How do I convince professors that I have enough math for the PhD position? It has been a month since I received the rejection email. I gave it a long thought for a month, about whether to pursue another try at the position, while applying for other PhD and job opportunities. I would still like to give it a shot, and the following email is what I am about to send. Please let me know if it sounds okay :) I took out the part pleading for a lower position (i.e. research assistant), as some comments pointed out that it sounded too desperate.

Dear Prof. A,
Despite my big disappointment about the decision, I would still like to thank you for taking your time to consider my candidacy and getting back to me with the result.
It took me some time to get back to you, because I just could not get over how much I find this project ideal for my research interests.  Hence, after a long thought, I decided to make my last attempt in convincing you to reconsider my candidacy for the position.
While I acknowledge that the &quot;Z&quot; project is a challenge, I also see it as a great opportunity to hone my mathematical training. I have proven records of success in facing such a challenge: I did not have solid mathematical or programming background for the Y master program. However, I put in a lot of efforts both prior to and during the program to thrive in mathematically rigorous courseworks (on my own and with the help of a mathematics professor affiliated with the Y program, Prof. X) and successfully completed a computational modelling project for my thesis. I am more than willing to do the same for the &quot;Z&quot; project, and I feel confident from the previous academic experience that I will not disappoint you if given a chance.
You could also provide me a test problem/project, with which you can gauge my abilities to work on the project.
In case you decide not to reconsider my candidacy, I would like to thank you anyways for the consideration and the close call again. I will remain dedicated to obtaining a PhD degree in the field of decision making under uncertainty and hope to meet you some day in a conference.

Below is the rejection email I've got last month:

&quot;...Unfortunately, I can not bring you good news. Among all candidates you were the one with the highest scientific ambitions which really set you a part from the rest. However, our concern remained that your mathematical training is not enough for the specific problem that is subject of this position. We wish you all the best and especially that you keep up your inspiring passion for science...
P.S. If that helps you somehow: We finally concluded that none of the other available candidates fulfilled all necessary requirements and hence the position remains open.&quot;

This was my initial reaction to the rejection email:

I really want to work on this project! Is it a good idea to tell them that I am willing to go down the hard road? (e.g. taking online math courses or working as an intern/assistant at their lab before the PhD studies to meet the mathematical requirements for the position)? Also, should I make a case that my master's program was in fact mathematically rigorous by outlining the course syllabi and requirements? I have already sent them a transcript for this purpose, but I feel that listing only course names and grades do not really tell them much about what kind of and how rigorous math I worked with.
Thanks for adding the text of the message you received.  The text makes it clear that this is a rejection, and it should be understood as final.  There is no point in following up to try to convince the professor that you should get the position; it will only annoy them.

The best thing you can do with this information is to improve your applications for other positions in the future.  It suggests that you need to improve your mathematics background if applying for positions like this one, and/or to review your application materials to make sure that they clearly demonstrate your preparation.