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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 "Z" 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 "Z" 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:

"...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."

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.

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    I'm curious what others here might suggest, but my personal gut feeling is that what you're wanting to do is something that should have been done during the interview in some way, perhaps in carefully walking a tightrope by providing answers to questions and steering conversations in such a way that your mathematical background could be inferred. The reason I say "treading a tightrope" is that if it's too obvious, then you might come off as showy or as not sufficiently respecting their ability to make such a judgement for themselves. – Dave L Renfro Apr 18 at 8:27
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    My personal gut feeling is that if the professor wanted to screen for mathematical ability, they would have made sure that the interview gauged mathematical ability. And for all we know, it did! – JeffE Apr 18 at 9:15
  • Thank you for the comments. You both are right. But since the position remains open, I could give it a shot by saying that I will put in extra-work prior to the project. After all, I have got nothing to lose. Or do you have other opinions? – grandukekj Apr 18 at 10:48
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    You can give it a shot but don't get your hopes up too high! They made a decision and presumably it was one reached after some thought and consideration. It's unlikely their decision would be completely different if only they had some additional input from you (remember they could -- and likely would -- have easily asked you about anything that would be a crucial dealbreaker like a commitment to take online math courses). I'd definitely for it. You never know, something useful could come of it! But don't get your hopes up too high. – user2705196 Apr 18 at 12:58
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    It seems you are interpreting "Among all candidates you were the one with the highest scientific ambitions which really set you a part from the rest" to mean you were the best candidate (i.e., closest to getting the position). I don't think that's necessarily correct. Every other candidate could have had the highest or most something else for them to compliment. – Bryan Krause Apr 18 at 22:26
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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.

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    This is exactly right. If all you were lacking was some skill-set easily and quickly obtainable, they wouldn't have had any objection. I'd wager that the questioner severely under-estimates the "mathematical deficit" that was perceived by the interviewers. Not to mention an apparent widespread belief that "oh, I'll take a course, and then I'll be up to speed on Mathematics"... It's not that "math is hard", but that it takes some time to refine one's intuitions, and acquire vocabulary and world-view. – paul garrett Apr 18 at 22:27
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This is a rejection and you are unlikely to be admitted. Still, you have nothing to lose.

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)?

Emotional pleas about "going down the hard road" just make you sound desperate. If there is a specific weakness, you should plan to patch it regardless of this application. That said, you have nothing to lose by saying "I agree that I don't have a strong background in topology, but I'm planning to take a graduate-level course in topology this summer."

Also, should I make a case that my master's program was in fact mathematically rigorous by outlining the course syllabi and requirements?

This should have been done during the interview. Stil, you have nothing to lose by saying "I can see how you might have that impression, but my background is actually quite rigorous -- we used X, Y, and Z books and I published Q paper."

If you decide to try either or both of these, it should be in the context of a brief, 1-2 paragraph e-mail. You should acknowledge the rejection, offer this additional information, and then state that you'd still be interested in being considered for this or other positions.

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Actions speak louder than words.

It's clear from the professor's message that (s)he cannot be persuaded based on your credentials right now. What you need therefore is to actually acquire the math. Intention to acquire it isn't enough; you need to actually do it. How you acquire it is up to you, but before having acquired it, attempting to persuade the professor is probably futile.

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Don;t get focused in so much on one opportunity. You need to apply to enough postings so you get multiple acceptable admissions. And you need to recognize that even from luck you may sometimes not get one particular one. This is even more the case with job interviewing (later).

Just say thank you, that you appreciate the close call, that you remain dedicated to getting a Ph.D. and are applying elsewhere. Definitely don't suggest cming to work in some reduced position (intern or the leak). That cheapens your market value.

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What you could do is to write them a (very) positive email outlining that you would see this position as a great chance to up your math skills and that is your dream position and that you are willing to put lots of time into improving your math (already before you actually start the position) and that you have not only succeeded before in doing difficult things but you have actually thrived in them (+example(s)) and if they would give you this chance you will not disappoint them.

Changes might be slim but worth a short - let us know how it went!

--- EDIT ---

Based on the comments below "dream position" used as phrase might be a little bit over the top but your email should transport the message that it is your dream position without explicitly mentioning it.

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    Sorry. "Dream position" and similar sounds desperate. It won't help. Say you understand and are working to gain additional math sophistication. Then do that. – Buffy Apr 18 at 11:19
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    Randomly bold facing words is academia's most convincing style trick! ;-) – user2705196 Apr 18 at 11:56
  • I think this is the right thing to do, in the wrong tone of voice. – Ethan Bolker Apr 18 at 12:58
  • I would first thank them, express my disappointment, then politely ask, since the position still remaisn open, if they are willing to reconsider me if i am willing to put in extra efforts in improving my math prior to the beginning of the project, possibly by joining their lab as a research assistant/intern. Does that sound better? – grandukekj Apr 18 at 13:48
  • I honestly wouldn’t join as a lower level. I would outline a very specific plan for gaining math knowledge. Do x course on x dates, y course on y dates, etc. – Dawn Apr 18 at 18:10
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What you wrote in a comment earlier (quote below) is a solid way to show your commitment and make the decision for your possible prospective supervisor easier:

possibly by joining their lab as a research assistant/intern

Another way is for her/him to give you a trial-problem for you to solve. This way, the supervisor can gauge your ability to work with him/her and your working style (persistence, frustration tolerance, creativity, etc.).

PS: That is, you should show your earnest motivation and problem-solving skills by asking for a small trial-project for you to work on (in the lab or from home, without being paid).

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