Educational Notes on Cosmology and Related Topics are intended to support/complement/supplement my course on cosmology (see Cosmology: Course Web Site / Extended Syllabus). They may or may not be posted someday at arXiv: astro-ph. Comments and corrections are welcome.

Notes:

- An Educational Note on Bayesian Analysis in Dialogue Form (2024)
- 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.

- An Educational Note on Cosmological Distance Measures:
Under construction.

- An Educational Note on the Cosmic Scale Factor for the Λ-CDM model
- An Educational Note on a toy model of dark matter halos: Under construction.
- An Educational Note on the Friedmann Equation and Elementary
Solutions: Under construction.

- 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.
- An Educational Note on the Planck Function:
Under construction.

- An Educational Note on the Gravity: Under construction.

- An Educational Note on the Saha Equation and its Solution
for the Ionization State of a Gas: Nearly complete.

- 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. - 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.
- An Educational Note on the Thermodynamics
and Statistical Mechanics: Under construction.
It will include the Debye function
maximum approximation.
See also Wolfram: Debye functions.