The second edition of At Play With J, collected from Eugene McDonnell’s columns for Vector, has been published at

Here in one volume are Eugene McDonnell’s 41 excellent articles published between 1993 and 2006. They form a series of straightforward but profound mathematical investigations which are not only entertaining but expand the mind.

The classical tradition founded by Fermat and Gauss mystifies the mathematical art by concealing the way in which the investigator found the solution in the first place. Trainee researchers will gain reassurance from the fact that the author does not shy away from expressing perplexity and puzzlement along the often rocky road to a solution. As such it constitutes a unique masterclass in how to do mathematical research.

The second edition has been produced by a team of J experts, revising and reworking the examples to correspond to best practice with J 6.02. With prefaces by Roger Hui and Chris Burke.

The first edition reproduced the original Vector articles with only minor amendments. But J evolved over the many years during which McDonnell wrote his column, and in the latest version of J not all the examples work as they were given. The first edition is of largely historical interest.

Some recent textbooks for the APLs

System Building with APL+Win
Ajay Askoolum is an experienced Windows developer; his 2006 cookbook was reviewed in Vector 23:1 and isavailable from Amazon.
Mastering Dyalog APL
Probably the best modern introduction to APL. A full introduction to the language, published in 2010, with ample examples and illustrations. 796pp. 

Available from or can be downloaded free as a PDF from the book’s website along with its companion files.
Dyalog manuals
can be bought from or downloaded free of charge.
A Practical Introduction to APL 1 & 2
A Practical Introduction to APL 3 & 4
Graeme Robertson has long experience with using and teaching APL. These two volumes draw on his teaching notes to produce a self-study course in Dyalog. The books cover the object-oriented features introduced in Version 11 (native support for the class-instance relationship) and how to exploit the .Net interface and work across the Internet. They were reviewed in Vector 24:2.
The J Dictionary
The J Primer
The J Dictionary
J Phrases
These three books, by Chris Burke, Roger K.W. Hui, Eric B. Iverson, Kenneth E. Iverson, Eugene E. McDonnell & Donald B. McIntyre, constitute the core reference for the J language and are available from Jsoftware.
Fractals, Visualization and J
Fractals, Visualization and J
Cliff Reiter teaches at Lafayette College in Pennsylvania; this textbook on computing and visualising fractals contains many illustrations and is now in its third edition.
Mathematical Computing in J
Mathematical Computing in J
An introduction to using J for mathematical computing, by Howard A. Peelle, available from Amazon.
More books on J at the J Wiki
q For Mortals
q For Mortals
Jeffry A. Borror’s 2008 textbook was reviewed in Vector 23:4and is available from
APL classics

Yale Idiom List
The APL Idiom List
Alan J. Perlis & Spencer Rugaber, 1977
The celebrated Yale Idiom List
A Programming Language
A Programming Language
Kenneth E. Iverson, Wiley, 1962
The companion to Brooks’ & Iverson’s classic Automatic Data Processing, now typeset in HTML by Roger Hui. Also available from the Software Preservation Group as a scan.

Inventing The PC
Inventing the PC: The MCM/70 story
Zbigniew Stachniak, 2011
In May 1973, Micro Computer Machines, a Toronto-based electronics company, gave a public demonstration of a small computer called the MCM/70. Powered by a microprocessor and operated with APL, a sophisticated programming language, the MCM/70 was positioned to be a practical, affordable, and easy-to-use personal computer - the very first of its kind.