Skip navigation

If you’d like to receive the latest updates from Northumbria about our courses, events, finance & funding then enter your details below.

* At Northumbria we are strongly committed to protecting the privacy of personal data. To view the University’s Privacy Notice please click here

CLOSE

Mathematics is the language of our data-driven society.

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.

Why choose Northumbria to study Mathematics?

Mathematics at Northumbria is ranked 1st in the UK for Teaching Quality & Student Experience (Times Good University Guide, 2024).

90% of students studying Mathematics at Northumbria believed their course challenged them to achieve their best work and felt free to express their ideas, opinions, and beliefs (NSS, 2023).

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

How does this course set me up for my future career? 

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.
 
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.

 

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

 

Mathematics is the language of our data-driven society.

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.

Why choose Northumbria to study Mathematics?

Mathematics at Northumbria is ranked 1st in the UK for Teaching Quality & Student Experience (Times Good University Guide, 2024).

90% of students studying Mathematics at Northumbria believed their course challenged them to achieve their best work and felt free to express their ideas, opinions, and beliefs (NSS, 2023).

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

How does this course set me up for my future career? 

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.
 
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.

 

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

 

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 2024 or September 2025

Fees
Fee Information

Modules
Module Information

Watch / Maths at Northumbria

Find out more about our Maths department and what it's really like to study here.

News / Maths, Physics and Electrical Engineering

Find out what our Maths, Physics and Electrical Engineering students and staff are taking part in and achieving.

light bulb on black background

This course is eligible for a scholarship

find out more →

Department / Mathematics, Physics and Electrical Engineering

Find out more about our department, facilities and what other students are taking part in.

a man standing in a kitchen preparing food

Study

a woman looking at a laptop

NUSTEM

Delve Deeper / Discover more about life at Northumbria

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.

Entry Requirements 2024/25

Standard Entry

112 UCAS Tariff points

From a combination of acceptable Level 3 qualifications which may include: A-level, T 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 by using the UCAS Tariff calculator: www.ucas.com/ucas/tariff-calculator

Northumbria University is committed to supporting all individuals to achieve their ambitions. We have a range of schemes and alternative offers to make sure as many individuals as possible are given an opportunity to study at our University regardless of personal circumstances or background. To find out more, review our Northumbria Entry Requirement Essential Information page for further details www.northumbria.ac.uk/entryrequirementsinfo

Subject Requirements:

Applicants will need Grade B in an A-level Mathematics, or a recognised equivalent.

GCSE Requirements:

Applicants will need Maths and English Language at minimum grade 4/C, or an equivalent.

Additional Requirements:

There are no additional requirements for this course.

International Qualifications:

We welcome applicants with a range of qualifications which may not match those shown above.

If you have qualifications from outside the UK, find out what you need by visiting www.northumbria.ac.uk/yourcountry

English Language Requirements:

International applicants should have a minimum overall IELTS (Academic) score of 6.0 with 5.5 in each component (or an 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 in our English Language section: www.northumbria.ac.uk/englishqualifications

Entry Requirements 2025/26

Standard Entry

112 UCAS Tariff points

From a combination of acceptable Level 3 qualifications which may include: A-level, T 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 by using the UCAS Tariff calculator: www.ucas.com/ucas/tariff-calculator

Northumbria University is committed to supporting all individuals to achieve their ambitions. We have a range of schemes and alternative offers to make sure as many individuals as possible are given an opportunity to study at our University regardless of personal circumstances or background. To find out more, review our Northumbria Entry Requirement Essential Information page for further details www.northumbria.ac.uk/entryrequirementsinfo

Subject Requirements:

Applicants will need Grade B in an A-level Mathematics, or a recognised equivalent.

GCSE Requirements:

Applicants will need Maths and English Language at minimum grade 4/C, or an equivalent.

Additional Requirements:

There are no additional requirements for this course.

International Qualifications:

We welcome applicants with a range of qualifications which may not match those shown above.

If you have qualifications from outside the UK, find out what you need by visiting www.northumbria.ac.uk/yourcountry

English Language Requirements:

International applicants should have a minimum overall IELTS (Academic) score of 6.0 with 5.5 in each component (or an 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 in our English Language section: www.northumbria.ac.uk/englishqualifications

Fees and Funding 2024/25 Entry

UK Fee in Year 1: £9,250

* The maximum tuition fee that we are permitted to charge for UK students is set by government. Tuition fees may increase in each subsequent academic year of your course, these are subject to government regulations and in line with inflation.


EU Fee in Year 1: £18,250

International Fee in Year 1: £18,250


Please see the main Funding Pages for 24/25 scholarship information.

 


ADDITIONAL COSTS

There are no Additional Costs

Fees and Funding 2025/26 Entry

UK Fee in Year 1*: TBC

* The maximum tuition fee that we are permitted to charge for UK students is set by government. Tuition fees may increase in each subsequent academic year of your course, these are subject to government regulations and in line with inflation.



EU Fee in Year 1: **TBC


International Fee in Year 1: TBC

ADDITIONAL COSTS

TBC

If you’d like to receive the latest updates from Northumbria about our courses, events, finance & funding then enter your details below.

* At Northumbria we are strongly committed to protecting the privacy of personal data. To view the University’s Privacy Notice please click here

How to Apply

Please use the Apply Now button at the top of this page to submit your application.

Certain applications may need to be submitted via an external application system, such as UCAS, Lawcabs or DfE Apply.

The Apply Now button will redirect you to the relevant website if this is the case.

You can find further application advice, such as what to include in your application and what happens after you apply, on our Admissions Hub Admissions | Northumbria University



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 its relation to limits; standard derivatives; product, quotient, and chain rules; implicit, parametric, and logarithmic differentiation; maxima / minima, curve sketching; Taylor and Maclaurin series; L’Hopital’s rule.
• Integration: standard integrals, definite integrals, area under a curve; integration using substitutions, partial fractions decomposition and integration by parts; calculation of solid volumes.
• Functions of several variables: partial differentiation and gradients; change of coordinate systems; stationary points, maxima / minima / saddle points of functions of two variables; method of Lagrange multipliers (constrained maxima / minima).
• Double integrals: standard integrals, change of order of integration.
• Ordinary differential equations: First-order differential equations solved by direct integration, separation of variables, and integrating factor. Second-order differential equations with constant coefficients solved by the method of undetermined coefficients.

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, script files, 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 probability and 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 sample mean and variance, 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.

More information

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.

More information

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, such as: 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.

More information

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.

The module will cover topics such as:
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.

More information

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.
The module will cover topics such as:

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, special functions

Partial Differential Equations (PDEs)

1. Introduction and classification of PDEs.
2. Method of characteristics for first order linear PDEs.
3. The method of separation of variables and Fourier series.
4. Solutions of Laplace, diffusion/heat and wave equations.
5. Applications

More information

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 mathematical concepts such as:
• 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.

More information

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.

More information

KL5004 -

Complex Variables (Core,20 Credits)

The module is designed for you to develop your understanding of the principles, techniques and applications of complex variables.

The module will cover topics such as:

Complex numbers: Basic algebraic properties and operations, Trigonometric and exponential forms; Products and powers; Stereographic projection.

Functions of one complex variable: Limits, continuity and mappings; Differentiability, analyticity of a function and Cauchy-Riemann equations; Exponential and trigonometric functions; branches and derivatives of logarithms.

Integrals: Contours, contour integrals, Cauchy’s integral theorem and formula; Liouville’s theorem; Fundamental theorem of algebra.

Series: Convergence of sequences and series; Laurent series; Integration and differentiation of power series.

Residues and poles: Types of isolated singular points; Cauchy’s residue theorem; Meromorphic functions; Applications of residues.

More information

KL5005 -

Statistical Modelling and Data Visualisation (Core,20 Credits)

This module will provide you with the fundamental tools to identify appropriate exploratory analysis techniques to uncover hidden patterns and unknown correlations in large data sets. You will be able to assess the strength of statistical evidence of the revealed patterns/correlations. You will also develop appropriate technique to visualise data/outputs, implement suitable analytical methods for big data and critically assess the suitability of the chosen analytical technique.
You will have the opportunity to analyse and visualise data for tackling real-life problems. You will work individually and in group and have the opportunity to critically appraise both your own work and the work of others.

The module will include topics such as:
? Exploratory analysis of big data;
? Data visualisation;
? Data manipulation (e.g. dealing with missing values, detecting outliers values, data transformation);
? Univariate statistical methods (e.g. simple linear regression, residual analysis);
? Techniques for predictive data mining (e.g. methods for binary/logistic classification);
? A suite of appropriate computer packages (including R) will be used.

More information

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.

More information

KL5006 -

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.

More information

KL5007 -

Study abroad year (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)”.

More information

KL5008 -

Work placement semester (Optional,60 Credits)

This module operates within a partnership between the University, employer and yourself, and provides you with the opportunity to develop core competencies and employability skills relevant to your programme of study in a work based environment.

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.

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.

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.

More information

KL5009 -

MPEE - Study Abroad Semester (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.

More information

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.

More information

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, physics 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.

More information

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.

More information

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.

More information

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

More information

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.

More information

KE6030 -

Geophysical Dynamics (Optional,20 Credits)

In this module you will learn basics concepts of continuum mechanics i.e. kinematics (material derivatives, kinematic boundary conditions), kinetics (stresses, traction), balance laws (mass, momentum, energy) and constitutive relationships (stress strain relationships for fluids).

You will learn the effects of rotation on the fluid flow and how these affect the large-scale flow of the ocean and the atmosphere. The focus is on understanding how the large-scale flow regime of the ocean, atmosphere, glaciers and the mantle can be described mathematically.

Your learning will be set within the context of global environmental changes. The module will provide you with the tool required to understand the physical principles of global circulations models used to describe the movement of the atmosphere, oceans, earth’s mantle and large ice sheets.


The course consists of lectures and exercises using a state-of-the art numerical ice sheet model. Assessment of the module is by one individual numerical modelling assignment (30%) and one formal examination (70%).

On completion of the module you will have developed an improved understanding of the earth system and the principles of climate change.
The module is designed to provide you with a useful preparation for employment in earth sciences with aim at pursuing graduate studies in environmental modelling.




Outline Syllabus

• Introduction and review of continuum mechanics, balance laws (mass, conservation, energy), kinematics of deforming bodies, constitutive laws (non-Newtonian rheology).

• Rotating shallow-water models. Large-scale flow approximations used in earth sciences. Large-scale features of ocean circulation and atmospheric circulation. Ocean gyres, boundary currents, eddy transport. Variation in flow with depth/height. Geostrophic balance. Ekman spiral.

• Hydrostasy in the ocean and atmosphere.

• Mechanics of glaciers and ice sheets. Commonly used flow approximations in glaciology. Ice-sheet instabilities. Grounding-line dynamics and instabilities.

• Scaling of flow equations and linearization. Systematic reduction of equations.

More information

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.

More information

KL6000 -

Data Science (Optional,20 Credits)

Data Science concerns extracting information from data – in other words giving a voice to the data. Different analysts may have different purposes when analysing data – the intention may be to describe the information in the data, explain the relationships between parts of the data or use a subset of the data to predict the outcome of a variable of interest. For example, that variable could be whether a customer with a particular profile may buy an item of interest. Most companies collect data on their customers and are interested in how this data can be used to improve customer experience as well as profits. Depending on the intention, the approach taken by the analyst will differ and this module will cover the main tools for classification, clustering, association mining and outlier detection allowing you to analyse data with confidence.

By the end of the module, you should have developed an awareness of different approaches to analysing various forms of data and should have an ability to appraise which analytical techniques are appropriate. You will be able to perform the analysis and interpret the results correctly.

Outline Syllabus

Classification techniques that may include decision trees, support vector machines, linear discriminant techniques and logistic regression.

Clustering techniques including k-means clustering, apriori association mining, naïve Bayes and dimensionality reduction.

More information

KL6002 -

Methods of Applied Mathematics (Optional,20 Credits)

With this module you will learn advanced methods and technical skills to find exact and approximate solutions to complex problems inspired by the real world. Examples of applications include traffic flow, waves in the ocean, optical telecommunications systems, models for climate and biological systems and magnetohydrodynamics.

Outline syllabus will develop the following three areas:

Exact methods

1) Integral transforms:
- Laplace transform,
- Fourier transform

2) Applications of integral transforms to linear differential equations.

3) Theory of quasilinear partial differential equations

4) Method of characteristics.

5) Conservation laws and shock waves.

6) Applications of exact methods to

- traffic flows
- water waves
- magnetohydrodynamics.



Asymptotic methods:

1) Asymptotic methods for algebraic equations
2) Regular and singular perturbation methods for ordinary differential equations;
3) Asymptotic methods for evaluations of integrals


Applications

1) Boundary layers
2) Linear and Nonlinear dispersive waves
3) Solitons.

More information

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.

You will achieve proficiency in using appropriate R and or Python statistical packages.

More information

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 state-of-the-art numerical methods. These may include but are not limited to

• Finite difference methods
• Finite element methods
• Finite volume methods
• Spectral methods
• Particle methods

More information

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. At the beginning of the academic year, the module will include taught sessions on research methodology and professional practice, providing guidance to complete a project plan prior to starting the project. The supervisor will guide the student through techniques and methods used in academic and professional research in mathematics, exploring philosophies underpinning research, stages of research and research approaches, discovery of new facts, testing and verifying hypotheses, analysing events, processes or phenomena, identifying cause and effect relationships, developing new scientific tools, concepts and theories to solve and understand scientific dilemmas, organising resources and bibliographies.
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 second semester.

More information

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.

More information

KL7015 -

Complex and Random Systems (Optional,20 Credits)

You will learn about a range of appropriate statistical techniques that are used to predict and analyse complex systems modelled by random matrices. You will be introduced to the generalisation of probability theory for multivariate calculus, the analysis of the most common ensembles (Gaussian Orthogonal and Unitary Ensembles, the Circular Ensembles) and methods for using these tools efficiently in numerical simulations.

Outline Syllabus
– Review of linear algebra and probability theory
– Numerical techniques to generate and analyse random matrices
– The Circular Unitary Ensemble (CUE): definition, spacing distribution, eigenvalues correlation functions
– The Circular Orthogonal Ensemble (COE)
– The Gaussian Ensembles: unitary, orthogonal, symplectic
– Orthogonal polynomial techniques (large N limit and universality)

Depending on the time the extrema statistics (Tracy-Widom distribution) will be derived as it can be found in numerous applications (combinatorics, biology)

More information

KL7016 -

Networks and Machine Learning (Optional,20 Credits)

This module will provide you the fundamentals and theoretical underpinnings of the theory of networks, machine learning and their applications, create a solid background to support professional work in relation to a rapidly evolving field of research such as machine learning and artificial intelligence.
You will learn fundamental concepts of graphs theory, representation and quantitative characterisation of networks, statistical mechanics of random networks and their deployment for the realisation of systems which can process information and learn. You will achieve proficiency in relevant computer programming (Python) and suitable packages for network analysis and machine learning.
Topics in the syllabus will include fundamentals of graph theory and elements of neural networks (degree distributions, clustering, shortest paths, portioning, modularity), probability and statistical mechanics of networks, supervised/unsupervised machine learning.

More information

KL7017 -

Mathematical Modelling and Simulations (Optional,20 Credits)

The module covers three broad topics: 1) Ordinary differential equations, 2) eigenvalue problems, and 3) random processes. For each topic, we will explore related techniques and apply them to specific problems.

The syllabus includes:

Ordinary differential equations
Numerical methods (Euler, Runge-Kutta); phase portraits; systems of ordinary differential equations; reflection and transmission; synchronisation (entraining, Adler’s model, Arnold tongues, mutual synchronisation, nonlinear oscillators).

Eigenvalue problems
Fourier transform and series; discrete Fourier transform; asymptotic expansion; dispersion relation in periodic potentials; Bloch theorem.

Random processes
Brownian motion; Langevin equations; Ito and Stratonovich calculus; noise in Fourier space; Wiener-Khinchin theorem; Monte-Carlo integration; metropolis algorithm.

More information

KL7020 -

Nonlinear Waves and Extreme Events (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 points of view.
You will learn the mathematical theory of nonlinear wave motion. 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 and the mechanisms of formation and propagation of anomalous waves such as tsunamis and rogue waves. The module is designed to give you a flavour of modern research in this actively developing area of applied mathematics.

Topics will include theory of linear dispersive waves (wave propagation, elements of Fourier analysis, modulated waves), nonlinear hyperbolic waves and integrable nonlinear wave equations and their applications.

More information

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 its relation to limits; standard derivatives; product, quotient, and chain rules; implicit, parametric, and logarithmic differentiation; maxima / minima, curve sketching; Taylor and Maclaurin series; L’Hopital’s rule.
• Integration: standard integrals, definite integrals, area under a curve; integration using substitutions, partial fractions decomposition and integration by parts; calculation of solid volumes.
• Functions of several variables: partial differentiation and gradients; change of coordinate systems; stationary points, maxima / minima / saddle points of functions of two variables; method of Lagrange multipliers (constrained maxima / minima).
• Double integrals: standard integrals, change of order of integration.
• Ordinary differential equations: First-order differential equations solved by direct integration, separation of variables, and integrating factor. Second-order differential equations with constant coefficients solved by the method of undetermined coefficients.

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, script files, 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 probability and 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 sample mean and variance, 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.

More information

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.

More information

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, such as: 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.

More information

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.

The module will cover topics such as:
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.

More information

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.
The module will cover topics such as:

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, special functions

Partial Differential Equations (PDEs)

1. Introduction and classification of PDEs.
2. Method of characteristics for first order linear PDEs.
3. The method of separation of variables and Fourier series.
4. Solutions of Laplace, diffusion/heat and wave equations.
5. Applications

More information

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 mathematical concepts such as:
• 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.

More information

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.

More information

KL5004 -

Complex Variables (Core,20 Credits)

The module is designed for you to develop your understanding of the principles, techniques and applications of complex variables.

The module will cover topics such as:

Complex numbers: Basic algebraic properties and operations, Trigonometric and exponential forms; Products and powers; Stereographic projection.

Functions of one complex variable: Limits, continuity and mappings; Differentiability, analyticity of a function and Cauchy-Riemann equations; Exponential and trigonometric functions; branches and derivatives of logarithms.

Integrals: Contours, contour integrals, Cauchy’s integral theorem and formula; Liouville’s theorem; Fundamental theorem of algebra.

Series: Convergence of sequences and series; Laurent series; Integration and differentiation of power series.

Residues and poles: Types of isolated singular points; Cauchy’s residue theorem; Meromorphic functions; Applications of residues.

More information

KL5005 -

Statistical Modelling and Data Visualisation (Core,20 Credits)

This module will provide you with the fundamental tools to identify appropriate exploratory analysis techniques to uncover hidden patterns and unknown correlations in large data sets. You will be able to assess the strength of statistical evidence of the revealed patterns/correlations. You will also develop appropriate technique to visualise data/outputs, implement suitable analytical methods for big data and critically assess the suitability of the chosen analytical technique.
You will have the opportunity to analyse and visualise data for tackling real-life problems. You will work individually and in group and have the opportunity to critically appraise both your own work and the work of others.

The module will include topics such as:
? Exploratory analysis of big data;
? Data visualisation;
? Data manipulation (e.g. dealing with missing values, detecting outliers values, data transformation);
? Univariate statistical methods (e.g. simple linear regression, residual analysis);
? Techniques for predictive data mining (e.g. methods for binary/logistic classification);
? A suite of appropriate computer packages (including R) will be used.

More information

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.

More information

KL5006 -

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.

More information

KL5007 -

Study abroad year (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)”.

More information

KL5008 -

Work placement semester (Optional,60 Credits)

This module operates within a partnership between the University, employer and yourself, and provides you with the opportunity to develop core competencies and employability skills relevant to your programme of study in a work based environment.

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.

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.

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.

More information

KL5009 -

MPEE - Study Abroad Semester (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.

More information

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.

More information

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, physics 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.

More information

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.

More information

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.

More information

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

More information

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.

More information

KE6030 -

Geophysical Dynamics (Optional,20 Credits)

In this module you will learn basics concepts of continuum mechanics i.e. kinematics (material derivatives, kinematic boundary conditions), kinetics (stresses, traction), balance laws (mass, momentum, energy) and constitutive relationships (stress strain relationships for fluids).

You will learn the effects of rotation on the fluid flow and how these affect the large-scale flow of the ocean and the atmosphere. The focus is on understanding how the large-scale flow regime of the ocean, atmosphere, glaciers and the mantle can be described mathematically.

Your learning will be set within the context of global environmental changes. The module will provide you with the tool required to understand the physical principles of global circulations models used to describe the movement of the atmosphere, oceans, earth’s mantle and large ice sheets.


The course consists of lectures and exercises using a state-of-the art numerical ice sheet model. Assessment of the module is by one individual numerical modelling assignment (30%) and one formal examination (70%).

On completion of the module you will have developed an improved understanding of the earth system and the principles of climate change.
The module is designed to provide you with a useful preparation for employment in earth sciences with aim at pursuing graduate studies in environmental modelling.




Outline Syllabus

• Introduction and review of continuum mechanics, balance laws (mass, conservation, energy), kinematics of deforming bodies, constitutive laws (non-Newtonian rheology).

• Rotating shallow-water models. Large-scale flow approximations used in earth sciences. Large-scale features of ocean circulation and atmospheric circulation. Ocean gyres, boundary currents, eddy transport. Variation in flow with depth/height. Geostrophic balance. Ekman spiral.

• Hydrostasy in the ocean and atmosphere.

• Mechanics of glaciers and ice sheets. Commonly used flow approximations in glaciology. Ice-sheet instabilities. Grounding-line dynamics and instabilities.

• Scaling of flow equations and linearization. Systematic reduction of equations.

More information

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.

More information

KL6000 -

Data Science (Optional,20 Credits)

Data Science concerns extracting information from data – in other words giving a voice to the data. Different analysts may have different purposes when analysing data – the intention may be to describe the information in the data, explain the relationships between parts of the data or use a subset of the data to predict the outcome of a variable of interest. For example, that variable could be whether a customer with a particular profile may buy an item of interest. Most companies collect data on their customers and are interested in how this data can be used to improve customer experience as well as profits. Depending on the intention, the approach taken by the analyst will differ and this module will cover the main tools for classification, clustering, association mining and outlier detection allowing you to analyse data with confidence.

By the end of the module, you should have developed an awareness of different approaches to analysing various forms of data and should have an ability to appraise which analytical techniques are appropriate. You will be able to perform the analysis and interpret the results correctly.

Outline Syllabus

Classification techniques that may include decision trees, support vector machines, linear discriminant techniques and logistic regression.

Clustering techniques including k-means clustering, apriori association mining, naïve Bayes and dimensionality reduction.

More information

KL6002 -

Methods of Applied Mathematics (Optional,20 Credits)

With this module you will learn advanced methods and technical skills to find exact and approximate solutions to complex problems inspired by the real world. Examples of applications include traffic flow, waves in the ocean, optical telecommunications systems, models for climate and biological systems and magnetohydrodynamics.

Outline syllabus will develop the following three areas:

Exact methods

1) Integral transforms:
- Laplace transform,
- Fourier transform

2) Applications of integral transforms to linear differential equations.

3) Theory of quasilinear partial differential equations

4) Method of characteristics.

5) Conservation laws and shock waves.

6) Applications of exact methods to

- traffic flows
- water waves
- magnetohydrodynamics.



Asymptotic methods:

1) Asymptotic methods for algebraic equations
2) Regular and singular perturbation methods for ordinary differential equations;
3) Asymptotic methods for evaluations of integrals


Applications

1) Boundary layers
2) Linear and Nonlinear dispersive waves
3) Solitons.

More information

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.

You will achieve proficiency in using appropriate R and or Python statistical packages.

More information

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 state-of-the-art numerical methods. These may include but are not limited to

• Finite difference methods
• Finite element methods
• Finite volume methods
• Spectral methods
• Particle methods

More information

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. At the beginning of the academic year, the module will include taught sessions on research methodology and professional practice, providing guidance to complete a project plan prior to starting the project. The supervisor will guide the student through techniques and methods used in academic and professional research in mathematics, exploring philosophies underpinning research, stages of research and research approaches, discovery of new facts, testing and verifying hypotheses, analysing events, processes or phenomena, identifying cause and effect relationships, developing new scientific tools, concepts and theories to solve and understand scientific dilemmas, organising resources and bibliographies.
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 second semester.

More information

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.

More information

KL7015 -

Complex and Random Systems (Optional,20 Credits)

You will learn about a range of appropriate statistical techniques that are used to predict and analyse complex systems modelled by random matrices. You will be introduced to the generalisation of probability theory for multivariate calculus, the analysis of the most common ensembles (Gaussian Orthogonal and Unitary Ensembles, the Circular Ensembles) and methods for using these tools efficiently in numerical simulations.

Outline Syllabus
– Review of linear algebra and probability theory
– Numerical techniques to generate and analyse random matrices
– The Circular Unitary Ensemble (CUE): definition, spacing distribution, eigenvalues correlation functions
– The Circular Orthogonal Ensemble (COE)
– The Gaussian Ensembles: unitary, orthogonal, symplectic
– Orthogonal polynomial techniques (large N limit and universality)

Depending on the time the extrema statistics (Tracy-Widom distribution) will be derived as it can be found in numerous applications (combinatorics, biology)

More information

KL7016 -

Networks and Machine Learning (Optional,20 Credits)

This module will provide you the fundamentals and theoretical underpinnings of the theory of networks, machine learning and their applications, create a solid background to support professional work in relation to a rapidly evolving field of research such as machine learning and artificial intelligence.
You will learn fundamental concepts of graphs theory, representation and quantitative characterisation of networks, statistical mechanics of random networks and their deployment for the realisation of systems which can process information and learn. You will achieve proficiency in relevant computer programming (Python) and suitable packages for network analysis and machine learning.
Topics in the syllabus will include fundamentals of graph theory and elements of neural networks (degree distributions, clustering, shortest paths, portioning, modularity), probability and statistical mechanics of networks, supervised/unsupervised machine learning.

More information

KL7017 -

Mathematical Modelling and Simulations (Optional,20 Credits)

The module covers three broad topics: 1) Ordinary differential equations, 2) eigenvalue problems, and 3) random processes. For each topic, we will explore related techniques and apply them to specific problems.

The syllabus includes:

Ordinary differential equations
Numerical methods (Euler, Runge-Kutta); phase portraits; systems of ordinary differential equations; reflection and transmission; synchronisation (entraining, Adler’s model, Arnold tongues, mutual synchronisation, nonlinear oscillators).

Eigenvalue problems
Fourier transform and series; discrete Fourier transform; asymptotic expansion; dispersion relation in periodic potentials; Bloch theorem.

Random processes
Brownian motion; Langevin equations; Ito and Stratonovich calculus; noise in Fourier space; Wiener-Khinchin theorem; Monte-Carlo integration; metropolis algorithm.

More information

KL7020 -

Nonlinear Waves and Extreme Events (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 points of view.
You will learn the mathematical theory of nonlinear wave motion. 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 and the mechanisms of formation and propagation of anomalous waves such as tsunamis and rogue waves. The module is designed to give you a flavour of modern research in this actively developing area of applied mathematics.

Topics will include theory of linear dispersive waves (wave propagation, elements of Fourier analysis, modulated waves), nonlinear hyperbolic waves and integrable nonlinear wave equations and their applications.

More information

To start your application, simply select the month you would like to start your course.

Mathematics MMath (Hons)

Home or EU applicants please apply through UCAS

International applicants please apply using the links below

START MONTH
YEAR

UniStats

Any Questions?

Our Applicant Services team will be happy to help.  They can be contacted on 0191 406 0901 or by using our Contact Form.



Accessibility and Student Inclusion

Northumbria University is committed to developing an inclusive, diverse and accessible campus and wider University community and are determined to ensure that opportunities we provide are open to all.

We are proud to work in partnership with AccessAble to provide Detailed Access Guides to our buildings and facilities across our City, Coach Lane and London Campuses. A Detailed Access Guide lets you know what access will be like when you visit somewhere. It looks at the route you will use getting in and what is available inside. All guides have Accessibility Symbols that give you a quick overview of what is available, and photographs to show you what to expect. The guides are produced by trained surveyors who visit our campuses annually to ensure you have trusted and accurate information.

You can use Northumbria’s AccessAble Guides anytime to check the accessibility of a building or facility and to plan your routes and journeys. Search by location, building or accessibility feature to find the information you need. 

We are dedicated to helping students who may require additional support during their student journey and offer 1-1 advice and guidance appropriate to individual requirements. If you feel you may need additional support you can find out more about what we offer here where you can also contact us with any questions you may have:

Accessibility support

Student Inclusion support




All information is accurate at the time of sharing. 

Full time Courses are primarily delivered via on-campus face to face learning but could include elements of online learning. Most courses run as planned and as promoted on our website and via our marketing materials, but if there are any substantial changes (as determined by the Competition and Markets Authority) to a course or there is the potential that course may be withdrawn, we will notify all affected applicants as soon as possible with advice and guidance regarding their options. It is also important to be aware that optional modules listed on course pages may be subject to change depending on uptake numbers each year.  

Contact time is subject to increase or decrease in line with possible restrictions imposed by the government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors if this is deemed necessary in future.

 

Useful Links

Find out about our distinctive approach at 
www.northumbria.ac.uk/exp

Admissions Terms and Conditions
northumbria.ac.uk/terms

Fees and Funding
northumbria.ac.uk/fees

Admissions Policy
northumbria.ac.uk/adpolicy

Admissions Complaints Policy
northumbria.ac.uk/complaints



If you’d like to receive the latest updates from Northumbria about our courses, events, finance & funding then enter your details below.

* At Northumbria we are strongly committed to protecting the privacy of personal data. To view the University’s Privacy Notice please click here

a sign in front of a crowd
+

Northumbria Open Days

Open Days are a great way for you to get a feel of the University, the city of Newcastle upon Tyne and the course(s) you are interested in.

a person sitting at a table using a laptop
+
NU World Virtual Tours
+

Virtual Tour

Get an insight into life at Northumbria at the click of a button! Come and explore our videos and 360 panoramas to immerse yourself in our campuses and get a feel for what it is like studying here using our interactive virtual tour.

Back to top