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I'm currently a sophomore majoring in pure math with the hopes of going to graduate school to study applied math, specifically numerical analysis, machine learning, statistics. I have A's in my courses such as Linear Algebra, Discrete Math, Calculus, etc. Real Analysis is the first course that is giving me lots of trouble, and I think it is because I was not well-versed in writing proofs coming into the course. I received a B-/C+ on the first exam, and expect to receive a similar grade in the overall course.

How heavily will my grade in this course affect my chances of getting into a good graduate school for applied math (numerical analysis) if I receive A's/A-'s in my all of my progamming (up to an Advanced Algorihms course) and applied classes (PDE, Numerical, Complex Variables)?

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    Sophomore - does that mean undergraduate?
    – Solar Mike
    Apr 16, 2019 at 18:36
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    It's a little unusual for most US math majors to have real analysis sophomore year. What book are you using for this course and what were the prereqs? Apr 16, 2019 at 18:59
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    @ElizabethHenning: At an elite undergraduate college/university, it's quite common for math majors to take their first analysis or algebra course in sophomore year. Generally speaking, the sophomores in the class will do better than the seniors. Apr 16, 2019 at 20:05
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    @Alexander At those schools, the freshman curriculum includes calc and linear algebra courses that are heavy on proofs and theory, which the OP said they lacked experience in. So it's hard to assess this particular situation without more information. Apr 16, 2019 at 21:05
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    @ElizabethHenning: Not in my experience. Students are just expected to pick up how to write proofs in their first upper level course, and, for the most part, given the student body, they do. Apr 16, 2019 at 21:41

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A poor grade in a single course (especially in your second year) is unlikely to have a lot of effect on your application most places. But it isn't an indicator of success. When you apply for grad school or a job you need to indicate in the application process that you are an excellent candidate for success going forward. Poor grades don't help you. If managing proofs is really your issue then it will be hard to be a success in mathematics no matter what the field.

On the other hand, insight into mathematical structures isn't uniform across disciplines. I was great in analysis and topology but marginal (at best) in abstract algebra. I could follow along OK, but had no real insight into the big ideas.

Analysis can be pretty important in statistics, of course, and probably also in numerical analysis. But much less so in most of CS.

But, there is tremendous competition for slots in doctoral studies. You will be competing with a lot of people with better grades. That doesn't necessarily make you worse overall, but you need to make the case that you are the one for whom they can easily predict success. Make it so.

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  • I'm not too worried about managing proofs in future courses now that I have been exposed to harder ones. I really just didnt have much proof experience before taking this course. I did receive a much better grade on my second test and may end up with a B or B+ depending on my final grade!
    – SciFiFish
    Apr 17, 2019 at 3:03
  • I agree, but I'd also claim that students' difficulties with "algebra", or "analysis", or "topology", or <whatever> are most likely due to adversarial instruction, dubious assigned texts, and similar, in their prior course on X. My experience as Dir of Grad Studies in math without-exception indicates that students having difficulty with X would admit to having "X-trauma", that is, an unpleasant experience in a prior course on X, which invariably involved an unpleasant instructor. No, surely "mathematical talent" is not homogeneous, but I also don't think it branches at basic grad levels. :) Jun 13, 2023 at 3:20

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