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Mathematics is the language of our data-driven society. Mathematics graduates understand the world in a special way, and their skills are in high demand. According to a report by the Council for Mathematical Sciences, demand is still rising, giving graduates access to a wide range of interesting and rewarding careers boasting excellent salaries.

Our Mathematics degree will build your analytical and quantitative skills, as well as develop you into a problem solver and a flexible thinker. You will explore the elegance of pure mathematics, apply your theories, use computers to solve mathematical equations and cultivate a strong modelling instinct to translate everyday problems into mathematics. Our Mathematics degree also includes the use of modern software, training on how to present your work professionally and learning to articulate how you have come to your conclusion.

Our approach works well with our students and employers, and our Mathematics graduates have gone on to work at Intel, NHS, the financial industry (including Accenture, Ernst & Young, Procter & Gamble), UK Government’s Department for Work and Pensions, Government Statistical Service, BAE Systems and Rolls-Royce. We have an Employer Advisory Board to ensure our course content is 100% relevant (members include Hewlett Packard and PriceWaterhouseCoopers).

In your final year, you can specialise in areas such as financial mathematics, cryptography, medical statistics or fluid dynamics and will dig even deeper with a specialist project. Recent specialist projects have investigated the volatility of shares, ocean modelling, mathematical modelling of cancer, kidney transplant survival data, and Bayesian modelling of Premier League results.

There are opportunities to do a work placement year as part of your mathematics course. This is a great way to help build your confidence in essential skills and gain valuable first-hand experience in the workplace. Undertaking a work placement year can help you to stand out to graduate recruiters. Our students have taken up placements with Nissan, Lloyds Bank plc and IBM.

In addition, you will have the option of study abroad at one of our partner institutions in Europe, USA, South East Asia and Australia. Studying abroad is a fantastic way to broaden your cultural awareness, gain experience of a different academic environment, and develop a range of personal and professional skills which enhance your employability.

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

This programme will meet the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications, when it is followed by subsequent training and experience in employment to obtain equivalent competences to those specified by the Quality Assurance Agency (QAA) for taught masters degrees.

Northumbria University - Maths Department from Northumbria University on Vimeo.

Mathematics is the language of our data-driven society. Mathematics graduates understand the world in a special way, and their skills are in high demand. According to a report by the Council for Mathematical Sciences, demand is still rising, giving graduates access to a wide range of interesting and rewarding careers boasting excellent salaries.

Our Mathematics degree will build your analytical and quantitative skills, as well as develop you into a problem solver and a flexible thinker. You will explore the elegance of pure mathematics, apply your theories, use computers to solve mathematical equations and cultivate a strong modelling instinct to translate everyday problems into mathematics. Our Mathematics degree also includes the use of modern software, training on how to present your work professionally and learning to articulate how you have come to your conclusion.

Our approach works well with our students and employers, and our Mathematics graduates have gone on to work at Intel, NHS, the financial industry (including Accenture, Ernst & Young, Procter & Gamble), UK Government’s Department for Work and Pensions, Government Statistical Service, BAE Systems and Rolls-Royce. We have an Employer Advisory Board to ensure our course content is 100% relevant (members include Hewlett Packard and PriceWaterhouseCoopers).

In your final year, you can specialise in areas such as financial mathematics, cryptography, medical statistics or fluid dynamics and will dig even deeper with a specialist project. Recent specialist projects have investigated the volatility of shares, ocean modelling, mathematical modelling of cancer, kidney transplant survival data, and Bayesian modelling of Premier League results.

There are opportunities to do a work placement year as part of your mathematics course. This is a great way to help build your confidence in essential skills and gain valuable first-hand experience in the workplace. Undertaking a work placement year can help you to stand out to graduate recruiters. Our students have taken up placements with Nissan, Lloyds Bank plc and IBM.

In addition, you will have the option of study abroad at one of our partner institutions in Europe, USA, South East Asia and Australia. Studying abroad is a fantastic way to broaden your cultural awareness, gain experience of a different academic environment, and develop a range of personal and professional skills which enhance your employability.

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

This programme will meet the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications, when it is followed by subsequent training and experience in employment to obtain equivalent competences to those specified by the Quality Assurance Agency (QAA) for taught masters degrees.

Northumbria University - Maths Department from Northumbria University on Vimeo.

Course Information

UCAS Code
G100

Level of Study
Undergraduate

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

Department
Mathematics, Physics and Electrical Engineering

Location
Pandon Building, Newcastle City Campus

City
Newcastle

Start
September 2019

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

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

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

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

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

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

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Book An Open Day / Experience Mathematics BSc (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.

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

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

Staff / Meet the Team

We are an enthusiastic, committed, knowledgeable and likeable staff team, who are here to motivate you and propel you through your degree and beyond.

Book An Open Day / Experience Mathematics BSc (Hons)

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

We have benefited from a £6.7m investment in STEM facilities (HEFCE teaching capital award 2014–2016) including a mathematical modelling lab and an MMath suite.

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

Mathematics, Physics and Electrical Engineering Facilities

The department has benefited from a £6.7M capital investment (HEFCE STEM) including a new Scanning Electron Microscope, Secondary Ion Mass Spectrometer and 3D printing facilities, in addition to existing specialist laboratories, including Smart Materials and Surfaces, Mathematical Modelling, Optical Communications and Microwave Technology.

Virtual Tour

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

University Library

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

Book An Open Day / Experience Mathematics BSc (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.

One of the main aims of the course is to stimulate your scientific curiosity and help you to develop you into a problem solver and a flexible thinker.

Teaching takes place in a research-rich environment and you’ll be gradually introduced to the advanced research methods and processes needed for the construction of new knowledge in mathematics and statistics.

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

Research / Mathematics, Physics and Electrical Engineering

A top-35 Engineering research department with 79% of our outputs ranked world-leading or internationally excellent in the latest UK wide research assessment exercise (Research Excellence Framework (REF) 2014, UoA15), placing us in the top quartile for world-leading publications among UK universities in General Engineering.

Book An Open Day / Experience Mathematics BSc (Hons)

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

Mathematics is a highly-respected degree and mathematicians and statisticians work across a wide range of disciplines in a variety of sectors.

By the end of the course you’ll be equipped with a range of advanced mathematical and statistical skills that are highly valued by employers, as well as advanced IT skills, communication skills and the ability to present complex information in a clear way.

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

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

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

Student Life

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

Book An Open Day / Experience Mathematics BSc (Hons)

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

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

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

Our graduates have found employment in the financial, retail, manufacturing and teaching sectors, including Intel, NHS, the financial industry (including Accenture, Ernst & Young, Procter & Gamble), UK Government’s Department for Work and Pensions, Government Statistical Service, BAE Systems, GlaxoSmithKline and Rolls-Royce, as well as advancing to postgraduate study.

Book An Open Day / Experience Mathematics BSc (Hons)

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

Course in brief

Your course in brief

Year 1

Year one Students benefit from lectures, group problem-solving sessions and computer laboratory software sessions covering topics such as calculus, algebra, modelling and computational mathematics.

Year 2

Year two This year will build on modules from the previous year as well as introducing topics such as operational research and vector calculus. Learning will take place through various mediums such as lectures, exams, problem solving and laboratory sessions.

Year 3

Year three You can choose to go out on industrial placement to put the skills you have learned in the previous modules into professional practice, or you have the option of studying abroad at one of our partner institutions.

Year 4

Year four Students choose from a variety of specialised modules including financial mathematics, fluid dynamics, cryptology and medical statistics, as well as completing an individual independent project.

Who would this Course suit?

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

It is a great route if you want to develop your mathematical talents and gain knowledge of contemporary theory, research and professional practice. A degree in Mathematics opens the door to a wide range of careers as a result of our graduates’ abilities to solve problems using a variety of approaches, build rigorous arguments, their analytical and quantitative skills and flexible thinking, and their ability to construct models to make testable predictions.

Entry Requirements 2019/20

Standard Entry

GCSE Requirements:

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

UCAS Tariff Points:

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

GCE and VCE Advanced Level:

From at least 2 GCE/VCE A Levels 

Edexcel/BTEC National Extended Diploma:

Distinction, Distinction, Merit 

Scottish Highers:

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

Irish Highers:

BBBBB  - ABBBB to include

IB Diploma:

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

Access to HE Diploma:

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

Qualification combinations:

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

Plus one of the following:

  • International/English Language Requirements:

    Applicants from the EU:

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

    International Qualifications:

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

    English Language Requirements:

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

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

Fees and Funding 2019/20 Entry

UK/EU Fee in Year 1**: £9,250

International Fee in Year 1: £15,000

ADDITIONAL COSTS

There are no Additional Costs

FUNDING INFORMATION

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

Click here for International undergraduate funding and scholarships information.

Click here for UK/EU undergraduate tuition fee information**.

Click here for International undergraduate tuition fee information.

Click here for additional costs which may be involved while studying.

Click here for information on fee liability.

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Modules Overview

Modules

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

KC4009 -

Calculus (Core, 20 Credits)

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

On this module you will learn:

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

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

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

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

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

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

More information

KC4011 -

Modelling (Core, 20 Credits)

This module provides a first course in mathematical and statistical modelling. You will solve a variety of real-life problems using a wide range of mathematical and statistical techniques. You will gain experience in tackling real world problems 'from scratch’, working individually as well as within a group. You will use MATLAB to solve these challenging problems.
OUTLINE SYLLABUS

Principles of modelling: formulation, solution and validation of data-driven models (e.g. data fitting using linear and quadratic models);
Discrete models: use of difference equations;
Modelling with differential equations: exponential growth/decay models and logistic models;
Developing modelling skills: simulation, dimensional analysis
Modelling a wide range of case studies: formulation and solution ab initio.

More information

KC4012 -

Computational Mathematics (Core, 20 Credits)

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

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

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

More information

KC4014 -

Dynamics (Core, 20 Credits)

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

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

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

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

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

More information

KC4015 -

Statistics (Core, 20 Credits)

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

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

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

Correlation and simple linear regression.

More information

KC4016 -

Algebra and Analysis (Core, 20 Credits)

The module is designed to introduce you to the concepts, definitions and methods of linear algebra and real analysis. In particular, you will learn the basic concepts and definitions of linear algebra, complex numbers, limits, properties of continuity, differentiability and integrability of mathematical functions, to enable you to formulate and solve problems algebraically and analytically.


Outline Syllabus:

Complex Numbers: fundamental operations in cartesian, polar and exponential forms; De Moivre's theorem, applications to roots and trigonometric identities.

Matrices and Determinants: definitions, addition, multiplication by a scalar, matrix multiplication, determinants; minors and cofactors; classical adjoint and inverse of a matrix; solution of simultaneous linear equations by matrix inversion and Cramer's rule; geometric interpretation of matrix multiplication; eigenvalues and eigenvectors. Solution of simultaneous linear equations with parameters.

Vectors in 2, 3 and n dimensions. Geometrical interpretation. Linear combinations. A geometric interpretation of Span{v} and Span{u,v}. Vector Spaces. Inner (dot) product, length, orthogonality. Vector (cross) product. The concept of vector spaces.

Real numbers: rational and irrational numbers, bounds of sets of real numbers.

Sequences and Series: convergence, bounded and monotonic sequences, convergence and sum of series; standard convergent and divergent series; absolute and conditional convergence; comparison, ratio and alternating series tests for convergence.

Continuity and Differentiability: Limits of functions: definitions, sums, products and quotients; one- and two-sided limits. Continuity at a point and on an interval; intermediate value theorem; differentiability, Rolle’s theorem, mean value theorem.

Integrability; area under a curve, Riemann integral, fundamental theorem of calculus.

More information

KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Optional, 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, including: systems of linear and nonlinear equations, eigensystems, optimisation, ordinary and partial differential equations. Theoretical aspects are illustrated and discussed at the lectures, and computational implementation developed at the computer-lab workshops, using appropriate software (e.g. MATLAB).

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

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.

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

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

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

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

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.

Outline Syllabus

Ordinary Differential Equations (ODEs)

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

Partial Differential Equations (PDEs)

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

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

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

More information

KC5026 -

Applied Modelling (Core, 20 Credits)

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

Outline Syllabus

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

More information

KC5027 -

Operational Research (Core, 20 Credits)

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

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

More information

KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Optional, 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

KA5029 -

International Academic Exchange 1 (Optional, 60 Credits)

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

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

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

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KA5030 -

International Academic Exchange 2 (Optional, 120 Credits)

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

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

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

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KF5000 -

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

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

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

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

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

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KF5001 -

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

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

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

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

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

More information

KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Optional, 0 Credits)

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

The topics you will cover on the module include:

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

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KC6001 -

Financial Mathematics (Optional, 20 Credits)

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


Outline Syllabus

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

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KC6007 -

Mathematical Cryptology (Optional, 20 Credits)

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

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

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

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

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KC6027 -

Fluid Dynamics (Optional, 20 Credits)

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

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

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

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

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

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

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KC6028 -

Dynamical Systems (Optional, 20 Credits)

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

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

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KC6029 -

Advanced Statistical Methods (Optional, 20 Credits)

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

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

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.

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KC6034 -

Complex Analysis (Optional, 20 Credits)

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

Outline Syllabus:

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

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

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

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

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

More information

KL5001 -

Academic Language Skills for Mathematics, Physics and Electrical Engineering (Optional, 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

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