The Applied Mathematics group in the School of Mathematics at the University of Manchester has a long-standing international reputation for its research. Expertise in the group encompasses a broad range of topics, including Continuum Mechanics, Analysis & Dynamical Systems, Industrial & Applied Mathematics, Inverse Problems, Mathematical Finance, and Numerical Analysis & Scientific Computing. The group has a strongly interdisciplinary research ethos, which it pursues in areas such as Mathematics in the Life Sciences, Uncertainty Quantification & Data Science, and within the Manchester Centre for Nonlinear Dynamics.
The Applied Mathematics group offers the MSc in Applied Mathematics as an entry point to graduate study. The MSc has two pathways, reflecting the existing strengths within the group in numerical analysis and in industrial mathematics. The MSc consists of five core modules (total 75 credits) covering the main areas of mathematical techniques, modelling and computing skills necessary to become a modern applied mathematician. Students then choose three options, chosen from specific pathways in numerical analysis and industrial modelling (total 45 credits). Finally, a dissertation (60 credits) is undertaken with supervision from a member of staff in the applied mathematics group with the possibility of co-supervision with an industrial sponsor.
The course aims to develop core skills in applied mathematics and allows students to specialise in industrial modelling or numerical analysis, in preparation for study towards a PhD or a career using mathematics within industry. An important element is the course regarding transferable skills which will link with academics and employers to deliver important skills for a successful transition to a research career or the industrial workplace.
The course features a transferable skills module, with guest lectures from industrial partners. Some dissertation projects and short internships will also be available with industry.
Students take eight taught modules and write a dissertation. The taught modules feature a variety of teaching methods, including lectures, coursework, and computing and modelling projects (both individually and in groups). The modules on Scientific Computing and Transferable Skills particularly involve significant project work. Modules are examined through both coursework and examinations.
Assessment comprises course work, exams in January and May, followed by a dissertation carried out and written up between June and September. The dissertation counts for 60 credits of the 180 credits and is chosen from a range of available projects, including projects suggested by industrial partners.
Course unit details
CORE (75 credits)
* Introduction to Uncertainty Quantification
* Mathematical Methods
* Partial Differential Equations
* Scientific Computing
* Transferable Skills for Applied Mathematicians
OPTIONAL (3 modules, 45 credits)
* Applied Dynamical Systems (IM)
* Continuum Mechanics (IM)
* Stability theory (IM)
* Transport Phenomena and Conservation Laws (IM)
* Advanced Uncertainty Quantification (IM,NA)
* Approximation Theory and Finite Element Analysis (NA)
* Numerical Linear Algebra (NA)
* Numerical Optimization and Inverse Problems (NA)
Students registered on the Numerical Analysis pathway must select modules marked NA, and those registered on the Industrial Modelling pathway must select modules marked IM.
Syllabuses for the modules Introduction to Uncertainty Quantification and Advanced Uncertainty Quantification are currently being finalized and details will be added here as soon as possible.
Modern computing facilities are available to support the course.
Practical support and advice for current students and applicants is available from the Disability Advisory and Support Service. Email: [email protected]
The programme will prepare students for a career in research (via entry into a PhD programme) or direct entry into industry. Possible subsequent PhD programmes would be those in mathematics, computer science, or one of the many science and engineering disciplines where applied mathematics is crucial. The programme develops many computational, analytical, and modelling skills, which are valued by a wide range of employers. Specialist skills in scientific computing are valued in the science, engineering, and financial sector.
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.
This course provides you with a sound general knowledge of advanced mathematics through study in several pure and applied areas of the subject, including Statistics and Operational Research. A wide choice of topics is available for your dissertation, taken under the supervision of a member of the academic staff.
If you wish to enter employment within the field of Mathematics then this course will enhance your career prospects by promoting a professional attitude to Mathematics. Mathematicians are warmly welcomed in industry, business and commerce for their analytical ability and logical approach to problem solving. The course is particularly suitable if you are planning a career in teaching Mathematics or are already a qualified teacher seeking to enhance your promotion prospects.
Research Methods and professional Skills
Introduction to Cybermetrics
Advanced Topics in Mathematics
The Mathematics department includes a team of researchers in the field of Introduction to Cybermetrics, led by a professor who has been recognised as a leading international authority on the subject and who achieved a very high rating in the latest Research Assessment Exercise.
We pride ourselves on the academic support and guidance given by our friendly and approachable staff. Students have shown their appreciation for this by the exceptionally high ratings they have given us in the National Student Survey in recent years.
Students will have developed advanced technical skills within the field of Mathematics together with an ability to critically analyse and evaluate complex problems. These skills should equip students to enter careers in Mathematics in a variety of roles.
There is a shortage of Mathematics-related skills both nationally and regionally, and in particular there is a recognised severe shortage of qualified Mathematics teachers. Hence the Mathematics qualification that this course offers will make its graduates highly employable.
Excellent career opportunities will also be open in operational research, statistics, information analysis, financial advising, actuarial work and accountancy.
You will be able to demonstrate a full understanding, knowledge and experience of complex and specialised areas of mathematics; Select and apply appropriate techniques to the analysis, design and synthesis of solutions to problems which require mathematics for their resolution.
Within this course, you will apply knowledge of mathematics with particular reference to its applications in other subject areas (e.g. mathematical education, analysis and modelling of business and finance, computing and scientific systems).
You will be able to demonstrate originality in the application of knowledge, together with a practical understanding of how established techniques of research and enquiry are used to create and interpret knowledge in mathematics.
Conduct research into current mathematical literature; review, analyse and evaluate findings in a professional manner.
This course will enable you to deal with complex issues both systematically and creatively, making sound judgements in the absence of complete data, and communicating conclusions clearly to specialist and non-specialist audiences.
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Computational Mathematics, in particular the physical applied areas and the theory and implementation of numerical methods and algorithms, have wide-ranging applications in both the public and private sectors. More recently, in this era of ubiquitous and cheap computing power, there has been an explosion in the number of problems that require us to understand processes by modelling them, and to use data sets that are large. Thus the subject of Computational Mathematics has become increasingly prominent. Consequently there is high demand also for computational modellers and data scientists. This programme concentrates on the overlap and synergy between these fields.
The programme consists of 120 credits of courses in total during Semesters 1 and 2, followed by a 60 credit dissertation which is completed during the Summer. The courses taken will be dependent on the availability of courses each year which may be subject to change as curriculum develops to reflect a modern degree programme.
The first semester is composed of a combination of compulsory and optional courses. The compulsory courses will build strong applied mathematical and computational foundations. The curriculum is completed with optional courses in related subjects such as statistics and optimization.
The second semester is again composed of a combination of compulsory and optional courses, building on the skills gained in Semester 1. The compulsory courses include Research Skills, which will prepare you for the Summer Dissertation Project. The optional courses cover a wide range of areas including, for example, data science, high performance computing, and related disciplines such as Informatics and Physics.
The 60 credit individual dissertation will take the form of a supervised research-style project on a topic proposed by a staff member of the Applied and Computational Mathematics group. The aim of the project is to provide practical experience and skills for tackling scientific problems which require both computational approaches and mathematical insight. This will include identifying and applying appropriate mathematical and numerical techniques, interpreting the results, and presenting the conclusions.
This programme will provide training in the tools and techniques of mathematical modelling and scientific computing, and will provide students with skills for problem solving using modern techniques of applied mathematics.