Teaching

Department of Mathematics, UCLA

• Spring 2023 -- Math 191 Variable Topics Research Seminar
  
  Title: What can neural networks learn?
  
  Description: In this course, our goal is to study the properties of neural networks (NN) through the lens of the approximation theory. Indeed, NNs are used to approximate (learn) complex mappings between input and output pairs based on available input-output data. Our goal is to understand classes of mappings that could be approximated (learned) or exactly recovered by NNs based on their structure. To this end, we will study classical approximation theorems and their modifications and see how they apply in the context of NN learning. We will emphasize the mathematical properties of NNs dictated by structural choices in their design. In particular, we will be interested in invariances, geometric properties, etc. In this course, we will not study algorithmic or training aspects of NN learning; instead, we will focus on the analytic and mathematical properties of NNs.
  
  Textbook: We will use the textbook “Deep Learning Architectures, A Mathematical Approach” by Ovidiu Calin. Going over the Appendix before attending the course is highly recommended.
  
  Prerequisites: The prerequisites for this course are Analysis 131A-B, Linear Algebra 115A-B, and Probability Theory 170A.
  
  Useful or related: Although we will try to cover necessary background material beyond the prerequisites as we go, familiarity with elementary measure theory would be helpful.
  
  

• Winter 2023 -- Math 131A Analysis

• Fall 2022 -- Math 131A Analysis

• Spring 2022 -- Math 115B Linear Algebra

• Winter 2022 -- Math 131A Analysis

• Winter 2022 -- Math 167 Mathematical Game Theory

• Fall 2021 -- Math 131AH Analysis (Honors)

• Winter, Spring 2021 -- Math 167 Mathematical Game Theory

• Winter 2021 -- Math 285J Graduate Seminar in Applied Mathematics on Mean-Field Games

• Fall 2020 -- Math 142 Mathematical Modeling

• Spring, Summer 2020 -- Math 115A Linear Algebra

• Summer 2020 -- Math 199 Directed Research on the Generalization Theory in Machine Learning

• Winter 2020 -- Math 131A Analysis

• Fall 2019 -- Math 31A Differential and Integral Calculus