Collection of interesting papers, including the famous MIT HAKMEM http://home.pipeline.com/~hbaker1/hakmem/hakmem.html
Lisp, garbage collection, modular arithmetic and more.

Apart from the blog, there are technical notes https://www.johndcook.com/blog/writing/ and on-line calculators https://www.johndcook.com/blog/online-calculators/
As an example, see Camp-Paulson normal approximation to the binomial distribution https://www.johndcook.com/blog/camp_paulson/
The articles https://www.johndcook.com/blog/2024/04/01/more-laguerre-images/ and
https://www.johndcook.com/blog/2024/03/22/laguerres-root-finding-method/ demonstrate the basins of attraction for Laguerre's root-finding method.
https://www.johndcook.com/blog/2018/11/24/spheroid-distance/ should be useful for azel.
https://www.johndcook.com/blog/2020/02/08/arenstorf-orbit/ shows a periodic solution to the restricted 3-body problem.
https://www.johndcook.com/blog/2022/11/14/simultaneous-root-finding/ describes the Durand-Kerner polynomial root finding method.
https://www.johndcook.com/blog/2022/11/01/kepler-newton/ discusses solving Kepler's equation

TODO: https://www.johndcook.com/blog/2022/10/30/arctan-k-tan-t/ states "This plot looks similar to the plot of true anomaly for a highly elliptical orbit. I’m sure they’re related, but I haven’t worked out exactly how."

https://www.johndcook.com/blog/2022/10/21/math-origins/ explains V.I. Arnolds comment
"All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines), and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA)."

https://www.johndcook.com/blog/2018/09/24/riemann-hypothesis-the-fine-structure-constant-and-the-todd-function/ is about  Sir Michael Atiyah's incorrect proof of Riemann's hypothesis, the article https://rjlipton.com/2018/09/26/reading-into-atiyahs-proof/ is an interesting read. (I had bookmarked this entry on Wed Sep 26 15:51:47 2018 and put it here 2024-04-03.)

The article https://www.johndcook.com/non_central_chi_square.pdf sounds interesting:
John D. Cook Upper bounds on non-central chi-squared tails and truncated normal moments (2010). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 62.
Abstract. We show that moments of the truncated normal distribution provide upper bounds on the tails of the non-central chi-squared distribution, then develop upper bounds for the former.

Recommended on MoHP.

There a number of interesting articles such as
- The Mystery of the Grazing Goat  http://www.mathpages.com/home/kmath074/kmath074.htm
- On The Solution of the Cubic Equation  http://www.mathpages.com/home/kmath444/kmath444.htm
- Infinite grid of resistors, ...

Just what it says.

spigot is a calculating program. It supports the usual arithmetic operations, square and cube roots, trigonometric and exponential functions, and a few other special functions such as erf.

spigot differs from the average calculating program in that it is an exact real calculator. This means that it does not suffer from rounding errors; in principle, it can keep generating more and more digits of the number you asked for until it runs out of memory.

In particular, if you ask for a complex expression such as sin(sqrt(pi)), then most calculating systems would compute first pi, then sqrt(pi) and finally sin(sqrt(pi)), accumulating a rounding error at each step, so that the final result had a build-up of error and you would have to do some additional error analysis to decide how much of the output you could trust.

spigot, on the other hand, does not output any digit until it is sure that digit is correct, so if you ask for (say) 100 digits of sin(sqrt(pi)) then you can be sure they are the right 100 digits.

Mark Chu-Carroll's blog covers many subjects, including mathematics, physics and programming. In this article he describes his design of a programming language suited for an editor (think about a more readable version of TECO's language).
As of 2021-06-21, the site cannot be reached. On 2021-12-22 it is on-line again.

In order to factor (relatively) large semi-primes (i.e. semi-primes larger than 150-bits), you should (probably) just ask YAFU (Yet Another Factoring Utility, https://github.com/DarkenCode/yafu) to try to factor the number for you in parallel using a highly-optimized number field sieve such as GGNFS (GPL General Number Field Sieve) or SIQS (Self-Initialising Quadratic Sieve). By using YAFU I was able to factor a 302-bit semi-prime in a little over half an hour , as opposed to over the course of 72 minutes using Sage’s Quadratic Sieve (QS).

Sounds like an interesting book. The blog is worth reading as well.