BSc Hons Mathematics & Physics

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, all demonstrated in application to practical problems including solving basic first and second-order differential equations.  

This class will introduce you to vectors and matrices.

This class will introduce basic ideas and techniques of statistics.

This class is an introduction to working in a laboratory environment. You'll undertake experiments related to the taught components of the first year physics curriculum, learning how to use standard equipment and handle experimental uncertainties.

This class 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.

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 will be presented.

This class 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 class 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 and the operation of lasers.

This class builds on the material you learned in year 1. you'll be introduced to the probabilistic nature of quantum mechanics and you'll develop a vector model of electromagnetism.

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

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.

This class 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. It'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.

This class will introduce you to the fundamentals of computer programming and the applications of computer programming, using Matlab, to solve physical problems.

This class 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.

Here 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 class 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 class will present the main results in Functional Analysis, give an introduction to linear operators on Banach and Hilbert spaces and study applications to integral and differential equations.

This class will provide you with a range of applied statistical techniques that can be used in professional life.

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.

You'll be presented with the basic theory and practice of finite element methods and polynomial and piecewise polynomial approximation theory.

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

Here you'll learn the application of mathematical models to a variety of problems in biology, medicine, and ecology. It'll 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, and 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 class 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.

Students will learn new statistical methodology and apply it to real data from medical research studies, with an emphasis on the interpretation of the statistical results in the context of the medical problem being investigated. This skill is necessary for the application of statistics to medical data and differs from the traditional, standard interpretation of statistical textbook problems.

Students will be introduced to modern experimental and theoretical developments in the field of quantum optics and atom optics. A great emphasis will be put on illustrating the theory by discussing state-of-the art experiments and research papers.  Students will gain a solid background in the field of quantum optics, with a specific focus on the subjects listed below. They will understand the key questions in modern research in this area and they will in particular learn to read and understand related research papers.