By Jonathan M. Borwein

ISBN-10: 1461442524

ISBN-13: 9781461442523

ISBN-10: 1461442532

ISBN-13: 9781461442530

Thirty years in the past mathematical, in preference to utilized numerical, computation was once tricky to accomplish and so particularly little used. 3 threads replaced that: the emergence of the non-public computing device; the invention of fiber-optics and the resultant improvement of the fashionable web; and the construction of the 3 “M’s” Maple, Mathematica and Matlab.

We intend to cajole that Mathematica and different comparable instruments are worthy understanding, assuming basically that one needs to be a mathematician, a arithmetic educator, a working laptop or computer scientist, an engineer or scientist, or someone else who wishes/needs to exploit arithmetic higher. We additionally wish to give an explanation for the best way to turn into an "experimental mathematician" whereas studying to be larger at proving issues. to complete this our fabric is split into 3 major chapters via a postscript. those conceal trouble-free quantity thought, calculus of 1 and a number of other variables, introductory linear algebra, and visualization and interactive geometric computation.

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64493 The computation took approximately three seconds on the author’s computer. Note that in order to use the N function, we could not use the variable N as the argument to our function. Instead we used n . It might be tempting to view the above numerical computation with some contempt. Decimal approximations are just that, approximations. Worse still, the above computation is adding approximations to approximations at every step, and doing it a million times. What’s more, we are using a CAS, the whole point of which is to allow the computer to perform exact symbolic calculations.

We want an answer in either case, so we need to use the optional third argument to the If function. First we must find the proper divisors and add them. In[188]:= With[{n = 6}, (Divisors[n] // Total) - n ] Out[188]= 6 Note that we only wanted to sum the proper divisors, but the Total command we used will sum every divisor, so we needed to subtract out n to compensate for this unwanted addition. We can clearly see that 6 is perfect (which we already knew). 30 1 Number Theory Despite the fact that we already know the answer, we will have Mathematica compute whether 6 is perfect, using the If function.

The first argument to the If function is a criterion for the expression that is the second argument to be carried out. If the criterion is met, the expression is evaluated, and if the criterion is not met, the expression is not evaluated. Note that in some cases (which we look at later), we may add an additional expression as a third argument, which will be carried out in the case that the criterion is not met. For the moment, let’s look at an example with a single piece of code that does not execute In[170]:= If[6 ~Mod~ 4 == 0, 6 / 3] Of course, we don’t want to have to type all of these in individually, so we now incorporate these decisions into our loop.

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An Introduction to Modern Mathematical Computing: With Mathematica® by Jonathan M. Borwein

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