Jonathan M. Borwein's An Introduction to Modern Mathematical Computing: With PDF

By Jonathan M. Borwein

ISBN-10: 1461442524

ISBN-13: 9781461442523

ISBN-10: 1461442532

ISBN-13: 9781461442530

Thirty years in the past mathematical, in place of utilized numerical, computation was once tricky to accomplish and so fairly little used. 3 threads replaced that: the emergence of the private computing device; the invention of fiber-optics and the ensuing improvement of the trendy web; and the development of the 3 “M’s” Maple, Mathematica and Matlab.

We intend to cajole that Mathematica and different comparable instruments are worthy figuring out, assuming basically that one needs to be a mathematician, a arithmetic educator, a working laptop or computer scientist, an engineer or scientist, or an individual else who wishes/needs to take advantage of arithmetic larger. We additionally wish to provide an explanation for tips on how to develop into an "experimental mathematician" whereas studying to be larger at proving issues. to complete this our fabric is split into 3 major chapters by means of a postscript. those disguise basic quantity thought, calculus of 1 and a number of other variables, introductory linear algebra, and visualization and interactive geometric computation.

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Example text

In[160]:= 3 ~Mod~ 4 9 ~Mod~ 7 10 ~Mod~ 5 Out[160]= 3 Out[161]= 2 Out[162]= 0 Returning to the question of finding the divisors of a number, we start with a straightforward approach. Given our number n, whatever it happens to be, we recognize that no number bigger than n can possibly be a divisor of n, so we check every single number a less than n and see if a|n. This is just the thing for which a loop would be good. We’ll start small with n = 6 In[163]:= With[{n = 6}, Do[ Print[n / a], {a, 1, n} ] ] Out[163]= 6 Out[164]= 3 Out[165]= 2 3 2 6 Out[167]= 5 Out[168]= 1 Out[166]= The With function allows us to temporarily set some variables for the purpose of a computation; in this case we set n = 6.

The second problem is that the L variable should only be temporary, yet in the above case it is not. This is the reason for the empty output, as the Cases function has tried to extract elements from a variable with no value, and finding no elements which matches the pattern, promptly returns to us an empty list. The solution to both of these problems is the same; we must use either the Block or With function. In general, the only mechanism Mathematica provides us for computing compound expressions as part of a function is for that compound expression to be an argument to a function.

This means losing the pattern, although we shall make use of it again when it is more appropriate to the desired actions of a function. Instead, we will use the IntegerQ function as part of our computation, as this should ensure that our function behaves similarly. 5] IntegerQ[x] IntegerQ[{6, 10, 28}] Out[220]= True Out[221]= False Out[222]= True Out[223]= False Out[224]= False Out[225]= False Out[226]= False One advantage of having this function as a function is that it greatly simplifies our code to compute perfect numbers less than N .

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


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