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Course content

If you have a mathematical background and want to apply your mathematical skills to understanding the complex behaviour of the Earth’s atmosphere and oceans then this could be the programme for you. This is an exciting interdisciplinary subject, of increasing importance to a society facing climate change.

You’ll be trained in both modern applied mathematics and atmosphere-ocean science, combining teaching resources from the School of Mathematics and the School of Earth and Environment. The latter are provided by members of the School’s Institute for Climate and Atmospheric Science, part of the National Centre for Atmospheric Science.

Only a handful of UK universities are positioned to offer similar interdisciplinary training in modern applied mathematics and atmosphere-ocean-climate science.

If you do not meet the full academic entry requirements then you may wish to consider the Graduate Diploma in Mathematics. This course is aimed at students who would like to study for a mathematics related MSc course but do not currently meet the entry requirements. Upon completion of the Graduate Diploma, students who meet the required performance level will be eligible for entry onto a number of related MSc courses, in the following academic year.

Course content

The focus of the course is on analysing the equations of fluid dynamics and thermodynamics, via mathematical and numerical modelling. The programme is highly flexible, meaning you are free to choose options from applied maths, atmosphere-ocean science, numerical methods and scientific computation alongside the compulsory core applied maths and fluid dynamics modules.

Topics are drawn from four broad areas:

  1. Applied mathematics: asymptotic methods, fluid dynamics, mathematical theory of waves and stability of flow
  2. Numerical methods and computing: discretization of ordinary and partial differential equations, algorithms for linear algebra, direct use of numerical weather and climate models
  3. Atmospheric dynamics: structure of the atmosphere, dynamics of weather systems and atmospheric waves
  4. Ocean dynamics: the large-scale ocean circulation, surface waves and tides

Modules are taught either by the School of Mathematics or the School of Earth and Environment.

The course is made up of two parts: a set of taught modules, and a research project. Two-thirds of the course consists of taught modules involving lectures and some computer workshops. Beyond a compulsory core of atmosphere-ocean fluid dynamics, students may choose options to suit their interests from applied maths (e.g. nonlinear dynamics), atmosphere-ocean science (e.g. climate change processes, weather forecasting), numerical methods and scientific computation. The final third of the course consists of an intensive summer project, in which students conduct an in-depth investigation of a chosen subject related to the course.

Course structure

Compulsory modules

  • Dissertation in Mathematics 60 credits

Optional modules

  • Scientific Computation 15 credits
  • Mathematical Methods 15 credits
  • Linear and Non-Linear Waves 15 credits
  • Hydrodynamic Stability 15 credits
  • Dynamical Systems 15 credits
  • Nonlinear Dynamics 15 credits
  • Analytic Solutions of Partial Differential Equations 15 credits
  • Introduction to Entropy in the Physical World 15 credits
  • Astrophysical Fluid Dynamics 15 credits
  • Numerical Methods 10 credits
  • Modern Numerical Methods 15 credits
  • Fluid Dynamics 2 15 credits
  • Advanced Mathematical Methods 20 credits
  • Advanced Linear and Nonlinear Waves 20 credits
  • Advanced Hydrodynamic Stability 20 credits
  • Advanced Dynamical Systems 20 credits
  • Advanced Nonlinear Dynamics 20 credits
  • Advanced Entropy in the Physical World 20 credits
  • Foundations of Fluid Dynamics 30 credits
  • Advanced Geophysical Fluid Dynamics 20 credits
  • Advanced Astrophysical Fluid Dynamics 20 credits
  • Advanced Modern Numerical Methods 20 credits
  • Independent Learning and Skills Project 15 credits
  • Atmosphere and Ocean Climate Change Processes 10 credits
  • Practical Weather Forecasting 10 credits
  • Dynamics of Weather Systems 15 credits
  • Weather, Climate and Air Quality 30 credits
  • Environmental Modelling 15 credits
  • Advanced Atmosphere and Ocean Dynamics 15 credits

For more information on typical modules, read Atmosphere-Ocean Dynamics MSc in the course catalogue

Learning and teaching

Teaching is by lectures, tutorials, practical classes, and one-on-one supervision (for research projects). Outside these formal sessions, students are able to study at their own pace, aided by our wide range of electronic teaching resources.


Assessment is by course work and written exams which take place at the end of the semester in which the module is taught.

Career opportunities

Students will be prepared for postgraduate research in applied mathematics or atmosphere-ocean science, or employment in the environmental sector.

However, given the interdisciplinary nature of the programme, graduates will have expertise and skills in a number of different areas, and should be attractive to a wide range of employers.

Careers support

We encourage you to prepare for your career from day one. That’s one of the reasons Leeds graduates are so sought after by employers.

The Careers Centre and staff in your faculty provide a range of help and advice to help you plan your career and make well-informed decisions along the way, even after you graduate. Find out more at the Careers website.

Visit the Atmosphere-Ocean Dynamics MSc page on the University of Leeds website for more details!






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