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.
Postgraduate combined research and teaching degree programme Applied Mathematics MRes:
This programme involves both taught classes in Applied Mathematics and a substantial MRes thesis which accounts for almost two-thirds of the total degree.
The MRes can be used as the first phase of our fast track PhD programme, in which the MRes thesis is extended over a further period of two years into a PhD thesis.
This programme involves both taught classes in Applied Mathematics and a substantial MRes thesis which accounts for almost two-thirds of the total degree. The minimum period of registration is 12 months.
The MRes is an ideal preparation for entry into a PhD programme. Indeed, the MRes programme can be used as the first phase of our fast track PhD programme. This is an excellent option for well-qualified mathematics students who do not have all the necessary mathematical background to start immediately on a PhD in their area of choice. In the fast track programme the MRes thesis is extended over a further period of two years into a PhD thesis.
Each MRes student is assigned a project supervisor who will act as director and mentor in the preparation of the MRes thesis. This gives each student the opportunity to work one-to-one with mathematicians who are international experts in their fields.
In addition to the assessed elements of the course, students are expected to play a full part in the research life of the School. The School has an active seminar programme, and organises international conferences in all areas of mathematics.
Related links
These courses are approximately one-third course work and two-thirds dissertation. The dissertation is completed under the direction of a project supervisor which gives our students the opportunity to work one-to-one with a leading expert in their field.
A regular programme of seminars and conferences takes place within the School in a wide range of subjects. Currently thriving at Birmingham are the following research groups:
This programme gives comprehensive training in mathematics and areas appropriate to professional development and research foundations. The MRes is an ideal preparation for entry into the PhD programme at Birmingham. In fact, the MRes programme can be used as the first phase of our ?Fast-track? PhD programme.
University Careers Network
Preparation for your career should be one of the first things you think about as you start university. Whether you have a clear idea of where your future aspirations lie or want to consider the broad range of opportunities available once you have a Birmingham degree, our Careers Network can help you achieve your goal.
Our unique careers guidance service is tailored to your academic subject area, offering a specialised team (in each of the five academic colleges) who can give you expert advice. Our team source exclusive work experience opportunities to help you stand out amongst the competition, with mentoring, global internships and placements available to you. Once you have a career in your sights, one-to-one support with CVs and job applications will help give you the edge.
If you make the most of the wide range of services you will be able to develop your career from the moment you arrive.
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.
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.
The approval from the Institute of Mathematics and its Applications is currently being sought.
A student obtaining an approved IMA award can qualify as a Chartered Mathematician once they have completed 5 years employment in a relevant occupation after graduating.
This programme is delivered full-time over 12 months or part-time over 24 months.
The course provides excellent training in many different areas of applied mathematics and equips students with a range of mathematical skills in problem solving, project work and presentation.
Our MSc in Applied Mathematics is delivered in small classes and offers a variety of optional modules. You complete a substantial research project, which in the past have often led to publication in scientific journals.
The skills you gain from this programme are highly transferable and open up opportunities for a career in industry, such as in the aerospace, petroleum and financial industries.
The solid training in applied mathematics provides the necessary background for further postgraduate study in diverse areas ranging from engineering and physics to finance.
For full information on this course, including how to apply, see: http://www.imperial.ac.uk/study/pg/mathematics/applied-mathematics/
If you have any enquiries you can contact our team at: [email protected]
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.
“There is no branch of mathematics, however abstract, which may not someday be applied to phenomena of the real world.” – Nikolai Ivanovich Lobachevsky
If you're looking to take your undergraduate mathematics experience to new levels and develop advanced research skills, this intensive programme covers the wide spectrum of discrete mathematics, applied mathematics and statistics, and addresses some of the key quantifiable challenges and opportunities in the world around us. An interdisciplinary subject by nature, we will help you to apply mathematical concepts and methods to the ever-changing worlds of science, engineering, business, digital technology and industry, and particularly to communication theory, mathematical physics and financial mathematics, where some of our key research interests lie.
The skills you gain will open up a range of career options and provide a solid foundation if you wish to progress to a PhD. You will be guided by renowned specialists in the field who publish in internationally competitive journals and work closely with partners in industry.
Join our friendly and inspiring department and you will benefit from a thoroughly supportive learning environment, with generous staff office hours and a dedicated personal advisor to help you with any queries and guide you through your degree. Our graduates are in demand for their skills in research, numeracy, data handling and analysis, logical thinking and creative problem solving.
Core modules
Optional modules
In addition to these mandatory course units there are a number of optional course units available during your degree studies. The following is a selection of optional course units that are likely to be available. Please note that although the College will keep changes to a minimum, new units may be offered or existing units may be withdrawn, for example, in response to a change in staff. Applicants will be informed if any significant changes need to be made.
You will initially choose eight modules from the list of available options, of which you specify modules during the second term that will count towards your final award. You will also complete a core research project under the supervision of one of our academic staff. There is a strong focus on small group teaching throughout the programme.
Assessment is carried out through a variety of methods, including coursework, examinations and the main project. End-of-year examinations in May or June will count for 66.7% of your final award, while the dissertation will make up the remaining 33.3%.
By the end of this programme you will have completed a major research project and acquired an advanced knowledge and understanding of: the role and limitations of mathematics in solving problems that arise in real-world scenarios. You will also have impressive skills in selected areas of mathematics and their applications, and the ability to synthesise and interpret information from multiple sources with insight and critical awareness. We will teach you to formulate problems clearly and express your technical work and conclusions clearly in writing, and you will develop valuable transferable skills such as time management, adaptability and self-motivation.
Our graduates have gone on to carry out cutting-edge research in the fields of communication theory and cryptography, as well as successful careers in industries such as: information security, IT consultancy, banking and finance, higher education and telecommunication. They have taken up roles such as: Principal Information Security Consultant at Abbey National PLC; Senior Manager at Enterprise Risk Services, Deloitte & Touche; Global IT Security Director at Reuters; and Information Security Manager at London Underground.
You will have a dedicated personal adviser to guide you through your studies and advise you on postgraduate opportunities, and the campus Careers team will be on hand to offer advice and guidance on your chosen career. The University of London Careers Advisory Service offers regular, tailored sessions for Mathematics students, on finding summer internships or vacation employment and getting into employment.
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