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The type of mathematical expertise needed in our modern world is changing. More than ever the need for flexibility, open-mindedness and abstract mathematical knowledge is in demand.

Is this course for me?

Aimed at those with a genuine interest in mathematics who are interested in exploring a range of career options, this Masters degree in Mathematics will provide an all-round experience and awareness of mathematics in the modern world. Using a combination of analytical and numerical techniques and computer simulations our Masters will enable you to tackle a variety of industry problems and apply new knowledge to enhance and expand understanding of original phenomenon and make predictions.


How will I be taught?

Blending traditional elements with the applied nature of mathematics this Masters course offers a unique opportunity to develop a solid scientific background as well as transferable practical skills. You will learn a range of mathematical and statistical approaches with advanced solution-based techniques for complex and nonlinear systems.

 

What themes can I expect to cover on this course?

Our MSc Mathematics will allow you to discover critical applications in a variety of contexts, from climate change, meteorology and space weather to ultra-fast optical communications, biological systems, machine learning and artificial intelligence.

 

Course Information

Level of Study
Postgraduate

Mode of Study
1 year full-time

Department
Mathematics, Physics and Electrical Engineering

Location
Coach Lane Campus, Northumbria University

City
Newcastle

Start
September 2023

Fee Information

Module Information

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Entry Requirements 2023/24

Standard Entry

Applicants should normally have:

A minimum of a 2:2 honours degree in in a subject related to Mathematics, Physics, Statistics, Computer Science, or Engineering. Other subject qualifications, equivalent professional qualifications and/or relevant work experience will be considered on an individual basis.

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 6.5 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 2023/24 Entry

Full UK Fee: £9,960

Full EU Fee: £17,500

Full International Fee: £17,500



Scholarships and Discounts

Click here for UK, EU and International scholarship, fees, and funding information.

ADDITIONAL COSTS

There are no Additional Costs

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

Modules

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

KC7015 -

Time Series & Forecasting (Core,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 (Core,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


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

More information

KL7003 -

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 institution 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 area in the Department of Architecture and Built Environment. 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.
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Discussing ethical issues in research, and analysing results.
• Describing bias and limitations of research.
• Developing self-reflection skills.

More information

KL7015 -

Complex and Random Systems (Core,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

More information

KL7016 -

Networks and Machine Learning (Core,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.
Syllabus:
1. Fundamentals of graph theory (graph representation, trees, planar graphs, paths, connectivity, Laplacian)
2. Networks structure and metrics: degree distributions, clustering, shortest paths, partitioning, modularity
3. Probability theory and statistical mechanics of networks
4. Random network models
5. Linear regression and Bayesian linear regression
6. Neural networks
7. Supervised machine learning
8. Unsupervised machine learning
9. Processes on networks, e.g. percolation, epidemics on networks, network search

More information

KL7017 -

Mathematical Modelling and Simulations (Core,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

KL7019 -

MSc Mathematics Project (Core,60 Credits)

The project requires you to develop and demonstrate the ability to do research and this is primarily demonstrated through your dissertation. Your dissertation will detail a systematic understanding of Mathematical Modelling and its real life application, a critical awareness of knowledge, a critical awareness of current problems and/or new insights into advanced mathematical methods and their importance for professional practice. You will develop a comprehensive understanding of techniques applicable to the research topic you have chosen and advanced scholarship. You will also develop skills for carrying out original research in Mathematical Modelling and practical understanding of how established techniques of research and enquiry are used to create and interpret knowledge in the specific area of interest. You will be trained on how to engage with relevant research articles for your chosen project. You will also learn from seminars in Mathematics that are regularly organised in the department. Importantly, you will learn by 1:1 meetings with your supervisor while working on a topic grounded in the staff research.

Specifically, you will learn how to do the following
1) Conduct a focused literature search of library and web-based materials and critically appraise and analyse the findings.
2) Integrate and/or modify ideas, concepts and theoretical models that have been selectively extracted from scholarly literature.
3) Critically appraise and test the applicability of theoretical models to their researchable topic.
4) Rationalise and defend the key aspects of the work undertaken in the form of a presentation using professional software (e.g. Microsoft PowerPoint, Beamer package in LaTex).
(5) Write an original dissertation in an academically acceptable format, which should be theoretically and methodologically linked, paying particular attention to the integration of the literature review, the methodology and the clear and concise presentation of results and conclusions.

More information

KL7020 -

Nonlinear Waves and Extreme Events (Core,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.

The syllabus includes topics from

Linear dispersive waves:
Wave propagation; elements of Fourier analysis; dispersion relations; phase and group velocity; wave energy; modulated waves, applications.

Nonlinear hyperbolic waves:
Conservation laws and hyperbolic waves; transport and travelling waves; method of characteristics and shock wave formation; dissipation and shock structures; Burger's equation; applications.

Nonlinear integrable waves equations:
Korteweg-de Vries (KdV) equation; solitons; Inverse Spectral Transform (IST); Nonlinear Schrodinger (NLS) equation; modulational instability and rogue waves; multiscale expansions and integrability of dispersive wave equations; 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.

KC7015 -

Time Series & Forecasting (Core,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 (Core,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


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

More information

KL7003 -

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 institution 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 area in the Department of Architecture and Built Environment. 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.
• Giving discipline-related academic presentations, experiencing peer observation, and receiving formative feedback.
• Speed reading techniques.
• Discussing ethical issues in research, and analysing results.
• Describing bias and limitations of research.
• Developing self-reflection skills.

More information

KL7015 -

Complex and Random Systems (Core,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

More information

KL7016 -

Networks and Machine Learning (Core,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.
Syllabus:
1. Fundamentals of graph theory (graph representation, trees, planar graphs, paths, connectivity, Laplacian)
2. Networks structure and metrics: degree distributions, clustering, shortest paths, partitioning, modularity
3. Probability theory and statistical mechanics of networks
4. Random network models
5. Linear regression and Bayesian linear regression
6. Neural networks
7. Supervised machine learning
8. Unsupervised machine learning
9. Processes on networks, e.g. percolation, epidemics on networks, network search

More information

KL7017 -

Mathematical Modelling and Simulations (Core,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

KL7019 -

MSc Mathematics Project (Core,60 Credits)

The project requires you to develop and demonstrate the ability to do research and this is primarily demonstrated through your dissertation. Your dissertation will detail a systematic understanding of Mathematical Modelling and its real life application, a critical awareness of knowledge, a critical awareness of current problems and/or new insights into advanced mathematical methods and their importance for professional practice. You will develop a comprehensive understanding of techniques applicable to the research topic you have chosen and advanced scholarship. You will also develop skills for carrying out original research in Mathematical Modelling and practical understanding of how established techniques of research and enquiry are used to create and interpret knowledge in the specific area of interest. You will be trained on how to engage with relevant research articles for your chosen project. You will also learn from seminars in Mathematics that are regularly organised in the department. Importantly, you will learn by 1:1 meetings with your supervisor while working on a topic grounded in the staff research.

Specifically, you will learn how to do the following
1) Conduct a focused literature search of library and web-based materials and critically appraise and analyse the findings.
2) Integrate and/or modify ideas, concepts and theoretical models that have been selectively extracted from scholarly literature.
3) Critically appraise and test the applicability of theoretical models to their researchable topic.
4) Rationalise and defend the key aspects of the work undertaken in the form of a presentation using professional software (e.g. Microsoft PowerPoint, Beamer package in LaTex).
(5) Write an original dissertation in an academically acceptable format, which should be theoretically and methodologically linked, paying particular attention to the integration of the literature review, the methodology and the clear and concise presentation of results and conclusions.

More information

KL7020 -

Nonlinear Waves and Extreme Events (Core,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.

The syllabus includes topics from

Linear dispersive waves:
Wave propagation; elements of Fourier analysis; dispersion relations; phase and group velocity; wave energy; modulated waves, applications.

Nonlinear hyperbolic waves:
Conservation laws and hyperbolic waves; transport and travelling waves; method of characteristics and shock wave formation; dissipation and shock structures; Burger's equation; applications.

Nonlinear integrable waves equations:
Korteweg-de Vries (KdV) equation; solitons; Inverse Spectral Transform (IST); Nonlinear Schrodinger (NLS) equation; modulational instability and rogue waves; multiscale expansions and integrability of dispersive wave equations; applications

More information

Any Questions?

Our admissions team will be happy to help. They can be contacted on 0191 406 0901.

Contact Details for Applicants:

bc.applicantservices@northumbria.ac.uk

All information is accurate at the time of sharing.

Full time Courses starting in 2023 are primarily delivered via on-campus face to face learning but may include elements of online learning. We continue to monitor government and local authority guidance in relation to Covid-19 and we are ready and able to flex accordingly to ensure the health and safety of our students and staff.

Contact time is subject to increase or decrease in line with additional restrictions imposed by the government or the University in the interest of maintaining the health and safety and wellbeing of students, staff, and visitors, potentially to a full online offer, should further restrictions be deemed necessary in future. Our online activity will be delivered through Blackboard Ultra, enabling collaboration, connection and engagement with materials and people.

 

Current, Relevant and Inspiring

We continuously review and improve course content in consultation with our students and employers. To make sure we can inform you of any changes to your course register for updates on the course page.


Your Learning Experience

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

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northumbria.ac.uk/terms

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northumbria.ac.uk/fees

Admissions Policy
northumbria.ac.uk/adpolicy

Admissions Complaints Policy
northumbria.ac.uk/complaints

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

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