Educational Notes on Cosmology, Galaxies, Radiative Transfer, and Related Topics

Notes:

1. An Educational Note on Bayesian Analysis: Under construction.
   
2. An Educational Note on the Central Limit Theorem: Under construction.
   A brief presentation of the central limit theorem (CLT) with a non-rigorous proof suitable for giving insight for astronomy and physics students.
   Relevant links: central limit theorem (CLT) (see also Wolfram Mathworld: Central Limit Theorem (with proof), Gaussian distribution (AKA normal distribution, AKA bell curve) (see also Wolfram Mathworld: Normal Distribution), Hagen derivation of the Gaussian, p. 4, History of the Central Limit Theorem: See p.~83-85 for the Hagen derivation of the Gaussian.
3. An Educational Note on Cosmological Distance Measures: Under construction.
   
4. An Educational Note on the Cosmic Scale Factor for the Λ-CDM model
5. An Educational Note on a toy model of dark matter halos: Under construction.
6. An Educational Note on the Friedmann Equation and Elementary Solutions: Under construction.
   
7. Exact Two-Density Component Solutions for the Cosmic Scale Factor from a General Approach Iincluding a Simplified Exact Solution Formula for the Radiation-Matter Universe: Under construction, but most important results are already in place.
8. An Educational Note on the Planck Function: Under construction.
   
9. An Educational Note on the Gravity: Under construction.
   
10. An Educational Note on the Saha Equation and its Solution for the Ionization State of a Gas: Nearly complete.
    
11. An Educational Note on Monte Carlo Radiative Transfer: CELL MONTE CARLO RADIATIVE TRANSFER: A RESEARCH NOTE ON AN IDEA FOR A SPEED-UP OF MONTE CARLO RADIATIVE TRANSFER: This is my first idea for Monte Carlo radiative transfer based on atmosphere cells and runtime lists. A key point is that it is a general method for all Monte Carlo radiative and not just for special cases.
    There may be smarter versions of the idea, but that will take some thought. For references, see Radtran: Radiative Transfer References, Resources, Etc. for Radiative Transfer Codes.
    For handwritten classroom lecture notes, see (whenever I can get them back online) 120_monte_carlo_notes_classroom.pdf which are primarily based on Lucy 1999 and Kasen et al. 2006.
12. An Educational Note PINN Radiative Transfer: This is a 2024jan01 update of arXiv paper Chen et al. 2022. On p. 3--5, it has a discussion of LTE temperature calculations and on p. 11--13, a discussion of P-Cygni line formation in supernovae.
13. An Educational Note on the Thermodynamics and Statistical Mechanics: Under construction. It will include the Debye function maximum approximation. See also Wolfram: Debye functions.