Students should know all relevant definitions, correct statements of the major theorems (including their hypotheses and limitations), and examples and non-examples of the various concepts. The students should be able to demonstrate their mastery by solving non-trivial problems related to these concepts, and by proving simple (but non-trivial) theorems about the concepts below, related to, but not identical to, statements proven by the text or instructor.

Students will be able to write programs and utilize existing libraries to implement deep neural networks.

The object of this course is to familiarize students with classical techniques in applied mathematics and demonstrate their application to specific problems. Possible topics include variational, integral, and partial differential equations; spectral and transform methods; nonlinear waves; Green's functions; scaling and asymptotic analysis; perturbation theory; continuum mechanics. For more detailed information visit the Math 522 Wiki page.

Students will explore recent progress in analyzing the stability, generalizability, and potential extension of neural networks to new datasets.