Mathematical Notes

Unless stated otherwise, all the documents below are mine. They are free to use with proper citation, etc. etc. If you see any mistake, please let me know.

Harmonic Analysis – I
Stein-Tomas restriction theorem and Stricharz estimate for Schrödinger equation
Stricharz estimate for wave equation
As taught by Steve Hofmann in University of Missouri, Fall 2019. Extra notes (Hofmann’s, not mine) added.
Thank you to John Hoffman, Tom Hogancamp, and Konstantinos Tselios for the corrections.

Harmonic Analysis – II
As taught by Steve Hofmann in University of Missouri, Spring 2020.

Convexity, Symmetrization, and Isoperimetry
A course on convex geometry, as taught by Peter Pivovarov in University of Missouri, Spring 2021.

Analysis Qualifying Problems Collection
chosen for University of Missouri quals. Mostly based on Folland’s Real Analysis. Topics include:

  • Measure & construction of Lebesgue measure
  • Integration theorems (Dominated convergence, etc.)
  • Modes of convergence (a.e., in norm, in measure)
  • \(L^p\) space (inequalities, duality, etc.)
  • Hilbert space (basis, projection, operator representation, weak convergence, extension theorem)

Potential Development for Al-TiN Nanolayers
My masters thesis at MSU. Not very interesting mathematically but the pictures are nice to look at. Upshot: the easiest way to make tough materials (with respect to mechanical strength) is to sandwich them, e.g. the soft (Al) – hard (TiN) ‘sandwiches’ done here.
This final version looks a bit weird, because I had to fit my Latex-typesetted draft to the school’s standard format.