So, like the title says, whats the difference between "Pure" and "Applied" mathematics? I'm starting to get to the point where I might need to choose which to go into. I'm wondering both about the content of each and the uses of each.

"Pure" math typically refers to the study of mathematics in and of itself, and for it's own sake, while "applied" math often entails using mathematical methods to solve "real world" problems. One way to look at the difference is to consider the kinds of problems that each kind of mathematician might be interested in. A pure mathematician, for example, may be interested in finding out whether the Euler-Mascheroni constant is or is not an irrational number. Such a question (arguably) only holds an interest for mathematics itself, not for any kind of "real world" problem. In contrast, an applied mathematican may be interested in discovering which class of partial differential equations best models the behavior of ocean currents during a specific weather phenomena. This kind of work can be used to better understand the physical world.

Pure mathematicians generally study mathemtics exclusively, though some may work intimately in the field of computer science. They usually work for universities.

Applied mathematicians can work in many diverse fields, including physics, chemistry, engineering, sociology, economics, computer science, earth scienes, statistics, actuary, etc. They typically work in industry.

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Two functions, meromorphic in the entire complex plane, that share five values are identical. —R. Nevanlinna

Could you perhaps clarify what you mean by this, as I would have thought that the maths of computer science would be classed as Pure rather than Applied. Although it has applications, it originated as Pure.

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What about encryption?

He said "Applied mathematicians can work in many diverse fields, including ... computer science ...". Which seems to be correct.

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I would have considered encryption to come under pure maths - it a subject that uses fields, number theory and, I believe, elliptical equations. All very pure stuff.

I am not saying there is nothing of applied maths that crops up in computer science, I am merely wondering where, and also perhaps questioning its inclusion in a list of important applications for Applied maths. Although an important subject, I am unsure how much applied maths is involved in it. In retrospect, I worded my reply a little clumsily.

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