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Background

I graduated with a BS in math about a year and a half ago from a not well known school and with a less than stellar academic record. I did not go to graduate school (I was not accepted). Since then, I have improved my mathematical ability considerably, but I have not kept in touch with my professors. I can demonstrate this improvement in many ways, the most obvious of which is by referring to my subject GRE score.

Given that I was a mediocre student, I assume that my professors' letters of recommendation did not paint me in as positive of a light as they would have if they knew me now.

I am now interested in applying to graduate school again but this time I would like to secure stronger letters of recommendation.

Question

Is it appropriate to ask a professor the following question:

"Is there any way I can demonstrate my current mathematical ability and thereby improve your letter of recommendation for me?"

If so, how should I ask this question?

Further Considerations

If the answer to the above question is "Yes", then for at least two of the professors, I can suggest showing them my typed solutions to every question (save the trivial ones) in the textbook used for their class. These classes were both upper level classes (second level Linear Algebra and second level Real Analysis). With the last professor, I can demonstrate knowledge of Calculus of Variations (a subject that this professor is interested in) as well as Functional Analysis. Should this be my approach?

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    If possible, you might want to publish some papers :) Considering the conditions you are under, this seems to be more effective way for your application. – Benicio Sep 12 '14 at 3:15
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    You can certainly publish without support, but it would require that you first do some original research, which is very rarely possible for undergraduates without very direct guidance to find a suitable open question. – Tobias Kildetoft Sep 12 '14 at 6:42
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    Is doing a smallish research project (e.g., over the summer) with one of those professors an option? This would help you on the paper front as well as with LoRs. – xLeitix Sep 12 '14 at 15:00
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    @xLeitix I am in the (strange) position that I was given an open research problem about 3 years ago but due to my negligence i produced no results on it. After graduating, however, I made significant progress on it but the professor does not know this and I am somewhat hesitant to show him the results because of my earlier lackadaisical efforts. – illysial Sep 12 '14 at 16:07
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    @illysial That shouldn't make you hesitant - any bad blood from those early efforts will likely be washed away when he discovers you've continued to work on it. – OJFord Sep 13 '14 at 19:23
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I think it is okay to ask the question. However, I do not think you should suggest that professors read your solutions since they are likely very busy.

You may do better to tell the professors what you have been working on, including your GRE score, and then ask them if there is anything else you can do to prepare yourself for graduate school. Then follow their suggestions. Essentially it is the same question, but I think it could show you are a "deep learner" rather than a "strategic learner" who only cares about the letter.

6

You're thinking about the problem a little bit sideways, as do many students.

First, when you originally request a letter of recommendation, ask the person your asking to support you if they can write you a strong letter. If they say no, they can write you a letter but they're not in a position to write a strong one, you can either move on to the next person (if there is one), or have a very mature conversation where you ask what's the best portrayal you can get. For example, if you feel like there's a hole in your application portfolio that this person can help fill, ask about it. Sometimes, if a student with average grade performance is a stand out in terms of writing, communication, leadership, I can focus on that and come out with an OK letter.

Now, to new recommendations from your original references: If your original recommenders have had no interactions with you that would change their opinion, its probably already too late to get a better recommendation. If there's something about your overall package that would change your likelihood to be admitted to a grad program, then you should be able to dig up a new reference to support your application. Your personal statement should be carefully crafted, stating very clearly what's changed about your situation, why you're a better candidate than you were originally, and some evidence to support it that an admissions committee can understand. A recommendation involving a recent interaction from a new person would be extremely helpful.

For what its worth, the admissions committee will be very interested in how you've spent your time since your BS. They might expect you to be showing maturity not typical of recent graduates. If you can show a solid understanding of why you are now seeking a graduate degree and how you expect it to impact your career in your application package, that will prove very helpful. If you've been twiddling your thumbs since you graduated, and that's apparent in your package, that will not go over very well. If that's the case, you might consider delaying your application until you can make your application package look right, and spend six months working very hard just to develop those good recommendations.

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