Dissertation topic in one field and degree in another field?

Question

Feeing kind of stuck here. I started out as a math PhD student then switched to engineering. I thought by doing so I would be able to learn new skills and expertise in that particular field. But I quickly realized my advisor had a side interest in a math-ish field that is tangentially related to his main area (maybe that’s THE reason I was hired in the first place) but obviously his knowledge is limited in this new field.

Somehow I managed to publish 3 papers in engineering/applied math journals (by fluke? I thinkso) but since everything I know about this field is self-taught I don’t feel confident in my knowledge. I don’t know enough math to become a mathematician nor can I claim expertise in this engineering field I am supposedly in and time is running out.

My biggest fear is actually that the committee members are going to think I have been doodling around doing some unrelated math stuff and reject my dissertation (does this happen? My advisor doesn’t seem worried about this possibility at all). What are my options here really? I suppose if I manage to graduate I will just get a regular job outside of academia, but I do want my degree as I have been here for too long.

Answer 1

You write that you do not feel confident in your knowledge. However, experts in your field have put your knowledge to the test, and deemed it worthy of publication in a journal. Not once, not twice, but three times. Trust those experts. If they think your knowledge is good enough for three journal publications, then the committee members are highly likely to think similarly positively about your dissertation.

A solid background in mathematics is fertile ground for an exceptional career in any engineering discipline. If you stop worrying about the limitations of your knowledge, and instead accept that everyone's knowledge is by definition limited, you have a bright future ahead of you.

Answer 2

Feeling nervous when you are approaching your thesis defense is the normal situation. If you were not nervous I would be surprised.

The chances of getting rejected outright are very small. By the time you get to your defense, it looks bad on everybody if you fail. Your school, your prof, your dean of admissions, all look bad for letting you go this far and not finish.

The very worst that happens is that you get told you must do some more work. That might delay your graduating by six months or something. And that is not usual, especially when you have three publications related to your thesis.

How many previous PhDs has your prof graduated? Your chance of getting rejected should be a lot less if your prof has several already graduated. It means that the "halls of academe" have been successfully navigated before. If you are not comfortable talking to your prof about such issues, you should be able to find out from your university. Many departments have collections of previous PhD theses available for you to look at. See if you can find some of the previous ones your prof supervised.

That might also tell you if you are in a line of research your prof has gone down before. Basically, that has two sides. If it's a familiar territory, you are less likely to get lost, but you are expected to put up something prettier. In brand new territory, you get a lot of credit for innovation even if it's ugly.

My prof gave me a "pep talk" just before my defense. Literally in the hallway outside the room, just before the oral. He said to remember that I had three publications. That I had done a lot of good work on the thesis and on the prep for the defense. That the committee had already seen the thesis and they had not reacted badly. Then he gave a strategy for answering questions. He said, listen to the entire question. Then give the simplest possible answer and look at the person expectantly. If they want more they will tell you.

Take heart.