At the simplest level, mathematics, sometimes called "pure mathematics" is the science of solving problems to obtain an answer. Applied mathematics is the science of solving problems in order to discover answers to problems outside of mathematics, such as within physics or economics.
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there is no difference between Mathematics and Arithmetic because Arithmetic is a branch of mathematics. there is no difference between Mathematics and Arithmetic because Arithmetic is a branch of mathematics.
There is simply no difference.
Algebra is a form (or subset) of mathematics.
As far as I know, there is no difference. "Math" is just short for "Mathematics".
There is no difference, they are the same.