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Independent Study Course in Mathematics


IlbeHighLevel
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Hi all, I am currently attending Top 10 Econ undergraduate in the U.S.

Eventually, my school allows students to take graduate level math courses if students show sufficient mastery of undergraduate mathematics and have certain grade point average. I was originally planning on taking graduate-level math courses such as Measure Theory, Functional Analysis and etc. Then, I noticed that our undergrad math department offers independent study course where students get to choose the topic and take the 1:1 course with a faculty member of their choice.

 

here are my questions: would it be better off learning the grad-level math topics through independent study? (I believe that this can help me adjust the pace of my study and lower the risk of getting a bad grade) or would it be better off taking the actual graduate courses? Would A-s in math courses send a negative signal when I apply to Econ Ph.D?

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Many schools/departments that allow UG independent study classes do not allow it for courses that you are otherwise able to take. So if they allow UG's to with good GPA's to take specific MA level classes (PhD classes might be different) and those MA level classes are offered at least annually, then they will likely not allow you to do an independent study. I know that this was the case with my UG school whose math department also allowed UG's to take MA level classes and allowed independent study classes.

 

Also, don't assume that it will be easier learning via independent study. The professor will probably set the pace, albeit with some input from you. Because there is no class to compare to, there will not be a curve and you will not have study groups. I know of some professors who actually grade independent study classes harder to make sure that it is really being used so that students can learn a topic that they otherwise would not be able to study and not to get an easy A. At my UG school, all independent study classes were required to have a research project component which depending on the professor could be easy or could be hard.

 

That being said, if you are using the independent study class to learn a topic you would otherwise not be able to take a class in, it can be very rewarding. When you take a class one on one it enables you to pick the professor's brain much more than you can in a regular class, and it enables you to develop a closer relationship with a professor which can help you with LOR's down the line (though a math professor is less useful for LOR's than an econ professor). I took an econ/finance independent study class as a UG nine years ago, and some of what I covered there is strongly relates to one of my current areas of research interest (I am starting a PhD in finance this fall) and the professor I took it with was one of my LOR writers and probably wrote the strongest, most personal letter of all my LOR's.

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Whether an independent study would be demanding depends entirely on the professor. I would only recommend an independent if it has a research component to it, or if it is on a topic that you’re very interested in and which is not offered at all by the math department at your school. If you’re going for signalling and content, I think a “standard” course like Measure Theory etc. would be better.
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Measure Theory and Functional Analysis should probably be taken in classes. They're very standardized, probably won't be fast paced, and you'll probably find 1-2 students in class who are capable of solving all of your problem set questions if you ever need help. And I really doubt the department will let you do independent study on those.
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