I have not enjoyed my undergraduate math program, primarily because it is not challenging enough - not enough advanced courses offered, too few research opportunities, classes are just not at the level I feel they should be for junior-senior math majors. I am choosing to apply to grad schools (pure math) which I know have elite and challenging programs. I do not want to spend 5 years repeating this undergraduate experience. In the statement of purpose one is asked to explain why they are applying to the particular program. Should I mention this desire to have a more challenging, competitive environment, as compared to the undergraduate program, as a reason? I do have other substantial things I will write about, but I'm wondering if I should also mention this, as it is one of the main motivations I have for applying to the programs I am applying to.


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    It's possible that too much emphasis on not having advanced courses or research opportunities, and desiring "a challenging, competitive environment" will backfire by making it seem as if you can only learn when being supported and pushed externally, which may be taken as evidence of poor future research potential. If I were reading your application, I would wonder why you didn't just work through several advanced texts obtained from the library or something similar, given that you would have had a lot of free time. – Dave L Renfro Apr 2 at 22:43
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    Is your record essentially perfect? – Buffy Apr 2 at 22:53
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    I strongly agree with @DaveLRenfro: I find it difficult to imagine how someone who is looking for challenges won't find them while studying mathematics. There's a library, there are other students (some of them are certainly very smart and motivated as well), and there are staff members/course instructors (some of them are certainly quite nice and helpful) - each of these can give you opportunities to learn much more than required for a degree. I'd argue that there is a considerable chance that someone reading your application might have the same impression. – Jochen Glueck Apr 2 at 23:13
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    Echoing @DaveLRenfro, why didn't you read books? – paul garrett Apr 2 at 23:30
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    Depending on what you mean by "elite and challenging programs," there are many very strong applicants who do not make it into "elite" programs. Just to pick a number, what if you don't make it into the "top" 10 programs? Would you no longer be interested in pursuing math? – Stephen McKean Apr 3 at 0:44

I think you'd disserve yourself by making such a "complaint". Colleges have limited resources, and especially these days tend to be squeezed by administration... to offer ever-fewer courses, as ridiculous as that sounds. (Our graduate program at an R1 in the U.S. currently is under even-more-extreme pressure in this direction, for financial reasons that are themselves fairly non-sensical, but nevermind. It's essentially impossible to "argue" with higher administration...)

Read books (or notes, from on-line). Get advice from faculty on books/notes.

Do not be passive. Be eager. Even if the environment wasn't what you'd have wished, that's not really an obstacle, just "less help".

And, as in comments, it would be unwise to give the impression that you "need to be pushed" to do anything. I am aware that there is some notion that this is ok, but it is corruptive to one's thinking to sit and wait... Do not be passive.

EDIT: in response to your comment appended to the original question... I'd recommend that you not feel disappointed that your were "not challenged in class". Things don't have to work as challenge-and-response. Can be opportunities...

I'd agree that a sluggish environment can drag a person down... but, well, don't let your environment determine you, even if it has an effect.

If anything, a person could argue that a not-too-stimulating environment is a nice quiet environment, so that a person is not coerced...

  • I like this phrase - "not an obstacle, just less help". Yeah, I have seen that some students who are good at "competing" in math often do not turn out to be good researchers in math, without the stimulating environment to motivate them. I have tried to make the most of my situation here, doing research etc. (I probably should have mentioned this in the original post), so I definitely do not want to give the impression that I am such a student who needs a competitive environment to succeed. – user138022 Apr 3 at 0:33
  • So should I just talk about what I have done beyond class, and not explicitly make complaints about classes at all, and just let the admissions committee "read between the lines"? – user138022 Apr 3 at 0:34
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    Overall I like the optimistic attitude which you are describing. I think I will try to convey this in my statement, and rather than complain I will emphasize my inner motivation to learn math (without the competition of peers), and the opportunities and time I had to explore subjects not taught in class. Thanks for your response. – user138022 Apr 3 at 1:16
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    @user138022: What you suggest in your third comment sounds like a very good approach. Do not describe the weaknesses of your school, but instead focus on your personal strengths. The sentences "My classes were very low-level, so I had to learn everything myself - I hope that will be different at your school" and "In addition to my course work, I read books A and B, participated in a reading course about topic C, and got some research experience by doing D" could both be based on the same experience, but it's not hard to guess which sentence will leave a positive impression and which won't. – Jochen Glueck Apr 3 at 2:24

I think it's great to mention it, but frame it in the way that shows you will be a good candidate for the program. "I realized I can perform at a high level and I'm looking for a place that will challenge me to grow my skills" sounds much better than "School XYZ was not good enough for me and I want an upgrade". I think a good statement of purpose shows the reader about your attitudes and potential to make your school or research team a better place, and that is more important than the bare facts of your history and goals (goals change all the time).

  • I think phrases like 'looking for a challenging environment' are now considered cliche and could be counterproductive. – AppliedAcademic Apr 5 at 21:43

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