What does "Mathematics of Computation" mean? I visited this link: http://www.ams.org/journals/mcom/1950-04-030/S0025-5718-50-99474-9/
And I a bit confused by its title "Mathematics of Computation".

I am not a native English speaker. Could anyone tell me what does this phrase really mean? What's the difference of:


*

*Mathematics

*Calculus

*Computation


And how could Mathematics be used together with Computation?
I think this could help me get a more deep understanding about What math is. Thanks.
 A: It seems to me that this journal deals with computational mathematics and numerical methods. We're talking about applied mathematics in the realm of computation. Computation in this sense means calculating something. It does not necessarily imply that we are using a modern, transistor based PC, but that is often related. 
Mathematics is a rather exact subject, but when it comes to actually computing numerical values, we are faced with challenges. As humans, our solution is to develop tools: stone tablets, the abacus, pencil and paper, the slide rule, the pocket calculator, the computer. These tools have advantages and disadvantages. 
Modern PCs are incredibly fast computers, but there are limitations. Take speed for instance. We're always striving for more powerful technology, but part of that research lies in the optimization of preexisting algorithms. For instance, you may be aware that matrices and computer graphics are intimately connected. Image processing and graphics rendering, to my knowledge, boils down to linear algebra. Even a basic operation such as matrix multiplication can turn into a burdensome task for a computer when matrix dimensions grow ever larger. To overcome these limitations, we develop more efficient algorithms. 
Another limitation is in the finite nature of computing calculations. How do we perform, say, integration when non-exact values and non-closed form problems are involved? Or forget that, how do we handle continuous real variables? We might, for example, employ finite difference methods. Most non-linear systems of differential equations rely on such methods. 
More often than not, we have to sacrifice numerical accuracy for practicality. Anyone who's used $\pi \approx 3.14$ is guilty of this! When employing numerical methods, we often are forced to accept that exact values are pipe dreams. I say this without even broaching the subject of floating point error...

... which would bridge us towards computer science. Anyway, the subject of computational mathematics can also deal with addressing these deficiencies. 
These are the sorts of maths that journal likely explores, both in a theoretical and applied sense.
A: *

*What is $42\times 31$?

*Why should $\underbrace{42+\cdots+42}_\text{31 terms}\vphantom{\dfrac\int{\displaystyle\int}}$ be the same as $\underbrace{31+\cdots+31}_\text{42 terms}$, and similarly for other pairs of numbers than $42$ and $31$?

*How efficiently can one calculate things like $42\times31$?


The first item above is a problem of computation.
The second is a problem of mathematics.
The third is a problem in the mathematics of computation.
