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Pure Mathematics is the branch of mathematics that deals only with mathematics and how it works - it is the HOW of mathematics. It is abstracted from the real world and provides the "tool box" of mathematics; it includes things like calculus.

Applied mathematics is the branch of mathematics which applies the techniques of Pure Mathematics to the real world - it is the WHERE of mathematics; it includes things like mechanics.

Pure Mathematics teaches you HOW to integrate, Applied mathematics teaches you WHERE to use integration.

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Q: What is pure math?
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Pure math is done as a kind of art, similar to music, without any concern about how the results may apply to science or daily life. The major concern is how the results improve on other math. Pure math is only concerned with improving upon itself. Pure Mathematicians are master in Mathematics. Applied math relates to other things. It is math used to help advance science, engineering, or other fields that are not related to just math. Applied mathematicians are well equiped in every related branches of science where mathematics is used thus they are "jack of all trades but master of none".


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