if you want to get a good job, you need to be an expert in maths and science. if you want to have a good job, you might work in numbers which is math, and you might have to know science stuff like nitrogen or titanium. mostly you are going to be working with science.
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Mathematics is the toolbox of science.
Yes mathematics are the tools of science
Giving the IIT exam is a suitable option as it has both engineering and science.
Mr.carl f gauss toldmaths is queen of science and theory of numbers is queen of maths
Mathematics is the medium language with definite instructive explaining how thing related or worked in science. Early learning in science (say primary school) might need a lot of memorizing and little calculation. At the higher end, it will be less memorizing and more to understanding of how thing work or relate. It is when Maths become the major part of science.