It would be advisable to avoid computer engineering/science for people who really hate math. The education required for computer engineering requires a lot of high level math, and chances are that a lot of sophisticated math skills are required for use on a daily basis even after getting a job in the field.
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Not really. Science Engineering deals basically with Math subjects. Therefore, if you're good in Math, you'll do good in Science Engineering.
Well if you are really good at math you could be a mathematician.
You don't really need much computer programming for most engineering courses - except those where you specifically concentrate on computer science. And I don't see any reason why you should fail at OTHER, unrelated, subjects, just because you are bad at writing code. Finally, I think you shouldn't be afraid of writing code - you can still learn it.
Basically anything related to engineering or science - except computer-related subjects. Engineering majors are those that have the name "engineering" in their names, and a few who don't - such as economy and architecture. You probably shouldn't be afraid of programming; if you are good at math, you should be able to learn that, as well. At least the basic subjects which you are likely to encounter in any engineering course. Also, you'll need SOME writing skills for ANY higher-level career; once again, there is really no reason to be afraid of it. While you might not get a prize for your writing style, you should still be able to write simple reports on your work, for example.
It really depends on fields. In my view the 3 most important math fields that are important in computer science are: Discrete maths - Set theory, logic, combinatorics Number theory - Vital in cryptography and security. Geometry and Matrices - Game theory etc.