Download PDF by Jonathan M. Borwein: An Introduction to Modern Mathematical Computing: With

Counting Numeration

By Jonathan M. Borwein

ISBN-10: 1461442524

ISBN-13: 9781461442523

ISBN-10: 1461442532

ISBN-13: 9781461442530

Thirty years in the past mathematical, rather than utilized numerical, computation was once tough to accomplish and so particularly little used. 3 threads replaced that: the emergence of the private machine; the invention of fiber-optics and the ensuing improvement of the fashionable net; and the development of the 3 “M’s” Maple, Mathematica and Matlab.

We intend to cajole that Mathematica and different related instruments are worthy realizing, assuming in basic terms that one needs to be a mathematician, a arithmetic educator, a working laptop or computer scientist, an engineer or scientist, or somebody else who wishes/needs to take advantage of arithmetic higher. We additionally wish to provide an explanation for tips on how to turn into an "experimental mathematician" whereas studying to be higher at proving issues. to complete this our fabric is split into 3 major chapters by means of a postscript. those hide straightforward quantity idea, calculus of 1 and several other variables, introductory linear algebra, and visualization and interactive geometric computation.

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Extra info for An Introduction to Modern Mathematical Computing: With Mathematica®

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We currently have 3 rules for our AmicableQ function; one for a pair of positive integer arguments, one for a single argument list containing exactly two positive integers as elements, and a default rule. We close this subsection by using this function to find, again, the amicable pairs where at least one of of the pair is less than some number N . 3 the case of N = 10,000, although we computed each pair twice. What’s more, the astute reader may have noticed that our previous computation was in fact a computation of all amicable pairs where one of the pair was less than N = 10,000.

In[89]:= a ~F~ b Out[89]= F [a, b] It should hopefully be expected, in light of the both pre- and postfix notation, that any function that can take exactly two inputs may be used in infix notation. Unfortunately, our previous example is not appropriate for infix notation; it does not have any functions that take two arguments. However, we have already seen a function which lends itself very nicely to infix notation, the Join function. In[90]:= {1, 2, 3} ~Join~ {3, 4, 5} Out[90]= {1, 2, 3, 3, 4, 5} We may chain these notations together, if we wish, and the results are fairly predictable.

We start by creating a function which takes two arguments. If we stop to think about this for a minute before proceeding, we should realize that we have 4 conditions to meet. We need to make sure that both our arguments are integers, and then we need to check that each one is equal to the sum of the divisors of the other. That’s going to be a large, and unwieldy, If statement. To alleviate this, we will use patterns to make sure the arguments are integers. In[229]:= AmicableQ[n_Integer /; n > 0, m_Integer /; m > 0] := If[ (Divisors[m ] // Total) - m == n && (Divisors[n ] // Total) - n == m , True, False ] This function, however, is a query function; it ought to always return True or False.

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

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