Good majors could be biology, psychology, social sciences, or maybe oceanography. In these majors, you have a good opportunity to branch out. Hope this helps!
Software programming is a good thing to study. Software programming pays good money.
Yes, math is more closely applicable to physics, chemistry, and engineering, than biology and programming are.
Most careers in engineering fit that description - except for computer engineering. In any case, if you are good at math, you really shouldn't have much trouble in programming, since it involves - not exactly math, but similar abstract thinking.
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Not so sure about economics but you will need physics.
There are several, two of them already listed in your question, engineering, definitely not programming, and more.
Just about any engineering course that's not specialized in computers. You might want to try your hand at computer programming anyway; you'll probably need SOME computer programming.
Math, physics, astronomy, architecture, actuarial science, statistics, possibly genetics.
Most university majors will require you to write essays regardless, but there are some majors that don't emphasize a lot of writing: Economics Math Engineering Science(except biology and some fields of chemistry)
Science, especially physics; any engineering discipline; architecture; economics and finance; computer programming; statistics...
Math, Engineering and the Hard Sciences(except biology lol), however, regardless of the major, you have to be good at some level of writing.