I think taking it would show a real commitment to being a graduate student. Get in a good study group and crack out the work. From what I have heard Grad class grades can be more inflated than UG classes.
I was curious what others would think. I am currently taking a graduate level "Probability and Statistics" course at my university. My gpa is perfect right now, but I am nervous about taking the class because I am not sure if it will look good if I don't do well in it.
Would a grade of a B in this graduate class actually be a good thing or would it be better to simply take an undergraduate class and get an A?
Zomgrogged is definately right. Good grades in grad classes go a long way to convincing admissions committees that you will be a good graduate student, for obvious reasons.
Of course, to answer your question, a B in a grad class would actually significantly weaken your current 4.0 profile, much worse than a B in any UG class could. However, if you work hard, theres no reason you couldn't pull off an A and significantly improve your profile.
It is certainly a calculated risk, but if you live your life only doing what you know you can do you will never do very much.
If you work hard you should be fine. Getting a B will certainly weaken your profile, but if your profile is strong enough to get you into a top program then you should be capable of getting A's in those classes.
So far I have a solid profile. But the case is that I know the undergraduate courses will be easy A's, and of course it's good to challenge myself, but what good would the challenge be if it ruins my chances of getting into the top programs? (since it pretty much comes down to finding reasons to admit one identical candidate over another).
Before giving any advice, I would like you to consider the following:
1. What other UGrad course are you talking about ? If it is an advanced math course such as Topology/Measure theory, then getting an 'A' in that course will be a pretty strong signal (nearly as much as the grad course).
2. What is your previous coursework in mathematics, and especially in probability ? If you already have a few courses in this topic, then the benefit of a marginal grade (even though in a grad class) IMHO will not be really strong.
3. The benefit from taking (and doing well) in grad courses often emerges from Micro/Macro/Metrics core. If possible, taking the PhD core of any of the 3 aforementioned will serve you better.
4. PhD students are often unwilling to allow UGrads enter their study group. I guess it would be even more difficult for an Econ student to enter a PhD math study group, than it would have been to enter an Econ PhD study group.
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