Transition from Math Theory to Practice w/ Computing Systems

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dslowik
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In applying theoretical math knowledge we use systems like R, numpy/scipy, sage etc. These systems provide a suit of tools to solve math problems. However the 'language' can be quite different from wht we learn in our (theoretical) math courses. For example I know how to solve a system of linear equations from any standard linear algebra text, but when I go into numpy or R I am lead to the function: solve() -solve a system of linear equations. If you read far enough down into the description of this function however, you find that it really only solves systems where the LHS is given by an invertable matrix. With a name like solve and a description as given, I would think that it might provide the rank, nullity, a basis for the kernel and the image, the homogenous solution and a particular solution -that would 'solve' it.

So my question is, how (maybe what book) are people transitioning from learning math to using it within these powerful computing systems? e.g. from knowing about linear algebra to using Cholesky decomposition, QR factorization, SVD etc? Currently I am using Numerical Recipes, and google searching functions alluded to by the computer systems documentation -often a wiki page describing the technique...
 
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There are books, but the best way to learn these math softwares is to use Google. Search with what you want to do (in layman terms) and mention the software. This is the way I am learning Matlab.

Another good option is to keep an eye on forums regarding the softwares. I learned a lot from the Math software forum in PF. Often you will find quests on functions that you don't know. Search Google and read the documentation. That's how you learn.