APL Programs for the Mathematics Classroom by Norman D. Thomson

By Norman D. Thomson

The proposal for this e-book grew out of proposals on the APL86 con­ ference in Manchester which ended in the initiation of the I-APL (International APL) venture, and during it to the provision of an interpreter which might deliver the benefits of APL in the technique of large numbers of college childrens and their academics. the inducement is that when tuition lecturers have glimpsed the chances, there'll be a spot for an "ideas" e-book of brief courses so that it will let valuable algorithms to be introduced quickly into school room use, and even perhaps to be written and built in entrance of the category. A test of the contents will express how the conciseness of APL makes it attainable to handle a tremendous variety of issues in a small variety of pages. there's clearly a level of idiosyncrasy within the number of issues - the choice i've got made displays algo­ rithms that have both proved valuable in genuine paintings, or that have stuck my mind's eye as applicants for demonstrating the price of APL as a mathematical notation. the place acceptable, notes at the courses are meant to teach the naturalness with which APL bargains with the maths involved, and to estab­ lish that APL isn't, as is frequently intended, an unreadable lan­ guage written in a extraordinary personality set.

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V RPT;I;J [1J [2J [3J [4J [5J [6J [7J I+10 L1:+0 IF 31

I) Define T+-15 PIB Oland compare (2-1-T) x-2-1-T with l-1--1-1-T*2. (ii) Define T+-30 PIB 1 1 and compare T[M] HCP T[N] and T[M HCP N] for pairs of integers M and N between 1 and 30. (iii) Define T+-60 PIB 1 1 and investigate T[N] I T[Nx 1 L60+N] for values of N in the range 3 to 10. Describe the property of the Fibonacci series which this shows. (iv) What is the result of (N PIB 0 1)+. xPAS N-l for an appropriate small integer value of N ? 7. Series relating to pi In each case R is the number of terms, and the function defines a series which converges to n.

2 t Z to print the ratios of successive terms. 625 O i l 2 3 5 8 13 A recursive function to output the terms of the series is FIB1 : R FIB1 R+D+L where Land Rare U o and Ul respectively. g. Adding a stopping 4. Series 47 PIB2 : R PIB2 R+O+L: L~1000 : L I. (i) Define T+-15 PIB Oland compare (2-1-T) x-2-1-T with l-1--1-1-T*2. (ii) Define T+-30 PIB 1 1 and compare T[M] HCP T[N] and T[M HCP N] for pairs of integers M and N between 1 and 30. (iii) Define T+-60 PIB 1 1 and investigate T[N] I T[Nx 1 L60+N] for values of N in the range 3 to 10.

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