What is the main purpose of getting a Ph.D. from an interdisciplinary doctoral school?
If someone completes a Ph.D. from an interdisciplinary doctoral school, can he work as a professor in CS/CSE?
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Yes, it is possible (in the US, at least). You need to get hired, so you need to meet the needs of a faculty position, both in teaching and research, but having an interdisciplinary degree doesn't rule that out.
Some places will be more receptive to the idea than others. Some universities value cross discipline collaboration and have, say, undergraduate programs that value cross discipline study. Applications of CS to other fields is fairly popular, though not universal.
Some large faculties have a few members who have quite diverse interests.
But, a person would likely have fewer opportunities with any degree that isn't, somehow, mainstream.
And, you also need to be able to earn tenure if you want a career. And once you do, you have the opportunity to expand diverse interests in the institution.
The interesting part about Computer Science as a field is that it has many applications to other fields. From my experience, I have seen people with doctorates in many fields become CS faculty, and vice-versa. At my undergraduate CS department, there are quite a few faculty who changed fields this way:
Getting an interdisciplinary degree can definitely open doors in this regard, but of course this will obviously depend on your specific research interests. If you're thinking of switching fields, you'll obviously want your interdisciplinary interests to kind of be related to what you are currently studying, as well as what you plan on doing in the future.
Keep in mind that this doesn't necessarily just apply to Computer Science, or necessarily even academia. My multivariable calculus professor was able to go into computational science (slightly related to CS, but not exactly the same as CS) after finishing a Chemistry PhD (they had also studied mathematics during their undergraduate). In industry, while the instinct of most undergraduates is to get a job at Google with their BS in CS, there are also people at such companies with PhD's in Chemistry, Physics, or other fields that also get jobs at such companies.