APL Programs for the Mathematics Classroom by Norman D. Thomson

By Norman D. Thomson

The concept for this publication grew out of proposals on the APL86 con­ ference in Manchester which ended in the initiation of the I-APL (International APL) undertaking, and during it to the supply of an interpreter which might convey some great benefits of APL in the technique of monstrous numbers of faculty youngsters and their academics. the inducement is that after institution academics have glimpsed the chances, there'll be a spot for an "ideas" e-book of brief courses in order to let important 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 exhibit how the conciseness of APL makes it attainable to deal with a massive variety of subject matters in a small variety of pages. there's obviously a level of idiosyncrasy within the number of themes - the choice i've got made displays algo­ rithms that have both proved invaluable 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 applicable, notes at the courses are meant to teach the naturalness with which APL bargains with the math involved, and to estab­ lish that APL isn't, as is frequently meant, an unreadable lan­ guage written in a weird and wonderful personality set.

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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. Describe the property of the Fibonacci series which this shows.

5. 1R[3J-1 R : initial value (a), difference (d), no of terms (n) and its sum is +/AP. Example: AP 1 2 6 1 3 5 7 9 11 +/AP 1 2 6 36 The formula for a geometric progression has the same structure, and differs only in the arithmetical functions involved: R : initial value (a), ratio (r), no of terms (n) APL Programs for the Mathematics Classroom 34 and its sum is +/GP . Example: GP 1 2 6 1 2 4 8 16 32 +/GP 1 2 6 63 I. 6. Sets A set is conveniently modelled as a vector (numeric or character) with no repeated elements.

3. Convergence The 1 function is valuable in helping to judge whether an infinite series is or is not convergent. The general principle is to define T+-125 say, and then do a + scan on an expression which defines the series. T +\+TxT+l ( ( ( ( Un Un Un Un l/n ) 1/n 2 ) l/n! ) l/n(n + 1) ) 4. Series 43 +\(fT)+-l*T ( +\fl-1-eT (Un = Un = (ljn)+(-I)n Ijin n ) ) Applying the DRAW function (see Appendix 1) with T as x-axis then gives a vivid realisation of the behaviour of the series. , 1:1jn 2 , and 1:1jn(n+ 1).

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