# Chemistry, Physics and Mathematical Sciences

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.

## Chemistry

40 compulsory credits:

To provide a fundamental understanding of the basics of organic chemistry, including nomenclature, molecular structure and bonding, stereochemistry and the chemical reactivity of common functional groups and reaction types through an understanding of their electronic properties.

To provide an introduction to fundamental physical aspects of chemistry, which underpins all areas of Chemistry - emphasis will be placed on being able to apply knowledge, especially in solving problems.

To introduce a range of chemical techniques appropriate to the study of inorganic, organic and physical chemistry at first year level, which will act as a foundation for more advanced work in subsequent years.

**40 compulsory credits throughout 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.**

## Mathematical Sciences

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.

## Chemistry

50 compulsory credits from your chosen sub-stream plus 10 optional credits:

#### Organic and Inorganic Chemistry

Develop an understanding of modern spectroscopic techniques (NMR, IR, UV and mass spectrometry) for the characterisation of organic and biological molecules to the extent that students have an intuitive approach to problem solving and structural analysis.

Aspects of the stereochemistry of bio-organic molecules, including prochirality, molecular chirality and properties of non-racemic compounds, conformational analysis and aspects of stereocontrol in bio-organic reactions are developed.

**10 credits in the Autumn semester.**

The module is divided into two parts:

1. Functional group chemistry: synthetic transformations of alcohols, amines, carbonyls, and alkenes, and how these transformations are used to synthesise complex molecules such as natural products or pharmaceutical agents.

2. Synthesis: Introduction to retrosynthetic analysis and synthesis of organic molecules using a selection of pharmaceutical agents as examples. Formative feedback is given on the material in this module at the associated workshops. Summative feedback is provided after the exam by the module convenor.

**10 credits in the Spring semester.**

This module builds on the practical, analytical and communication skills acquired in the first year and introduces more advanced experiments across Inorganic, Organic and Physical chemistry (note – students choose 2 of the 3 from Inorganic, Organic and Physical Chemistry). Increasing use is made of spectroscopic and other analytical techniques in the characterisation of compounds. More detailed laboratory reports will be required.

Students will:

• Be able to perform a range of standard & more advanced synthetic and analytical practical procedures safely and reliably using Good Chemistry Laboratory Practice (GCLP).

• Know how to prepare Control of Substances Hazardous to Health (COSHH) and risk assessments.

• Be proficient in planning and organising time so that experiments are performed efficiently in the allocated time.

• Be competent in calculating amounts of reagents accurately.

• Be capable of accurately and precisely measuring reagents and preparing solutions.

• Be able to scientifically interpret results and observations and report your findings in a concise manner.

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

In this module students will gain knowledge and understanding of the importance of Main Group compounds across all branches of chemistry and materials science.

Education aims:

To survey the classical and new chemistry of the main group elements.

To use group theory as a tool in the analysis of vibrational spectra in inorganic chemistry.

To give a concise introduction to the organometallic chemistry of the transition metals.

To use multinuclear NMR spectroscopy as a tool for the characterisation of molecules.

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

Or

#### Inorganic and Physical Chemistry specialism

This module introduces and builds on theories that can predict and describe accurately the physical principles underlying chemical phenomena, with emphasis on energy, quantum mechanics, spectroscopy and the solid state.

The module includes a basic introduction to quantum mechanics in Chemistry and an introduction to a range of spectroscopies applied to diatomic molecules. It will be shown how these methods are used to find out and understand information about the structure and bonding in diatomic molecules. Methods for calculating thermodynamic properties of single-component and multi-component materials in different phases will be developed, and there will be an introduction to solid-state chemistry, including the structure, characterisation, energetics and simple band theory of solids.

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

This module builds on the practical, analytical and communication skills acquired in the first year and introduces more advanced experiments across Inorganic, Organic and Physical chemistry (note – students choose 2 of the 3 from Inorganic, Organic and Physical Chemistry). Increasing use is made of spectroscopic and other analytical techniques in the characterisation of compounds. More detailed laboratory reports will be required.

Students will:

• Be able to perform a range of standard & more advanced synthetic and analytical practical procedures safely and reliably using Good Chemistry Laboratory Practice (GCLP).

• Know how to prepare Control of Substances Hazardous to Health (COSHH) and risk assessments.

• Be proficient in planning and organising time so that experiments are performed efficiently in the allocated time.

• Be competent in calculating amounts of reagents accurately.

• Be capable of accurately and precisely measuring reagents and preparing solutions.

• Be able to scientifically interpret results and observations and report your findings in a concise manner.

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

In this module students will gain knowledge and understanding of the importance of Main Group compounds across all branches of chemistry and materials science.

Education aims:

To survey the classical and new chemistry of the main group elements.

To use group theory as a tool in the analysis of vibrational spectra in inorganic chemistry.

To give a concise introduction to the organometallic chemistry of the transition metals.

To use multinuclear NMR spectroscopy as a tool for the characterisation of molecules.

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

#### Optional Chemistry modules

And select an additional 10 credits from the following options:

You’ll be introduced to the principles of analytical chemistry, including the principal types of instrumentation used and the statistical treatment of analytical results.

You’ll attend two lectures each week studying this module.

**10 credits in the Autumn semester.**

This module covers material related to developing a more sustainable approach to chemistry. You will learn what constitutes sustainable chemistry, the significance of new technologies such as synthetic biology, and recognise the problems in achieving sustainability.

**10 credits in the Autumn semester.**

## Physics

Students taking Physics must take a total of 60 credits.

If you've chosen Chemistry 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.**

## Mathematical Sciences

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 throughout 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 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** 50 credits in each**.

### 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.**

## Chemistry

Students taking Chemistry must take a total of 40-50 credits from their chosen specialism. 30 compulsory credits and 10-20 optional credits*.*

#### Organic and Inorganic Chemistry

30 compulsory credits:

This module will:

• Teach advanced experimental techniques in one of the areas of organic, inorganic and physical chemistry

• Provide experience in the recording, analysis and reporting of physical data

• Put into practice the methods of accessing, assessing and critically appraising the chemical literature. This will be achieved through a focused literature search culminating in a mini research project followed by individual oral and written presentations.

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

On this module, students will develop an understanding of the mechanisms, regiocontrol and stereochemical outcome of organic reactions. You will also learn how to to predict the regiochemical and stereochemical outcome of organic reactions; and to use organometallics to create organic structures.

This module will also introduce students to a range of reagents and synthetic methodology, and to describe how it is applied to the synthesis of organic target molecules.

**10 credits in the Autumn semester.**

On this module, students will learn:

- To consolidate and develop concepts of organic reactivity and mechanism, primarily using qualitative frontier molecular orbital theory
- To illustrate and rationalise molecular rearrangements in organic chemistry
- To give an appreciation of the generation and use of reactive intermediates in organic chemistry

**10 credits in the spring semester.**

#### Optional Organic and Inorganic Chemistry modules

And select an additional 10-20 optional credits:

At the end of this module the student should be able to:

1. Recognise the roles of metalloproteins and metalloenzymes in controlling key biological processes.

2. Understand the chelate effect, and apply the principle to explain the stability and reactivity of polychelate complexes and the properties of the active sites of metalloenzymes.

3. Assess the structure-function relationships that control the reactivity and catalysis achieved by the metal centres involved in dioxygen transport, electron transfer, photosynthesis and nitrogen fixation.

4. Relate the chemical properties of complexes incorporated into supramolecular systems, metal organic frameworks, metalloproteins and metalloenzymes to the electronic structure of the metal centre.

5. Understand the role that transition metal centres can play in the rational design and chemistry of supramolecular assemblies, and metal organic frameworks.

6. Apply the above knowledge and understanding to a range of inorganic complexes relevant in biological and supramolecular chemistry.

7. Develop key written and communication skills

**10 optional credits in the Autum semester.**

This module will develop an understanding of protein structure, stability, design and methods of structural analysis. In addition you will understand the protein folding problem and experimental approaches to the analysis of protein folding kinetics and the application of site-directed mutagenesis.

You will also be expected to develop a number of spectroscopic experimental techniques to probe protein structures.

There will be two hours of lectures a week.

**10 credits in the Autumn semester.**

On this module, students should gain a good appreciation of the applications for a range of enzymological, chemical and molecular biological techniques to probe cellular processes and catalysis at the forefront in Chemical Biology research.

This module represents a culmination of principles and techniques from a biophysical, molecular, biochemical and genetic perspective.

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

This module increases the student's knowledge and understanding of

(a) heterogeneous and homogeneous catalysis

(b) catalyst promotion and the concept of catalytic cycles.

The physical basis of the structure-property relationships of heterogeneous catalysts is explained and the link between various organo-transition metal complexes and homogenous catalysis is explored. Comparisons between homogeneous and heterogeneous catalysis are highlighted. A review of the 18- and 16- electron rules and fundamental metal-centred bond-forming and bond-breaking reactions is undertaken and applied to several catalytic cycles. The influence of catalyst design in homogeneous catalysts, with respect to choice of metal ion and ligands, is discussed relating to product selectivity, in particular chirality. A qualitative appreciation of scale up for industrial application.

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

**Or choose this Chemistry specialism:**

#### Inorganic and Physical Chemistry specialism

30 compulsory credits:

This module will:

• Teach advanced experimental techniques in one of the areas of organic, inorganic and physical chemistry

• Provide experience in the recording, analysis and reporting of physical data

• Put into practice the methods of accessing, assessing and critically appraising the chemical literature. This will be achieved through a focused literature search culminating in a mini research project followed by individual oral and written presentations.

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

This module aims to:

- provide a fundamental understanding of molecular structure and of the requirements for reactivity
- introduce modern electronic structure theory and demonstrate how it can be applied to determine properties such as molecular structure, spectroscopy and reactivity.

At the end of the module, a student should be able to:

1. Understand the information contained in a simple potential energy contour plot

2. Appreciate the origin of the normal mode separation and the reasons for its breakdown

3. Appreciate the origin of the Born-Oppenheimer approximation and the reasons for its breakdown

4. Appreciate the role of symmetry in spectroscopic selection rules

5. Perform simple calculations of partition functions

6. Appreciate the concepts underlying RRK and Transition State theories and how they overcome limitations in simple collision theory

7. Describe and understand different electronic structure methods including Hartree-Fock theory and density functional theory

8. Understand the electron correlation problem

9. Appreciate the strengths and weaknesses of different electronic structure methods

10. Understand how theoretical methods can be used to model chemical reactions and spectroscopy.

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

This course aims to teach the relationship between structure and properties of solids, structure of Solids and characterisation.

It aims to teach a general introduction to Interfaces and Surfaces.

**10 credits in the spring semester.**

#### Optional Inorganic and Physical Chemistry modules

And select an additional 10-20 optional credits:

At the end of this module the student should be able to:

1. Recognise the roles of metalloproteins and metalloenzymes in controlling key biological processes.

2. Understand the chelate effect, and apply the principle to explain the stability and reactivity of polychelate complexes and the properties of the active sites of metalloenzymes.

3. Assess the structure-function relationships that control the reactivity and catalysis achieved by the metal centres involved in dioxygen transport, electron transfer, photosynthesis and nitrogen fixation.

4. Relate the chemical properties of complexes incorporated into supramolecular systems, metal organic frameworks, metalloproteins and metalloenzymes to the electronic structure of the metal centre.

5. Understand the role that transition metal centres can play in the rational design and chemistry of supramolecular assemblies, and metal organic frameworks.

6. Apply the above knowledge and understanding to a range of inorganic complexes relevant in biological and supramolecular chemistry.

7. Develop key written and communication skills

**10 optional credits in the Autum semester.**

This module increases the student's knowledge and understanding of

(a) heterogeneous and homogeneous catalysis

(b) catalyst promotion and the concept of catalytic cycles.

The physical basis of the structure-property relationships of heterogeneous catalysts is explained and the link between various organo-transition metal complexes and homogenous catalysis is explored. Comparisons between homogeneous and heterogeneous catalysis are highlighted. A review of the 18- and 16- electron rules and fundamental metal-centred bond-forming and bond-breaking reactions is undertaken and applied to several catalytic cycles. The influence of catalyst design in homogeneous catalysts, with respect to choice of metal ion and ligands, is discussed relating to product selectivity, in particular chirality. A qualitative appreciation of scale up for industrial application.

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

Various structure determination methods will be presented, covering a selection of spectroscopic and scattering methods. Advanced light and neutron sources will be introduced, moving on to their use in determining the structures of both isolated molecules and of solids (both crystalline and amorphous) and liquids.

**10 credits in the Spring semester.**

A general introduction to lasers, including laser radiation and its properties will be given, leading to why lasers have such widespread uses in Chemistry.

The bulk of the module is devoted to selected applications, which will include some of:

- atmospheric measurements
- combustion
- photochemistry and synthesis
- chemical kinetics
- spectroscopic studies of isolated molecules (stable and reactive)
- studies of van der Waals complexes
- studies of small metal clusters and nanoparticles
- time-resolved studies

**10 credits in the spring semester.**

## Physics

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

If you've chosen Chemistry 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.**

## Mathematical Sciences

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.**

#### Mathematical Physics specialism

Select 50 credits from the below modules:

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 Autumn 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.

## Chemistry

Students taking Chemistry must take a minimum of 80 and a maximum of 120 credits from this subject.

60 compulsory credits:

You will be welcomed into one of the research groups within the School of Chemistry to undertake an in-depth research project.

All projects will involve a review of relevant published work and the planning and execution of a research topic under the guidance of two supervisors.

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

And a minimum of 20 credits to a maximum of 60 credits from the following optional modules:

Students will learn about the factors that lead to successful innovation, including evaluation and management of an idea/concept.

In addition, students will consider the factors required to extract the value from a product/concept (e.g. market awareness) and the potential routes to market available from both an academic and industrial viewpoint.

**10 optional credits throughout the full year.**

Building on your knowledge from the previous years' modules in inorganic chemistry, you’ll study topics including:

- electron transfer pathways
- inorganic chemistry in biological systems
- the principles of molecular and supramolecular photochemistry
- applications of inorganic photochemistry
- photocatalysis

You’ll attend two lectures each week in this module.

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

Explore the synthesis of a variety of natural (and unnatural) compounds of relevance to biology and medicine, with reference to the goals and achievements of contemporary organic synthesis through a range of case studies. There is an emphasis on the use of modern synthetic methodology to address problems such as chemoselectivity, regiocontrol, stereoselectivity, atom economy and sustainability.

You will also study the application of new methodology for the rapid, efficient and highly selective construction of a range of target compounds - particularly those that display significant biological activity. There will also be an opportunity to address how a greater understanding of mechanism is important in modern organic chemistry. This module is assessed by a two hour exam.

**10 optional credits in the Autumn semster.**

In this module you will explore inorganic photochemistry, electron transport pathways, molecular and supramolecular photochemistry, and artificial photosynthesis together with the principles that underpin green chemistry.

You will attend two lectures per week in this module.

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

This module focuses on Inorganic Photochemistry, Molecular Machines and the applications of photochemistry tochemical manufacture.

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

Advanced Chemical Biology:

To introduce concepts of chemical genetics and including activity-based protein profiling, non-natural amino acid incorporation, bio-orthogonal reactivity and the use of bump-and-hole strategies, applied to various challenges such as finding kinase/target pairs.

Biocatalysis

To introduce enzyme engineering and the synthetic utility of designer biocatalysts, especially highlighting chemo-enzymatic approaches toward chiral commodity molecules (e.g. pharmaceuticals) and their precursors.

Biosynthesis

To introduce the biosynthetic pathways and enzyme catalysed reactions leading natural products polyketides, terpenes, fatty acids and non-ribosomal peptides.

**10 optional credits in the Autumn semster.**

Building on your knowledge from the previous years' modules in inorganic chemistry, you’ll study topics including:

- electron transfer pathways
- inorganic chemistry in biological systems
- the principles of molecular and supramolecular photochemistry
- applications of inorganic photochemistry
- photocatalysis

You’ll attend two lectures each week in this module.

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

This module consists of two separately taught topics in advanced organic chemistry: Medicines from Nature (Dr Francesca Paridisi ) and Pharmaceutical Process Chemistry (Dr Andrew Nortcliffe).

**Medicines from Nature**

To provide an appreciation of the importance of natural products from plants, micro-organisms and marine life in providing leads for today’s drugs and medicines in the fight against cancer, blood pressure, pain, inflammation, bacterial infection, AIDS, Alzheimer’s, Parkinson’s and other diseases. How the discovery of biological activity in a natural product can be turned into a useful medicine. The topic will include descriptions of the biosynthesis and total synthesis of natural products.

**Pharmaceutical Process Chemistry**

This topic explores the role of the chemist in developing a viable commercial synthesis of medicines starting from a small scale. After a description of the place process chemistry takes within drug discovery as a whole, the topic will cover the following: Selection of chemical routes to medicines and assessment of their worth; Safety; Reagent selection; synthesis of chirally pure compounds; How reactions and reaction workups may be optimised.

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

In this module you will learn about the importance of intermolecular forces, across a wide cross-section of subject areas from biology through to supramolecular chemical systems.

You will study molecular organisation, assembly and recognition in biological and supramolecular systems.

In addition to appreciating the rich chemistry underlying self-assembling systems, you'll learn about the phenomena that impact on the properties of materials and important interactions in biology.

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

During this module you will learn to understand in depth the structure, chemistry and molecular recognition of nucleic acids and their reactivity towards mutagens, carcinogens and ionising radiation and anti-tumour drugs. You will appreciate the plasticity and dynamics of the DNA duple helix through base motions that underpin its function.

The bacterial replisome will be used as the prime example to highlight the problems associated with DNA replication and the significance of telomeres will be discussed. Alongside this you will develop an understanding of the chemical reactivity of coenzymes and how these add significantly to the functionality of the 20 amino acids found in proteins.

**10 optional credits in the Spring 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.**

## Mathematical Sciences

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 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**

The module introduces and explores methods, concepts and paradigm models for classical and quantum mechanical dynamics. The course explores how classical concepts enter quantum mechanics, and how they can be used to find approximate “semiclassical” solutions.

**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.