# Teaching

Here are some pedagogical notes on physics/math/astronomy (click on title to access PDF/Jupyter notebook).

**Introduction to Numerical Integrators (and Orbits Around Black Holes)**

Numerical integration is a very powerful tool for an astrophysicist. In this Jupyter notebook, we will build a simple numerical integrator from scratch and employ it to solve for the motion of particles around black holes.

**Tensors for Physicists and Astronomers in Two Class Periods**

Tensors are everywhere in physics, and it is nearly impossible to do physics without meeting them in one form or another. However, they are also one of those things that a physics student is expected to understand, but is never taught properly. This note is written to help alleviate this problem.

**A Pictorial Guide to (One of) the Singularity Theorems**

The singularity theorems are some of the most fascinating results in general relativity. In this series of pictures, we go through the proof of the original Penrose singularity theorem for globally hyperbolic manifolds. While this theorem is most suited for cosmology, the proof of the other singularity theorems (e.g. the one for black holes) are similar in spirit.

**Why the Stupid Integrals in Stellar Structure Works**

When studying stellar structures, astrophysicists tend to replace differential quantities with the quantity themselves: dQ~Q. This method of "stupidly integrating" the stellar structure equations has created consternation for many students. In this note we show that this method is well motivated and justifiable.

# List of classes taught:

2018 FS21G: (Teaching Assistant) How Did the First Stars and Galaxies Form? (Harvard)

2018 Astronomy 16: (Teaching Assistant) Stellar and Planetary Astronomy (Harvard)

2016 Astronomy 16: (Teaching Assistant) Stellar and Planetary Astronomy (Harvard)

2015 Astronomy 16: (Teaching Assistant) Stellar and Planetary Astronomy (Harvard)

2013 Astronomy 200: (Teaching Assistant) Radiative Processes in Astronomy (Harvard)

2012 Astronomy 7B: (Teaching Assistant) Introduction to Astronomy (UC Berkeley)

2011 Astronomy 122: (Teaching Assistant) Infrared/Optical Laboratory (UC Berkeley)

2011 Astronomy 198: IDL Decal: Programming Course for Astronomers (UC Berkeley)