Teaching at NUS
2023 Spring: Partial Differential Equations.
I received the "Professor Joel Dean Excellence in Teaching" award for TAs in 2021.
2018 Spring: Partial Differential Equations.
2018 Fall: Calculus 2 (Eng).
2020 Fall: Honour Analysis 1, Differential Equations and Applications.
2021 Fall: Real Variables, Introduction to Proofs.
2022 Spring: Honour Analysis 2, Differential Equations and Applications.
I received the "Outstanding TA in USTC" award in 2016(rank 6/703, score 4.95/5.00) and 2017(rank 7/562, score 4.98/5.00).
- My Teaching Preferrences: PDE(Grad)>Real Analysis(Grad)>Harmonic Analysis>Real Analysis(Undergrad)
>ODE/PDE(Undergrad)>Mathematical Analysis>Functional Analysis>>Others.
- Here, in my understanding,
- Real Analysis(Grad)=Folland Ch 1-3, 6-9.
- Real Analysis(Undergrad)=Stein Ch 1-3, 6 plus more about convergence theorems and Lp spaces.
- PDE grad=Evans Ch 5, 6, 7.1, and part of Ch 8, 9 for elliptic and parabolic PDEs, and materials concerning wave equations (Sogge's book, Jonathan Luk's notes, Qian Wang's notes) and first-order symmetric hyperbolic system (e.g., Chen Shu-Xing's PDE book, Alinhac's hyperbolic PDE book. Evans Ch 7.3.2 and Ch 11).
- PDE undergrad=Evans Ch 2-4.
- Functional Analysis=Reed/Simon Ch 1-6. (Banach/Hilbert Space, Hahn-Banach thm and related,
Weak topology, Spectrum of Compact operators)
- Harmonic Analysis(based on Grad Real Analysis, with prerequisites on Lp interpolation, Fourier transform, Hardy-Littlewood maximal function) should include
Singular Integral (cf. Stein's book Ch 1-4)
Littlewood-Paley and almost orthogonality+T1 Theorem(based on Cotlar's Lemma) (cf. Muscalu-Schlag, Ch 8-9, or Appendix A in Tao's dispersive PDE book)
H1 and BMO (cf. Duoandikoetxea)
Oscillatory Integrals (cf. Stein's"bible" Ch 9-10, Muscalu-Schlag Ch 11, Sogge's book Ch 0-2).