How to email a professor requesting to supervise a PhD thesis?
I don't think you need to send a &quot;learning roadmap&quot; or solved exercises. A learning roadmap doesn't really convey whether you have learned the subject. The University of Luxembourg requires that you have a masters degree before you start your PhD. If you have a masters in math, then you've probably solved a few exercises in the process.
Having ideas for future research projects is a very good thing, especially if they are ideas relating to the work of a potential advisor. My advice is to keep the initial email short and to the point -- you can add more details once you get a response. Something like:
&quot;Dear Prof. [So and So],
I am interested in applying for a PhD position at the University of Luxembourg. I obtained my Masters from [the Institute of Such and Such]. I would be interested in working on a project relating to your work on [informal group laws]. I have a few ideas for potential projects in this direction. Please let me know if you would be willing to discuss these.
Thank you in advance for your time,
user454229&quot;
Of course, don't just copy this and insert the relevant details. You want to write the email in your own voice. This is just to give you an idea of how to keep it short and to the point. And good luck!