This is a list of books that use array programming languages like APL or J to teach or explain subjects in mathematics. I compiled it because I wanted to. If I may editorialize, I think there should be more of these. I think such was much of Ken Iverson's purpose.
It is based on a Reddit post I made in October 2023. I have added books that use the J language and would for any other array language if I knew of any such books.
I believe all of these are out of print. Where there is a PDF available online that appears to me to be legitimate (not a copyright infringement) I have linked to that. Additionally, where possible, I have linked to the Google Books page on the book, which in turn often links to sellers like Amazon. Please note that I have not personally seen all of these, so if you know that something does not belong on this list, please let me know.
The references attempt to be approximately in AMA style, in alphabetic order by author, and then by title under a given author, with the additional prefix listing what language is used.
I would very much welcome any additions or corrections. No need for a formal pull request unless you want to. Just send me a reference or correction.
Thanks to Reddit users from r/apljk moon-chilled, Embarrassed_Ba, maa49, and cratylus for some of these. Much else comes from the J Wiki Books page.
Alvord, L. Probability in APL. APL Press; 1984. Google Books.- Anscobm, FJ. Computing in Statistical Science through APL. APL Press; 1981. Google Books.
- Grenander, U. Mathematical Experiments on the Computer. Academic Press; 1982. Google Books.
- Helzer, G. Applied Linear Algebra with APL. Springer New York; 1983. Google Books.
- Iverson, KE. Algebra: An Algorithmic Treatment. APL Press; 1977. PDF. Google Books
Iverson, KE. Arithmetic. J Software; Date unknown. PDF.- Iverson, KE. Applied Mathematics for Programmers. Pub unknown; 1984.
- Iverson, KE. Calculus. Iverson Software, Inc.; 1993. PDF. Google Books.
- Iverson, KE. Concrete Math Companion. Pub unknown; 1995. PDF. Google Books.
- Iverson, KE. Elementary Algebra. IBM Corporation; 1971. PDF.
- Iverson, KE. Elementary Analysis. APL Press; 1976. Google Books.
- Iverson, KE. Elementary Functions: An Algorithmic Treatment. Science Research Associates, Inc; 1966. PDF.
- Iverson, KE. Exploring Math. J Software; 1996. PDF. Google Books.
- Iverson, KE. Mathematics and Programming. Pub unknown; 1986.
- Iverson, KE. Math for the Layman. J Software; Date unknown. zipped HTML.
- LeCuyer, EJ. Introduction to College Mathematics with A Programming Language. Springer-Verlag; 1961. PDF.
- Musgrave, GL, Ramsey, JB. APL-STAT: A Do-It-Yourself Guide to Computational Statistics Using APL. Lifetime Learning Publications; 1981. PDF.
- Peelle, HA. Mathematical Computing in J. Research Studies; 2005. Google Books.
- Orth, DL. Calculus in a New Key. APL Press; 1976. Google Books.
- Reiter, CA, Jones, WR. APL With a Mathematical Accent. Routledge; 1990. Google Books.
- Sims, CC. Abstract Algebra: A Computational Approach. John Wiley & Sons; 1984. Google Books.
- Reiter, CA. Fractals, Visualization and J. Fourth Ed. Part 1. Lulu.com; 2016. Google Books
- Reiter, CA. Fractals, Visualization and J, Fourth Ed. Part 2. Lulu.com; 2016. Google Books
- Thompson, ND. APL Programs for the Mathematics Classroom. John Wiley & Sons; 1989. Google Books.
