What would be the opportunity cost of just majoring in general engineering versus a specific type?which one do you think is better?
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Agree with Alex. Very few jobs are geared towards general engineers and the engineer with the more specific degree will beat out the general engineer. It is practically impossible to roll the vast amount of topics under the title of "engineer" into one major. There are such a variety of subjects relating to engineering that one degree could not even begin to cover it. You would gain a shallow knowledge of many subjects but not enough depth to get a good job without further education. Definitely do a specific degree.
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I am a general engineer major. It really depends on the school. I have noticed that general engineering is less intense than the specific engineering majors. It also gives you some time to try other classes so you could switch if you wanted. However, if you graduate with a degree in general engineering and apply for a mechanical or other specific type job, it is likely that an actual mechanical engineer will beat you out of the job.
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A specific one. I can't really think of any benefits to general engineering. My university didn't even offer it as a major.