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If you're interested in developing your mathematical talents and learning how to apply mathematics and statistics to real life problems, then this degree will give you an enjoyable route to becoming a mathematics graduate. It focuses on showing you how to apply a range of mathematical and statistical tools in order to get results, as well as learning to articulate how you have come to your conclusion. Our degree also includes the use of modern software and training on how to present your work professionally.

The university’s strong research culture feeds into the course, together with direct feedback from employers about the skills that they want our graduates to develop. These combine to ensure that you gain the most relevant up-to-date knowledge and skills on which to build your career.

We’re particularly proud of our high performance in the NSS (National Student Survey), steadily performing well above national averages.

Your first two years will offer fundamental knowledge in mathematics and statistics, then you’ll specialise your studies through a choice of optional modules such as financial mathematics, cryptography, medical statistics or fluid dynamics among others.

This integrated undergraduate course is underpinned by our research strengths in areas of applied mathematics and in your final year you will have the opportunity to do a substantial piece of research in areas such as biomathematics, classical and quantum dynamical systems, symmetries and integrable systems, magnetohydrodynamics and nonlinear waves.

In addition, you’ll have the option of a work-based placement year in industry or to study abroad at one of our partner institutions, enabling you to develop additional personal and professional skills.

Northumbria Mathematics Department achieved an overall satisfaction score of 97% (National Student Survey, 2018)

This programme is accredited to meet the educational requirements of the Chartered Mathematician designation awarded by the Institute of Mathematics and its Applications.

Northumbria University - Maths Department from Northumbria University on Vimeo.

If you're interested in developing your mathematical talents and learning how to apply mathematics and statistics to real life problems, then this degree will give you an enjoyable route to becoming a mathematics graduate. It focuses on showing you how to apply a range of mathematical and statistical tools in order to get results, as well as learning to articulate how you have come to your conclusion. Our degree also includes the use of modern software and training on how to present your work professionally.

The university’s strong research culture feeds into the course, together with direct feedback from employers about the skills that they want our graduates to develop. These combine to ensure that you gain the most relevant up-to-date knowledge and skills on which to build your career.

We’re particularly proud of our high performance in the NSS (National Student Survey), steadily performing well above national averages.

Your first two years will offer fundamental knowledge in mathematics and statistics, then you’ll specialise your studies through a choice of optional modules such as financial mathematics, cryptography, medical statistics or fluid dynamics among others.

This integrated undergraduate course is underpinned by our research strengths in areas of applied mathematics and in your final year you will have the opportunity to do a substantial piece of research in areas such as biomathematics, classical and quantum dynamical systems, symmetries and integrable systems, magnetohydrodynamics and nonlinear waves.

In addition, you’ll have the option of a work-based placement year in industry or to study abroad at one of our partner institutions, enabling you to develop additional personal and professional skills.

Northumbria Mathematics Department achieved an overall satisfaction score of 97% (National Student Survey, 2018)

This programme is accredited to meet the educational requirements of the Chartered Mathematician designation awarded by the Institute of Mathematics and its Applications.

Northumbria University - Maths Department from Northumbria University on Vimeo.

Course Information

UCAS Code
G101

Level of Study
Undergraduate

Mode of Study
4 years full-time or 5 years with a placement (sandwich)/study abroad

Department
Mathematics, Physics and Electrical Engineering

Location
City Campus, Northumbria University

City
Newcastle

Start
September 2019 or September 2020

Department / Mathematics, Physics and Electrical Engineering

The Hub / For Students, By Students

Read our student blog and find out what student life is like at Northumbria from real students, tips and advice and much more.

Book An Open Day / Experience Mathematics MMath (Hons)

Visit an Open Day to get an insight into what it's like to study Mathematics. Speak to staff and students from the course and get a tour of the facilities.

From the outset, we’ll help you to take responsibility for your own learning as you develop the skills to investigate the frontiers of mathematics and statistics.

You’ll be taught through lectures, classes, seminars and workshops in computer labs where you’ll work with your fellow students, supported by academic staff.

You’ll be able to use the university’s online resources to support your study, including the e-learning portal where you can access course materials and develop discussions with your peers.

We’ll also encourage you to take an independent approach to problem solving and you’ll develop skills in computer programming and data analysis using a range of specialist applications.

At the start of each module, we’ll be really clear about its content and what you should expect to achieve. Assessment will be through a mix of practical and theoretical approaches including coursework and exams and we’ll provide regular and high-quality feedback with every piece of work, as well as throughout the course, to ensure you develop the skills and knowledge you need to succeed.

We’ll help you take responsibility for your learning as you develop skills to investigate the frontiers of mathematics, leading to an open-ended research project in your final year. This will include an emphasis on problem solving, particularly using IT packages. 

Your optional industrial placement will help to reinforce and develop your knowledge and skills, bringing real context to your studies.

Book An Open Day / Experience Mathematics MMath (Hons)

Visit an Open Day to get an insight into what it's like to study Geography. Speak to staff and students from the course and get a tour of the facilities.

You’ll learn from a team of leading mathematicians and statisticians. Our internationally diverse teaching team come from a wide range of backgrounds and have a wealth of experience between them.

You can find out more about our teaching staff and their specific areas of interest and expertise in the staff profiles section.

  

Book An Open Day / Experience Mathematics MMath (Hons)

Visit an Open Day to get an insight into what it's like to study Mathematics. Speak to staff and students from the course and get a tour of the facilities.

Technology will play a big part in your learning and is embedded throughout the course and you will be able to benefit from an extensive range of specialist facilities to support all aspects of your studies.


Facilities / Mathematics, Physics and Electrical Engineering

Take a look at the facilities for the Mathematics, Physics and Electrical Engineering department.

Virtual Tour

Come and explore our outstanding facilities in this interactive virtual tour.

University Library

At the heart of each Northumbria campus, our libraries provide a range of study space and technology to suit every learning style.

Book An Open Day / Experience Mathematics MMath (Hons)

Visit an Open Day to get an insight into what it's like to study Mathematics. Speak to staff and students from the course and get a tour of the facilities.

The course is underpinned by our research strengths and one of its main aims is to stimulate your scientific curiosity and help you to develop your own research potential.

Teaching is both research-orientated and research-led and you’ll be gradually introduced to the advanced research methods and processes needed for the construction of new knowledge in mathematics and statistics.

As you progress through your studies, you’ll develop your critical thinking skills and academic rigour and have lots of opportunities to engage with analytical and computational techniques, including your final year independent project where you’ll be expected to demonstrate your independent research and inquiry skills.


Book An Open Day / Experience Mathematics MMath (Hons)

Visit an Open Day to get an insight into what it's like to study Mathematics. Speak to staff and students from the course and get a tour of the facilities.

Mathematics is a high-respected degree and mathematicians and statisticians work across a wide range of disciplines in a variety of sectors.
By the end of the course you’ll be equipped with a range of advanced mathematical and statistical skills that are highly valued by employers, as well as advanced IT skills, communication skills and the ability to present complex information in a clear way.

Your research project will require you to apply qualitative and quantitative analysis, form objective judgments, justify and communicate outcomes and contribute to the creation of new knowledge, and these high-level skills will really enhance your employability.

You’ll also have a good understanding of the wider global issues around mathematics, statistics and their applications.

If you choose the option of a sandwich year placement, you’ll also develop project management experience, enhanced technical skills, awareness of business models and a valuable contact network, giving you a real head start in the job market on graduation.

Student Life

A great social scene can be found at the heart of our campuses, featuring award-winning bars and a huge range of clubs and societies to join you'll be sure to meet people who share your enthusiasms.

Book An Open Day / Experience Mathematics MMath (Hons)

Visit an Open Day to get an insight into what it's like to study Mathematics. Speak to staff and students from the course and get a tour of the facilities.

We’ll place great emphasis on supporting you to develop the knowledge and skills that employers value the most, including transferable skills such as creative thinking while applying structure to complex problems, communication, analysis and IT.

Mathematics graduates are highly sought after in a variety of sectors, both in the UK and internationally, including the financial sector and public sector, as well as in commerce, industry and teaching.

Our graduates have found employment in the banking, retail, manufacturing and teaching sectors, including BAE Systems, Department of Work and Pensions, GlaxoSmithKline, Northumbrian Water, London Transport System, Nissan, as well as advancing to postgraduate study.

Book An Open Day / Experience Mathematics MMath (Hons)

Visit an Open Day to get an insight into what it's like to study Mathematics. Speak to staff and students from the course and get a tour of the facilities.

Course in brief

Your course in brief

Year 1

Year one You will study core modules in Calulus, Modelling, Computational Mathematics, Dynamics, Statistics and Algebra and Analysis.

Year 2

Year two In year two you will undertake modules in Further Computational Mathematics, Applied Statistical Methods, Ordinary and Partial Differential Equations, Vector Calculus and Further Dynamics, Applied Modelling and Operational Research.

Year 3

Year three You will have the option to go out on an industrial placement to put the skills you have learned in the previous modules into professional practice, or on study abroad.

Year 4

Year four In the fourth year you will study modules such as Financial Mathematics, Advanced Mathematical Modelling, Mathematical Cryptology, Fluid Dynamics, Dynamic Systems, Advanced Statistical Methods, Medica Statistics and Complex Analysis. You will also undertake a major Investigative Project in a topic of your choice.

Year 5

Year five You will study modules such as Bayesian Statistics, Time Series and Forecasting, Linear and Non Linear Waves, Numerical Solutions of PDEs and Research Methods and Professional Practice. A major aspect of this year is to complete a Masters project in a relevant subject area of your choice.

Who would this Course suit?

If you are fascinated by mathematics and have a passion for numbers, statistics, structure and space then this course is for you.

It is a great route if you want to develop your mathematical talents and gain knowledge of contemporary theory, research and professional practice. It allows you to explore the subject of mathematics at an advanced level, with a specialised final year that leads to an integrated masters qualification.

A degree in mathematics opens the door to a wide range of careers as a result of our graduates’ ability to solve problems using a variety of approaches, build rigorous arguments and their ability to construct models to make testable predictions.

Entry Requirements 2019/20

Standard Entry

GCSE Requirements:

A good GCSE profile is expected including Maths and English Language at minimum grade C or equivalent.  If you have studied for a new GCSE for which you will be awarded a numerical grade then you will need to achieve a minimum grade 4.

UCAS Tariff Points:

120-128 UCAS Tariff points including one or more of the following:

GCE and VCE Advanced Level:

From at least 2 GCE/VCE A Levels including GCE A level Mathematics grade B 

Edexcel/BTEC National Extended Diploma:

Distinction, Distinction, Merit

Scottish Highers:

BBBCC - BBBBC at Higher level, CCC - BCC at Advanced Higher including Mathematics

Irish Highers:

BBBBB  - ABBBB including Mathematics

IB Diploma:

120-128 UCAS Tariff points including minimum score of 4 in at least three subjects at Higher level including Mathematics

Access to HE Diploma:

Award of full Access to HE Diploma in Engineering including 18 credits at Distinction and 27 at Merit

Qualification combinations:

The University welcomes applications from students studying qualifications from different qualification types - for example A level and a BTEC qualification in combination, and if you are made an offer you will be asked to achieve UCAS Tariff points from all of the qualifications you are studying at level 3.  Should the course you wish to study have a subject specific requirement then you must also meet this requirement, usually from A level or equivalent study.

Plus one of the following:

  • International/English Language Requirements:

    Applicants from the EU:

    Applicants from the EU are welcome to apply and if the qualification you are studying is not listed here then please contact the Admissions Team for advice or see our EU Applicants pages here www.northumbria.ac.uk/international/european-union/eu-applications/

    International Qualifications:

    If you have studied a non UK qualification, you can see how your qualifications compare to the standard entry criteria, by selecting the country that you received the qualification in, from our country pages. Visit www.northumbria.ac.uk/yourcountry

    English Language Requirements:

    International applicants are required to have a minimum overall IELTS (Academic) score of 6.0 with 5.5 in each component (or approved equivalent*).

    *The university accepts a large number of UK and International Qualifications in place of IELTS. You can find details of acceptable tests and the required grades you will need in our English Language section. Visit www.northumbria.ac.uk/englishqualifications

Entry Requirements 2020/21

Standard Entry

120 UCAS Tariff points
From a combination of acceptable Level 3 qualifications which may include: A level, BTEC Diplomas/Extended Diplomas, Scottish and Irish Highers, Access to HE Diplomas or the International Baccalaureate

Find out how many points your qualifications are worth using the UCAS Tariff calculator: www.ucas.com/ucas/tariff-calculator

Subject Requirements:
Grade B in an A level Mathematics or recognised equivalents

GCSE Requirements:
Students will need Maths and English Language at minimum grade 4 or C, or the equivalent.

Additional Requirements:
There are no additional requirements for this course

International Qualifications:
We welcome applicants with a range of qualifications from the UK and worldwide which may not exactly match those shown above. If you have taken qualifications outside the UK you can find out how your qualifications compare by visiting our country page www.northumbria.ac.uk/yourcountry

English Language Requirements:
International applicants are required to have a minimum overall IELTS (Academic) score of 6.0 with 5.5 in each component (or approved equivalent*).

*The university accepts a large number of UK and International Qualifications in place of IELTS. You can find details of acceptable tests and the required grades you will need in our English Language section. Visit www.northumbria.ac.uk/englishqualifications

Fees and Funding 2019/20 Entry

UK/EU Fee in Year 1: £9,250

International Fee in Year 1: £15,000

ADDITIONAL COSTS

There are no Additional Costs

Scholarships and Discounts

Click here for UK and EU undergraduate funding and scholarships information.

Click here for International undergraduate funding and scholarships information.

Fees and Funding 2020/21 Entry

UK/EU Fee in Year 1**: TBC

Undergraduate fees are set by Government and are subject to annual review. Once these have been approved we will update fees/funding information for UK and EU students.


International Fee in Year 1: £15,500

Scholarships for 2020/2021 entry have not been announced. Please visit the 2019/2020 international scholarship page for the 2019/2020 scholarship offer.


ADDITIONAL COSTS

TBC


Scholarships and Discounts

20/21 fees and funding information has not been confirmed. 19/20 information is listed below.

Click here for UK and EU undergraduate funding and scholarships information.

Click here for International undergraduate funding and scholarships information.

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* By submitting your information you are consenting to your data being processed by Northumbria University (as Data Controller) and Campus Management Corp. (acting as Data Processor). To see the University's privacy policy please click here

How to Apply

Applications via UCAS

Most full-time and sandwich first degrees, extended degrees, DipHE and HND courses require that application is made through the Universities and Colleges Admissions Service (UCAS) Clearing House.

If you are at school or college, staff there will advise you on how to apply. If you are not at school or college, you can apply using the UCAS secure, web-based online application system ucasapply.

Applicants apply via UCAS apply wherever there is access to the internet, and full instructions and an online help facility is available. Application details can be checked and printed at any time, text for personal statements and references can be copied and pasted into applications from a word processing package, and applications can normally be processed by the relevant Clearing House within one working day once submitted. More details on apply can be found on the UCAS website at www.ucas.com.

  • The UCAS institution code for Northumbria University is NORTH N77

If you wish to defer your entry, you should ensure you indicate this in section 3i of the application form. Full details of application deadlines and the application fee can be found on the UCAS website. Please note, however, we are unable to consider applications for deferred entry to our Teacher Training, Nursing, Midwifery and Operating Department Practice programmes.

Application Deadlines

Equal consideration is given to all applications received at UCAS by 6.00pm on 15 January. Details of all UCAS deadlines can be found on the UCAS website www.ucas.com.

UCAS will accept applications up to 30 June, but we can only consider these if there are still vacancies in relevant subjects. You are advised to check with the University before applying for popular courses which may already be full. Candidates applying for any courses after early September must follow the UCAS Late Registration Procedure, and we will provide the appropriate form.

Decision Making Process

When we receive your application it will be forwarded to the Admissions Tutor who will consider your application in accordance with the University’s Admissions Policy.

Most subject areas do not require applicants to attend an interview as part of the selection procedure. However, if the standard procedure is to interview candidates, this is specified in the degree programme entrance requirements. Some courses, such as Health, Social Work and Teacher Training, require specific checks or requirements to be put in place during the normal selection process. These are detailed on the individual course details pages.

Fairness and Transparency

The University is committed to a system of admissions that ensures fairness, transparency and equal opportunities within the legal framework of the UK and best practice. All reasonable effort will be made to ensure that no prospective or existing student is unreasonably treated less favourably on the grounds of age, race, colour, nationality, ethnic origin, creed, disability, sexual orientation, gender, marital or parental/carer status, political belief or social or economic class, or any other type of discrimination.

What Happens Next

You will receive one of the following from UCAS or our Admissions Office:

  • Conditional offer which depends on you achieving certain grades from forthcoming examinations, completing relevant checks, or other requirements prior to entry. You may be asked to send us a copy of your certificates/qualifications once these have been received to enable us to confirm your offer. Not all examination results are sent to Universities via UCAS.
  • Unconditional offer if you have already satisfied entry requirements.
  • Reject your application.

Tuition Fee Assessment

Tuition fees are set at different levels for Home/EU and International Students. Before you begin your course the University must establish your tuition fee status. In many cases, the University will be able to make this assessment without requiring any additional information.

Guidance can be found on the UK Council for International Student Affairs (UKCISA) website www.ukcisa.org.uk to help you understand how Higher Education Institutions (HEI’s) make an assessment on your fee status.

Selection Process

Interviews

Applicants who may not have the standard entry qualifications are welcome to apply and may be interviewed. Some courses will interview as part of the selection process. This applies particularly to courses in art and design, teaching and health.

Health Screening

Applicants for Nursing, Midwifery, Physiotherapy, Occupational Therapy, Primary (Early Years) and Social Work will be required to complete a health questionnaire, and you may be required to attend a doctor or nurse assessment at the University Health Centre.

Prior to beginning your programme, all applicants to Nursing, Midwifery, Physiotherapy and Occupational Therapy are advised to start a course of Hepatitis B vaccinations, available from your own GP. In addition, Midwifery applicants must provide evidence before they commence training that they are immune to Hepatitis B or have Hepatitis B non-carried status.

Applicants to these courses who have had contact with MRSA in the previous 6 months may be asked to provide evidence that they are not colonised by submitting negative swabs results prior to commencement of training. Alternatively, you may be screened on commencement of the programme.

All applicants will receive vaccination screening at the University Health Centre on commencement of their programme.

Disclosure of Criminal Background

To help the University reduce the risk of harm or injury to any member of its community caused by the criminal behaviour of other students, it must know about any relevant criminal convictions an applicant has.

Relevant criminal convictions are only those convictions for offences against the person, whether of a violent or sexual nature, and convictions for offences involving unlawfully supplying controlled drugs or substances where the conviction concerns commercial drug dealing or trafficking. Convictions that are spent (as defined by the Rehabilitation of Offenders Act 1974) are not considered to be relevant and you should not reveal them - unless you are applying for one of the courses outlined within the following paragraph.

If you are applying for courses in teaching, health, social work and courses involving work with children or vulnerable adults, you must complete the section of your UCAS application form entitled ‘Criminal Convictions’. You must disclose anycriminal convictions, including spent sentences and cautions (including verbal cautions) and bindover orders. Further information on how to complete this section is available from the UCAS booklet ‘How to Apply’. For these courses, applicants are required to undergo police clearance for entry and will need to complete a Disclosure and Barring Service (DBS) enhanced disclosure form. 

The Disclosure and Barring Service (DBS) helps employers make safer recruitment decisions and prevent unsuitable people from working with vulnerable groups, including children. It replaces the Criminal Records Bureau (CRB) and Independent Safeguarding Authority (ISA). Access to the DBS checking service is only available to registered employers who are entitled by law to ask an individual to reveal their full criminal history, including spent convictions - also known as asking 'an exempted question'. The University is such a 'registered employer' and will send you the appropriate documents to fill in if you are offered a place in the course.

If you are convicted of a relevant criminal offence after you have applied, you must tell UCAS and the University. Do not send details of the offence; simply tell UCAS and the University that you have a relevant criminal conviction. You may then be asked to supply more details.

Anti-fraud Checks

Please note that both UCAS and the University follow anti-fraud procedures to detect and prevent fraudulent applications. If it is found that an applicant supplies a fraudulent application then it will be withdrawn.

Plagiarism

Applicants suspected of providing, or found to have provided, false information will be referred to UCAS if their application was made via UCAS. The same is true for applicants who are suspected of omitting, or found to have omitted, information that they are required to disclose according to UCAS regulations. Applications identified by UCAS’s Similarity Detection software to contain plagiarised material will be considered on an individual basis by Admissions Staff, taking into account the nature, relevance and importance of the plagiarism. The University reserves the right to cancel an application or withdraw any offer made if it is found that an application contains false, plagiarised or misleading information.

Extra

The Extra process enables applicants who have not been offered a place, or have declined all offers received, can use EXTRA to apply for other courses that still have vacancies before Clearing starts. The Extra process normally operates from late February until the end of June and Applicants should use the Course Search facility at UCAS to find which courses have vacancies.

Clearing

If you have not succeeded in gaining a place at your firm or insurance university, UCAS will send you details about Clearing, the procedure which matches course vacancies with students who do not have a university place. Information about degree vacancies at Northumbria is published in the national press; and you can also find information on our dedicated Clearing web pages during this period. We operate a Helpline - 0191 40 60 901 - throughout the Clearing period for enquiries about course vacancies.

Adjustment
If an applicant has both met and exceeded the conditions of their firmly accepted offer, they will have up to five calendar days from the time their place was confirmed (or A level results day, whichever is the later) to research places more appropriate to their performance. Applicants will have to nominate themselves for this system, and their eligibility will be confirmed by the institution they apply to adjust to.

Going to University from Care
Northumbria University is proud of its work in widening participation of young people and adults to university. We have recently been successful in being awarded the Frank Buttle Trust Quality Mark for Care Leavers in Higher Education. This mark was created to recognise institutions who go that extra mile to support students who have been in public care. To find out more, visit our Going to University from Care web page.

Disabled Students

Northumbria welcomes enquiries and applications from disabled students whether disability is due to mobility or sensory impairment, specific learning difficulties, mental health issues or a medical condition. Applications from disabled students are processed in the usual way, but applicants should declare their disability at the application stage so that the University can contact them to assess how to meet any support needs they may have. Disabled applicants may be invited to visit the University so that this can be done in person.

To find out more contact:
Disability Support Team
Tel +44 (0)191 227 3849 or
Minicom +44 (0)191 222 1051

International Students

The University has a thriving overseas community and applications from International students are welcome. Advice on the suitability of overseas qualifications is available from:

International Office
Northumbria University
Newcastle upon Tyne
NE1 8ST
UK
Email: international@northumbria.ac.uk
Tel +44 (0)191 227 4274
Fax +44 (0)191 261 1264

(However, if you have already applied to Northumbria and have a query, please contact internationaladmissions@northumbria.ac.uk or telephone 00 44 191 243 7906)

Provision of Information

The University reserves the right at any stage to request applicants and enrolling students to provide additional information about any aspect of their application or enrolment. In the event of any student providing false or inaccurate information at any stage, and/or failing to provide additional information when requested to do so, the University further reserves the right to refuse to consider an application, to withdraw registration, rescind home fees status where applicable, and/or demand payment of any fees or monies due to the University.

Modules Overview 2019/20

Modules

Module information is indicative and is reviewed annually therefore may be subject to change. Applicants will be informed if there are any changes.

KC4009 -

Calculus (Core,20 Credits)

The module is designed to introduce you to the principles, techniques and applications of calculus. The fundamentals of differentiation and integration are extended to include differential equations and multivariable calculus.

On this module you will learn:

Differentiation: derivative as slope and rate of change, standard derivatives; product, quotient, function of a function rules; implicit, parametric and logarithmic differentiation; maxima / minima, curve sketching; Maclaurin's and Taylor's series.

Integration: standard integrals, definite integrals, area under a curve; using substitution, partial fractions and by parts; applications (eg volumes, r.m.s. values).

Ordinary differential equations: Solution by direct integration. Solution of first order equations by separation of variables and use of an integrating factor. Solution of homogeneous and non-homogeneous second order equations with constant coefficients.

Functions of several variables: partial differentiation, Taylor's series in two variables, total first order change, analysis of errors, total rate of change, change of variables; stationary points, maxima / minima / saddle points of functions of two variables.

Method of Lagrange Multipliers: constrained maxima / minima, classification of stationary points.

Multiple integrals: double and triple integrals, change of order of integration, use of polar coordinates, simple applications.

More information

KC4012 -

Computational Mathematics (Core,20 Credits)

Mathematics students require knowledge of a range of computational tools to complement their mathematical skills. You will be using MATLAB, an interactive programming environment that uses high-level language to solve mathematics and visualise data. In addition, you will be investigating the development of algorithms through a selection of mathematical problems. Elements of the MATLAB language will be integrated throughout with various methods and techniques from numerical mathematics such as interpolation, numerical solution of differential equations, numerical solution of non-linear equations and numerical integration.

The computer skills you will become conversant with include programming concepts such as the use of variables, assignments,
expressions, scriptfiles, functions, conditionals, loops, input and output. You will be applying MATLAB to solve mathematical problems and display results appropriately.

The range of numerical techniques that will be covered will include a selection from the following topics:
• Solution of non-linear equations by bisection, fixed-point iteration and Newton-Raphson methods.
• Interpolation using linear, least squares and Lagrange polynomial methods.
• Numerical differentiation.
• Numerical integration using trapezoidal and Simpson quadrature formulae.
• Numerical solution of Ordinary Differential Equations using Euler and Taylor methods for first-order initial value problems.
• Numerical solution of systems of linear equations using elementary methods.

More information

KC4014 -

Dynamics (Core,20 Credits)

This module is designed to provide you with knowledge in a special topic in Applied Mathematics. This module introduces Newtonian mechanics developing your skills in investigating and building mathematical models and in interpreting the results. The following topics will be covered:

Mathematics Review
Euclidean geometry. Vector functions. Position vector, velocity, acceleration.
Cartesian representation in 3D-space. Scalar and vector products, triple scalar product.

Newton’s Laws
Inertial frames of reference. Newton's Laws of Motion. Mathematical models of forces (gravity, air resistance, reaction, elastic force).

Rectilinear and uniformly accelerated motion
Problems involving constant acceleration (e.g., skidding car), projectiles with/without drag force (e.g., parabolic trajectory, parachutist). Variable mass. Launch and landing of rockets.
Linear elasticity. Ideal spring, simple harmonic motion. Two-spring problems. Free/forced vibration with/without damping. Resonance. Real spring, seismograph.

Rotational motion and central forces
Angular speed, angular velocity. Rotating frames of reference.
Simple pendulum (radial and transverse acceleration). Equations of motion, inertial, Coriolis, centrifugal effects. Effects of Earth rotation on dynamical problems (e.g. projectile motion).
Principle of angular momentum, kinetic and potential energy. Motion under a central force. Kepler’s Laws. Geostationary satellite.

More information

KC4020 -

Probability and Statistics (Core,20 Credits)

This module is designed to introduce you to the important areas of Statistics. In this module, you will learn about data collection methods, probability theory and random variables, hypothesis testing and simple linear regression. Real-life examples will be used to demonstrate the applications of these statistical techniques. You will learn how to use R to analyse data in various practical applications.

Outline Syllabus
Data collection: questionnaire design, methods of sampling - simple random, stratified, quota, cluster and systematic. Sampling and non-sampling errors. Random number generation using tables or calculator.

Population and sample, types of data, data collection, frequency distributions, statistical charts and graphs, summary measures, analysis of data using R.

Probability: sample space, types of events, definition of probability, addition and multiplication laws, conditional probability. Discrete probability distributions including Binomial, Poisson. Continuous probability distributions including the Normal. Central Limit Theorem. Mean and variance of linear combination of random variables. Use of Statistics tables.

Hypothesis tests on one and two samples, confidence intervals using the normal and Student t distributions.

Correlation and simple linear regression.

More information

KL4001 -

Real Analysis (Core,20 Credits)

The module is designed to i) introduce you to the notion of convergence as this applies to sequences, series and functions of one variable; ii) to provide a firm basis for future modules in which the idea of convergence is used; iii) to help you recognize the necessity and power of rigorous argument.

Outline Syllabus:

1) Introduction to propositional logic and sets.
2) Real numbers: equations, inequalities, modulus, bounded sets, maximum, minimum, supremum and infimum.
3) Sequences: convergence, boundedness, limit theorems; standard sequences and rate of convergence, monotone sequences, Cauchy sequences.
4) Series: standard series (geometric, harmonic series, alternating harmonic series, etc ); absolute and conditional convergence; convergence tests.
5) Power Series.
6) Functions: continuity, the intermediate value theorem, the extreme value theorem.
7) Differentiability: basic differentiability theorems, differentiability and continuity, Rolle’s theorem, Lagrange theorem, Taylor’s theorem.
8) Riemann’s Integrability: properties of integrable functions, modulus and integrals, The fundamental theorem of Calculus.

More information

KL4002 -

Linear Algebra and Geometry (Core,20 Credits)

The module is designed to introduce you to the concepts, definitions and methods linear algebra, coordinate transformations and geometry of curves and surfaces.

Outline Syllabus:

1. Sets, Rings, Groups (basic definitions)
2. Vector Spaces
3. Linear maps (basis expansions, rank, kernel)
4. Matrices (determinants, systems of linear equations, eigenvalues and eigenvectors, similarity transformations)
5. Quadratic forms
6. Euclidean vector spaces
7. Affine spaces
8. Projective spaces
9. Conics
10. Curves in the plane (length of a curve and natural parametrisation, tangent vector, normal vector and curvature)
11. Quadrics
12. Surfaces.

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KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Core – for International and EU students only,0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

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KC5000 -

Further Computational Mathematics (Core,20 Credits)

This module continues the numerical methods and computational mathematics thread established with KC4012: Computational Mathematics. The module aims to present an introduction to advanced numerical mathematics, in particular multivariable problems, and associated transferable skills. Numerical methods are applied to the solution of several classes of problems, including: systems of linear and nonlinear equations, eigensystems, optimisation, ordinary and partial differential equations. Theoretical aspects are illustrated and discussed at the lectures, and computational implementation developed at the computer-lab workshops, using appropriate software (e.g. MATLAB).

Topics may include (note this is indicative rather than prescriptive):
1. Vector and matrix spaces: normed spaces; vector norms; matrix norms; compatible norms; spectral radius; condition number.
2. Systems of linear equations: direct and iterative methods.
3. Matrix eigensystems: iterative methods for eigenvalues and eigenvectors.
4. Systems of nonlinear equations: multidimensional Newton method; fixed-point iterations method.
5. Numerical optimization: pattern search methods; descent methods.
6. Ordinary differential equations (ODEs): forward and backward Euler methods; Crank-Nicolson method; convergence, consistency and stability of a method; conditional stability; simple adaptive-step methods; Runge-Kutta methods; predictor-corrector methods; Heun method; systems of ODEs; stiff problems.
7. Numerical approximation of initial, boundary value problems (IBVP) for ordinary and partial differential equations (PDEs): finite difference method for the (Dirichlet) IBVP for the one- and two-dimensional Poisson equations; finite difference method for the (Dirichlet) IBVP for the one-dimensional heat equation; finite-difference method for the (Dirichlet) IBVP for the one-dimensional wave equation.

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KC5001 -

Applied Statistical Methods (Core,20 Credits)

The aim of the module is to enhance your hands-on statistical modelling expertise The module considers important continuous probability distributions leading on to parameter estimation and goodness of fit. Hypothesis testing for both parametric and non-parametric situations are introduced for each of one and two - possibly paired - samples. This is extended to design, and analysis, of experiments. You will also study residual analysis for model assessment and goodness-of-fit with examples based on the classic simple linear regression model.

Outline Syllabus
Probability distributions including standard continuous distributions.
Central Limit Theorem.
Mean and variance of a linear combination of random variables.
Principles of estimation and estimation via the method of moments.
Maximum likelihood estimation. Goodness-of-fit test and contingency tables.
Tests for variances and proportions. Test and confidence intervals using F- and chi-squared distributions.

Nonparametric statistics
Sign test; Wilcoxon signed rank test; Mann-Whitney U-test; Wald-Wolfowitz runs test; Spearman's rank correlation coefficient.

Regression Analysis
(Pearson’s) correlation coefficient; simple linear regression. Transformations of variables. Residual Analysis.

Design and Analysis of Experiments
Completely randomised, randomised block, Latin square and missing values.

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KC5008 -

Ordinary & Partial Differential Equations (Core,20 Credits)

The module is designed to introduce you to a first mathematical treatment of ordinary and partial differential equations. You will learn fundamental techniques for solving first- and second-order equations as well as approximation methods. These are used to explore the question of the existence of solutions and provide a qualitative behaviour of the solutions. Examples are drawn from applications to physics, engineering, biology, economics and finance and modelling of complex systems.

Outline Syllabus

Ordinary Differential Equations (ODEs)

1. First-order ODEs: Classification of ODEs, separable, Bernoulli, Riccati and exact equations as well as integrating factors. Picard iterations and existence of solutions.
2. Second-order ODEs: Solutions of linear equations, independence of solutions, linear stability, initial and boundary value problems, series solutions about ordinary and singular points.

Partial Differential Equations (PDEs)

1. Introduction and classification of PDEs. The method of separation of variables and Fourier series. Solutions of Laplace, diffusion/heat and wave equations.
2. Applications to physics, engineering, biology and finance.

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KC5009 -

Vector Calculus & Further Dynamics (Core,20 Credits)

You will learn about vector calculus and tensor analysis and their applications in ‘Vector Calculus and Further Dynamics’. These powerful mathematical methods provide convenient tools for the description and analysis of the physical world. You will be introduced to the fundamentals of vector calculus and Cartesian tensors, as well as their application to the development and analytical solution of problems in rigid body dynamics. Throughout, the real-world motivation for the techniques chosen and the interpretation of the solutions will be emphasised.

You will learn about the following topics:
• Line, surface and volume integrals;
• Vector fields and operators, including Gauss' (Divergence) Theorem, Stokes' Theorem and the Transport Theorem;
• Introduction to Cartesian tensors.

You will be applying these powerful mathematical techniques to planetary motion and rigid body dynamics in ‘Vector Calculus and Further Dynamics’. By studying point particle motion you will become acquainted with the fundamental concepts of central forces and through the application of the principles of linear and angular momentum you will be investigating the dynamics of rigid bodies.

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KC5026 -

Applied Modelling (Core,20 Credits)

The module will give you the confidence to tackle real world problems in a supported environment. You will work in groups under supervision. Two real world problems are considered. The two real world problems do not rely on you already having the necessary mathematical knowledge and may require you to research various techniques. You would be expected to apply these techniques to the problems, solve them and analyse their results. This module also prepares students for the level 6 Advanced Mathematical Modelling module in Final Year (core on the Maths degree, option on Maths with Business Management degree) where students are expected to work much more independently.

Outline Syllabus

This module provides an opportunity for students to develop their ability to model and solve real world problems. For a given problem students work in groups and might not have studied all the mathematical/statistical methods needed to solve it.
The students work on two case studies in a different group each time. The groups meet with their supervisor once a week, who supports and guides them through the modelling and solution process.
The case studies are assessed by a variety of methods, which may include giving a PowerPoint presentation, producing a written report, creating a poster. The module enhances their abilities in critical thinking, research skills and other transferable skills.
Students are given oral and written feedback after every case study by the supervisor involved.

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KC5027 -

Operational Research (Core,20 Credits)

Operational Research is designed to introduce students to the operational research methods that apply to specific business problems. You will learn about linear programming, inventory control, quality control, network analysis, queueing theory and simulation – topics created to analyse and solve everyday business problems. A range of business optimisation problems will be presented, and theoretical aspects of the solutions considered. Various quality control techniques will be examined and you will learn how to use software such as Excel and Matlab to solve such problems.

Outline syllabus
Simulation Models: Properties and transformations of pseudo random numbers. Developing Witness models to simulate various situations.
Queuing Theory: Queue discipline; traffic intensity; single server queues with random arrivals and random service times; more than one server; cost comparisons.
Network Analysis: Construction of the network; critical path analysis; resource levelling; crash costs and crashing the network; variation in the duration of activities.
Linear Programming: Formulation of a problem for two or more variables; graphical solution; sensitivity analysis; simplex algorithm. Use of Excel to solve linear programming problems. Integer programming using Branch and Bound Algorithm. Transportation problems.
Inventory Control: Economical order quantity; price breaks; buffer stocks.
Quality Control techniques to include control charts and acceptance sampling.

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KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Core – for International and EU students only,0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

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KA5029 -

International Academic Exchange 1 (Optional,60 Credits)

This module is designed for all standard full-time undergraduate programmes within the Faculty of Engineering and Environment and provides you with the option to study abroad for one semester as part of your programme.

This is a 60 credit module which is available between Levels 5 and 6. You will undertake a semester of study abroad at an approved partner University where you will have access to modules from your discipline, but taught in a different learning culture. This gives you the opportunity to broaden your overall experience of learning. The structure of study will be dependent on the partner and will be recorded for an individual student on the learning agreement signed by the host University, the student, and the home University (Northumbria).

Your study abroad semester will be assessed on a pass/fail basis. It will not count towards your final degree classification but, if you pass, it is recognised in your transcript as an additional 60 credits for Engineering and Environment Study Abroad Semester.

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KA5030 -

International Academic Exchange 2 (Optional,120 Credits)

This module is designed for all standard full-time undergraduate programmes within the Faculty of Engineering and Environment and provides you with the option to study abroad for one full year as part of your programme.

This is a 120 credit module which is available between Levels 5 and 6. You will undertake a year of study abroad at an approved partner University where you will have access to modules from your discipline, but taught in a different learning culture. This gives you the opportunity to broaden your overall experience of learning. The structure of study will be dependent on the partner and will be recorded for an individual student on the learning agreement signed by the host University, the student, and the home University (Northumbria).

Your study abroad year will be assessed on a pass/fail basis. It will not count towards your final degree classification but, it is recognised in your transcript as a 120 credit Study Abroad module and on your degree certificate in the format – “Degree title (with Study Abroad Year)”.

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KF5000 -

Engineering and Environment Work Placement Year (Optional,120 Credits)

This module is designed for all standard full-time undergraduate programmes within the Faculty of Engineering and Environment to provide you with the option to take a one year work placement as part of your programme.

You will be able to use the placement experience to develop and enhance appropriate areas of your knowledge and understanding, your intellectual and professional skills, and your personal value attributes, relevant to your programme of study, as well as accreditation bodies such as BCS, IET, IMechE, RICS, CIOB and CIBSE within the appropriate working environments. Due to its overall positive impact on employability, degree classification and graduate starting salaries, the University strongly encourages you to pursue a work placement as part of your degree programme.

This module is a Pass/Fail module so does not contribute to the classification of your degree. When taken and passed, however, the Placement Year is recognised both in your transcript as a 120 credit Work Placement Module and on your degree certificate.

Your placement period will normally be full-time and must total a minimum of 40 weeks.

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KF5001 -

Engineering and Environment Work Placement Semester (Optional,60 Credits)

This module is designed for all standard full-time undergraduate programmes within the Faculty of Engineering and Environment to provide you with the option to take a one semester work placement as part of your programme.

You will be able to use the placement experience to develop and enhance appropriate areas of your knowledge and understanding, your intellectual and professional skills, and your personal value attributes, relevant to your programme of study, within the appropriate working environments. Due to its overall positive impact on employability, degree classification and graduate starting salaries, the University strongly encourages you to pursue a work placement as part of your degree programme.

This module is a Pass/Fail module so does not contribute to the classification of your degree. When taken and passed, however, the placement is recognised both in your transcript as a 60 credit Work Placement Module and on your degree certificate.

Your placement period will normally be full-time and must total a minimum of 20 weeks.

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KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Core – for International and EU students only,0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

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KC6001 -

Financial Mathematics (Optional,20 Credits)

The module introduces the concepts and terminology of financial mathematics and modelling in finance. You will learn about
the properties of interest rates and the key tools of compound interest functions for modelling a range of annuity schemes. The module develops models for life insurance and endowment schemes and enables the students to analyse the behaviour of share prices. The generalised cash-flow model is introduced to describe financial transactions. The student learns how to develop simple models of financial instruments such as bonds and shares.


Outline Syllabus

Interest: Simple and compound interest. Effective and nominal interest rates. Force of interest. Interest paid monthly. Present values. Cash flows and equations of value.
Annuities: Annuities with annual payments, and payments more regularly. Payments in arrear and in advance. Deferred and varying annuities, annuities payable continuously. Loans, loan structure and equal payments.
Discounted cash flow: Generalised cash flow model. Project appraisal at fixed interest rates. Comparison of two investment projects. Different interest rates for lending and borrowing. Payback periods. Measurement of investment performance.
Investments: Types of investments. Valuation of fixed interest securities and uncertain income securities. Real rates of interest. Effects of inflation. Capital gains tax.
Arbitrage in financial mathematics: Forward contracts. Calculating delivery price and delivery value of forward contracts using arbitrage-free pricing methods. Discrete and continuous time rates.
Life Insurance: Term insurance and whole life insurance. Curtate future lifetime. Life tables, expectation of life. Annual and monthly premium. Endowments. Payment at death.
Stochastic Interest Rates: Varying interest rates. Independent rates of return. Expected values. Application of the lognormal distribution. Brownian motion.

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KC6007 -

Mathematical Cryptology (Optional,20 Credits)

Mathematical cryptology concerns the creation and analysis of secret messages using mathematical techniques. You will learn about both classical and contemporary cryptology from the time of Julius Caesar until the present day. Mathematical techniques have been at the heart of many of these approaches and, on this module, you will be able to see, for example, how modular algebra can be a powerful cryptographic tool. Large prime numbers are another useful tool at the heart of modern cryptology and you will learn how to formulate an efficient approach to determining whether a large number is prime or composite.

By the end of the module, you should have developed an awareness of different approaches to deciphering various forms of ciphertext and should have an ability to appraise which cryptographical techniques are robust.

Outline Syllabus
Classical Cryptology: Encryption and decryption using direct standard alphabets and alphabets created using classical techniques from the shift cipher to polygraphic ciphers.

Contemporary Cryptology: Encryption and decryption using techniques based on boolean functions and exploring the mathematical theorems and approaches at the heart of modern cryptology practices.

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KC6027 -

Fluid Dynamics (Optional,20 Credits)

This module is designed to introduce fundamental concepts in the mathematical area of Fluid Dynamics. You will analyse the equations of continuity and momentum, and will investigate key concepts in this area. We will introduce the Navier-Stokes equations, and case studies will be used to visualise and analyse real-world problems (using appropriate software) as appropriate to delivery of the module. Initially, we will use the inviscid approximation and then utilise analytical and computational techniques to investigate flows. The second half of the module is a specialist course in laminar incompressible viscous flows, encompassing background mathematical theory allied to a case study approach, with solution to problems by both analytical and computational means.

Assessment of the module is by one individual assignment (30%) and one formal examination (70%).

The module is designed to provide you with a useful preparation for employment in an applied mathematical environment or engineering environment.

Outline Syllabus
• Introduction of fluid dynamics, Navier-Stokes equations, equations of continuity and momentum for inviscid flow, unsteady one-dimensional flow along a pipe, irrotational flow, Bernouilli's equation, stream function formulation, flow past a cylinder, velocity potential.

• Low Reynolds Number Flow including: (i) lubrication theory, slider bearing, cylinder-plane, journal bearing, Reynolds equation, short bearing approximation; (ii) Flow in a corner, stream function formulation, solution of the biharmonic equation by separation of variables.

• High Reynolds Number Flow including boundary layer equations, skin friction, displacement and momentum thickness, similarity solutions, momentum integral equation, approximate solutions.

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KC6028 -

Dynamical Systems (Optional,20 Credits)

The module aims to present an introduction to Dynamical Systems and associated transferable skills, providing the students with tools and techniques needed to understand the dynamics of those systems. You will analyse non-linear ordinary differential equations and maps, focusing on autonomous systems, and will learn analytical and computational methods to solve them. This module offers the additional opportunity of research-orientated learning through a hands-on approach to selected research-based problems.

Topics may include (note this is indicative rather than prescriptive):
1. Autonomous linear systems, fixed points and their classification.
2. 1-dimensional non-linear systems: critical points; local linear approximations; qualitative analysis; linear stability analysis; bifurcations.
3. Multi-dimensional non-linear systems: linearisation about critical points, limit cycles, bifurcations.
4. Discrete systems: maps (such as tent map, logistic map, Henon map, standard map).
5. Numerical schemes for ordinary differential equations, such as the embedded Runge-Kutta method.
6. Numerical applications and programming: generation of the orbit of a map, Lorenz map for a dynamical system, orbit diagrams, cobwebs, simple fractals.
7. Elements of Chaos theory: Lyapunov exponents, sensitive dependence on initial conditions, strange attractors, Hausdorff dimension, self-similarity, fractals.

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KC6029 -

Advanced Statistical Methods (Optional,20 Credits)

This module covers the three important areas of experimental design, multivariate techniques and regression. Experimental design will be developed using analysis of variance techniques to compare treatments meaningfully using replication, factorial experiments and balanced incomplete block designs. You will then move on to multivariate techniques including multivariate inference, data reduction using principal component analysis and classification with linear discriminant analysis. You will also learn how to extend regression models to the case where there are several explanatory variables including indicator variables. The models will subsequently be scrutinised using variable selection criteria and regression diagnostics to improve the model. Curvilinear and non-linear regression models cover the important aspect where different types of curves are appropriate for the data. The generalised linear model will be introduced and the specific case of a count response variable is developed.

Outline Syllabus
Experimental Design: design and analysis of 2n factorial experiments with replication, a full replicate and balanced
incomplete block designs.
Multivariate techniques: the multivariate normal distribution and its properties. Hotellings T2 test for one, two and paired
samples. Manova, linear discriminant analysis and principal component analysis.
Multiple linear regression: least squares estimation of the parameters of the model and their properties. The analysis of variance
and the extra sum of squares method. Variable selection techniques and regression diagnostics.
Non-linear and generalised linear models: Non-linear regression models, estimation of parameters and testing the model. Analysis of deviance and the Poisson regression model.

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KC6030 -

Medical Statistics (Optional,20 Credits)

You will learn about a range of appropriate statistical techniques that are used to analyse medical data. You will be introduced to the design and analysis of clinical trials and learn how to design the statistics of clinical trials for a variety of scenarios. These trials are the scientific tests that all medical advances need to go through to assess whether they have merit. You will learn techniques that can be used to handle various types of medical data found in epidemiology and learn when to apply them. You will investigate some of the statistical models used in survival data analysis for the analysis of time to failure data such as transplant data.

By the end of the module, you should have developed an ability to design clinical trials that are scientifically sound and be able to select and apply the appropriate statistical techniques to analyse medical data in a variety of forms.

Outline Syllabus

Design and analysis of Clinical Trials including the four main phases, estimation of sample size and power of a test. Parallel group and cross-over trials.

Categorical data analysis using contingency tables, McNemar's test, Fishers Exact test and test for trend.
Epidemiology: Prospective, retrospective and cross-sectional studies. Analysis of trials including dichotomous response and dichotomous risk factors. Study bias and reliability of a trial. Observer bias and diagnostic tests
Mortality statistics. Survival data analysis

Analysis of covariance, logistic regression

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KC6031 -

Project (Core,40 Credits)

This module is designed specifically to enhance your graduate skills that are essential to your future career and/or postgraduate study. This is achieved by an individual, research-based project work in an area appropriate to your degree.

You will develop the ability to undertake independent research in an area of interest, requiring a survey of current literature, synthesis of ideas, find solutions where required and drawing a coherent appraisal of conclusions. In this process you will learn how to defining clearly a mathematical and/or statistical problem to be investigated/solved, research and appraise current thinking as regards the subject, select methodologies, include appropriate mathematical exemplars to justify your argument and present a well-integrated set of conclusions.

You will also develop the ability to critically appraise both your own work and the work of others in the field.

You will be research-tutored through the module, and you will be assessed by a written project proposal, a poster presentation and a final written report.

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KC6034 -

Complex Analysis (Optional,20 Credits)

The module is designed for you to develop the principles, techniques and applications of Complex Analysis.

Outline Syllabus:

Complex numbers: Basic algebraic properties; vectors and moduli; exponential form; products and powers.

Functions of complex variable: Mappings; limits; continuity; derivatives; Cauchy-Riemann equations; analytic functions; harmonic functions; exponential function; logarithmic function; branches and derivatives of logarithms; trigonometric functions; hyperbolic functions.

Integrals: Contours; contour integrals; brunch cuts; Cauchy’s integral theorem; Cauchy integral formula; Liouville’s theorem; fundamental theorem of algebra; maximum modulus principle.

Series: Convergence of sequences; converges of series; Taylor series; Laurent series; integration and differentiation of power series; multiplication and division of power series.

Residues and poles: Isolated singular points; residues; Cauchy’s residue theorem; three types of isolated singular points; residues at poles; zeros of analytic functions; behaviour of functions near isolated singular points; applications of residues.

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KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Core – for International and EU students only,0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

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KC7014 -

Bayesian Statistics (Optional,20 Credits)

You will gain an understanding of Bayesian statistics. The module introduces Bayes’ Theorem and its application to both simple and complex problems. It examines the algebraic and numerical techniques used to handle different problems and the important concept of combining prior information with data to form a posterior distribution. A wide range of real-life problems will be used to motivate the subject matter. Both conjugate and non-conjugate problems will be considered.

The module will be delivered using a combination of lecture and computer laboratory sessions. Assessment will be via a formal examination.

OUTLINE SYLLABUS

Bayes’ Theorem and its application. Bayesian inference.
Prior distributions, maximum likelihood estimation, posterior distributions.
Single-parameter models, multi-parameter models. Vague and informative priors.
Large-sample inference. Normal approximation to the posterior distribution.
Monte Carlo method and simulation of data. Markov Chain Monte Carlo (MCMC) methods for non-conjugate problems, including the Gibbs sampler and Metropolis-Hastings.
Introduction to Bayesian regression modelling.

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KC7015 -

Time Series & Forecasting (Optional,20 Credits)

You will learn about a range of appropriate statistical techniques that are used to analyse time series data. You will be introduced to the different methods that can be used to remove any trend or seasonality that are present in the data and learn how to determine the appropriate time series model for this modified time series. Once the model is chosen, you will learn verification techniques to confirm that you have selected the correct model and then, if required, learn how to forecast future values based on this model.

By the end of the module, you will have developed an awareness of different approaches to analysing time series data and to be able to tailor these techniques based on the initial assessment of the time series data.

Outline Syllabus
On this module, you will cover:
• Differencing methods to remove trends and/or seasonality.
• Diagnostic tools to select appropriate model
• Autoregressive Integrated Moving Average (ARIMA) models
• Model identification methods
• Verification of model
• Seasonal Autoregressive Integrated Moving Average (SARIMA) models and their identification and modelling.

An appropriate statistical computer package will be used.

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KC7016 -

Linear & Non Linear Waves (Optional,20 Credits)

Wave phenomena appear everywhere in nature, from water waves to magnetic materials, from optics to weather forecasts, hence their description and understanding is of fundamental importance both from the theoretical and the applicative point of view.
You will learn the mathematical theory of wave motion including both linear and nonlinear behaviour. Applications include the understanding of shock waves and coherent structures, such as solitons, of some famous integrable partial differential equations that arise from standard modelling processes.

The syllabus includes topics from

Linear wave equations
Wave propagation; characteristics; dispersion relations; group velocity; wave energy; applications.

Nonlinear wave equations
Dispersive and hyperbolic waves; stationary waves; transport and travelling waves; dissipation and shock structures; Burger's equation; applications.

Nonlinear integrable waves equations
e.g. Korteweg-de Vries (KdV) equation; solitons; Inverse Spectral Transform (IST) for the KdV; examples of nonlinear integrable waves and their applications; multiscale expansion and integrability of dispersive wave equations.

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KC7017 -

Numerical Solutions of Partial Differential Equations (Optional,20 Credits)

You will learn the various numerical techniques used to solve partial differential equations (PDEs). PDEs are widely used to describe phenomena in the natural world as well as in cultured and manufactured reality. These powerful numerical methods often provide the only means to explore and analyse the PDEs. Various methods will be investigated with emphasis on the underlying ideas and principles of each method. This theoretical understanding will be underpinned by practical implementation of the numerical methods throughout the module. This approach will allow you to develop a well-grounded theoretical base as well as the necessary programming skills to implement solutions in real-life situations.

You will become conversant in the classification of PDEs as well as the stability and convergence of numerical schemes. Using this knowledge as a foundation, you will investigate and appraise the following numerical methods:

• Finite difference methods
• Finite element methods
• Finite volume methods
• Spectral methods
• Particle methods
• Numerical methods for solving nonlinear PDEs
• Numerical methods for solving PDEs in conservative form

Evaluating each numerical method in depth, you will be able to make informed choices when selecting the optimal solution method for different types of PDEs. Also, you will become proficient in writing and implementing computer codes (e.g. using MATLAB) by solving the various types of PDEs.

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KC7018 -

Masters Project (Core,60 Credits)

The module provides the opportunity to apply the concepts studied in the MMath degree to a problem with mathematical or real world application interest and do analytical and/or numerical exploration of this problem using mathematical techniques and models.

Outline Syllabus

This module will allow you to engender a spirit of enquiry into a practical or theoretical dissertation. The aim of this module is to provide the opportunity for students to work independently, under supervision of the project supervisor, on a project topic, research the background, develop the appropriate methodology, construct the model and apply to appropriate data (if necessary) to verify and evaluate the model performance. The project can be a theoretical or laboratory-based exercise. The module will include an aspect of research and critical appraisal; development of practical skills and/or discussion of results; and an opportunity to compose a written dissertation. The module will be assessed by viva and dissertation bringing out the key aspects of the project. The dissertation would vary with subject area but would typically be within the range 50 to 70 pages. A project plan should be completed as part of KC7023 Research Methods and Professional Practice module and should be available prior to starting the project.
Assessment of the module is written dissertation and oral Viva examination (70% and 30% respectively). Students will receive feedback on their Viva first; this will enable students to act on the feedback received. Feedback for the Dissertation will be given at the end of the semester.

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KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Core – for International and EU students only,0 Credits)

Academic skills when studying away from your home country can differ due to cultural and language differences in teaching and assessment practices. This module is designed to support your transition in the use and practice of technical language and subject specific skills around assessments and teaching provision in your chosen subject. The overall aim of this module is to develop your abilities to read and study effectively for academic purposes; to develop your skills in analysing and using source material in seminars and academic writing and to develop your use and application of language and communications skills to a higher level.

The topics you will cover on the module include:

• Understanding assignment briefs and exam questions.
• Developing academic writing skills, including citation, paraphrasing, and summarising.
• Practising ‘critical reading’ and ‘critical writing’
• Planning and structuring academic assignments (e.g. essays, reports and presentations).
• Avoiding academic misconduct and gaining credit by using academic sources and referencing effectively.
• Listening skills for lectures.
• Speaking in seminar presentations.
• Presenting your ideas
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Developing self-reflection skills.

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KL7000 -

Research Methodology (Core,20 Credits)

You will learn about the techniques and methods used in academic and professional research in mathematics. You will also develop your understanding of the philosophies underpinning research, as well as how to design and run research in an applied context. You will explore various stages of research and research approaches and methodologies which can be applied to academic and professional practice.

In particular you will learn how to discover and classify new facts, to test and verify hypothesis, to analyse an event, process or phenomenon, to identify the cause and effect relationship, to develop new scientific tools, concepts and theories to solve and understand scientific problems. You will thus develop critical arguments in support of your own research.

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No module Data

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Mathematics MMath (Hons)

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