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My friend is studying a subject called 'Numerical Mathematics and Computer Algorithms'. Surely mathematics is all about 'Numbers', so is ''Numerical Mathematics' a redundant statement?

Please excuse my ignorance.

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And computers are all about algorithms, no? –  FumbleFingers Aug 5 '11 at 3:25
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Whether maths is intrinsically "necessarily about numbers" is something you could debate. You could probably argue that topology and group theory are still "about numbers" in some loose sense. But I think they're basically saying "Numerical algorithms" in a long-winded way. And there are definitely Non-numerical algorithms (as well as what we might call "Semi-numerical" algorithms). –  Neil Coffey Aug 5 '11 at 5:30
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@Neil: I would say that only a small part of math deals with numbers, and certainly wouldn't consider either topology or algebra (group theory, field theory, etc.) as being about numbers at all. There are applications of, say, group theory to numbers -- algebraic number theory, for example -- but that doesn't make group theory itself about them. –  Charles Aug 5 '11 at 8:52
    
When I got to university I found out that maths with numbers was called physics. –  Optimal Cynic Nov 17 '11 at 14:25
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2 Answers

As @Charles said in a comment above:

I would say that only a small part of math deals with numbers, and certainly wouldn't consider either topology or algebra (group theory, field theory, etc.) as being about numbers at all. There are applications of, say, group theory to numbers -- algebraic number theory, for example -- but that doesn't make group theory itself about them.

So the term is not redundant. Specifically, the term refers to a specific field of mathematics:

Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions.

A more concise definition is:

n:

(Mathematics) a branch of mathematics concerned with methods, usually iterative, for obtaining solutions to problems by means of a computer

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Right. It's actually a fairly specialized branch of math -- not nearly all of math as a nonmathematician might guess. Closely related is numerical analysis which ensures that the answers returned are as precise as possible. –  Charles Aug 5 '11 at 8:15
    
@Bogdan I apologize for the incorrect wording. I edited -- is it a better answer now? –  simchona Aug 7 '11 at 3:15
    
@Bogdan Thank you for the constructive comments. –  simchona Aug 7 '11 at 3:18
    
I think that's an example that there is no "best answer", but all the answers and the comments contributed partly to one answer. –  Theta30 Aug 7 '11 at 3:23
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You should probably read it as Numerical Methods or Computational Mathematics.

But lots of mathematics isn't about numbers, topology, group theory, set theory - numbers (and number theory) is a small part of pure maths, although a big part of applied maths.

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