Mathematics involves adding, subtracting, multiplying, and dividing. It also involves using Inductive and Deductive Reasoning, Trigonometry, Radicals, Statistical Reasoning, etc.. Whoever has not tried it has something wrong with them. Try out math. It is really fun.
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In mathematics, a coefficient is a multiplicative factor in some term of an expression (or of a series); it is usually a number, but in any case does not involve any variables of the expression.
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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.
Only a person who does not understand mathematics is disadvantaged. Mathematics in itself has no disadvantages.
Depending on what type of science, yes mathematics can be science. Like if you're doing physics that can be mathematics.