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

Notes:

1. An Educational Note on Bayesian Analysis in Dialogue Form (2024)
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.
    A smarter version may be An Educational Note on Monte Carlo Radiative Transfer.
    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.