Natural Sciences
   
   
  

Physics, Psychology 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. The combination of subjects which you study in the first year allows you to find out what each subject is like at university before you specialise further. You will also have the opportunity to explore specialist areas through optional modules as you progress through the course. Both of the subjects taken beyond the first year will be studied to degree level. This degree aims to provide you with a broad knowledge and understanding of your chosen areas of science, as well as experience of interdisciplinary study.

Year One

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

Physics


40 compulsory credits:

From Newton to Einstein (40 credits, full year)
This module aims to provide students with a rigorous understanding of the core concepts of physics at an introductory level. The module underpins all other physics modules in all years.
 
 

Psychology


20 compulsory credits:

Cognitive Psychology 1 (20 credits, Autumn semester)
Cognitive psychology is the study of mental processes, and this module will provide an introduction to the methods used by cognitive psychologists in their investigations of mental processes in humans. A wide range of topics will be discussed, with some introductory discussion of how they limit human performance in applied contexts. The mental processes to be covered include those that support attention, perception, language, memory, and thinking. You will have two one-hour lectures per week for this module.
 


20 compulsory credits from your chosen pathway:

Social and Development Psychology subpathway

Social Psychology (10 credits, Autumn semester)

This module introduces you to the core topics in social psychology, which is concerned with trying to understand the social behaviour of individuals in terms of both internal characteristics of the person (e.g. cognitive mental processes) and external influences (the social environment). Lectures will cover topics including how we define the self, attitudes, attribution, obedience, aggression, pro-social behaviour and formation of friendships. You will have a one-hour lecture weekly.

 
Developmental Psychology (10 credits, Spring semester)
You will receive an introduction to the fascinating world of the developing child. Lectures consider different theoretical, applied, and experimental approaches to cognitive, linguistic, and social development from early to late childhood. Topics include the development of thinking, perception, drawing, understanding the mind, intelligence, attachment, language, and moral development. You will have a one-hour lecture weekly.
 


Biological Psychology subpathway

Biological Psychology 1 (20 credits, Spring semester)
This module will give you an introduction to the neural and biological bases of cognition and behaviour. You will learn about the structure and evolution of the brain and the main functions of the different parts. You will examine how the brain receives, transmits, and processes information at the neural level, as well as its visual pathways. The main scientific methods for investigating brain and behaviour will also be covered. You will have two hours of lectures weekly.
 
 

Mathematical Sciences


40 compulsory credits:

Analytical and Computational Foundations (20 credits, full year)
This module introduces students to a broad range of core mathematical concepts and techniques. It has three components.
  • Mathematical reasoning (the language of mathematics, the need for rigour, and methods of proof).
  • The computer package MATLAB and its applications.
  • Elementary analysis.
 
Calculus and Linear Algebra (20 credits, full year)

The module consolidates core GCE mathematical topics in the differential and integral calculus of a function of a single variable and used to solving some classes of differential equations. 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. An emphasis in the module is to develop general skills and confidence in applying the methods of calculus and developing techiniques and ideas that are widely applicable and used in subsequent modules.

Major topics are:

  • differential and integral calculus of a single variable;
  • differential equations;
  • differential calculus of several variables;
  • multiple integrals;
  • complex numbers;
  • matrix algebra;
  • vector algebra and vector spaces.
 
 

 

Year Two

You will continue on a pathway 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.

Physics


60 compulsory credits:

Compulsory with Biological Sciences

  • Classical Fields (20 credits, full year)
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.
 
  • Experimental Techniques and Instrumentation (20 credits, full year)

In this module students will receive:

  • an introduction to the the basic techniques and equipment used in experimental physics
  • training in the analysis and interpretation of experimental data
  • a basic practical introduction to geometrical and physical optics
  • opportunities to observe phenomena discussed in theory modules
  • training in the skills of record keeping and writing scientific reports
 
  • The Quantum World (20 credits, 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.
 

 

Compulsory with Mathematical Sciences

  • Experimental Techniques and Instrumentation (20 credits, full year)

In this module students will receive:

  • an introduction to the the basic techniques and equipment used in experimental physics
  • training in the analysis and interpretation of experimental data
  • a basic practical introduction to geometrical and physical optics
  • opportunities to observe phenomena discussed in theory modules
  • training in the skills of record keeping and writing scientific reports
 
Optics and Electromagnetism (20 credits, full year)
The first half of the module will focus on optics: the study of light. Topics to be covered will include geometrical optics, wave description of light, interference and diffraction and optical interferometry. There will be a small number of practical sessions illustrating the ideas developed. The second half of the module will cover various aspects of electromagnetism including the treatment of dielectric and magnetic media, the propagation of electromagnetic waves and various techniques for the solution of electromagnetic problems.
 
  • Thermal and Statistical Physics (20 credits, full year)

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.

 
 

Psychology


Biological Psychology subpathway

40 compulsory credits:

Cognitive Psychology 2 (20 credits, Autumn semester)
You will examine in greater depth perception, language, human memory, thinking, and problem solving. For each topic you will explore existing theories and contemporary issues to enable you to take an interdisciplinary perspective. You will have four hours of lectures per week.
 
Neuroscience and Behaviour (20 credits, Spring semester)
This module will cover issues in neuroscience and behaviour that are particularly relevant to understanding the biological bases of psychological functions. Among the topics to be covered are psychopharmacology, psychobiological explanations of mental disorders, dementia, sexual development, and behaviour and methods of studying neuropsychological processes. You will also examine the effects of brain damage on mental functioning including amnesias, agnosias, and aphasias, among other topics. You will have four hours per week of lectures for this module.
 


A further 20 credits from the options below:

  • Practical Methods 2 (20 credits, full year)
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These practicals are designed to give students hands-on experience with designing, running, analysing and reporting Psychology experiments. These practical skills require the content taught in statistical courses. These practicals will provide students with the ability to conduct and evaluate scientific studies. Students will how interpret findings from inferential statistical test. The small-group approach helps students develop skills in project management and teamwork.
 
  • Statistical Methods 2 (20 credits, full year)
  This module will cover the basic concepts and assumptions with respect to univariate and multivariate statistics, as well as issues relating to field studies, ethics, the reliability and validity issues as well as basic qualitative techniques. The module will cover ANOVA, post-hoc tests, power, multiple linear regression, factor analysis, the nature of causality and field designs (both experimental and quasi-experimental), ethics, the reliability and validity of measures and field designs, as well as exploring some basic issues in questionnaire design and qualitative methods. 
 
Conceptual and Historical Issues in Psychology and Individual Differences
(10 credits, Autumn semester)
You’ll learn about the scientific, historical, and philosophical underpinnings of psychology as a discipline, which will demonstrate the inherent variability and diversity in the theoretical approaches to psychology. By the end of the module, you will have a good knowledge and critical understanding of the influences of history on psychological theories. There will be two hours of lectures per week.
 
Personality and Individual Differences (10 credits, Autumn semester)
You will cover the psychological explanations of personality and individual differences. The relationship between the individual and society will be highlighted. In particular, the major personality theories are considered in detail and the application of these theories to areas such as abnormal psychology, criminal behaviour, and health are discussed. IQ is also covered along with the evolutionary bases of traits. You will have two hours of lectures per week.
 


Social and Developmental Psychology subpathway

Cognitive Psychology 2 (20 credits, Autumn semester)
You will examine in greater depth perception, language, human memory, thinking, and problem solving. For each topic you will explore existing theories and contemporary issues to enable you to take an interdisciplinary perspective. You will have four hours of lectures per week.
 
  • Conceptual and Historical Issues in Psychology and Individual Differences 
    (10 credits, Autumn semester)
You’ll learn about the scientific, historical, and philosophical underpinnings of psychology as a discipline, which will demonstrate the inherent variability and diversity in the theoretical approaches to psychology. By the end of the module, you will have a good knowledge and critical understanding of the influences of history on psychological theories. There will be two hours of lectures per week.
 
  • Personality and Individual Differences (10 credits, Autumn semester)
You will cover the psychological explanations of personality and individual differences. The relationship between the individual and society will be highlighted. In particular, the major personality theories are considered in detail and the application of these theories to areas such as abnormal psychology, criminal behaviour, and health are discussed. IQ is also covered along with the evolutionary bases of traits. You will have two hours of lectures per week.
 
  • Social and Developmental Psychology (20 credits, Spring semester)
You will examine theories and experimental studies of social processes and human development. Topics relating to social processes will include: social cognition and social thinking, conformity and obedience, intergroup behaviour, theories of attraction and relationships, prosocial behaviour and intrinsic motivation, and self-determination, among others. Human development topics are also explored in depth such as the development of phonology, the importance of social referencing in early language acquisition, and atypical socio-cognitive development in people with autism. You will have four hours of lectures weekly.
 
 

Mathematical Sciences


40 compulsory credits:

Modelling with Differential Equations (20 credits, 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. This course leads to further study of mathematical models in medicine and biology and fluid mechanics. It also provides a foundation for further study of differential equations.
 
Vector Calculus (10 credits, Autumn semester)
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 course is an important pre-requisite for a wide range of other courses in Applied Mathematics.
 
Differential Equations and Fourier Analysis (10 credits, Spring semester)
This course aims to introduce standard methods of solution for linear ordinary and partial differential equations and to introduce the idea and practice of Fourier series and integral transforms. The mathematical methods taught in this module find wide application across a range of courses in applied mathematics.
 

 

20 compulsory credits from your chosen subpathway:

Modelling 1 subpathway

  • Introduction to Scientific Computation (20 credits, 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) 
 


Modelling 2 subpathway

  • Introduction to Mathematical Physics (20 credits, full year)
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.
 
 

 

Year Three

You will continue with the same two subjects studied in the second year, taking 50 credits in each. Alongside subject-specific study, you will undertake a 20-credit synoptic module which aims to tie together the subjects you are studying through an interdisciplinary group project.

Physics


50 compulsory credits:

  • Natural Sciences Synoptic Module (20 credits, full year)
  • Physics Project (10 credits, Autumn semester)
  • Atoms, Photons and Fundamental Particles (20 credits, 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 compulsory credits from your chosen subpathway:

Compulsory with Biological Sciences

Thermal and Statistical Physics (20 credits, full year)

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.

 


Compulsory with Mathematical Sciences

Introduction to Solid State Physics (20 credits, full year)
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
 
 

Psychology


20 compulsory credits:

  • Natural Sciences Synoptic Module (20 credits, full year)


Biological Psychology subpathway

30 compulsory credits:

  • Neuropsychology of Action: The Body in the Brain (10 credits, Autumn semester)
This module examines the psychological and neural basis for the planning and control of human action. Students will be introduced to scientific research, through their guided exploration of the neuropsychological bases for human action. During the course students will experience the multi-disciplinary nature of research into human behaviour, and by the end of the course, will understand how a single issue can be addressed from multiple perspectives including: experimental psychology, neurophysiology, neuroanatomy, neuropsychology, and functional brain-imaging.
 
  • Neuropsychology and Applied Neuroimaging (10 credits, Autumn semester)
You will examine the deficits seen in individuals who have suffered brain damage. You will learn about the impairments to language, memory, perception, attention, motor control, executive control, and emotion. This module evaluates both the clinical and theoretical aspects of these syndromes. In particular, you will evaluate the implications regarding how the healthy brain functions. There are two hours per week of lectures for this module.
 
The Visual Brain: Evolution, Development, Learning and Adaptation (10 credits, Autumn semester)
The central theme of this module is to explore how the architecture and function of the visual brain has been designed and shaped by experiences over a range of timescales. The innate properties of the eye and visual brain that are present at birth have been designed over millions of years of evolution. The brain continues to physically change it structure and function within a lifetime  a property termed brain plasticity. Over the years of development, brain plasticity is the driving force for the maturation of different visual brain functions. Even well into adulthood, plasticity is retained in the form of learning, which can optimise performance for certain visual tasks and be exploited for therapeutic uses. Another prominent form of plasticity in the visual brain is that caused by adaptation effects of visual experience over the preceding tens of milliseconds to minutes. The module will examine the consequences of evolution, development, learning and adaptation for visual brain function and perception. 
 


A further 20 credits from the options below:

Mechanisms of Learning and Psychopathology (20 credits, full year)
To provide students with an understanding of the findings of, and theories derived from, experimental studies of learning in humans and animals and the application of this research to instances of psychopathology in people. To provide knowledge about: the principles and properties of associative learning; instances in which learning produces undesirable behaviour; attentional processes and biases in animals and humans; the representation of conditional knowledge; the effects of neural manipulations on these processes. To encourage critical appraisal of models and experimental evidence. To encourage high-quality written communication skills.
 
  • Social Neuroscience Research (20 credits, full year)
To provide students with an advanced understanding of current social and cognitive neuroscience topics, as well as an understanding of the methods and analyses required to test specific theories related to that topic, and guidance on the critical evaluation of research papers. Students will receive lectures on and study a specific social neuroscience issue in detail, and will devise ways to further research into that issue. The course will provide an introduction to neuroscience methods and will focus on current research and theory behind various aspects of human social interaction, speech communication and body perception from a neuroscience perspective. Complementary evidence from different branches of behavioural and cognitive sciences will be integrated with current neuroscientific research. The course will focus predominantly on the neural mechanisms thought to be involved in the interpretation of our own and others’ bodies, actions, faces, voices and emotions. The course will also provide advice on developing ideas for research as well as how to write for each assessment.
 


Social and Developmental Psychology subpathway

40 compulsory credits:

Cognitive Development and Autism (10 credits, Autumn semester)
You will cover modern version of nativist and empiricist theories of cognitive development. This module will also give you an overview of current theories which have been proposed to explain Autism Spectrum Disorder. It will provide an evaluation of these theories using behavioural, clinical and neurophysiological evidence from a range of domains including drawing and musical skills (savant skills), scientific knowledge, maths, social learning (trust and imitation) and social motivation. You will have two hours of lectures per week for this module.
 
Applied Psychology: Road User Behaviour (10 credits, Spring semester)
The course will cover road user behaviour from a number of psychological perspectives. Topics will include a critical review of brain scanning studies of driving, the visual skills required for driving, the effects of aging and experience, distraction (from in-car devices such as mobile phones, and from out-of-car objects such as road-side advertisements), and the skill of hazard perception (and whether this can be adequately measured as part of the licensing procedure). The course will also cover memory for driving events (from everyday driving to road traffic accidents), influences of emotion on driving (e.g. does the aggression-frustration hypothesis explain road rage?), and social and individual differences related to crash risk (e.g. sensation-seeking and risk propensity).
 
Developmental Dyslexia: Psychological and Educational Perspectives (10 credits, Spring semester)
This module will give students an in depth understanding of the characteristics of developmental dyslexia. They will also learn about the main theories used to explain the presence of this developmental disorder and their relative merits in explaining components of dyslexia. Students will also gain an appreciation of developmental dyslexia within the context of research and educational environments where reasons for assessment and identification of dyslexia may differ. Students will gain experience of: synthesising and critically evaluating information; the methods used to assess children and adults with dyslexia; and the educational and environmental accommodations made for those with a diagnosis of dyslexia. This module should benefit students with an interest in developmental, cognitive or educational psychology, and those wishing to pursue a career in child psychology, educational psychology, general teaching practice and/or special needs education.
 
Understanding Developmental Disorders (10 credits, Spring semester)

This module explores how psychologists study and understand disorders of cognitive development. The course focuses largely on disorders which include impairments in attention, memory and/or executive function. Disorders covered include attention deficit hyperactivity disorder (ADHD), autism, reading disorders and Down Syndrome. List of lectures
1. General introduction and research methods
2. Typical development of attention/memory and executive function
3. ADHD
4. Autism
5. Developmental Coordination Disorder
6. Fragile X Syndrome
7. Down Syndrome
8. Preterm Birth
9. Interventions
10. Revision

 


A further 10 credits from the options below:

Educational Psychology (10 credits, Autumn semester)
This module provides an introduction to the contexts in which educational psychologists operate by examining the historical development of this profession within a set of major legislative and policy contexts, such as the recent drive to increase social inclusion. The module will concentrate on assessment and intervention work with specific populations such as young people who display challenging behaviour in schools, vulnerable adolescents, and bilingual learners. You will also examine psychological approaches to group work with teachers and pupils as well as the application of system theory in helping transform aspects of schools and other organisations. There will be two hours of lectures per week.
 
Forensic and Mental Health (10 credits, Autumn semester)
You will receive an introduction to this growing area of psychology, with a focus on criminality. The module will concentrate on offending behaviours, typical categorisation of those who commit crimes or harm themselves, standard interventions for offenders, and the neuroscience of offending. The module will also cover the current research on specific offending behaviours, and examine the role of the criminal justice system and health service in dealing with individuals who offend. You’ll have two hours of lectures per week for this module.
 
Clinical Psychology (10 credits, Spring semester)
The aim of the course is to introduce the students to the concept of abnormal psychology and the application of psychology in clinical settings. The course will illustrate how psychological models are developed and how they are applied in developing interventions. The emphasis will be on examining theory and evaluation of interventions for a number of disorders/clinical issues.
 
 

Mathematical Sciences


20 compulsory credits:

  • Natural Sciences Synoptic Module (20 credits, full year)


30 compulsory credits from your chosen subpathway:

Modelling 1 subpathway

  • Mathematical Medicine and Biology (20 credits, 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.
 
  • Game Theory (10 credits, Spring 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.
 

 

Modelling 2 subpathway

  • Coding and Cryptography (10 credits, 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.
 
  • Differential Equations (20 credits, 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 MATH2012.
 

 

Optional mathematics modules

A further 20 credits from the options below:

  • Differential Equations (20 credits, 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 MATH2012.
 
  • Electromagnetism (20 credits, Spring semester)

The course complements others in the Waves Pathway by providing an introduction to electromagnetism and the electrodynamics of charged particles. The aims of this course are:

  • to develop an appropriate mathematical model of electromagnetic phenomena that is informed by observations;
  • to understand electromagnetic configurations of practical importance and to relate predictions made to everyday phenomena;
  • to illustrate the use of solutions of certain canonical partial differential equations for determining electrostatic fields and electromagnetic waves in vacuum and in matter;
  • to illustrate the interplay between experimental input and the development of a mathematical model, and the use of various mathematical techniques for solving relevant problems.
 
  • Fluid Dynamics (20 credits, 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.
 
  • Topics in Scientific Computation (20 credits, 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. Alongside the project you take taught modules in your main subject and if you wish to maintain some breadth you can also take options from your other third year subject.

Physics


60 compulsory credits:

  • Natural Sciences Physics Project (60 credits, full year)


Compulsory (if Introduction to Solid State Physics not taken)

Solid State Physics for Natural Sciences (20 credits, full year)
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
 

 

Minimum of 20 credits, maximum of 60 credits from the options below:

  • Atmospheric Physics (10 credits, Autumn semester)
From Accelerators to Medical Imaging (10 credits, Autumn 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).
 
  • Introduction to Cosmology (10 credits, 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).
 
Soft Condensed Matter (10 credits, Autumn semester)
The aim of this module will be to give students a basic grounding in key concepts in soft condensed matter physics, with emphasis being placed on the dynamic, structural and kinematic properties of these materials. Key differences and similarities between soft matter, hard matter and liquid systems will be highlighted and discussed throughout the module. Material that will be covered includes:
  1. Introduction to Soft Matter
  2. Forces, energies and timescales in soft matter
  3. Liquids and glasses
  4. Phase transitions in soft matter (solid-liquid and liquid-liquid demixing)
  5. Polymeric materials
  6. Gelation
  7. Crystallisation in soft systems
  8. Liquid crystals
  9. Molecular order in soft systems
  10. Soft Nanotechnology
 
  • Extreme Astrophysics (10 credits, Spring semester)
To develop an understanding of high-energy phenomena in astrophysics and the relative importance of different processes in different situations.
To make models of extreme astrophysical sources and environments basedon physical theory.
To interpret observational data in the light of relevant physical theory.
 
  • Functional Medical Imaging (10 credits, Spring semester)
The techniques for magnetic resonance imaging (MRI) and spectroscopy (MRS) are explored. The course aims to introduce the brain imaging technique of functional magnetic resonance imaging (fMRI), giving an overview of the physics involved in this technique. The electromagnetic techniques of electroencephalography (EEG) and magnetoencephalography (MEG) will then be outlined, and the relative advantages of the techniques described.
 
  • Imaging and Manipulation at the Nanoscale (10 credits, Spring semester)
The invention of the scanning tunneling microscope (STM) in the 1980s has led to a revolution in the imaging of surfaces and has provided an enormous stimulus for the development of nanoscience. The operation of a scanning probe microscope relies on the interaction between a local probe and a surface. A family of techniques has been derived from the STM which exploit a range of different forces and other interactions for image formation. The most widely-used of these techniques is atomic force microscopy which, unlike, STM, can be used to image insulating samples. In this module the focus will be on the development of physical models to describe the interaction between a local point-like probe and a surface. The operation of the STM will be considered in detail together with design considerations which are common across all scanning probe microscopes. In the second half of the course, forces between the tip and sample will be considered and methods for measuring these interactions will be discussed. The probe-surface interaction can also be used to modify the surface with a specificity which can result in placement of single atoms and molecules and these patterning processes will be discussed. Throughout the course images from the current research literature will be introduced to inform students of the range of possible applications of this these techniques.
 
Semiconductor Physics (10 credits, 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.
 
  • Quantum Coherent Phenomena (10 credits, Spring semester)
This module will introduce a number of systems in which quantum coherent phenomena are observed, discuss their common features and the general underlying theoretical ideas for their description as well as some of their applications.
  • Bose condensation review of Bose statistics, BEC, BEC in cold atomic gases.
  • Superfluidity in Helium-4 quantum fluids, macroscopic wave functions, superfluidity, non-classical rotational inertia and vortices, phonon and roton excitations.
  • Superconductivity conduction in metals, superconducting materials, zero-resistivity, Meissner effect, perfect diamagnetism, type I and type II behaviour, London theory.
  • BCS theory of superconductivity.- electron-phonon interaction, Cooper pairs, BCS wave function, order parameter and microscopic origin of GL.
  • Applications: squids, superconducting magnets etc.
 
  • Theoretical Elementary Particle Physics (10 credits, 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.
 
 

Mathematical Sciences


60 compulsory credits:

  • Mathematics Project (60 credits, full year)


Minimum of 40 credits, maximum of 60 credits from the options below:

  • Advanced Techniques for Differential Equations (20 credits, Autumn semester)

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.

 
  • Computational and Systems Biology (20 credits, Autumn semester)
The purpose of this module is to deepen and broaden the students’ knowledge and experience of computational and systems biology techniques, including the use of numerical solutions of ODEs and PDEs, and of relevant computer packages (eg MATLAB, Python/Scipy).
 
  • Quantum Information Science (20 credits, Autumn semester)
This Quantum Theory Pathway course gives a mathematical introduction to quantum information theory. Its content builds on MATH2013 with the aim of providing the student with a background in quantum information science which will facilitate further independent learning and the access to current research topics.
 
  • Scientific Computation and C++ (20 credits, 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++.
 
  • Applied Nonlinear Dynamics (20 credits, Spring semester)
The course will cover Nonlinear oscillations, including the linear stability of limit cycles (Floquet theory), the Mathieu equation, and relaxation oscillators (using geometric singular perturbation theory). Synchronisation by periodic forcing will be discussed using the notion of isochrons and phase-response curves, as well as Poincaré sections, circle-maps, mode-locking, and Arnol’d tongues. The treatment of Chaos will cover tests for chaos (Liapunov exponents and spectral analysis), strange and chaotic attractors, fractal boundaries, and routes to chaos in nonlinear dynamical systems. The analysis of Oscillator networks will cover weakly coupled phase-oscillators, Kuramoto networks, and the master-stability theorem for linearly coupled limit-cycle networks. The extension of techniques to Non-smooth dynamical systems will be developed for piece-wise linear systems (exact analysis), impact oscillators (with grazing bifurcations), and integrate-and-fire models (from neurons to networks). The course will conclude with a treatment of Spatially extended systems, covering pattern formation (in both PDE and integral equation models), and weakly nonlinear analysis (amplitude equations and pattern selection).
 
  • Advanced Fluid Mechanics (20 credits, Spring semester)
This course forms part of the Fluid and Solid Mechanics pathway within Applied Mathematics. Students taking this course will develop their knowledge of specialised topics within fluid mechanics and be introduced to areas of active research.
 
  • Computational Applied Mathematics (20 credits, 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.
 
 

 

The following is a sample of the typical modules that we offer as at the date of publication but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Due to the passage of time between commencement of the course and subsequent years of the course, modules may change due to developments in the curriculum and the module information in this prospectus is provided for indicative purposes only.

Natural Sciences

School of Chemistry, University of Nottingham
University Park
NG7 2RD

Tel: +44 (0) 115 823 2376
Fax: +44 (0) 115 951 3555
Email: naturalsciences@nottingham.ac.uk