well, you gotta know physics and good communication skills because engineers work in groups on projects.
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That should be rather obvious as these people seem to speak in math. Computer science to theoretical mathematics.
yeah
Yes
All of those topics are very heavy in math. If you have a good math background and are very good at math, these topics will be easier for you to understand them.
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.