Engineering is an applied science that is heavily involved with mathematics. Every discipline of engineering (chemical, mechanical, structural, electrical, computer, etc.) uses a vast amount of mathematics ranging from algebra to Laplace Transforms to define, explain and understand the problems that arise with its area of expertise. Many other fields of pure science use mathematics beyond engineering but the aim of engineering is to apply mathematics to real world problems.
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Structural engineering uses a tremendous amount of math.
Possibly. You also have to be good at and enjoy engineering concepts which do involve math.
Math and physics are extremely important for an aerospace engineer. The first 3 levels of calculus are a basis. Any university engineering program will be heavily loaded with math and math related courses.
Of course not. Certainly, you won't be bad at physics or engineering BECAUSE OF your math skills. You NEED math for physics, and both math and physics for engineering, so somebody who is not good at math is more likely to have trouble with physics or engineering.
Other than math subjects, such as geometry, algebra, calculus, etc., math is important in science, especially computer sciences, physics, and engineering. You may also be good at economics, business, and accounting. Music is also math-related, actually, and graphic design can be very math intensive. Architecture is also a good option.