APL and Insight: Using Functions to Represent Concepts in Teaching

[Alexey Slyusar]

Hello,
I am at the moment investigating APL applications in teaching elementary math - I mean such topics like elementary algebra, elementary functions, and several others like combinatorics, probability and number theory discussed on high school level of sophistication.

And It seems that the father of APL - Dr. Kenneth Iverson - and other people from APL community have developed several brilliant text for such a level of sophistication:
- Iverson K.E. Algebra
- Iverson K.E. Elementary Functions
- Iverson K.E. The use of APL in Teaching
- Iverson K.E. Introducing APL to Teachers
- Thomson N. APL Programs for the Mathematics Classroom

I have all the above texts at hand and experimenting with the material using genuine APL\360 (many thanks to Jürgen Winkelmann https://wotho.ethz.ch/mvt4apl-2.00/ and all the people who made it possible to run the system on GNU/Linux as well as on Windows and MacOS)
and I-APL (https://code.jsoftware.com/wiki/Essays/History_of_I-APL)

I want to learn more on this direction and wonder does someone here could point me on some other texts (digital copies preferred)?

In particular I am searching for digital copy of:
- Berry P. at al. APL and Insight: Using Functions to Represent Concepts in Teaching, IBM, 1971.
- Linda Alvord's book "Probability in APL".

APL physics text at similar level of sophistication would be interesting also. (Physics in APL2 by G.J. Ghaitin is awesome and it would be great to learn something else in this direction).

Any help would be highly appreciated.

Thanks in advance,
Alexey

-Marry Christmas to all here

[DaveW]

Digital design, using an APL-derived syntax:

Hill, Fredrick J & Peterson, Gerald R
Digital Systems Hardware Organization and Design
John Wiley & Sons
The 2nd edition is 1978: ISBN 0-471-39608-7

Dave Weintraub

[barry_...@yahoo.com]

I was involved in APL and Education in Canada in the 80's. I knew Linda and Tama and at one time had all their little books. All I can find at the moment are three booklets on J by Iverson. I also have Calculus in a New Key by Orth somewhere..... Things may have been lost when I moved.

Physics in APL2 does sound awesome. Where can I find it?

Barry

[DaveW]

At APL83 (I'm pretty sure), there was a speaker who talked about teaching subjects in Japan using APL. You might find the paper and look for references there. There was also a later presentation (I do not recall which year) on teaching APL in France.

(Our house is in the middle of renovations, so I can't get to my APL Conference Proceedings.)
Dav

[Curtis Jones]

On Monday, December 26, 2022 at 9:44:46 AM UTC-8, barry_...@yahoo.com wrote:
>
> Physics in APL2 does sound awesome. Where can I find it?
>
> Barry

Barry,
Have a look at
https://www.softwarepreservation.org/projects/apl/Papers/ComputerGallery
G. J. Chaitin, "A Computer Gallery of Mathematical Physics - A Course Outline"
Curtis

[Alexey Slyusar]

> Digital design, using an APL-derived syntax:
>
> Hill, Fredrick J & Peterson, Gerald R
> Digital Systems Hardware Organization and Design
> John Wiley & Sons
> The 2nd edition is 1978: ISBN 0-471-39608-7
>
> Dave Weintraub

Thank you for the reply.
1st edition of the book accessible through "borrow" option from Archive.org.
Here is a link:
https://archive.org/details/digitalsystemsha00hill

Alexey.

[Rav]

Hi, Dave. I have the proceedings from '83, '84, and a few more. I
quickly skimmed the table of contents in the '83 and didn't see anything
you might be referring to, but in the '84 there is an article titled
"Word, Image and Metaphor To Name APL Concepts in Many Tongues."
Perhaps this is what you are referring to? If this isn't it, let me
know and I can send you the table of contents for '83 and '84. This is
the abstract:

"APL notation uses symbols rather than words. But discussion and
education require the use of words. A well-chosen term can make a new
concept plain, or link it effectively to related topics. The
English-speaking originators of APL took some pains to avoid jargon, and
to select terms rooted in metaphors to help convey the meaning of
symbols. This paper identifies several goals in the choice of English
terms for APL concepts, and then lists problems that arise when
corresponding terms must be found in other languages, with examples from
French, German, Spanish and Japanese. It notes both strengths and
weaknesses of current APL terminology in English. It exhorts
translators and writers in languages other than English to avoid
transliterating English terms, and urges them instead to convey the
relevant images implied in the English source, or, better yet, to
contribute new images to enrich the international vocabulary of APL."

- Rav

[Alexey Slyusar]

> I was involved in APL and Education in Canada in the 80's. I knew Linda and Tama and at one time had all their little books. All I can find at the moment are three booklets on J by Iverson. I also have Calculus in a New Key by Orth somewhere..... Things may have been lost when I moved.
>
> Physics in APL2 does sound awesome. Where can I find it?
>
> Barry

Yes, the author masterly added to awesome "The Evolution of Physics" by Albert Einstein and Leopold Infeld a computational dimension using APL2 models for physical phenomena discussed through the book and got his awesome "Physics in APL2". Here is a link:
https://www.softwarepreservation.org/projects/apl/Books/Physics%20in%20APL2

Possibly not so relevant for comp.lang.apl, but there are at least two wonderful texts that used Lisp (more precisely Scheme) and Haskell in order to get deeper insight in physics:
1. Gerald Jay Sussman and Jack Wisdom, Structure and Interpretation of Classical Mechanics, second edition, MIT Press
available through open access from the publisher:
https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/9579/sicm_edition_2.zip/book.html
There is MIT OCW also:
https://ocw.mit.edu/courses/12-620j-classical-mechanics-a-computational-approach-fall-2008/resources/12-620jf08/
It has to be noted that it is graduate level text.

2. Scott N. Walck Learn Physics with Functional Programming. A Hands-on Guide to Exploring Physics with Haskell.
The book available from No Starch Press.

Both above books, I believe, inspired by Seymour Papert who pioneered these ideas in 60-70s at MIT's AI Lab and Logo Lab.

Alexey.

[DaveW]

I found the Proceedings:

APL83 Pg 1:
Traberman, Tama: "Teaching Social Studies Concepts Using Concrete Models Expressed in APL
I had the country wrong: She was from NJ, but an *example* in the paper used Japan
(I apologize for the error, but after all, it has been 40 years since I edited those Proceedings).

There are a few other papers there. A fair number in APL89.

[Alexey Slyusar]

Thank you.

Here is a link for the paper:
https://dl.acm.org/doi/abs/10.1145/800062.801188