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I am currently an undergraduate student studying in an area of mathematics and am planning to apply to do a masters research degree next year. I have been doing research with my supervisor who works in some topic say X and will be doing more research throughout the remainder of the year with him.

I am still very interested in topic X and consider this a large option for my masters, however, I have greater interests in another topic say Y. There is another university in our country that has a specialist research group in topic Y. I am looking into changing to this alternative university to study topic Y for my masters, however, I have had no conversations about my future research with people at either university.

Would it be considered rude for me to leave my supervisor now, who currently offers me a lot of support during my undergraduate, to pursue research in this other area of mathematics solely because I am more interested in this alternative topic? And what would be the correct way to go about this without burning any bridges with my current supervisor?

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If Y is what you really want to do then go for it. There is no point in going down a career path just to please someone else.

Talk in person to your current supervisor once you have a written offer from the university that does Y. Explain to him that it is your dream to do Y and you hope to keep in contact with him even though you are leaving the university.

A good supervisor will understand - if not then he was not a good supervisor anyway. It's a win-win for you.

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If you have spent the time to earn a degree somewhere and have interacted with the faculty there who are closest to your interests, then it is actually a good thing to move on to another university for continued education. Don't get too comfortable early on.

You have learned a lot from a few people, but other people have different ways to think and it is good to get exposed to that early in your career.

Many, maybe most, faculty understand this. Especially undergraduate faculty. I always thought it was best if my best students left me behind and found inspiration elsewhere. My view is that it is much better if my students can surpass me than if they wind up just like me.

So, don't worry much about rudeness as much as you worry about maximizing your own opportunities. Thank your professor for all that s/he has done for you and for making it possible for you to move on. In a few years, return and thank them again and bring them up to date on your success.

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A good advisor will tell you to explore the new areas and make new connections, even if that means you will be leaving them. Both my MS and PhD advisors told me to go to different institutions whenever my degree was completed, but still kept their labs open in case I don't feel like doing that. Therefore, as a result I have my BS, MS, and PhD from three different institutions. And I believe that attending different institutions, meeting different people, learning and embracing their different operating styles, prepared me much better for job hunting and future career.

If your supervisor is understanding, he will put your interests and career ahead of his comfort of not finding another student. However, you have mentioned that you haven't talked about this to any of the people yet (current or future potential supervisor). I would talk to your future potential supervisor if s/he is interested in supervising you before you talk to your current supervisor about leaving. You don't want to be standing in two boats with one foot in each, because if the boats drift apart, you could fall in the lake. Once you have a confirmation from your potential future advisor then you can talk to your current supervisor, and if he is understanding, then he will understand and will let you go without burning the bridge.

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