# Biology, Physics and Maths

Natural Sciences is a multidisciplinary degree which allows you to study three subjects in the first year and continue with two subjects in the second and third year.

## Year One

You will study **40 credits of each subject** from your chosen three-subject streams.

## Biology

40 compulsory credits can be from your chosen specialism.

#### Molecular Biology and Genetics specialism

This module combines lectures and laboratory classes and introduces you to the structure and function of significant molecules in cells, and the important metabolic processes which occur inside them. You will study, amongst other topics, protein and enzyme structure and function, the biosynthesis of cell components, and the role of cell membranes in barrier and transport processes. You'll examine how information in DNA is used to determine the structure of gene products. Topics include DNA structure, transcription and translation and mutation and recombinant DNA technology.

#### 40 credits throughout the full year.

#### Evolutionary Biology and Ecology specialism

Starting with Darwin’s theory of evolution, you will learn how natural selection and other evolutionary forces have shaped the ways in which organisms interact with each other and their environment. In addition to lectures, practical classes will give you hands-on experience with a range of ecological and behavioural concepts in the laboratory and the field.

**20 compulsory credits throughout the full year.**

Life on Earth provides an introduction to the fundamental characteristics and properties of the myriad of organisms which inhabit our planet, from viruses, bacteria and Archaea, to plants and animals. In weekly lectures, and regular laboratory practical classes, you will consider how living organisms are classified, how they are related genetically and phylogenetically, and basic aspects of their structure and function.

**20 compulsory credits throught the full year.**

## Physics

Students taking Physics must take 40 compulsory credits.

This module is based on the textbook "Physics for Scientists and Engineers" by Knight (all first years are provided with a copy of this book). The module aims to introduce core topics in physics which will underpin all subsequent physics modules. The module begins by discussing classical mechanics in the language of vectors and the key notion of harmonic motion which is extended to cover wave phenomena. The first semester ends with an introduction to Einstein's special theory of relativity. The second semester introduces the basic ideas of electromagnetism and electrical circuits and quantum physics.

- Vectors and Coordinate systems
- Kinematics and Motion in 1D and 2D
- Newton's Laws
- Conservation Laws
- Rotation of a Rigid Body
- Micro-macro connection
- Oscillations
- Travelling Waves
- Superposition of Waves
- Galilean Relativity
- Relativity of Time
- Spacetime
- Relativistic Energy and Momentum

**40 compulsory credits over the full year.**

## Maths

Students must take 40 compulsory credits.

Basic theory is extended to more advanced topics in the calculus of several variables. In addition, the basic concepts of complex numbers, vector and matrix algebra are established and extended to provide an introduction to vector spaces. Students are introduced to different types of proof, such as direct proof, proof by contradiction and proof by induction, as well as theorems and tests for determining the limits of sequences and series. An emphasis in the course is to develop general skills and confidence in applying the methods of calculus and developing techniques and ideas that are widely used and applicable in subsequent modules.

**40 compulsory credits throughout the year**

### Compulsory module

All students are required to take a compulsary module, **Academic and Transferable Skills Portfolio**. This will be taught throughout the first full year. It will support organisational and professional competancies which will be used during the course.

## Year Two

You will continue on your stream comprising of **two of your first year subjects**. You will take **60 credits of modules from each subject** and greater emphasis will be put on studying outside of formal classes.

## Biology

40 compulsory credits from your chosen specialism:

#### Molecular Biology and Genetics specialism

- The Genome and Human Disease

In this module you will learn about the structure and function of the eukaryotic genome, including that of humans, and the approaches that have led to their understanding. You will learn about techniques that are employed to manipulate genes and genomes and how they can be applied to the field of medical genetics. By using specific disease examples, you will learn about the different type of DNA mutation that can lead to disease and how they have been identified. Practical elements will teach you about basic techniques used in medical genetics such as sub-cloning of DNA fragments into expression vectors. Practical classes and problem based learning will be used to explore the methods used for genetic engineering and genome manipulation.

**20 compulsory credits throughout the year.**

You'll cover the key groups of eukaryotic and prokaryotic microorganisms relevant to microbial biotechnology, principles of GM, and strain improvement in prokaryotes and eukaryotes. The impact of “omics”, systems biology, synthetic biology and effects of stress on industrial microorganisms are explored, alongside the activities of key microorganisms that we exploit for biotechnology.

**10 compulsory credits in the Spring Semester.**

- Bacterial Genes and Development

Molecular events that occur during the control of gene expression in bacteria will be explored. You'll learn by considering case studies, which will show you how complex programmes of gene action can occur in response to environmental stimuli. You will also study the regulation of genes in pathogenic bacteria.

**10 compulsory credits in the Spring Semester.**

Plus a further 20 credits from the following for the Molecular Biology and Genetics specialism:

You will study microbiology, learning about pathogenic microbes including viruses, fungi, parasites and the roles of bacteria in health and disease. You will learn how the body generates immunity; the causes of diseases associated with faulty immune responses will be considered. In applied microbiology you will be introduced to recombinant DNA technology and prokaryotic gene regulation.

**20 credits in the Autumn Semeseter.**

This module will teach you the underlying neurophysiology and pathology associated with several common CNS disorders and the neuropharmacology of currently available medication. You will learn about the neurotransmitters and pathways involved in normal brain function and how changes in these contribute to abnormal function. You will also decipher the pharmacological mechanisms of drugs used to treat these CNS disorders. You will cover numerous human diseases including those with great significance such as Alzheimer's disease, epilepsy, schizophrenia and autism.

**20 credits in the Spring Semester.**

Introduces key evolutionary concepts and their application in the animal kingdom. Areas you will study include the history of evolutionary thinking, natural selection versus the neutral theory, sexual selection and human evolution.

**10 credits in the Autumn Semester.**

Examines the basic concepts of vertebrate embryonic development. You will discuss specific topics including germ cells, blood and muscle cell differentiation, left-right asymmetry and miRNAs. The teaching for this module is delivered through lectures.

**10 credits in the Spring Semester.**

Or

#### Evolutionary Biology and Ecology specialism

40 credits from the following:

You will learn about the forces determining the distribution and abundance of species and be able to use models to predict the dynamics of populations under a range of conditions. You will recognise how interactions between species can drive co-evolutionary processes leading to an understanding of the organisation of natural systems working systematically from populations through to communities, ecosystems and biogeographical scales.

**20 compulsory credits in the Autumn Semester.**

This module explores the evolution of key plant systems through deep time, and the significance of this process for understanding modern ecology and food security. You will learn about the challenges that plants faced when moving onto land and evolutionary innovations within the early spermatophytes. You will also gain an understanding of the power of natural selection in producing plant diversity over deep time.

**20 compulsory credits in the Spring Semester.**

Plus a further 20 credits from the following options:

A comprehensive introduction to the study of animal behaviour, from the physiological and genetic bases of behaviour to its development through learning and its adaptive significance in the natural environment. Through practical classes, you will learn about the physiological basis of fundamental behaviours. Using examples from across the animal kingdom, you will learn how predictive modelling, experimental and observational approaches integrate to explain how and why animals behave as they do.

**20 credits in the Spring Semester.**

Studying this module, you'll be able to explain how the nervous system develops, is organised, and processes information. This will be achieved through presentation of comparative invertebrate and vertebrate studies, consideration of evolutionary concepts, and a detailed analysis of the development, structure, and function of the mammalian brain. The lecture sessions are complemented by workshops on Drosophila and chick embryo development, on the neuroanatomy of the human spinal cord, and dissection of pig brains subject to the availability of tissue.

**20 credits in the Autumn Semester.**

You will study microbiology, learning about pathogenic microbes including viruses, fungi, parasites and the roles of bacteria in health and disease. You will learn how the body generates immunity; the causes of diseases associated with faulty immune responses will be considered. In applied microbiology you will be introduced to recombinant DNA technology and prokaryotic gene regulation.

**20 credits in the Autumn Semeseter.**

Introduces key evolutionary concepts and their application in the animal kingdom. Areas you will study include the history of evolutionary thinking, natural selection versus the neutral theory, sexual selection and human evolution.

**10 credits in the Autumn Semester.**

Reproductive Physiology of both male and female mammals including comparative information for farm animals and human. Reproductive physiological processes and their regulation from gametogenesis to fertilization and preparations for a successful pregnancy. Development of mammary glands and hormonal regulation of lactation will also be discussed. Principal features of avian reproduction and the avian maintenance of calcium homeostasis for efficient egg formation. Hormonal regulation of egg laying with emphasis on the nutritional and metabolic challenges associated with commercial rates of egg lay.

Hands-on practical's have been changed to online dissection demonstrations that are performed by experts and are very nicely recorded. This helps students to understand the taught subject matter and provide additional understanding when observing live dissection. This can be viewed multiple times and helps students when preparing for assessment.

**10 credits in the Autumn Semester.**

## Physics

Students taking Physics must take a total of 60 credits.

If you've chosen Biology as one of your subjects you will study these compulsory modules in year three:

In the module From Newton to Einstein, you learnt about the idea of a field a quantity which is defined at every point in space. In this module, the description of fields will be extended by introducing the mathematics of vector calculus.

The module will begin with an introduction to vector calculus, illustrated in the context of the flow of ideal (non-viscous) fluids.

The mathematics will then be used to provide a framework for describing, understanding and using the laws of electromagnetism. We discuss how electric and magnetic fields are related to each other and to electrical charges and electrical currents. The macroscopic description of electric fields inside dielectric materials and magnetic fields inside magnetizable materials will be described, including the boundary conditions that apply at material interfaces.

The last section of the module will discuss Maxwells equations of electrodynamics and how they lead to the vector wave equation for electromagnetic waves.

**20 compulsory credits over the full year.**

In this module you will develop your experimental technique and gain experience of some key instruments and methods. The experiments will cover electrical measurements, optics and radiation. You will also learn how to use a computer to control experiments and to record data directly from measuring instruments.

**20 compulsory credits over the full year.**

This module will provide an introduction to the theory and elementary applications of quantum mechanics, a theory that is one of the key achievements of 20th-century physics.

Quantum mechanics is an elegant theoretical construct that is both beautiful and mysterious. Some of the predictions of quantum mechanics are wholly counter-intuitive and there are aspects of it that are not properly understood but it has been tested experimentally for over 50 years and, wherever predictions can be made, they agree with experiment.

**20 compulsory credits over the full year.**

If you've chosen Maths as one of your subjects you will study these compulsory modules in year two:

Macroscopic systems exhibit behaviour that is quite different from that of their microscopic constituents studied in isolation. New physics emerges from the interplay of many interacting degrees of freedom. In this module you will learn about the important physical properties of matter and the two main approaches to their description. One, thermodynamics, treats macroscopically relevant degrees of freedom (temperature, pressure and so on) and find relations between these and the fundamental laws which govern them, independent of their microscopic structure. The other approach, statistical mechanics, links the macroscopically relevant properties to the microphysics by replacing the detailed microscopic dynamics with a statistical description. The common feature of both of these methods is the introduction of two macroscopic quantities, temperature and entropy, that have no microscopic meaning.

**20 compulsory credits over the full year.**

**20 compulsory credits over the full year.**

**Plus** **select an additional 20 credits** from these optional modules to cover in year two:

You will develop your knowledge of the various physical processes occurring in stars of different types. You’ll use this knowledge to build both mathematical models and your qualitative physical understanding of stellar structure and evolution will be enhanced. You’ll have two hours per week of lectures studying this module.

**10 credits in the Autumn semester.**

You’ll be given an overview of how forces at the nanoscale are different to those observed in macroscopic systems and will consider how they can be exploited in nanometre-scale processes and devices.

You’ll focus on the physical basis and measurement of forces operating on the nanoscale, considering van der Waals, electrostatic, hydrophobic and hydrophilic interactions.

You’ll spend around three hours per week in lectures and workshops studying this module.

**10 compulsory credits in the Autumn semester.**

This module will develop your current understanding of the various physical processes that dictate the formation, evolution and structure of galaxies. You’ll explore a number of topics including The Milky Way, The Dynamics of Galaxies, Active Galaxies and Galaxy Evolution among others. You’ll spend two hours per week in lectures studying this module.

**10 compulsory credits in the Spring semester.**

This module introduces basic techniques in numerical methods and numerical analysis which can be used to generate approximate solutions to problems that may not be amenable to analysis.

Specific topics include:

- Implementing algorithms in Matlab
- Discussion of errors (including rounding errors)
- Iterative methods for nonlinear equations (simple iteration, bisection, Newton, convergence)
- Gaussian elimination, matrix factorisation, and pivoting
- Iterative methods for linear systems, matrix norms, convergence, Jacobi, Gauss-Siedel
- Interpolation (Lagrange polynomials, orthogonal polynomials, splines)
- Numerical differentiation & integration (Difference formulae, Richardson extrapolation, simple and composite quadrature rules)
- Introduction to numerical ODEs (Euler and Runge-Kutta methods, consistency, stability)

**20 credits throughout the full year.**

## Maths

Students taking Maths must take 60 credits from their chosen specialism:

#### Applied, Computation and Statistics specialism

20 compulsory credits:

This course aims to give students a sound grounding in the application of both differential and integral calculus to vectors, and to apply vector calculus methods and separation of variables to the solution of partial differential equations. The module is an important pre-requisite for a wide range of other courses in Applied Mathematics.

**10 credits in the Autumn Semester**

This course is an introduction to Fourier series and integral transforms and to methods of solving some standard ordinary and partial differential equations which occur in applied mathematics and mathematical physics.

The course describes the solution of ordinary differential equations using series and introduces Fourier series and Fourier and Laplace transforms, with applications to differential equations and signal analysis. Standard examples of partial differential equations are introduced and solution using separation of variables is discussed.

**10 credits in the Spring Semester**

And 40 optional credits from the following modules:

The module covers introductory topics in statistics and probability that could be applied to data analysis in a broad range of subjects. Topics include probability distributions, parameter estimation, confidence intervals,hypothesis testing and an introduction to statistical modelling. Consideration is given to issues in applied statistics such as sample size calculations, the multiple comparison problem,data collection, design of experiments, critiquing and interpreting statistical reports and papers.

**20 credits in the Autumn Semester.**

This course aims to provide students with tools which enable them to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations.

**20 credits throughout the full year.**

This module introduces basic techniques in numerical methods and numerical analysis which can be used to generate approximate solutions to problems that may not be amenable to analysis.

Specific topics include:

- Implementing algorithms in Matlab
- Discussion of errors (including rounding errors)
- Iterative methods for nonlinear equations (simple iteration, bisection, Newton, convergence)
- Gaussian elimination, matrix factorisation, and pivoting
- Iterative methods for linear systems, matrix norms, convergence, Jacobi, Gauss-Siedel
- Interpolation (Lagrange polynomials, orthogonal polynomials, splines)
- Numerical differentiation & integration (Difference formulae, Richardson extrapolation, simple and composite quadrature rules)
- Introduction to numerical ODEs (Euler and Runge-Kutta methods, consistency, stability)

**20 credits throughout the full year.**

#### Mathematical Physics specialism

60 compulsory credits:

This course develops Newtonian mechanics into the more powerful formulations due to Lagrange and Hamilton and introduces the basic structure of quantum mechanics. The course provides the foundation for a wide range of more advanced courses in mathematical physics.

**20 credits through the full year.**

This course aims to provide students with tools which enable them to develop and analyse linear and nonlinear mathematical models based on ordinary and partial differential equations. Furthermore, it aims to introduce students to the fundamental mathematical concepts required to model the flow of liquids and gases and to apply the resulting theory to model physical situations.

**20 credits throughout the full year.**

This course aims to give students a sound grounding in the application of both differential and integral calculus to vectors, and to apply vector calculus methods and separation of variables to the solution of partial differential equations. The module is an important pre-requisite for a wide range of other courses in Applied Mathematics.

**10 credits in the Autumn Semester.**

This course is an introduction to Fourier series and integral transforms and to methods of solving some standard ordinary and partial differential equations which occur in applied mathematics and mathematical physics.

The course describes the solution of ordinary differential equations using series and introduces Fourier series and Fourier and Laplace transforms, with applications to differential equations and signal analysis. Standard examples of partial differential equations are introduced and solution using separation of variables is discussed.

**10 credits in the Spring Semester.**

## Year Three

You will continue with the **same two subjects studied in the second year**, taking** 40-50 credits**.

### Compulsory year three module

Alongside subject-specific study, you will undertake a **20-credit compulsory synoptic module** which aims to tie together the subjects you are studying through an interdisciplinary group project.

The Natural Sciences programme is by nature interdisciplinary but is mostly taught via specialized modules delivered by individual Schools with little exploration of the interfaces between the sciences. The synoptic module (C13602) gives students the opportunity to combine knowledge and skills acquired whilst on their pathway to carry out a (number of) interdisciplinary piece(s) of work.

**20 credits throughout the full year.**

## Biology

Students must take 40-50 credits in total from one of the specialisms.

#### Molecular Biology and Genetics specialism

30 compulsory credits:

Examines genetic variation in humans, including variation at the DNA level, and the study of human population history using genetic methods. Around three hours per week will be spent within lectures studying this module.

**10 compulosry credits in the Autumn Semester.**

Examines the mechanisms through which eukaryotic genes are expressed and regulated, with emphasis placed on recent research on transcriptional control in yeast and post-transcriptional control in eukaryotes. Studying this module will include having three hours of lectures per week.

**10 compulsory credits in the Autumn Semester.**

Examines the mechanisms through which eukaryotic genes are expressed and regulated, with emphasis placed on recent research on transcriptional control in yeast and post-transcriptional control in eukaryotes. Studying this module will include having three hours of lectures per week.

**10 compulsory credits in the Spring Semester.**

And 10-20 credits from the following:

This course, taught by 5 lecturers will give students an in depth understanding of the genetics, evolution and biochemistry behind the pathogenic properties of parasites and micro-organisms that cause major human disease in the present day. We will concentrate mainly on microbial aspects with one week on the genetics of human susceptibility. Students will learn about the specialised features of parasites and micro-organisms that make them pathogenic, how the genes encoding these features are regulated, and how biological, genetic and chemical tools can be used to develop preventative and curative treatments (two weeks). Model organisms to be studied include the agents of malaria (two weeks), leishmania (one week), candidiasis (one week), aspergillosis (one week), Salmonella, Escherichia and Shigella dysenteries (one week), and tuberculosis (one week). Students will also take part in a group-learning activity to produce a poster on an emerging or persistent pathogen explaining the molecular biology of its virulence. They will learn to use a questioning approach to gain an understanding of microbiological processes in the literature and how to present a scientific poster at a conference by presenting their group's work for peer and staff judging at a poster conference for 35% of the module mark.

**10 credits in the Autumn Semester.**

You will consider the molecular mechanisms underlying stem cell function during embryogenesis and adulthood. This will involve studies of regeneration and repair of tissues and pluripotency. You will have one two-hour lecture per week in this module.

**10 credits in the Autumn Semester.**

Considers ion channels at the molecular level, with topics including the structure and function of different ion channel groups and their modulation by drugs, pesticides and natural toxins. You will also consider the synthesis and transport of neurotransmitters and the formation and release of synaptic vesicles. This module involves one three hour session per week incorporating eight lectures and two practical sessions.

**10 credits in the Autumn Semester.**

Examine the molecular causes of the ageing and malignant transformations of somatic cells that are observed during a single lifespan, and gain an understanding of the necessity to maintain the genome intact from one generation to the next. Around three hours per week will be spent within lectures studying this module.

**10 credits in the Spring Semester.**

Examine a selection of acquired and inherited cancers, and develop an understanding of the role of the genes involved and how they can be analysed. To study for this module you will have a two- or three-hour lecture once per week.

**10 credits in the Spring Semester.**

Or 50 credits from this specialism:

#### Evolutionary Biology and Ecology specialism

30 compulsory credits:

Approximately one week will be spent on each of the following topics:

- Natural selection and the causes of evolution
- The genetic basis of variation and its maintenance
- Evolutionary stable strategies
- Evolution of life histories
- Competition and evolution
- Coevolution of predators and prey
- Coevolution of hosts and parasites
- Coevolution of mutualists
- Ecology and the origin of species
- Genomics in evolutionary ecology

**10 compulsory credits in the Autumn Semester.**

**20 compulsory credits in the Spring Semester.**

And 20 credits from the following:

Considers ion channels at the molecular level, with topics including the structure and function of different ion channel groups and their modulation by drugs, pesticides and natural toxins. You will also consider the synthesis and transport of neurotransmitters and the formation and release of synaptic vesicles. This module involves one three hour session per week incorporating eight lectures and two practical sessions.

**10 credits in the Autumn Semester.**

The module examines how we can use DNA and protein sequences to investigate evolutionary relationships among organisms.

The subject matter includes the alignment of DNA and protein sequences, the way in which DNA and protein sequences evolve and how these processes can be modeled, the construction of evolutionary trees (phylogenies) to determine relationships among organisms, and the use of molecular clocks to place evolutionary events within a timeframe.

The course provides numerous examples of the uses of molecular sequence data in evolutionary studies, highlighting the way in which sequence data are revolutionising our understanding of the living world and shows how understanding molecular evolution to produce accurate trees is crucial to understanding evolutionary mechanisms.

In depth examples include the uses of molecular data to resolve the deep-level relationships in the ‘tree of life’ (relationships among the three domains of life), the origins of mitochondria and chloroplasts, and the application of molecular data to study relationships in the Mammalia and in particular the Cetacea.

The use of molecular data in understanding phylogeography is also discussed, with particular emphasis on the recolonisation of Europe following the retreat of the ice at the end of the last glacial period. We also discuss the uses of genomic data to examine evolution.

**10 credits in the Autumn Semester.**

Scientific discoveries are not isolated from the society within which they exist. This module will explore the interactions between science and society through a series of lectures, discussion groups and workshops.

Topics that will be explored include the ethical parameters that govern how scientific work is constrained, ways in which scientific discoveries can/should be disseminated to the wider community, the wider responsibilities that follow the acquisition of new knowledge and the concept of 'citizen science', where science takes place outside the traditional academic centres of work.

**10 credits in the Spring Semester.**

Examines the mechanisms through which eukaryotic genes are expressed and regulated, with emphasis placed on recent research on transcriptional control in yeast and post-transcriptional control in eukaryotes. Studying this module will include having three hours of lectures per week.

**10 compulsory credits in the Spring Semester.**

## Physics

Students taking Physics must take 50 compulsory credits from your chosen specialism.

If you've chosen Biology as one of your subjects you will study these compulsory modules in year three:Macroscopic systems exhibit behaviour that is quite different from that of their microscopic constituents studied in isolation. New physics emerges from the interplay of many interacting degrees of freedom. In this module you will learn about the important physical properties of matter and the two main approaches to their description. One, thermodynamics, treats macroscopically relevant degrees of freedom (temperature, pressure and so on) and find relations between these and the fundamental laws which govern them, independent of their microscopic structure. The other approach, statistical mechanics, links the macroscopically relevant properties to the microphysics by replacing the detailed microscopic dynamics with a statistical description. The common feature of both of these methods is the introduction of two macroscopic quantities, temperature and entropy, that have no microscopic meaning.

**20 compulsory credits over the full year.**

This module will introduce students to the physics of atoms, nuclei and the fundamental constituents of matter and their interactions. The module will also develop the quantum mechanical description of these.

Topics to be covered are:

- Approximation techniques first order perturbation theory, degeneracies, second order perturbation theory, transition rates, time-dependent perturbation theory, Fermi's golden rule
- Particle Physics protons and neutrons, antiparticles, particle accelerators and scattering experiments, conservation laws, neutrinos, leptons, baryons and hadrons, the quark model and the strong interaction, weak interactions, standard model
- Introduction to atomic physics review of simple model of hydrogen atom, Fermi statistics and Pauli principle, aufbau principle, hydrogenic atoms, exchange, fine structure and hyperfine interactions, dipole interaction, selection rules and transition rates
- Lasers optical polarization and photons, optical cavities, population inversions, Bose statistics and stimulated emission, Einstein A and B coefficients
- Nuclear Physics Radioactivity, decay processes, alpha, beta and gamma emission, detectors, stability curves and binding energies, nuclear fission, fusion, liquid drop and shell models.

**20 credits over the full year.**

You will carry out a project drawn from one of several areas of physics. The project may be experimental or theoretical in nature. Many of the projects reflect the research interests of members of academic staff. You’ll work in pairs and will be expected to produce a plan of work and to identify realistic goals for your project. Each pair has a project supervisor responsible for setting the project.

**10 credits in the Autumn semester.**

If you've chosen Maths as one of your subjects you will study these compulsory modules in year three:

This module will provide a general introduction to solid state physics. Topics covered include:

- Bonding nature of chemical bonds, thermodynamics of solid formation
- Crystal structures description of crystal structures, k-space, reciprocal lattice, Bragg diffraction, Brillouin zones
- Nearly-free electron model - Bloch's theorem, band gaps from electron Bragg scattering, effective masses
- Band theory Fermi surfaces, qualitative picture of transport, metals, insulators and semiconductors
- Semiconductors - doping, inhomogeneous semiconductors, basic description of pn junction
- Phonons normal modes of ionic lattice, quantization, Debye theory of heat capacities, acoustic and optical phonons
- Optical properties of solids absorption and reflection of light by metals, Brewster angle, dielectric constants, plasma oscillations
- Magnetism- Landau diamagnetism, paramagnetism, exchange interactions, Ferromagnetism, antiferromagnetism, neutron scattering, dipolar interactions and domain formation, magnetic technology

**20 compulsory credits over the full year.**

This module will introduce students to the physics of atoms, nuclei and the fundamental constituents of matter and their interactions. The module will also develop the quantum mechanical description of these.

Topics to be covered are:

- Approximation techniques first order perturbation theory, degeneracies, second order perturbation theory, transition rates, time-dependent perturbation theory, Fermi's golden rule
- Particle Physics protons and neutrons, antiparticles, particle accelerators and scattering experiments, conservation laws, neutrinos, leptons, baryons and hadrons, the quark model and the strong interaction, weak interactions, standard model
- Introduction to atomic physics review of simple model of hydrogen atom, Fermi statistics and Pauli principle, aufbau principle, hydrogenic atoms, exchange, fine structure and hyperfine interactions, dipole interaction, selection rules and transition rates
- Lasers optical polarization and photons, optical cavities, population inversions, Bose statistics and stimulated emission, Einstein A and B coefficients
- Nuclear Physics Radioactivity, decay processes, alpha, beta and gamma emission, detectors, stability curves and binding energies, nuclear fission, fusion, liquid drop and shell models.

**20 credits over the full year.**

You will carry out a project drawn from one of several areas of physics. The project may be experimental or theoretical in nature. Many of the projects reflect the research interests of members of academic staff. You’ll work in pairs and will be expected to produce a plan of work and to identify realistic goals for your project. Each pair has a project supervisor responsible for setting the project.

**10 credits in the Autumn semester.**

## Maths

Students taking Maths must take a total of 50 credits from their chosen specialism:

#### Applied, Computation & Statistics specialism

Select 50 credits from the below modules:

In this module a variety of techniques and areas of mathematical optimisation will be covered including Lagrangian methods for optimisation, simplex algorithm linear programming and dynamic programming. You’ll develop techniques for application which can be used outside the mathematical arena.

**20 credits in the Autumn Semester.**

Mathematics can be usefully applied to a wide range of applications in medicine and biology. Without assuming any prior biological knowledge, this course describes how mathematics helps us understand topics such as population dynamics, biological oscillations, pattern formation and nonlinear growth phenomena. There is considerable emphasis on model building and development.

**20 credits in the Autumn Semester.**

This course provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. It also provides an introduction to to cryptography, including classical mono and polyalphabetic ciphers as well as modern public key cryptography and digital signatures, their uses and applications.

**10 credits in the Autumn Semester.**

Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The module starts with an investigation into normal-form games, including strategic dominance, Nash equilibria, and the Prisoner’s Dilemma. We look at tree-searching, including alpha-beta pruning, the ‘killer’ heuristic and its relatives. It then turns to mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.

**10 credits in the Spring Semester.**

This course aims to extend previous knowledge of fluid flow by introducing the concept of viscosity and studying the fundamental governing equations for the motion of liquids and gases. Methods for solution of these equations are introduced, including exact solutions and approximate solutions valid for thin layers. A further aim is to apply the theory to model fluid dynamical problems of physical relevance.

**20 credits in the Spring Semester.**

Differential equations play a crucial modelling role in many applications, such as fluid dynamics, electromagnetism, biomedicine, astrophysics and financial modelling. Typically, the equations under consideration are so complicated that their solution may not be determined by purely analytical techniques; instead one has to resort to computing numerical approximations to the unknown analytical solution. In this module we study numerical techniques for approximating data, ordinary and partial differential equations, and solving, or finding eigenvalues and eigenvectors of, the large linear systems of equations that result from these approximations. The module covers:

- Initial value problems (ODEs): multistage and multistep methods; convergence and stability; higher order ODEs; systems of first order ODEs; implicit methods
- Partial differential equations: finite differences for elliptic, parabolic and hyperbolic PDEs; truncation error and stability analysis; finite volume methods
- Approximation theory: least squares approximation; trigonometric polynomial approximation
- Eigenvalues and eigenvectors: power method; inverse iteration; Householder transformations; QR algorithm; singular value decomposition
- Large linear systems: Krylov subspace methods; conjugate gradient method; preconditioning

**20 credits in the Spring Semester.**

#### Mathematical Physics specialism

Select 50 credits from the below modules

**20 credits in the Autumn Semester**

This course introduces various analytical methods for the solution of ordinary and partial differential equations, focussing on asymptotic techniques and dynamical systems theory. Students taking this course will build on their understanding of differential equations covered in Modelling with Differential Equations.

**20 credits in the Spring Semester.**

This course aims to extend previous knowledge of fluid flow by introducing the concept of viscosity and studying the fundamental governing equations for the motion of liquids and gases. Methods for solution of these equations are introduced, including exact solutions and approximate solutions valid for thin layers. A further aim is to apply the theory to model fluid dynamical problems of physical relevance.

**20 credits in the Spring Semester.**

In this module you’ll have an introduction to Einstein’s theory of general and special relativity. The relativistic laws of mechanics will be described within a unified framework of space and time. You’ll learn how to compare other theories against this work and you’ll be able to explain new phenomena which occur in relativity.

**20 credits in the Spring Semester.**

This course provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. It also provides an introduction to to cryptography, including classical mono and polyalphabetic ciphers as well as modern public key cryptography and digital signatures, their uses and applications.

**10 credits in the Autumn Semester.**

Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The module starts with an investigation into normal-form games, including strategic dominance, Nash equilibria, and the Prisoner’s Dilemma. We look at tree-searching, including alpha-beta pruning, the ‘killer’ heuristic and its relatives. It then turns to mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.

**10 credits in the Spring Semester.**

## Year Four (MSci students only)

You will choose one of your third-year subjects to focus on in the fourth year, spending half your time working on an independent research project aiming to develop the skills needed to pursue a career in research.

All students take 120 credits of modules in the fourth year and each subject has a minimum number of credits listed. Students can take 120 credits from a single subject (where available) or they can use modules from their second subject to make up the difference between the minimum and the required number of credits.

## Biology

**You must take a total of 120 credits from biology throughout the year.**

100 compulsory credits:

The project involves an extensive piece of detailed research on the topic chosen after discussion with the supervisor. The practical component will involve collection of data from a laboratory or field investigation and appropriate analysis. The findings will be interpreted in the context of previous work, and written-up in a clear and concise final report in the form of a research paper manuscript or end-of-grant report. The main findings will also be delivered in an assessed oral presentation and discussed with two assessors in a viva voce.

**60 compulsory credits throughout the full year.**

**20 compulsory credits throughout the full year.**

**20 compulsory credits throughout the full year.**

Plus a further 20 credits from the following options:

- Cutting-edge Research Technologies and Ideas in Molecular Biology

**10 credits in the Autumn Semester.**

- Advanced Experimental Design and Analysis

**10 credits in the Autumn Semester.**

- Process and Practice in Science

**10 credits in the Autumn Semester.**

## Physics

**You must take a total of 120 credits from physics throughout the year.**

60 compulsory credits:

In this year-long module you’ll aim to solve a theoretical or practical problem. You’ll spend semester one researching your chosen project and carry out your original research in semester two. You’ll have the opportunity to work with external parties such as an industrial laboratory, school or hospital if appropriate to your topic.

**60 credits over the full year.**

Plus 20 compulsory credits if you haven't chosen Maths from year two or three.

This module will provide a general introduction to solid state physics. Topics to be covered will include:

- Fermi Dirac and Bose-Einstein Statistics, Fermi Wave-vector, temperature
- Introduction to Fourier Transforms and Associated Techniques
- bonding nature of chemical bonds, thermodynamics of solid formation
- crystal structures description of crystal structures, k-space, reciprocal lattice, Bragg diffraction, Brillouin zones
- Nearly-free electron model - Bloch's theorem, band gaps from electron Bragg scattering, effective masses
- Band theory Fermi surfaces, qualitative picture of transport, metals, insulators and semiconductors
- Semiconductors - doping, inhomogeneous semiconductors, basic description of pn junction
- Phonons normal modes of ionic lattice, quantization, Debye theory of heat capacities, acoustic and optical phonons
- Optical properties of solids absorption and reflection of light by metals, Brewster angle, dielectric constants, plasma oscillations
- Magnetism, Landau diamagnetism, paramagnetism, exchange interactions, Ferromagnetism, antiferromagnetism, neutron scattering, dipolar interactions and domain formation, magnetic technology

**10 credits in the Autumn semester.**

And an additional 40 to 60 credits to be selected from the below optional modules:

In this module you’ll explore the theoretical aspect of atmospheric physics. Topics will include planetary atmosphere, troposphere, solar radiation and the Energy budget, radiation transfer and Photochemistry among others. You’ll have two hours of lectures per week studying this module.

**10 credits in the Autumn semester.**

Cosmology is the scientific study of the universe as a whole. The module provides an introduction to modern cosmology, including some of the more recent observational and theoretical developments. No prior knowledge of General Relativity is required. Topics covered include: observed features of the universe, the Cosmological Principle, Newtoniaan and Relativistic cosmology, the Friedmann Models, cosmic expansion, the cosmological constant, evidence for the big bang model, the thermal history of the big bang, the early universe and inflation, the classical cosmological tests, structure formation (brief treatment only).

**10 credits in the Autumn semester.**

To make models of extreme astrophysical sources and environments basedon physical theory.

To interpret observational data in the light of relevant physical theory.

**10 credits in the Spring semester.**

This module introduces you to the physical properties of semiconductors and low-dimensional systems, such as quantum wells, wires and dots. The aim is to explain the physics that underlies optical and transport properties of these structures and and their applications in advanced technologies.

This course is structured in two main parts. The first part focuses on the foundation of quantum mechanics and solid state physics needed to describe a low dimensional system. The module then moves on describing the physical principles of semiconductor junction and devices.

**10 credits in the Spring semester.**

To introduce the key theoretical ideas of elementary particle physics, such as symmetry and conservation laws, and to build the foundations for a mathematical description of particle properties and interactions.

**10 credits in the Spring semester.**

The first half of this module will describe radiation sources and detectors, with particular reference to those used in the medical imaging applications described in the second half. It will include the physics of accelerators such as linacs, cyclotrons and synchrotrons, of detectors such as ionization chambers, scintillators and solid state detectors and of X-ray imaging, nuclear imaging and positron emission tomography (PET).

**10 credits in the Autumn semester.**

- Introduction to Soft Matter
- Forces, energies and timescales in soft matter
- Liquids and glasses
- Phase transitions in soft matter (solid-liquid and liquid-liquid demixing)
- Polymeric materials
- Gelation
- Crystallisation in soft systems
- Liquid crystals
- Molecular order in soft systems
- Soft Nanotechnology

**10 credits in the Autumn semester.**

Description under review.

**10 credits in the Autumn semester.**

## Maths

**You must take a minimum of 80 and a maximum of 120 credits from maths throughout the year.**

40 compulsory credits:

This module consists of a self-directed investigation of a project selected from a list of projects or, subject to prior approval of the School, from elsewhere.

The project will be supervised by a member of staff and will be based on a substantial mathematical problem, an application of mathematics or investigation of an area of mathematics not previously studied by the student. The course includes training in the use of IT resources, the word-processing of mathematics and report writing.

**40 compulsory credits throughout the year**

And select a minimum of 40 credits and a maximum of 80 credits from the optional modules:

The development of techniques for the study of nonlinear differential equations is a major worldwide research activity to which members of the School have made important contributions. This course will cover a number of state-of-the-art methods, namely:

- use of green function methods in the solution of linear partial differential equations
- characteristic methods, classification and regularization of nonlinear partial differentiation equations
- bifurcation theory

These will be illustrated by applications in the biological and physical sciences.

**20 credits in the Autumn Semester**

The course introduces notions of topology and differential geometry which are required for modern research in relativity and other topics involving geometry. The course will be illustrated with a body of concrete geometrical examples drawn from general relativity. The modern study of general relativity requires familiarity with a number of tools of differential geometry, including manifolds, symmetries, Lie Groups, differentiation and integration on manifolds. These are introduced using examples of curved space-times whose context is familiar from the study of general relativity, the presentation of geometric concepts will be significantly more abstract and powerful than in Relativity MATH3018

**20 credits in the Autumn Semester**

The first part of the module introduces no-arbitrage pricing principle and financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part of the module considers the pricing and hedging of options and discrete-time discrete-space stochastic processes. The final part of the module focuses on the Black-Scholes formula for pricing European options and also introduces the Wiener process. Ito integrals and stochastic differential equations.

**20 credits in the Autumn Semester**

The purpose of this course is to introduce concepts of scientific programming using the object oriented language C++ for applications arising in the mathematical modelling of physical processes. Students taking this module will develop knowledge and understanding of a variety or relevant numerical techniques and how to efficiently implement them in C++.

**20 credits in the Autumn Semester**

In this course the fundamental principles and techniques underlying modern statistical and data analysis will be introduced. The course will cover a 'common core' consisting of statistical concepts and methods, linear models, probability techniques and Markov chains.

You will gain experience of using a statistical package and interpreting its output. The common core material will be covered primarily at the beginning of the semester.

**20 credits in the Autumn Semester**

General relativity predicts the existence of black holes which are regions of space-time into which objects can be sent but from which no classical objects can escape. This course uses techniques learnt in MATH4015 to systematically study black holes and their properties, including horizons and singularities. Astrophysical processes involving black holes are discussed, and there is a brief introduction to black hole radiation discovered by Hawking.

This course aims to introduce the physics of black holes and its mathematical description, giving insight into problems of research interest. It provides an opportunity to apply techniques and ideas learned in previous modules to important astrophysical problems. Students will acquire knowledge and skills to a level sufficient to begin research in general relativity.

**20 credits in the Spring Semester**

This module illustrates the applications of advanced techniques of mathematical modelling using ordinary and partial differential equations. A variety of medical and biological topics are treated bringing students close to active fields of mathematical research.

**20 credits in the Spring Semester**

This module will provide a general introduction to the analysis of data that arise sequentially in time. You will discuss several commonly-occurring models, including methods for model identification for real-time series data. You will develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values. You will gain experience of using a statistical package and interpreting its output.

**20 credits in the Spring Semester**

This course introduces computational methods for solving problems in applied mathematics. Students taking this course will develop knowledge and understanding to design, justify and implement relevant computational techniques and methodologies.

**20 credits in the Spring Semester**

**Disclaimer**This online prospectus has been drafted in advance of the academic year to which it applies. Every effort has been made to ensure that the information is accurate at the time of publishing, but changes (for example to course content) are likely to occur given the interval between publishing and commencement of the course. It is therefore very important to check this website for any updates before you apply for the course where there has been an interval between you reading this website and applying.