Psychology, Biology and Maths

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 in the Autumn Semester.

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.

20 compulsory credits in the Spring Semester.

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 in the Autumn Semester.

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.

10 compulsory credits in the Autumn Semester.

An introduction 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.

10 compulsory credits in the Spring Semester.

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

40 credits throughout the full year.

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

20 compulsory credits throughout the full year.

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

20 compulsory credits throught the full year.

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

This module will examine:

• Perception, with particular emphasis on vision, but also hearing, taste, touch and smell;
• The Psychology of Language, including linguistic theory, speech, parsing, word meaning, and language production
• The Psychology of Reading, including word recognition, theories of eye-movement control, and reading multi-media displays
• Human Memory, covering the basics of encoding, storage and retrieval with particular reference to real-world applications of memory research
• Thinking and Problem Solving, including heuristics, biases, evolutionary perspectives on human rationality, and group decision making

20 compulsory credits in the Autumn Semester.

This module will cover several 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
• methods of studying neuropsychological processes
• the effects of brain damage on mental functioning including amnesias, agnosias and aphasias
• introduction to classical and instrumental conditioning
• theories of associative learning and memory
• what forgetting might tell us about learning
• topics in comparative cognition and cognitive abilities
• can animals do anything apart from conditioning?

20 compulsory credits in the Spring Semester.

The module is intended to support the development of practical skills in running experiments in psychology. Skills include experimental design; interpretation summary data and inferential statistics; ‘building’ experiments withthe computer-based user-interface, PsychoPy. Small groups will work on supervisor-guided projects in thedevelopment of these skills and will submit a report for assessment.

20 compulsory credits throughout the full year.

This module will examine:

• Perception, with particular emphasis on vision, but also hearing, taste, touch and smell;
• The Psychology of Language, including linguistic theory, speech, parsing, word meaning, and language production
• The Psychology of Reading, including word recognition, theories of eye-movement control, and reading multi-media displays
• Human Memory, covering the basics of encoding, storage and retrieval with particular reference to real-world applications of memory research
• Thinking and Problem Solving, including heuristics, biases, evolutionary perspectives on human rationality, and group decision making

20 compulsory credits in the 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.

10 compulsory credits in the Autumn Semester.

This module covers the psychological explanations of personality and individual differences, and 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 and health psychology are discussed. IQ is also covered and evolutionary bases of traits.

10 compulsory credits in the Autumn Semester.

This module examine a range of issues in social and developmental psychology including:

• Current issues in social psychology
• Social cognition and social thinking
• Attribution
• Attitudes
• Persuasive communication and attitude change
• Social Influence
• Conformity and obedience
• Group decision making and behaviour change culture
• Intergroup behaviour
• Prejudice and discrimination
• Perceptions and motivations
• Evolution of mentalising and theory of mind
• Ontology of mentalising: Development of theory of mind in children
• Mindblind: Autism spectrum disorder
• Phylogeny: The mental world of Apes
• Development of synaesthesia
• Language acquisition
• Adult perceptual development: sensory substitution and augmentation
• Conceptual development: colour cognition
• Reading and spelling development

20 compulsory credits in the Spring Semester.

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

20 compulsory credits throughout the year.

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

10 compulsory credits in the Spring Semester.

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

10 compulsory credits in the Spring Semester.

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

20 credits in the Autumn Semeseter.

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

20 credits in the Spring Semester.

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

10 credits in the Autumn Semester.

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

10 credits in the Spring Semester.

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

20 compulsory credits in the Autumn Semester.

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

20 compulsory credits in the Spring Semester.

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

20 credits in the Spring Semester.

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

20 credits in the Autumn Semester.

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

10 credits in the Autumn Semester.

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

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

10 credits in the Autumn Semester.

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

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

20 credits in the Autumn Semester.

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

20 credits throughout the full year.

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

Specific topics include:

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

20 credits throughout the full year.

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.

10 compulsory credits in the Autumn Semester.

This module examines the psychological and neural basis for the planning and control of human action. You will be introduced to scientific research through guided exploration of the neuropsychological bases for human action. You will experience the multi-disciplinary nature of research into human behaviour and, by the end of the module, will understand how a single issue can be addressed from multiple perspectives including: experimental psychology, neurophysiology, neuroanatomy, neuropsychology, and functional brain-imaging.

10 compulsory credits in the Autumn Semester.

The central theme of this module is to explore how the architecture and function of the visual brain have been designed and shaped by experiences over a range of timescales. 

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.

This module will examine the consequences of evolution, development, learning and adaptation for visual brain function and perception.

10 compulsory credits in the Spring Semester.

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.

20 credits throughout the full year.

Supported by lectures, seminars and tutorials, this module aims to provide you with an understanding of the mechanisms of learning and memory in human and non-human animals, and an analysis of pathological conditions involving these systems.

You’ll study topics that include:

• perceptual learning
• the contextual and attentional modulation of learning and behaviour
• neuroscience-focused topics such as the role of the hippocampus in memory

Clinical topics include:

• the acquisition of phobias
• memory discords
• the psychological side effects of cancer treatment
• depression

There are two hours per week of lectures for this module.

20 credits throughout the full year.

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.

10 credits in the Spring Semester.

The course will cover theories and models of altruism, cooperation and helping form the perspective of psychology, economics and evolutionary biology. Among the theories examined will be reputation-based, strong-reciprocity, warm-glow and crowding and altruistic punishment from economics; kin selection, reciprocity, coercion, mutualism, cooperative breeding from biology; and empathy, personality, sexual selection and situational constraints from psychology.

You will consider why people sometimes don't help and actively try to benefit from others and apply these models to anti-social behaviour, and how we cooperate to inflict injury on other groups. It will also examine not just models of helping others, but also why people ask for help. You will finally look at how charities implement some of these principles and if they are successful.

10 credits in the 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. 

10 compulsory credits in the Spring 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.

10 credits in the Spring 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.

10 credits in the Autumn Semester.

An introduction to the concepts of clinical psychology and the application of psychology in clinical settings.

The module illustrates how psychological models are developed and how they are applied in developing interventions. You will examine theory and evaluation of interventions for a number of disorders/clinical issues.

During this module you will have two hours of lectures weekly. 

10 credits in the Spring Semester.

The course will cover theories and models of altruism, cooperation and helping form the perspective of psychology, economics and evolutionary biology. Among the theories examined will be reputation-based, strong-reciprocity, warm-glow and crowding and altruistic punishment from economics; kin selection, reciprocity, coercion, mutualism, cooperative breeding from biology; and empathy, personality, sexual selection and situational constraints from psychology.

You will consider why people sometimes don't help and actively try to benefit from others and apply these models to anti-social behaviour, and how we cooperate to inflict injury on other groups. It will also examine not just models of helping others, but also why people ask for help. You will finally look at how charities implement some of these principles and if they are successful.

10 credits in the Spring Semester.

Description under review

20 credits

Description under review

10 credits

Description under review

10 credits

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

10 credits in the Spring Semester.

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

10 compulsory credits in the Spring Semester.

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

10 credits in the Autumn Semester.

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

10 credits in the Autumn Semester.

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

10 credits in the Spring Semester.

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

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

10 compulsory credits in the Autumn Semester.

20 compulsory credits in the Spring Semester.

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

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

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

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

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

10 credits in the Autumn Semester.

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

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

10 credits in the Spring Semester.

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

20 credits in the Autumn Semester.

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

20 credits in the Autumn Semester.

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

10 credits in the Autumn Semester.

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

10 credits in the Spring Semester.

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

20 credits in the Spring Semester.

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

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

20 credits in the Spring Semester.

This module will provide students with: The opportunity to research in depth a topic of their choice, under the direction of a subject specialist. The skills and methodologies required to carry out sustained independent research.

40 credits throughout the year

Problem-based learning to support lectures on neuroimaging topics. Topics covered include an introduction to computer programming with MATLAB, the design and analysis of behavioural experiments, and the analysis of functional MRI data.

10 credits in the Autumn term

This module provides students with the knowledge to be able to select, administer, score, interpret, and provide feedback on educational tests of the kind used when assessing individuals with learning difficulties. They will learn about the advantages and disadvantages of different types of assessment and how to make decisions about test selection for assessments. Students will gain an understanding of test theory including the concepts of reliability, validity and the standardization of tests.  The module will provide a skill set that will be useful to students completing their project in which they may have to administer psychometric tests. It will also be useful to students wishing to pursue a career in education or educational psychology.

20 credits in the Autumn term

This module is an opportunity to work in depth on a specific topic in Cognitive Neuroscience. Students explore their chosen topic and its related methodological issues to their own research interests. The topic is based on a seminar provided in the School of Psychology, with approval from the convenor. The module concerns independent study in addition to supervision sessions.

10 credits in the Spring term

Topics include more advanced concepts in MATLAB programming and the analysis of functional MRI data.

10 credits in the Spring term

The module provides an insight into some more advanced or specialised techniques of data collection, organisation and analysis in psychological research (e.g., eye-tracking, EEG, fMRI, TMS, computational modelling, diary methodologies and Workshops Lectures will include implementation of analytical procedures in for example specialised data management and statistical packages and on specialised data gathering equipment and software.

20 credits in the Spring term

This module will examine:  Conduct disorder – Oppositional Defiant Disorder – Depression – Anxiety – Childhood onset schizophrenia – Therapies for young people – Pharmacological interventions – Comorbidity of mental health problems and developmental disorders

20 credits in the Spring term

Description under review

20 credits

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

60 compulsory credits throughout the full year.

20 compulsory credits throughout the full year.

20 compulsory credits throughout the full year.

10 credits in the Autumn Semester.

10 credits in the Autumn Semester.

10 credits in the Autumn Semester.

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

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

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

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

20 credits in the Autumn Semester

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

20 credits in the Autumn Semester

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

20 credits in the Autumn Semester

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

20 credits in the Autumn Semester

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

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

20 credits in the Spring Semester

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

20 credits in the Spring Semester

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

20 credits in the Spring Semester

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

20 credits in the Spring Semester