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A solid background in Math is important to those subjects because they all involve a lot of math. If you don't already know a lot of math (i.e algebra, geometry, trigonometry, calculus) then those subjects will be extremely difficult to get into and more importantly to do well in.

In physics you might have to calculate the force of an object in motion, the speed of light through a substance, or the frictional constant of a surface. All of those would require you to at least already understand varying levels of algebra. Engineering is based off of physics.

In computer programming, you will be doing a lot of explicit logical thinking and having a strong background in math will have developed such logical thinking skills. You will be asked to solve problems and to write a variety of programs and they will require you to understand math: whether your writing a program to calculate and display the slope of an equation or if your writing a program to calculate a business' taxes, you will first need to understand how to do that yourself before you can instruct the computer on how to do it.

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Q: Why does having a solid background in mathematics so important in physics as well as engineering and computer sciences as well as computer programming?
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