Precisely formulate, and understand the distinction between, mathematical learning and control problems.

Be familiar with common methods for solving learning problems. Note the role of optimization as a method for separating solution design from specific computational methods, and understand the role of key ideas like gradient descent and convexity.

Apply learning techniques to model classes of controlled dynamical systems. Understand notions of data informativity, model identifiability, and the spectrum of model classes linking phenomenological (black box) and mechanistic (white box) models.

Understand how uncertainty is modeled and its role in learning and control problems. Be familiar with ways in which machine learning fails.

Understand the ideas of coarse-graining, universality classes, the renormalization group, and other methods for approaching model approximation. Understand information geometry and be able to apply the model boundary approximation method for a class of models.

Be familiar with a rich collection of model classes used in a wide variety of disciplines. Explore one area deeply in the construction of a specific, predictive model as part of a semester-long project.