Teaching

Teaching is a great way to learn (for me). I wish I was better at it though. Hence these subsequent videos, lectures, notes and resources are my attempts at improving my teaching abilities! These range from topics that I am studying to topics that are just for "fun". If I really want to master something I should be able to explain it in depth.

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Table of Contents

  1. Astrophysical Fluid Dynamics \(\approx \text{7hr}\) Long
    • A course originally taught by Prof. Chung-Pei Ma, to which I model the a class that covers graduate level fluid dynamics but at 2x the speed...
  2. Applied Machine Learning Lab \(\approx \text{tbd...hr}\) Long
    • A course I developed to focus on major machine learning algorithms and building them from scratch. Too much content is focused on calling packages and models without understanding fundamentals. This course changes that.

Astrophysical Fluid Dynamics

A course derived from Prof. Chung-Pei Ma in Berkeley when I first took the class. I hope to cover a bit more than what was originally planed with some exploration on numerical solvers and also General Relativistic Magneto Hydrodynamics. (also some notes were Howard Huang when I couldnt read my own hand writing)

  1. Intro Fluids \(\approx\) 2 Lectures [[Lec 1], [Lec 2]] and [[Video 1], [Video 2]]
    • Fluid approximation; fluid element [Lec 1]
    • Eulerian vs Lagrangian Derivatives [Lec 1]
    • Conservation [Mass, Momentum and Energy] [Lec 1]
    • Examples of simple solutions: hydrostatic equilibrium; polytropic star; Lane-Emden equation [Lec 2]
    • Bernoulli's principle [Lec 2]
  2. Waves and Shocks[[Lec 3], [Lec 4]] and [[Video 3], [Video 4]]
    • Sound waves [lec 3]
    • Gravity waves, surface water waves, capillary waves [lec 3]
    • Shock waves: jump conditions [lec 4]
    • Blast waves; Sedov-Taylor similarity solutions; supernova remnants [lec 4]
  3. Instabilities [[Lec 5]] and [[Video 5]]
    • Gravitational instability: Jeans length, static vs expanding medium
    • Gravitational instability in rotating disks: uniform vs differential rotation, epicycle frequency
    • Rayleigh-Taylor instability
    • Kelvin-Helmholtz instability
  4. Viscocity [[Lec 6]] and [[Video 6]]
    • Viscous stress tensor and force: heuristic and mathematical derivations
    • Navier-Stokes equation; Reynolds number
    • Accretion disk: molecular vs turbulent viscosity
  5. Computational Fluid Simulation [[Lec7]] and [[Video 7]]
    • Numerical Stability Intro
    • Ordinary Differential Equation solving
      • Foreward Euler Method
      • Backward Euler Method
      • Symplectic Euler Method
      • Runge-Kutta (RK) Methods (2nd and 4th order)
    • Partial Differential Equation solvers
      • Elliptical PDE integrator (Laplace)
      • Hyperbolic PDE integrator (Wave Equation)
    • Integrating Navier Stokes with Viscocity (driven lid example)
  6. Magneto-hydro-dynamic Model [[Lec 8]] and [[Video 8]]
    • Motivation; Maxwell's equations
    • Ohm's law; induction equation; magnetic Reynolds number
    • Ideal MHD; magnetohydrodynamic waves; Alfven speed
    • Magnetorotational instabilities
  7. General Relativistic Magneto-hydro-dynamic Model

Applied Machine Learning Lab

This will be a lab like course where I explain key algorithmic machine learning techniques and then manually implement them myself live (or go line-by-line atleast). My rule is I am NOT allowed to call any major computational package unless I have handwrote some version of it myself already. Note: this is a lab course and thus can only be best experienced through engaging with the interactive component of writing key concepts with me. This is usually a few lines of code each lecture which describe the heart of the algorithm.

  1. Intro!
  2. Supervised Learning
    • Linear Regression
    • Logistic Regression
    • Support Vector Machines
    • Decision Trees
    • Symbolic Regression
    • Neural Networks
      1. Forward Neural Network
      2. Autograd
      3. Backprop
      4. Optimizers (SGD and ADAM)
    • Convolutional Neural Networks (and variants)
    • Recurrent Neural Networks (and variants)
    • Transformers
  3. Unsupervised
    1. K means clustering
    2. Spectral Clustering
    3. DBSCAN
    4. Generative Adversarial Networks
    5. Diffusion Models
  4. Others:
    1. Simulation Based Inference
    2. Normalising flows