Applied Science MRes

On completion of the taught modules, students will have developed their knowledge base and attained a high level of competence in the application, analysis and evaluation of theory and practice. This knowledge and critical skills will have been assessed in all previous assignments, thereby providing students with the opportunity to undertake a research project relevant to their taught programme of study. The dissertation subject will be agreed with an appropriate supervisor and the Dissertation Module Leader (Research Co-ordinator). The subject matter may be related to any area of the scientific discipline chosen by the student.

1. To provide the student with an opportunity to investigate systematically and in depth a scientific topic of direct relevance to the programme of study and his/her personal interests.
2. To enable the student to draw on and contribute to the development of the growing body of knowledge in their chosen broad scientific field.
3. To present the outcomes of personal research in the form of two publishable scientific papers.
4. To be able to discuss their findings in an oral examination

To include:

• Time management, library skills and literature search
• Evaluation of information sources
• Critical analysis of information
• Ethical issues in science, technology and engineering research (including intellectual property and plagiarism)
• Writing for research: styles and rules for presentation (including referencing standards)
• Choosing a research area and evaluating source material
• Hypothesis formation
• Research approaches and methodologies
• Design and application of questionnaires & interviews
• Quantitative and statistical tools for researchers (e.g. R, Python, SPSS)

• To clarify the distinctions between undergraduate and postgraduate level work and expectations
• To increase students' experience in order to conduct a professional study and to use sampling procedures and analysing techniques.
• To improve students' appreciation of time management and how to conduct a literature search
• To reinforce students' research skills
• To consolidate students' appreciation of professional issues such as copyright and ethics

The module draws on the research expertise and investment in virtual reality hardware that exists within the Department of Computer Science to instruct students in an exciting area of computer science that is growing in commercial importance. The module content will include lecture material on:

How virtual environments work; seeing in 3D; Presence and Immersion. Social and ethical considerations.

Characteristics of displays.

Content creation for Virtual Environments.

Input and output devices.

Real time Interaction.

Augmented Reality.

Case studies from medical, oil and gas industry, manufacturing, car design, entertainment industry, and more.

To study the technology elements needed to build and interact with a Virtual Environment. To provide an overview of Human Perception and how it works. The technologies discussed will be illustrated by a series of state-of-the-art case studies and hands-on demonstrations.

The course has been designed to conform with the QAA Subject Benchmark Statement for Computing (2011) and delivers specialised instruction in the subject matter that  contributes to improving a student's computing-related cognitive skills, computing-related practical skills, and generic skills for employability. The module covers a greater range and depth of specialist knowledge than that that would be obtained at Bachelor degree level and provides a unique opportunity to design and develop real time 3D content that utilises a person's natural senses and skills.

Computability, Time and space complexity, asymptotic notation, polynomial and exponential time

Determinism, Nondeterminism, Complexity classes including P, NP, Co-NP, the polynomial time hierarchy and PSPACE

Reductions, proofs and practical case studies

Algorithmic approaches such as meta-heuristics, natural computation and mathematical programming

By the end of this module, students should be able to apply a range of problem solving techniques and to analyse the performance of such techniques with regard to resource consumption and accuracy. Students will gain a grasp of the limits of computation and of the complexity of both theoretical and real word problems as well as learning how to adjust problem solving processes to tackle highly complex scenarios.

The module draws on the research expertise in bio-inspired computing that exists within the Department of Computer Science to instruct students in an exciting area of computer science that is growing in research and commercial importance. The module content will include lecture material on:

-Evolutionary and genetic algorithms.

-Swarm behaviour

-Cellular automata 

-Chaos and fractals

-Neural computation

-Agent based models

-Complex adaptive systems

-Biologically inspired optimisation and behaviour search

To study elements of bio-inspired computing techniques which can be applied in simulation and modelling. To provide an overview of existing platforms and frameworks for bio-inspired computing. To gain experience and practical application of research and development techniques related to bio-inspired computing.

• Evolution of Robotics
• Microcontrollers: Arduino and Raspberry Pi
• Computer Vision
• Agents and Multi-Agent Systems
• Machine learning and robotics

• To introduce the concept of artificial intelligence (AI) and to evaluate its role in the development of robotics.
• To introduce theoretical approaches to the development of intelligent robots.
• To undertake practical tasks to demonstrate how AI techniques can be implemented for robotics.
• To analyse methods for designing and deploying robotic systems.
• To critically evaluate the ways in which intelligent robots can be used in real world situations

• Digital system forensics
  • Disk
  • Memory
  • Mobile
  • Cloud
• Live forensics
• Encryption and obfuscation
• Malware analysis and investigation
• Network forensics
• Anti-forensics
• Methodologies, approaches, and techniques
• Cyber Threat Intelligence and attribution
• Incident Response
• Ethical issues in digital forensics and incident response

This module aims to introduce the student to the need for and uses of digital forensics and incident response from an organisational security perspective.

The aim of this module is to introduce, study, understand and practice digital forensics techniques, and to understand the limitations of common techniques.  It aims to develop in the student an appreciation and understanding of anti- and counter-forensics, including falsification of data.  Finally, it aims to build the students' understanding of malware, how it operates, and practices to deal with it.

Students will gain an understanding of Incident Response and Cyber Threat Intelligence.

• Network security and attacks
• The current threat landscape
• Social engineering
• Penetration testing tools
• Active defence
• Threat hunting
• Defensive strategies and tools 
• Hack back and the legal implications
• Hacker tools
• Penetration testing; methodologies, approaches, and techniques
• Penetration test reporting
• Ethical issues in penetration testing and active defence

This module aims to:

• introduce the student to the need for and uses of penetration testing and active defence from an organizational security perspective;
• introduce, study, understand and practice active defence and the limitations of common techniques. This will also look at relevant tools and the legal aspect of 'hack back';
• help the student study, understand, and practice penetration testing techniques, developing skills in 'access' over networks, and how attackers look at a target; 
• the relevant skills, knowledge and usage of hacker tools and how to stop/deter attackers

These will be built upon to allow the student to better understand network and holistic defenses and to be able to design secure interconnected systems.

Mathematical models can be used to describe real world phenomena and to make predictions about the future behaviour of the system modelled.  Mathematical modelling lies at the heart of Applied Mathematics.

Topics to be covered on this course may be drawn from the following list which is not exhaustive but is presented by way of illustration:

• Birth & Death process.
• Game Theory.
• Queuing Theory.
• Markov Chains.
• Mathematical Biology.
• Financial Mathematics.
• Heat Conduction Models.

We aim to:

10.1  Introduce students to the theory and practice of the art of mathematical modelling. 

Computers are increasingly all pervasive throughout mathematics, science and technology.  This ranges from every-day tasks, such as surfing the web, or communicating securely with your bank, to more specialist scientific questions such as using mathematical computer simulations to model real-world phenomena.  As a result, possessing proficient computer and programming skills is indispensable not only in academic and scientific research but also for future-focused business and industry.

This module is designed with dual objectives. Firstly to provide an in-depth introduction to algorithms and the process of translating these into computer programs, using state-of-the-art software tools. This will provide you with a solid foundational understanding to tackle any future computational and programming challenges.  Secondly, you will develop important research and writing skills.  You will learn to use LaTeX, an industry-standard typesetting system for produce professional scientific documents.

• Introduction to algorithms and how to translate them into computer programs.
• Introduction to computer programming software, for example Python.
• Learn about basic programming concepts including algorithms, loops, conditional statements and functions.  Also learn about more advanced scientific functions.
• Introduction to numerical algorithms from a variety of mathematical areas.
• Develop research and writing skills through LaTeX and online mathematics resources.

Note: Applications within this course will be chosen to suit the interests and background of the students.  Typical application areas may be to the numerical and symbolic solution of equations of various type, and to the graphical representation of mathematical models.

1. Introduce the student to new opportunities for researching and tackling mathematical problems which are provided by modern software tools.

This module describes the classification and solution of integral equations which arise in a variety of situations: Integral equations (and differential equations) arise in the mathematical modelling of many real-world phenomena.

• Integral Equations.
• Equations of Fredholm type.
• Equations of Volterra type.
• Singular integral equations.
• Relationship to differential equations.
• Linear and non-linear equations.
• Discretisation methods.
• Existence, Uniqueness of solutions.
• Equations with multiple soulutions.

We aim to:

10.1  Provide students with an understanding of the main types and methods applicable to integral equations.

Ordinary differential equations (ODEs) play a crucial role in modelling many problems in science and engineering.  Despite their significance, finding analytic solutions for these differential equations is often challenging. In this module, we will study the methods for numerically solving ODEs, analysing their behaviour, and gaining practical experience in their application. Our focus will be on first-order ODEs, examining a variety of algorithms such as forward and backward Euler, the family of Runge-Kutta methods, and multistep methods. We will discuss the zero stability, absolute stability, and convergence of the proposed numerical methods. To implement these methods in practice, we will utilise ODE solvers in MATLAB and Python to address different types of differential equations. Additionally, we will consider the finite difference method for solving the boundary value problems and the heat equation.

• Concepts of convergence, consistency and zero stability of the numerical methods.
• Forward Euler method, backward Euler method, Runge-Kutta method
• Multistep methods
• absolute stability
• Finite difference method for solving boundary value problem
• Finite different methods for solving heat equation
• Discussion of examples drawn from: difference equations; non-linear equations; ordinary differential equations; partial differential equations.

We aim to:

1. Introduce students to some modern numerical methods and to provide an opportunity for them to undertake some convergence and stability analysis, assisted by appropriate software.

The two most common types of mathematical model studied result in differential equations and integral equations.  This modules describes the classification and solution of differential equations which arise in a variety of situations.

• Differential equations and why they are important.
• Relationships to other types of equations, including difference equations and integral equations.
• Simple methods of solution.
• Solution in series and the method of Frobenius.
• Picard's method.
• Systems of linear first order differential equations
• Phase space, orbits
• Stability
• Introduction to non-linear systems

Additional material which may be drawn from the following list:

• Numerical Methods
• Orthogonal functions; Introduction to Sturm - Liouville theory
• Transformations
• Pertubation Methods
• Second Order Systems

We aim to:

10.1  Introduce the student to fundamental ideas and methods relating to differential equations, their derivation and their solution.

10.2  Encourage students to relate real-world experience, mathematical models and mathematical theory.

10.3  Give flexibility for students to develop their interest in areas which might lead to research projects.

10.4  Encourage students to work more independently with the help of guided study and supervision.

10.5  Develop the students' research ability.

Partial differential equations
(PDEs) serve as mathematical models for a wide range of physical, biological, and economic phenomena and are foundational tools across various branches of pure and applied mathematics. In 1822, Fourier provided uniform solutions for significant PDEs, such as the wave and heat equations, along with Laplace's equation. This course will concentrate on these three equations, considering auxiliary initial or boundary conditions.  Throughout the course, we will explore diverse techniques, including separation of variables, Fourier methods, Laplace transform methods, among others, to effectively solve various types of partial differential equations.

• Mathematical techniques relevant to the solution of PDEs; e.g. Fourier series, Laplace Transforms.
• Introduction to partial differential equations. First order partial differential equations (linear and quasi-linear). Well-posedness.
• Linear partial differential operators: characteristic curves and surfaces.
• Classification of second order partial differential equations. Canonical form and reduction to canonical form.
• Initial value and boundary value problems.
• Existence and uniqueness of solutions.
• Laplace's equation; The Heat equation; The Wave equation; The Diffusion equation.
• Methods for solving PDEs: e.g. separation of variables, difference methods, transform methods, Fourier's method, Green's functions.
• Applications of partial differential equations.
• Systems of first-order partial differential equations.
• An introduction to the numerical Solution of PDEs.

1. Develop an understanding of theory relating to partial differential equations.
2. Develop skills in solving partial differential equations.
3. Introduce students to modelling using partial differential equations.
4. Give students an appreciation of the importance and relevance of numerical methods in solving partial differential equations.

The research project gives the student an opportunity to apply theory learned on the programme and to develop skills of self-discipline, project management and written communication.

Students will negotiate with tutors the precise title and objectives of the project.

Students will study the art of mathematical writing and communication.

Tutors will provide appropriate levels of support and advice.

The Level 7 module dissertation is designed to enable students to complete an independent research project written up in the form of a thesis that conforms with normal requirements for presentation of mathematical results. The demonstration of advanced competence in: formulating a valid research question; conducting an empirical investigation; analysing and interpreting results; writing up findings to a standard suitable for publication. 

This module allows the student to gain an advanced understanding of their chosen research area and to design a proposal for a research project for completion within the MRes module SE7035 Independent Research Project for Science and Engineering.  In particular, the module content points towards aspects such as critical surveying of scientific literature, effective design of a research project and awareness of responsible research practice. 

To provide the student with the means and opportunity to read widely in their chosen area of the Natural Sciences.

To enable the student to develop their independent study and reading skills.

To enable students to realise the importance of experiment, theory and modelling as they all link to provide research findings of sufficient evidence to support their research objectives.

To equip students with the ability form an independent research proposal using the knowledge gained from the literature and consultation with their supervisor.

To provide the student with an overview of the relevant and appropriate accepted methods of research within the natural sciences.

To equip students with the ability to communicate their research ideas and proposals through the written and spoken word.

This module ensures that the student gains an advanced understanding of the logistics of research in science and engineering. The students will also participate in a course of study on the ethical management of research work and their responsibilities with respect to safe working practices.

To enhance awareness in terms of responsible conduct of research, and to ensure that the student can plan and complete research work safely and ethically.

To give the student an advanced understanding of the importance of risk assessment and of complying with the procedure of safe systems of work in written form.

To familiarise the student with advanced techniques particular to their research area.

To ensure that the student gains a clear understanding of the responsibilities of the worker and supervisor in the research environment.

To enable the student to develop a data management plan along with an awareness of the requirements of accessing and using shared computing resources if applicable.

This module is linked to the completion of the other taught components in the programme. On completion of the taught modules, students will have developed a project proposal and appropriate research knowledge within an area of research in science and engineering. The research project subject will be agreed with an appropriate supervisor and the Research Project Module Leader.  The agreed Research Project will be carried out and assessed within this module.

To provide the student with an opportunity to investigate systematically and in depth a scientific topic within the general areas of competence of the Departmental staff.

To enable the student to draw on and contribute to the development of the growing body of knowledge in their chosen broad scientific field.

To equip the student with the ability to present the outcomes of personal research in the form of a research thesis.

To enhance the ability to communicate and defend their findings in an oral examination.

To allow the student to achieve proficiency in advanced experimental and/or computational techniques and to acquire instrumental skills in the relevant research area.