learn about the fundamentals of wave propagation and the superposition of waves as well simple optical phenomena such as diffraction.

This module is designed to introduce you to quantum mechanics and electromagnetism. It highlights experimental observations that resulted in the development of quantum mechanics, such as the photoelectric effect and blackbody radiation. In terms of electromagnetism, you'll cover basic electrostatics and magnetostatics and develop an understanding of Maxwell’s equations and the Lorentz force law.

This module will introduce you to the basic ideas of linear algebra, such as matrices and determinants, vector spaces, bases, eigenvalues and eigenvectors. You'll study various standard methods for solving ordinary differential equations and understand their relevance.

This module will present basic ideas, techniques and results for calculus of two and three variables, along with differentiation and integration over curves, surfaces and volumes of both scalar and vector fields.

This module will introduce you to the R computing environment. It'll enable you to use R to import data and perform statistical tests, allow you to understand the concept of an algorithm and what makes a good algorithm and will equip you for implementing simple algorithms in R.

This module builds on Mechanics and Waves from year 1. You'll be introduced to special relativity, the vector treatment of rotational motion and the behaviour of systems when forced to oscillate. To extend your understanding of wave phenomena you'll be introduced to the wave equation, Fresnel and Fraunhofer diffraction, interference, geometrical optics, and the operation of lasers.

This module builds on the material you learned in year 1. You'll be introduced to the probabilistic nature of quantum mechanics, including wave particle duality and Heisenberg uncertainty principle. You'll learn about AC theory, covering inductors, capacitors and transmission lines. You’ll extend your knowledge of Maxwell’s equations to develop a vector model of electromagnetism and the theory of the plane electromagnetic wave in vacuum.

This module will introduce functions of a complex variable, define concepts such as continuity, differentiability, analyticity, line integration, singular points, etc. You will examine some important properties of such functions and consider some applications of them, for example, conformal mappings and the evaluation of real integrals using the Residue Theorem. You will also be introduced to Fourier and Laplace transform methods for solving linear ordinary differential equations and convolution type integral equations.

In this module we’ll introduce you to analytical methods for solving ordinary and partial differential equations, so you'll develop an understanding along with technical skills in this area.

Building on what you learned in year 2, this module will extend your understanding of quantum mechanics. We'll introduce operators, expectation values and commutation relationships, and advanced concepts like time independent perturbation theory. In electromagnetism you will exploring the wave like nature of electromagnetism as predicted by Maxwell's equations, Poynting’s theorem, reflection and transmission at a dielectric interface, potentials and gauge transformations, and retarded potentials.

Here you'll cover condensed matter physics and be introduced to concepts such as the Fermi surface, superconductors, phonons and other forms of collective excitations.

This module covers the physics of gases and liquids and the fundamentals of thermodynamics. This includes the ideal gas law, hydrostatics, isothermal and adiabatic processes, and the laws of thermodynamics. We also present the basic principles of statistical mechanics, and various distributions such as Maxwellian, Fermi-Dirac and Bose-Einstein.

In this module we'll introduce basic algebraic structures, with particular emphasis on those pertaining to finite dimensional linear spaces and deepen your understanding of linear mappings. We'll also provide an introduction to inner product spaces and bilinear forms.

This module will:

• convey the generalisation of the mechanics of single-particle systems to many-particle systems
• convey the central ideas of a continuum description of material behaviour and to understand relevant constraints
• ground students in the basic principles governing three-dimensional motions of rigid bodies
• convey how the ideas of continuum theory are applied to static and inviscid fluids

This module will motivate the need for numerical algorithms to approximate the solution of problems that can’t be solved with pen and paper. You’ll develop your skills in performing detailed analysis of the performance of numerical methods and will continue to develop your skills in the implementation of numerical algorithms using R.

During this module, you’ll be introduced to the best practises in software development, and the numerical methods that are most commonly used to solve physical problems including linear algebra, partial, ordinary and stochastic differential equations, and Fourier methods.  To undertake this module, a prior understanding of Python is required.

This module provides you with experience of the skills required to undertake project work, and to communicate the findings in written and oral form using a variety of sources, such as books, journals and the internet. You will undertake an individual research project, researching a mathematical or statistical topic and writing a short report on it.

The aim of this module is to help you develop as an enquiring, independent physicist, by undertaking a research project. You'll be under the supervision of a member of staff from the department.

In this module you'll get an introduction to ideas in mathematics and statistics that can be used to model real systems, with an emphasis on the valuation of financial derivatives. This module places equal emphasis on deterministic analysis (calculus, differential equations) and stochastic analysis (Brownian motion, birth and death processes). In both cases, in addition to theoretical analysis, appropriate computational algorithms are introduced.

The first half of the module introduces general modelling and simulation tools, and the second half focuses on the specific application of valuing financial derivatives, including the celebrated Black-Scholes theory.

This module will present the main results in Functional Analysis. You will also be introduced to linear operators on Banach and Hilbert spaces and study applications to integral and differential equations.

You will be provided with a range of applied statistical techniques that can be used in professional life. This module provides you with the fundamental principles of statistical modelling through experimental design and multivariate analysis.

In this module you'll be introduced to the theory of Newtonian fluids and its application to flow problems and the dynamics of waves on water and in other contexts.

In this module you'll be presented with the basic theory and practice of finite element methods and polynomial and piecewise polynomial approximation theory.

In this module you'll be introduced to a range of modern statistical methods and practices used in industry, commerce and research, and you will develop skills in your application and presentation.

In this module, you'll learn the application of mathematical models to a variety of problems in biology, medicine, and ecology. The module will show:

• the application of ordinary differential equations to simple biological and medical problems
• the use of mathematical modelling in biochemical reactions
• the application of partial differential equations in describing spatial processes such as cancer growth and pattern formation in embryonic development
• the use of delay-differential equations in physiological processes.

The marine population modelling element will introduce the use of difference models to represent population processes through applications to fisheries, and the use of coupled ODE system to represent ecosystems. Practical work will include example class case studies that will explore a real-world application of an ecosystem model.

This module will demonstrate the central role network theory plays in mathematical modelling. It'll also show the intimate connection between linear algebra and graph theory and how to use this connection to develop a sound theoretical understanding of network theory. Finally, it'll apply this theory as a tool for revealing structure in networks.

This module will cover the application of classical statistical methods to data collected for health care research. There will be an emphasis on the use of real data and the interpretation of statistical analyses in the context of the research hypothesis under investigation. Topics covered will include:

• survival analysis
• experimental design and sampling
• categorical data analysis
• clinical measurement

Here you'll track the development of key concepts in solid state physics and how these concepts can be exploited to form functional optical and electronic devices. You will look at the chemistry and physics of crystalline and amorphous materials, with a focus on semiconductor materials, optical activity in solid-state materials, the interaction of semiconductors with light, transistors (bipolar and unipolar), quantum wells and microstructured materials.

Here you'll be introduced to state-of-the-art developments in generation and use of charged particles in various forms such as free electron beams, plasmas and astrophysical plasmas. This will include basic plasma physics theory (particle orbit theory, fluid equations, ideal and magnetohydrodynamics, wave equations and kinetic theory), electron optics and electron microscopes, free electron devices and radiation sources. You will also look at the history and geography of our galactic environment, red giants, white dwarfs, supernovae, neutron stars, black holes and physics of the Big Bang.

This module will provide an overview of modern nanoscience. It will discuss basic physics related to low dimensional nanostructures and nanoclusters, nanofabrication including top-down and bottom up approaches, characteristics techniques including electron spectroscopy and microscopy, scanning probe microscopy, and optical spectroscopy and microscopy. Noble metal nanoparticles, quantum dots, carbon nanomaterials will be introduced. In particular it will cover the physical and chemical properties of nanoparticles, their production, applications in physics, chemistry and medicine along with issues relating to nanotoxicity and the ethics of medical nanoscience.

During this module you'll gain an insight into laser physics, laser optics and nonlinear optics as used in many photonic laboratories. This will include properties of laser radiation, beam propagation and ray transfer matrices, nonlinear polarization, and second and third order nonlinear effects such as second harmonic generation and the optical Kerr effect.

In this module we’ll demonstrate the large-scale structure of space-time. You will develop the necessary mathematical concepts (4-vectors, the metric tensor, covariant derivatives, connection coefficients and the Riemann curvature tensor) and use them to derive Einstein's gravitational field equation and look at idealized cosmological solutions for the large-scale structure of the universe, including the standard model. You will study gravitational collapse and the properties of black holes.

This module aims to give a general overview and understanding of atomic and molecular physics and relate these to practical applications and related fields of study. You will learn about optical selection rules, atomic structure, and atom-light interactions, and applications such as Atomic Clocks; Laser Cooling; Ion Traps; Magnetic Trapping; Optical Trapping; Quantum Degenerate Gases; Atom Interferometry; Laser frequency calibration and combs. In molecular physics you will learn about: Diatomic molecules; Rotational Modes; Vibrational Modes; Symmetries and Selection Rules.

This module will provide a broad foundation in concepts and techniques from quantum mechanics, and provide experience in the practical application of these techniques to describing state-of-the-art experiments and quantum technologies.

During this module you will learn about simple systems that exhibit non-linear and complex behaviour. You will find how to analyse non-linear systems and find stationary points, learn to analyse bifurcation diagrams and identify key features on these diagrams, look at periodic solutions to non-linear systems and recognise oscillations, and key features of these oscillations, and understand the origin of deterministic chaos and explain key features relating to chaos.

This module provides an up-to-date introduction to High Performance Computing (HPC) and the use of modern parallel computers to tackle the most demanding problems in science in general and Physics in particular. It provides an overview of the basic building blocks of High-Performance Computers and how they can be utilised effectively. The practical use of HPC will be demonstrated using application examples drawn from several areas of relevance to 4th year modules offered by the Department.