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MSc Applied Mathematics / Course details

Year of entry: 2022

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Course description

The Applied Mathematics group in the Department 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, 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 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, from a list including specialist options relevant to 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 selection of optional courses in the MSc are centred around numerical analysis and industrial mathematics, reflecting research strengths within the Applied Mathematics group at Manchester.

Numerical Analysis - the study of algorithms for the problems of continuous mathematics - has been an area of strength since the first stored-program electronic digital computer, the Baby, was born at the University of Manchester in 1948, and we have run an MSc course in numerical analysis continuously since 1959. The optional numerical analysis modules develop essential skills for analysing, designing and implementing mathematical algorithms for leading edge scientific computing.

Industrial Mathematics and Industrial Modelling (any aspect of mathematics that can influence the way industry approaches or solves problems) is having an increasing importance within a variety of industrial sectors. Typical examples of industrial modelling problems are modifications to the way that fluid is pumped through a pipe, the design of algorithms for data encryption, modelling new types of materials used for sound reduction, understanding the instability between fluids of different viscosities, and determining how soft tissue deforms under applied forces.


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 of the course is 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 may be available with industry.

Teaching and learning

Your teaching will be delivered by a combination of lectures and other in-person classes such as tutorials, computer labs and project supervision meetings, together with online learning materials.

Coursework 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 unit details

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

 * Continuum Mechanics

 * Stability theory

 * Transport Phenomena and Conservation Laws

 * Advanced Uncertainty Quantification

 * Approximation Theory and Finite Element Analysis

 * Numerical Linear Algebra

 * Numerical Optimization and Inverse Problems  

Course unit list

The course unit details given below are subject to change, and are the latest example of the curriculum available on this course of study.

TitleCodeCredit ratingMandatory/optional
Mathematical Methods (as MAGIC022) MATH64051 15 Mandatory
PDEs: Theory and Practice (MAGIC058) MATH64062 15 Mandatory
Introduction to Uncertainty Quantification MATH64071 15 Mandatory
Transferable Skills for Applied Mathematicians MATH65740 15 Mandatory
Scientific Computing MATH69111 15 Mandatory
Dynamical Systems MATH64041 15 Optional
Advanced Uncertainty Quantification MATH64082 15 Optional
Transport Phenomena and Conservation Laws MATH65122 15 Optional
Stability Theory MATH65132 15 Optional
Approximation Theory and Finite Element Analysis MATH66052 15 Optional
Numerical Linear Algebra MATH66101 15 Optional
Numerical Optimization and Inverse Problems MATH66132 15 Optional
Displaying 10 of 12 course units

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