Masters degrees in Mathematical Methods involve advanced study of the specific techniques associated with solving mathematical problems.
Related subjects include Statistics and Operational Research. Entry requirements usually include an undergraduate degree in a relevant Mathematics discipline.
Mathematical Methods may be applied to a range of purposes across various industries and sectors. As a result, courses in this field offer a broad selection of specialisms for you to choose from, with others allowing you to study the field more generally.
For example, you may wish to focus your studies towards economic practices, combining methodology from Economics, Mathematics and Business Studies. Within this, you may undertake financial forecasting, modelling trade activities and analysing data on national and international scales to predict shortfalls in areas such as stocks.
Mathematical methods like linear algebra, differential equations and vector calculus, are also applicable to fields as diverse as Architecture, Robotics, Computer Science and Automotives. So, you could be employed to apply methodology to develop computer software, improve human-computer interfaces, or calculate the performance of different vehicle prototypes.
This one-year master's course provides training in the application of mathematics to a wide range of problems in science and technology. Emphasis is placed on the formulation of problems, on the analytical and numerical techniques for a solution and the computation of useful results.
By the end of the course students should be able to formulate a well posed problem in mathematical terms from a possibly sketchy verbal description, carry out appropriate mathematical analysis, select or develop an appropriate numerical method, write a computer program which gives sensible answers to the problem, and present and interpret these results for a possible client. Particular emphasis is placed on the need for all these parts in the problem solving process, and on the fact that they frequently interact and cannot be carried out sequentially.
The course consists of both taught courses and a dissertation. To complete the course you must complete 13 units.
There are four core courses which you must complete (one unit each), which each usually consist of 24 lectures, classes and an examination. There is one course on mathematical methods and one on numerical analysis in both Michaelmas term and Hilary term. Each course is assessed by written examination in Week 0 of the following term.
Additionally, you must choose at least least one special topic in the area of modelling and one in computation (one unit each). There are around twenty special topics to choose from, spread over all three academic terms, each usually consisting for 12 to 16 lectures and a mini project, which culminates in a written report of around 20 pages. Topics covered include mathematical biology, fluid mechanics, perturbation methods, numerical solution of differential equations and scientific programming.
You must also undertake at least one case study in modelling and one in scientific computing (one unit each), normally consisting of four weeks of group work, an oral presentation and a report delivered in Hilary term.
There is also a dissertation (four units) of around 50 pages, which does not necessarily need to represent original ideas. Since there is another MSc focussed on mathematical finance specifically, the MSc in Mathematical and Computational Finance, you are not permitted to undertake a dissertation in this field.
You will normally accumulate four units in core courses, three units in special topics, two units in case studies and four units in the dissertation. In addition, you will usually attend classes in mathematical modelling, practical numerical analysis and additional skills during Michaelmas term.
In the first term, students should expect their weekly schedule to consist of around seven hours of core course lectures and seven hours of modelling, practical numerical analysis and additional skills classes, then a further two hours of lectures for each special topic course followed. In addition there are about three hours of problem solving classes to go through core course exercises and students should expect to spend time working through the exercises then submitting them for marking prior to the class. There are slightly fewer contact hours in the second term, but students will spend more time working in groups on the case studies.
In the third term there are some special topic courses, including one week intensive computing courses, but the expectation is that students will spend most of the third term and long vacation working on their dissertations. During this time, students should expect to work hours that are equivalent to full-time working hours, although extra hours may occasionally be needed. Students are expected to write special topic and case study reports during the Christmas and Easter vacations, as well as revising for the core course written examinations.
The part-time MSc in Mathematical Finance aims to develop your mathematical modelling, data analysis and computational skills as applied to finance, without the need to take time out of your career to study.
Incorporating concepts from applied and pure mathematics, statistics, computing and corporate finance, the course gives you a broad intellectual perspective and covers, from fundamentals to the latest research, the most important aspects of quantitative finance currently in use in the finance industry.
It is possible to exit the course early and be awarded the Postgraduate Diploma in Mathematical Finance, should work pressures intervene before it is possible to write a dissertation.
In order to complete the MSc each student must attend and be assessed on four core modules, three advanced modules and to submit a dissertation. Students are expected to take seven terms (28 months) to complete the course.
Modules are taught through a series of lectures, practical sessions, guided reading, guest lectures and course assignments.
The core modules cover the mathematical foundations of probability, statistics and partial differential equations, stochastic calculus and martingale theory, portfolio theory, the Black-Scholes model and extensions, numerical methods (finite differences and Monte Carlo), interest rate modelling, stochastic optimisation, exotic derivatives and stochastic volatility. MATLAB and Python are used as a practical computing languages.
Attendance at the four core modules is compulsory. For each module there is an assignment for which feedback and an indicative mark is given to assist you in improving your future performance. Assessment for these compulsory modules consists of two two-hour written examinations held in September of the first year.
Each of the advanced modules explores a key area in contemporary mathematical finance. The programme of advanced modules is published in July each year, and you will be asked to register your choice of three modules. Attendance at these three assessed modules is compulsory. Advanced modules will be assessed by short ‘special project’ reports, each submitted on a subject chosen by you that is covered in the module.
You will complete a dissertation on a topic chosen in consultation with your supervisor and the Course Director.
Manchester is a leading centre for economics and research-led teaching. Graduate students from across the globe come to study economics at Manchester, attracted by its first-class postgraduate training and supervision in the core and specialist areas of economics.
Many famous names from the world of economics have worked here at Manchester, including three Nobel Prize winners. Interdisciplinary study is also actively pursued here with many course units involving a number of different Schools at the university.
The Economics MA course is designed to meet the growing demand for those students who seek a degree that combines a solid training in microeconomic and macroeconomic principles with quantitative methods and research informed applied economics units.
This course is clearly different from the existing MSc Economics courses at Manchester because of its focus on mainstream but less theoretical units that need to be completed.
Students who choose the Economics MA will take compulsory courses in both Microeconomics and Macroeconomics; they will further advance their quantitative skills and techniques in the core courses in Introduction to Econometrics, Mathematical Methods in Economic Analysis and Further Econometrics; and, as part of their MA dissertation, they will focus on applied and/or policy-oriented research of economic data as relevant to policy makers and economics professionals.
The programme suits students who are interested in a career straight after the MA and not those students interested in postgraduate research. The latter group may find our MSc Economics more appropriate.
Quantitative methods preparation for the MA
1. Please visit our Introduction to Quantitative Methods in Economics website where you will find information about the minimum level of knowledge of mathematics and statistics that you should possess from your current or previous training.
2. On the same website, please look at the details and content of our Introduction course on Quantitative Methods in Economics which builds on the knowledge resumed in (1) and which is designed to equip you with further technical skills that you will require before starting the MSc. You are strongly advised to attend this course which is offered, free of charge. The course will run during induction week and we recommend that you spend some time between July 1 and September studying and familiarising yourself with the course material on the website, especially if you might not be able to attend the course. The significance of this course is illustrated by the fact that the obtained marks contribute 10% to the final marks of the Maths Methods and Econometrics compulsory units of semester 1.
IMPORTANT NOTE ON PART-TIME STUDY
Part-time students complete the full-time programme over two years. There are NO evening or weekend course units available on the part-time programme.
You must first check the schedule of the compulsory modules and then select your optional modules to suit your requirements.
Updated timetable information will be available from mid-August and you will have the opportunity to discuss your module choices during induction week with your Course Director
Practical support and advice for current students and applicants is available from the Disability Advisory and Support Service. Email: [email protected]
The demand for economists continues to grow worldwide. This demand exists across a host of institutions ranging from the public sector (like universities, central banks, international organisations) to the private sector (commercial banks and insurance providers).
With the range of applied economics skills provided in the MA Economics students are perfectly place to seek a career in business and place themselves ahead of competition. At the same time this degree is ideal for students who seek further education via MSc-research degrees across the UK and the world.
In addition to being a science in its own right, mathematics plays a fundamental role in the quantitative areas of practically all other academic disciplines, particularly in the natural sciences, engineering, business administration, economics, medicine and psychology. Mathematical results permeate nearly all facets of life and are a necessary prerequisite for the vast majority of modern technologies – and as our IT systems become increasingly powerful, we are able to mathematically handle enormous amounts of data and solve ever more complex problems.
Special emphasis is placed on developing students' ability to formalise given problems in a way that facilitates algorithmic processing as well as enabling them to choose or develop, and subsequently apply, suitable algorithms to solve problems in an appropriate manner. The degree programme is theoretical in its orientation, with strongly application-oriented components. Studying this programme, you can gain advanced knowledge in the mathematical areas of Cryptography, Computer Algebra, Algorithmic Algebra and Geometry, Image and Signals Processing, Statistics and Stochastic Simulation, Dynamical Systems and Control Theory as well as expert knowledge in Computer Science fields such as Data Management, Machine Learning and Data Mining.
Furthermore, you will have the chance to learn how to apply your knowledge to tackle problems in areas as diverse as Marketing, Predictive Analytics, Computational Finance, Digital Humanities, IT Security and Robotics.
The core modules consist of two mathematics seminars and the presentation of your master's thesis.The compulsory elective modules are divided into eight module groups:
1) Algebra, Geometry and Cryptography
This module group imparts advanced results in the areas of algebra and geometry, which constitute the fundament for algorithmic calculations, particularly in cryptography but also in many other mathematical areas.
2) Mathematical Logic and Discrete Mathematics
The theoretical possibilities and limitations of algorithm-based solutions are treated in this module group.
3) Analysis, Numerics and Approximation Theory
Methods from the fields of mathematical analysis, applied harmonic analysis and approximation theory for modelling and approximating continuous and discrete data and systems as well as efficient numerical implementation and evaluation of these methods are the scope of this module group.
4) Dynamical Systems and Optimisation
Dynamical systems theory deals with the description of change over time. This module group is concerned with methods used for the modelling, analysis, optimisation and design of dynamical systems, as well as the numerical implementation of such techniques.
5) Stochastics, Statistics
This module group deals with methods for modelling and analysing complex random phenomena as well as the construction, analysis and optimisation of stochastic algorithms and techniques used in statistical data analysis.
6) Data Analysis and Data Management and Programming
This module group examines the core methods used in computer science for the analysis of data of heterogeneous modalities (e.g. multimedia data, social networks and sensor data) and for the realisation of data analysis systems.
In this module group, you will practise applying the mathematical methods learned in module groups 1 to 6 to real-world applications such as Marketing, Predictive Analytics and Computational Finance.
8) Key Competencies and Language Training
In this module group, you will choose seminars that develop your non-subject-specific skills, such as public speaking and academic writing and other soft skills; you may also undertake internships. This serves to complement your technical expertise gained during your degree studies and helps to prepare you for your professional life after university.
The Masters in Mathematics/Applied Mathematics offers courses, taught by experts, across a wide range. Mathematics is highly developed yet continually growing, providing new insights and applications. It is the medium for expressing knowledge about many physical phenomena and is concerned with patterns, systems, and structures unrestricted by any specific application, but also allows for applications across many disciplines.
Modes of delivery of the Masters in Mathematics/Applied Mathematics include lectures, laboratory classes, seminars and tutorials and allow students the opportunity to take part in project work.
If you are studying for the MSc you will take a total of 120 credits from a mixture of Level-4 Honours courses, Level-M courses and courses delivered by the Scottish Mathematical Sciences Training Centre (SMSTC).
You will take courses worth a minimum of 90 credits from Level-M courses and those delivered by the SMSTC. The remaining 30 credits may be chosen from final-year Level-H courses. The Level-M courses offered in a particular session will depend on student demand. Below are courses currently offered at these levels, but the options may vary from year to year.
The project titles are offered each year by academic staff and so change annually.
Career opportunities are diverse and varied and include academia, teaching, industry and finance.
Graduates of this programme have gone on to positions such as:
Maths Tutor at a university.
You’ll study interdisciplinary applied mathematics and modern scientific computing, with an emphasis on problem solving. You will gain an understanding of different disciplines and industrial problems. The course links mathematics with engineering, biology and other sciences, and gives students direct contact with industry.
You will develop an awareness of modern applications of mathematics in an interdisciplinary environment. You will get professional level training in mathematical methods, mathematical modelling, scientific computation and other applied techniques, combining both theory and applications.
The course specialises in interdisciplinary applications of mathematics, notably in industry and mathematical biology. You’ll have the opportunity to choose from a wide scope of interdisciplinary units, ranging from astrophysics over cryptography to computational chemistry.
You can choose to do a three month project which can be linked to industry or a six month work placement with a company. The placement route offers a chance to experience first-hand how mathematics can be applied in industry.
You will benefit from the close interactions that the department has with many industrial companies, who come and work with students and help to run projects.
Our graduates have gone on to further research in Lausanne, Berlin, Brussels, Frankfurt, and have taken up academic posts in Malaysia, Sweden, Germany, Canada, US and in the UK.
Recent employers of Bath graduates include British Aerospace, Network Rail, Pfizer, Barclays Capital and Powergen.
- In the 2014 Research Excellence Framework (REF), 88% of our research in all areas (Pure and Applied Mathematics, Statistics and Probability) was rated world leading/internationally excellent. The results of REF 2014 confirm the excellence of the research carried out in the Department of Mathematical Sciences.
- The most recent assessment of the quality of research being done in academic departments across the UK, (RAE 2008), confirms that our research activity is at the forefront of international excellence
- We have a fully-supported professional placement programme.
- The National Student Survey 2016 - 91% satisfaction with Mathematical Sciences.
Our graduates have gone on to further research in Lausanne, Berlin, Brussels, Frankfurt, and academic posts in Malaysia, Sweden, Germany, Canada, the US and in the UK. Recent employers of Bath graduates include:
MBDA UK Ltd
Find out more about the department here - http://www.bath.ac.uk/math-sci/
Find out how to apply here - http://www.bath.ac.uk/science/graduate-school/taught-programmes/how-to-apply/
Visit our website for more information on fees, scholarships, postgraduate loans and other funding options to study Mathematics at Swansea University - 'Welsh University of the Year 2017' (Times and Sunday Times Good University Guide 2017).
As an MSc by Research in Mathematics student you will be guided by internationally leading researchers and will carry out a large individual research project.
You will be fully integrated into one of our established research groups and participate in research activities such as seminars, workshops, laboratories, and field work.
Swansea is a research-led University and the Mathematics Department makes a significant contribution, meaning that as a postgraduate Mathematics student you will benefit from the knowledge and skills of internationally renowned academics.
In the Department of Mathematics at Swansea you will find friendly teaching staff that are fully committed to providing you with a supportive teaching and learning environment. This includes outstanding student support.
All postgraduate Mathematics programmes at Swansea will equip you with skills relevant for a rewarding career in a range of diverse fields. You will also further develop your communication, presentation and analytical skills.
The Mathematics Department’s research groups include:
Algebra and Topology Group
Areas of interest include: Noncommutative geometry, Categorical methods in algebra and topology, Homotopy theory and homological algebra and others.
Analysis and Nonlinear Partial Differential Equations Group
Areas of interest include: Reaction-diffusion and reaction-diffusion-convection equations and systems, Navier–Stokes equations in fluid dynamic, Complexity in the calculus of variations and others.
Stochastic Analysis Group
Areas of interest include: Functional inequalities and applications, Lévy-type processes, Stochastic modelling of fractal, multifractal and multiscale systems, Infinite dimensional stochastic analysis and others.
Mathematical Methods in Biology and Life Sciences Group
Areas of interest include: Mathematical pharmacology; heat and mass transfer models for plant cooling; modelling cellular signal transduction dynamics; mathematical oncology: multi-scale modelling of cancer growth, progression and therapies, and modelling-optimized delivery of multi-modality therapies; multi-scale analysis of individual-based models; spreading speeds and travelling waves in ecology; high performance computing
The ability to think rationally and to process data clearly and accurately are highly valued by employers. Mathematics graduates earn on average 50% more than most other graduates. The most popular areas are the actuarial profession, the financial sector, IT, computer programming and systems administration, and opportunities within business and industry where employers need mathematicians for research and development, statistical analysis, marketing and sales.
The Aubrey Truman Reading Room, located in the centre of the Department of Mathematics, houses the departmental library and computers for student use, and is a popular venue for students to work independently on the regular exercise sheets set by their lecturers, and to discuss mathematics together.
The main university library, the Learning and Information Centre (LIC), contains a notably extensive collection of mathematics books.
As part of our expansion, we are building the Computational Foundry on our Bay Campus for computer and mathematical sciences. This development is exciting news for Swansea Mathematics who are part of the vibrant and growing community of world-class research leaders drawn from computer and mathematical sciences.
The results of the Research Excellence Framework (REF) 2014 show that our research environment (how the Mathematics Department supports research staff and students) and the impact of our research (its value to society) were both judged to be 100% world leading or internationally excellent.
All academic staff in Mathematics are active researchers and the department has a thriving research culture.
The fields of graphics, vision and imaging increasingly rely on one another. This unique and timely MSc provides training in computer graphics, geometry processing, virtual reality, machine vision and imaging technology from world-leading experts, enabling students to specialise in any of these areas and gain a grounding in the others.
Graduates will understand the basic mathematical principles underlying the development and application of new techniques in computer graphics and computer vision and will be aware of the range of algorithms and approaches available, and be able to design, develop and evaluate algorithms and methods for new problems, emerging technologies and applications.
Students undertake modules to the value of 180 credits.
The programme consists of four core modules (60 credits), four optional modules (60 credits) and a research project (60 credits).
Students must choose a minimum of 15 and a maximum of 30 credits from Group One options. Students must choose a minimum of 30 and a maximum of 45 credits from Group Two options.
Group One Options (15 to 30 credits)
Group Two Options (30 to 45 credits)
Please note: the availability and delivery of optional modules may vary, depending on your selection.
All students undertake an independent research project related to a problem of industrial interest or on a topic near the leading edge of research, which culminates in a 60–80 page dissertation.
Teaching and learning
The programme is delivered through a combination of lectures and tutorials. Lectures are often supported by laboratory work with help from demonstrators. Student performance is assessed by unseen written examinations, coursework and a substantial individual project.
Further information on modules and degree structure is available on the department website: Computer Graphics, Vision and Imaging MSc
Graduates are ready for employment in a wide range of high-technology companies and will be able to contribute to maintaining and enhancing the UK's position in these important and expanding areas. The MSc provides graduates with the up-to-date technical skills required to support a wealth of research and development opportunities in broad areas of computer science and engineering, such as multimedia applications, medicine, architecture, film animation and computer games. Our market research shows that the leading companies in these areas demand the deep technical knowledge that this programme provides. Graduates have found positions at global companies such as Disney, Sony and Siemens. Others have gone on to PhD programmes at leading universities worldwide.
Recent career destinations for this degree
UCL received the highest percentage (96%) for quality of research in Computer Science and Informatics in the UK's most recent Research Excellence Framework (REF2014).
Our graduates have some of the highest employment rates of any university in the UK. This degree programme also provides a foundation for further PhD study or industrial research.
Careers data is taken from the ‘Destinations of Leavers from Higher Education’ survey undertaken by HESA looking at the destinations of UK and EU students in the 2013–2015 graduating cohorts six months after graduation.
UCL Computer Science contains some of the world's leading researchers in computer graphics, geometry processing, computer vision and virtual environments.
Research activities include geometric acquisition and 3D fabrication, real-time photo-realistic rendering, mixed and augmented reality, face recognition, content-based image-database search, video-texture modelling, depth perception in stereo vision, colour imaging for industrial inspection, mapping brain function and connectivity and tracking for SLAM (simultaneous localisation and mapping).
The Research Excellence Framework, or REF, is the system for assessing the quality of research in UK higher education institutions. The 2014 REF was carried out by the UK's higher education funding bodies, and the results used to allocate research funding from 2015/16.
The following REF score was awarded to the department: Computer Science
96% rated 4* (‘world-leading’) or 3* (‘internationally excellent’)
Learn more about the scope of UCL's research, and browse case studies, on our Research Impact website.