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"I failed an important course due to some justified reasons or terrible excuses, can I get into a decent PhD program?" is probably one of the most asked questions on the Academia Stack Exchange. However, I have a different question.

My question is, what if my low grade is due to my incompetence? No excuses, no external reasons. The only reason is my unsatisfactory intellectual capacity. How should I address this issue on my application?

Let me give more context. I am applying for a PhD in computer science, but my math proficiency is terrible. (Probably above average, but certainly not on par with the top students in my department, let alone those from the prestigious schools) There are several important courses in math and theoretical CS that I did poorly, such as B or C, but never F. (In our school, B and C are usually considered to be the bottom half of students, and are usually regarded as mediocre or poor, but not bad enough to fail the student.)

I have some research experience and have published in decent conferences. There are times when I use some sophisticated math in my research, but certainly not often. When this has happened, I have been given enough time and support to figure out complicated things, so my math incompetence has never held me back except to trigger my math anxiety (which happens quite often). My advisors also wrote strong LoRs (at least that is what they said) and they all believed that I was suitable for graduate studies. One advisor even told me that while it was true that my math skills were not as good as others, they were good enough to do graduate studies in my research areas.

I am now preparing to apply to graduate school, and it is certain that some, if not most, of the people on the admissions committees would notice these outliers on the transcript. How should I address this issue? I am quite concerned that my argument that math incompetence has never held me back will not convince others. I want to (and probably should) be honest and not make excuses.

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    Country? Where I am, B and C would be considered the second- and third best grade and definitely not bad.
    – user111388
    Dec 1, 2023 at 17:02
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    I'm surprised about the downvotes. Admittedly, the question is a bit uncoventional, but it appears to be asked in good faith and I can't find anything wrong with it. Dec 1, 2023 at 19:51
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    @CalFang: "bottom half of students" is meaningless when we don't know the population of students - the 5th-percentile student at MIT would probably be a 90th-percentile student here. Dec 1, 2023 at 21:16
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    Have you considered whether you would like to apply your CS knowledge to a field which is not specifically mathematically focused e.g. business/healthcare IT implementation, user experience, Web design etc. I think you may find that there are many jobs/research fields where your CS experience will be valued without specifically requiring that you excel at mathematics
    – user160623
    Dec 3, 2023 at 10:24
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    I want to commend you for your candidness and honesty Dec 4, 2023 at 0:13

5 Answers 5

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I don't think this is something you mention.

You present your grades; you present your research experience. You let the person judging your application make observations like "this person has done well in research despite their poor mathematics performance" on their own, rather than giving them the thought directly. You should do the best you can to highlight your achievements, talking about this more will instead highlight the poor grade you'd like to move beyond.

That said, I don't really believe incompetence or unsatisfactory intellectual capacity are useful excuses on an application for a poor grade in an undergraduate math course. I think the perception of this reasoning will be closer to "You could have done better" rather than "You did your absolute best and are being honorably honest about it".

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    Since there is a cap on how much effort you can invest into a single subject in a given semester, it's probably more fair to say that it shows that the required effort to get an A exceeded that cap. Dec 1, 2023 at 17:49
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    @AdamPřenosil That's what I meant by writing "Perhaps it's because they've chosen to prioritize other things, and that choice may be reasonable" - other reasonable things can include everything from other courses to recreation time to keep up a study/life balance. But it is not "incompetence or unsatisfactory intellectual capacity".
    – Bryan Krause
    Dec 1, 2023 at 17:55
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    Right, but the point is that whether or not you have the time to put it the required effort to get an A in a math class very much does depend on one's mathematical abilities. Dec 1, 2023 at 18:11
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    @BryanKrause: I've certainly had students who put in a lot of effort into an upper level undergraduate mathematics course and did not have the intellectual capacity to earn an A. Dec 1, 2023 at 18:16
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    Thanks, @BryanKrause. I have to admit that I should have put more effort into these classes. It's true that I might not get an A, but the situation would be much better than the one I'm in now. This is painfully obvious in hindsight. I am convinced that "I could have done better" or "I should have devote more time and effort into it" is a better reason. Thanks for the advice. It is really helpful.
    – Cai Fang
    Dec 3, 2023 at 11:37
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As in Bryan Krause's answer, I don't believe your should bring up weak points (such as poor grades) unprompted. While I think you see "being honest about math incompetence" as a positive, it might come across as you being unwilling to engage with subjects that are difficult for you.

Generally speaking, the program/PIs you're applying to probably care most about your directly CS-research related qualifications (experience, publications, LoRs, etc.) than your grades in ancillary subjects.

If you do get asked about the grades, a (somewhat honest?) response could be that you're not very interested in Math, but you've taken courses and acquired the necessary skills to tackle the research problems you're interested in. (+ argument about using x math method in research experience y)

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I think you need a better understanding of why you underperformed in math before you complete your application, if only because you need to question your motivations in applying. Internalizing your failure by saying "I am unable do math" is not an explanation; it's an excuse that suggests you aren't willing to examine your failures in depth. This is a big red flag for graduate studies. In grad school you will be frequently confronted with problems you won't be able to immediately overcome, no matter how capable you are. Persistence in the face of failure is essential in graduate studies. Why would an adviser want to take you on as a student if you limit your self-analysis to "I just don't have what it takes" when something difficult arises? I'm sure you can see why this is a disastrous perspective to put in your application, but I'd like you to consider that the perspective itself may be a larger underlying problem.

If you can understand abstract concepts in computer science, you can definitely learn to do math with sufficient time and effort—certainly at the level needed for most CS PhD programs. While it's possible you have a math-related learning disability that makes this more difficult, it's more likely that the math you have done (or the manner in which you were instructed, as math is notoriously difficult to instruct) did not interest or excite you sufficiently to push you to learn properly. When work is very difficult, there needs to be something about it that you can enjoy in order to motivate progress. You don't need to be thrilled by everything about the process, but there must be something interesting about it to keep you going.

To put it in terms you're no doubt familiar with, nearly anypony can learn to code, but you won't get good at it unless there's some aspect of the process you find interesting. Coding isn't the heart and soul of computer science, but it's the manner in which the craft is expressed, so you have to be able to do it without feeling like it's pure drudgery. This is similar to how a century ago you needed to be able to draw with a pencil to be an architect. Pencils have nothing to do with what architectural design actually is, but you needed to use them to express your designs.

Most computer science PhD work is not what I would consider math-heavy. To pass quals you'll need the ability to analyze algorithmic complexity, and you should be comfortable with basic concepts from discrete math. If it's electrical engineering focused you may need some math related to circuit theory. But math that students tend to hate like multivariate calculus is not directly relevant. Apart from specialized cases, the only reason advisers will care about your advanced math ability is as a metric for your ability to push yourself to learn hard things. The coursework you'll need to do in a PhD program isn't the hard part, and except for subjects directly relevant to your specific focus it's unlikely your advisers will care much about your grades (apart from keeping them at a nominal level to show you're actually learning, though this can vary by institution and program).

As for the application itself, I wouldn't mention the grades at all. Your grades speak for themselves. The only reason you would want to add an explanation is if the explanation shows how you have overcome whatever problem led to your poor performance, and this is something you don't yet understand about yourself. Suggesting to potential advisers that you falsely believe you contain a permanent, unfixable inability to do math will warn them not to accept you into the program.

One last thing: even though CS is not math-heavy, you should probably ask yourself why you're seeking a PhD in a math-related field if you think you can't do math well. You can make more money going directly into employment with a BS in a CS discipline, so you should only be here if CS is something you love, in spite of the mathematical warts (from your perspective).

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Computer science is a rather confusing degree, because there are areas of it which are very mathematical (formal verification, for example) and areas which aren't (human computer interaction is one such area). So you need to be clear about what you can offer. This also means that some schools will be very interested in you, and some schools will not be interested at all. Just be clear about yourself and what you have to offer, and good luck.

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Present the transcript as it is.

The admissions tutor will know the actual maths requirement of the program. S/he may say to a colleague something like, I have a candidate who is weak on maths but looks strong on lah dee dah. Would you have a project that is a good fit?

If your application is rejected because even the most "maths light" option at that place is too rich for you, then both yourself and the institute are best served by a rejection.

(Remember, rejection sounds like a negative word, but it can often be the best thing to happen to you.)

Remind the academics who are going to write your letters of support that modules XYZ were your favourites, that you did very well in them, and accordingly that you would like to pursue further research in diddle dee dum.

Chances are that the academic will copy-paste-lightly edit your remarks into their letter, and that will really help.

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