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Mathematics Department

The Mathematics Department systematically teaches the mathematical tools that underpin geophysical modeling. Students work through PDEs for wave propagation, inverse theory and regularization, Bayesian inference and uncertainty quantification, and stochastic processes for reservoir modeling; by graduation, they can reach for this mathematical foundation without hesitation whenever a quantitative modeling problem arises across the geosciences.

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Field-based Curriculum · 16

This department's curriculum is built directly on the GeoVerse Lab research fields its professors hold — click a field to see how it is taught.

Fourier Analysis & Spectral Methods
Fourier Analysis & Spectral Methods
A course on Fourier analysis and spectral methods, running from the idea of repr…
Peter Gustav Lejeune Dirichlet
Regularization Theory & Functional Analysis
Regularization Theory & Functional Analysis
A course on regularization theory and functional analysis, using Banach-space an…
Stefan Banach
Bayesian Inference
Bayesian Inference
A course on the theory and practice of Bayesian inference, building understandin…
Dennis Lindley
Stochastic Processes
Stochastic Processes
A course on stochastic processes organized around the classification by memory—i…
Paul Lévy
Optimization Theory & Linear Programming
Optimization Theory & Linear Programming
A course on optimization theory and linear programming, training the formulation…
Leonid Kantorovich
Numerical Methods for PDEs
Numerical Methods for PDEs
A course on the numerical analysis of PDEs centred on the triad of discretizatio…
Peter Lax
Linear Algebra & Matrix Theory
Linear Algebra & Matrix Theory
A foundational course in linear algebra and matrix theory, firmly establishing t…
Arthur Cayley
Complex Analysis
Complex Analysis
A foundational course in complex analysis taking the rigidity of holomorphy—Cauc…
Augustin-Louis Cauchy
Differential Geometry
Differential Geometry
A foundational course in differential geometry centred on the manifold-metric-cu…
Bernhard Riemann
Topology & Dynamical Systems
Topology & Dynamical Systems
A course pairing topology and dynamical systems—spatial properties invariant und…
Henri Poincaré
Probability Theory & Stochastic Calculus
Probability Theory & Stochastic Calculus
A course on probability theory and stochastic calculus, building measure-theoret…
Kiyosi Itô
Wave Equation Mathematics
Wave Equation Mathematics
A course on the mathematics of the wave equation, running from d'Alembert's solu…
Jean Le Rond d'Alembert
Calculus of Variations & Optimal Control
Calculus of Variations & Optimal Control
A course on the calculus of variations and optimal control, building the Euler-L…
Leonhard Euler
Random Matrix Theory
Random Matrix Theory
A course on random matrix theory, running from spectral statistics of classicall…
Freeman Dyson
Tensor Analysis
Tensor Analysis
A foundational course in tensor analysis, starting from the need for coordinate-…
Tullio Levi-Civita
PDE Theory & Sobolev Spaces
PDE Theory & Sobolev Spaces
A course on modern PDE theory teaching, through Sobolev spaces and weak solution…
Sergei Sobolev