Many problems across geoscience share mathematical challenges: incomplete observations, uncertainty, nonlinear and multiscale dynamics, model error, large datasets, and limited predictability. The course introduces applied mathematical ways of thinking about such problems arising throughout atmospheric and oceanic science, biogeosciences, hydrology, cryosphere, and many other subfields. Rather than teaching several techniques in depth, it helps participants recognize the mathematical structure of a scientific problem, understand what different approaches can and cannot provide, and identify pathways for deeper learning. Such insights will give participants complementary skills to their own expertise that help them refine scientific questions and produce a more meaningful formulation.
The course is organized around four questions: What can we predict? How uncertain are we? What can we infer from incomplete observations? What can we learn from data? Through a small number of representative examples, we show how perspectives from dynamical modeling and predictability, uncertainty quantification, data assimilation and inverse problems, and data-driven and machine-learning approaches can address different aspects of these questions. Short explanations will be paired with browser-based interactive experiments using simple models.
Participants will receive an Applied Mathematics for Geoscience Starter Kit containing reusable tutorials, interactive examples, a scientific-question-to-method roadmap, and curated resources for further learning, software, online materials, scientific communities, and meetings. The course concludes with practical guidance on choosing next steps, finding relevant expertise, and building collaborations across applied mathematics, data science, and geoscience.