Sean P. Carney

Instructor experience (UCLA):

• Math 151BH - Honors Applied Numerical Methods (Spring 2023)
  
• Math 151AH - Honors Applied Numerical Methods (Winter 2023)
  
• Math 135 - Ordinary Differential Equations (Winter 2022)
  
• Math 151B - Applied Numerical Methods (Winter 2021)
  
• Math 151A - Applied Numerical Methods (Fall 2020, Spring 2022, Fall 2022)
  

Sample course materials: course syllabus (151BH) (credit to Nicholas Hu, my TA, for helping create this), lecture notes (151A), homework assignment (151AH), homework assignment (135).

Mentoring:

• UCLA Computational and Applied Maths REU (Summer 2022)
  With Arnav Gangal (now Stanford, previously UCLA) and Luis Kim (now GA Tech, previously UT Austin); our team proved a negative result for a class of neural network based methods based on the strong formulation of a PDE (such as PINNs) with highly oscillatory coefficients in the differential operator. The work was published in TMLR and can be found here.
• Cal-State/UCLA Summer Bridge Program (August 2021)
  This was a week-long problem solving session on Fourier analysis and its applications. Here is a collection of notes and directed exercises.

Expository notes:

• Some lecture notes covering selected topics in numerical analysis: conditioning & stability, discrete least-squares problems, Cholesky decomposition, QR factorization, Singular Value Decomposition, and the Conjugate Gradient method.
  

Other experience:

• At UT Austin, I was a teaching assistant for the following courses: probability theory (graduate and introductory undergraduate), numerical analysis (graduate), differential equations (introductory undergraduate) and differential calculus.
  
• For three years, I worked as an undergraduate tutor for about 10 hours per week at the University of Michigan Math Lab.