Welcome to the Applied Mathematics Reading Seminar, organized by Nathan Soedjak, Han Yong Wunrow, and Edith Zhang. The purpose of this seminar is to build community among the applied mathematics graduate students and to create a space for students to teach and learn topics in applied mathematics. There will be an emphasis on applications to supplement APAM coursework.
Graduate students will sign up for either 2-3 seminar dates to cover their proposed topic. Prior to each seminar, speakers will email the attendees an abstract of their talk and any relevant textbook chapters or papers for attendees to read prior to the seminar.
This Spring we will continue studying Data Assimilation, Diffusion, and the Radiative Transfer Equation. Our talks will be held in-person in Columbia University (Mudd 210) on Mondays from 3 p.m. to 4 p.m. EDT.
If you would like to come or to be added on the mailing list, please email [email protected].
| Date | Presenter | Title/Abstract | Materials |
|---|---|---|---|
| 5/1 | Dion Ho | RTE II In the second talk we survey a variety of topics which we did not cover in the first talk. The topics we will prioritize are: the use of auto-differentiation to verify solutions, the delta-M scaling method, and tips and tricks for coding vector products in Python. |
| Date | Presenter | Title/Abstract | Materials |
|---|---|---|---|
| 4/24 | Dion Ho | RTE I We introduce the Radiative Transfer Equation (RTE), discuss its use as a model for atmospheric radiation and tomography, as well as discuss the phase function which is an essential part of the RTE. We proceed to solve the 1D, time-independent RTE using the Discrete Ordinates Method (DOM). We will focus on the series expansions, choice of quadrature schemes, and linear algebra + optimization + stability. We will present from the Jupyter Notebook documentation of PythonicDISORT which is a pure-Python implementation of the DOM. |
GitHub Repo |
| 4/17 | Edith Zhang | Diffusion II |
|
| 4/10 | Edith Zhang | Diffusion I A probabilistic introduction to diffusion and the heat equation using random walks. An introduction to graph random walks, graph Laplacian, and the corresponding eigenvalue problem. |
Slides |
| 4/3 | Nathan Soedjak | Data Assimilation III We continue our discussion of data assimilation by introducing the Extended and Unscented Kalman Filters using the framework of Gaussian Projected Filters. |
Slides |
| 3/27 | Han Yong Wunrow |
Data Assimilation II We will be covering chapters 9 and 10 from Sanz-Alonso, Stuart, and Taeb's notes, covering 3DVAR and 4DVAR variational methods and then introducing the Extended Kalman Filter (ExKF) and Ensemble Kalman Filter (EnKF). |
Slides |
| 3/20 | Han Yong Wunrow |
Data Assimilation I We will be covering chapters 7 and 8 from Sanz-Alonso, Stuart, and Taeb's notes, introducing the notion of data assimilation (what is the best estimate of the model state given a prior estimate and set of noisy measurements) and well-posedness of smoothing and filtering problems. We will then walk through the algorithms for the Kalman Filter and Kalman Smoother. |
Slides |