Read e-book online 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, rather than utilized numerical, computation used to be tough to accomplish and so particularly little used. 3 threads replaced that: the emergence of the private computing device; the invention of fiber-optics and the resultant improvement of the trendy web; and the construction of the 3 “M’s” Maple, Mathematica and Matlab.

We intend to cajole that Mathematica and different related instruments are worthy understanding, assuming simply 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 greater. We additionally desire to provide an explanation for how you can turn 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 conceal common quantity idea, calculus of 1 and several other variables, introductory linear algebra, and visualization and interactive geometric computation.

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New PDF release: An Introduction to Modern Mathematical Computing: With

Thirty years in the past mathematical, in place of utilized numerical, computation was once tricky to accomplish and so rather little used. 3 threads replaced that: the emergence of the non-public desktop; the invention of fiber-optics and the resultant improvement of the trendy net; and the development of the 3 “M’s” Maple, Mathematica and Matlab.

Additional resources for An Introduction to Modern Mathematical Computing: With Mathematica®

Example text

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. In[170]:= With[{n = 6}, Do[ If[n ~Mod~ a == 0, n / a // Print], {a, 1, n} ] ] Out[170]= 6 Out[171]= 3 Out[172]= 2 Out[173]= 1 In fact, it is usually quite rare that we use a decision manually when using Mathematica, where we can make these decisions for ourselves.

This isn’t really telling us very much, but we have digressed somewhat, so we do not explore this avenue any further. Getting back to the topic of large partial sums being computed quickly, we might be tempted to conclude that computer technology is just so fast nowadays that such a performance is simply to be expected. Unfortunately, this is not true. For instance, if we try to compute the 1,000,000th partial sum, we find it to be surprisingly slow. In[152]:= par[10ˆ6] // N Out[152]= $Aborted The author stopped the computation after approximately thirty to sixty seconds had elapsed.

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. For instance both a // F // G and G @ F @ a are equivalent to G[F[a]]. However, the effect of chaining infix notations together is not immediately obvious. Observe the following. In[91]:= {1, 2, 3} ~Join~ {3, 4, 5} ~Join~ {5, 6, 7} Out[91]= {1, 2, 3, 3, 4, 5, 5, 6, 7} We have produced exactly the same output, as if we had issued the command Join[{1, 2, 3}, {3, 4, 5}, {5, 6, 7}].

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


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