Applied Mathematics MSc

View tabbed content | View all content (for printing)

Course description

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.

Special features

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.

Teaching and learning

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.

Progression and assessment

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 units overview

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.

Disability support

Practical support and advice for current students and applicants is available from the Disability Advisory and Support Service. Email:

Previous tab | Next tab

▲ Up to the top