Mathematical Modelling for Sustainable Development

Aim

Through various learning elements in the course, students gain a deeper insight into how mathematics is relevant to other subject areas and the important role mathematics plays in sustainable development. After completing the course, the student is expected to be able to:

• M1 (Modeling): Understand the need for different modeling methods in natural sciences and technology, with a focus on sustainable development. Account for different mathematical and statistical models and explain the different steps of the modeling process. Plan and select the appropriate method considering the purpose of the modeling. Define an appropriate mathematical or statistical model that takes into account the chosen modeling method. Master and explain some general tools for mathematical modeling and have an understanding of the role of mathematics and statistics for modeling in sustainable development.
• M2 (Analysis): Use the modeling process to solve problems in natural sciences and technology, both individually and in groups, with a particular focus on sustainable development.
• M3 (Implementation): Develop programs in Python or an equivalent programming language, both independently and in collaboration with others. Document and present the results, both orally and in writing, also to a non-specialist audience

Content

The course Mathematical Modeling for Sustainable Development balances an exciting combination of advanced mathematical and statistical modeling and machine learning with a focus on sustainable development in the natural sciences, and especially climate modeling. The course aims to provide an understanding of the use, role and limitations of mathematics in modeling. The course places great emphasis on integrating research into the education, with the goal of deepening students' knowledge of both theoretical and practical aspects of mathematical modeling with applications.

The course covers examples of mathematical and statistical models with special emphasis on the different steps in the modeling process, including problem formulation, analysis, calculations, simulation and feedback.

With a focus on climate modeling, the fundamentals and rationale for transforming climate physics into a mathematical climate model are considered and discussed, where the language of computational physics and mathematics consists of ordinary and partial differential equations (ODEs and PDEs). The analysis is done at both continuous and discrete levels to provide a deeper understanding of how the solutions behave and how uncertainty in the data (through error terms) affects them. In modeling, the mathematical model needs to be discretized effectively to calculate an approximate solution for various uncertain parameters. The results then need to be interpreted, used in prediction and the conclusions should be presented in an appropriate way. The visualization of the results from a climate model requires mathematical knowledge of how to plot spherical data using post-processing tools.

The mathematical models involved are within several subject areas, such as computational mathematics, mathematical statistics, optimization theory and applied mathematics.