## The Numerical Analysis Undergraduate Study Pathway

This page is for students studying in the Department of Mathematics at The University of Manchester.

Since navigating your way through the list of undergraduate options can be tricky, we have grouped together below all the courses that have a numerical analysis flavour. Together, these courses provide a study pathway** **for those students wishing to specialise in numerical analysis during their BSc or MMath degree. Our courses range from purely theoretical ones on approximation theory to practical computing.

## Second Year

In the compulsory course PDEs and Vector Calculus, all students will start to gain insight into the science of numerical analysis. In particular, approximation schemes are introduced for solving ordinary and partial differential equations.

- MATH20401: PDEs and Vector Calculus A (core for Single Honours students)
- MATH20411: PDEs and Vector Calculus B (core for Joint Honours students)

The first optional course that is wholly dedicated to numerical analysis is:

- MATH20602: Numerical Analysis 1 (second semester)

This course is a pre-requisite for some of the numerical analysis options in the third and fourth years.

## Third Year

In the third year, there are currently five numerical analysis lecture courses to choose from.

- MATH36001: Matrix Analysis
- MATH36041: Essential Differential Equations
- MATH36022: Numerical Analysis 2
- MATH36032: Problem Solving by Computer
- MATH36061: Convex Optimisation

The following project options are also available:

- MATH3000: Double Project – Semesters 1 and 2
- MATH3011: Project – Semester 1 only
- MATH3022: Project – Semester 2 only

Members of staff who supervise numerical analysis projects include:

- Simon Cotter
- Stefan Guettel
- Nick Higham
- Françoise Tisseur
- Catherine Powell
- David Silvester
- Marcus Webb

A list of specific numerical analysis (and other applied) projects is available in our Study section. Please contact individual supervisors from the above list for more up to date details. We welcome enquiries by students interested in doing a project on any aspect of numerical analysis, not just those listed.

## Fourth Year

MMath students may choose the following numerical analysis courses.

- MATH46101: Numerical Linear Algebra
- MATH49111: Scientific Computing
- MATH46132: Numerical Optimization and Inverse Problems
- MATH46052: Approximation Theory and Finite Element Analysis

All MMath students are required to do a project. As in the third year, the following options are available:

- MATH4000: Double Project – Semesters 1 and 2
- MATH4011: Project – Semester 1 only
- MATH4022: Project – Semester 2 only

Please contact the staff members listed above if you are interested in doing a numerical analysis project in the fourth year.

## FAQs

**What is Numerical Analysis?**

Numerical Analysis is an exciting branch of applied mathematics, that is concerned with approximation (e.g. eigenvalues of matrices, solutions of linear systems or differential equations), and analysing the resulting errors.

### What do Numerical Analysts do?

Numerical Analysts strive to develop practical algorithms to approximate solutions to complex real-world problems, as well as to develop rigorous theory to establish error bounds and convergence.

### What can I do with Numerical Analysis?

Numerical Analysts are employed, e.g., in finance, industry, and research institutions, as well as in academia.

Numerical Analysts make computers solve real-world problems.