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Importance of A in Real Analysis


econ girl

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I'm a junior at a USNews T40 American college. I have a near perfect GPA in the economics department, as well as a summer research project and TA experience. But, my math grades have left something to be desired: B+ in calc III, A in linear algebra, B in intro to proofs (ouch), A in differential equations, A in abstract algebra. It seems like to get into a T20 university you need A's in most math classes, so I don't have much room for subpar grades. I'm taking real analysis and probability theory this semester - probability looks like A or A-, but I ****ed up a real analysis midterm to the point that I probably can't get a better grade than a B in the course.

 

Have I completely shut myself out of the Top 20? What about Top 30, or Top 50? I still have next semester to take more math classes before applying next fall, but it seems like real analysis is one of the most important courses you can take to signal your intelligence.

 

Thanks for any advice, I just want to have a realistic understanding of what schools I can shoot for.

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There's a handy rule of thumb: as an American undergrad, to get into a doctoral program at the same ranking as your undergrad institution, you should probably be around 90th percentile in aggregate performance in relevant coursework; this provides a rough conditional mean of your target with most of the rest of the variance (which is very high) coming from LORs. So if you're 90th percentile in a top 40 undergrad with an economics major and decent amount of math, you can probably land somewhere around #40 economics PhD.

 

Right now I'm guessing (depending on level of grade inflation at your university) you're sitting on something like a 75th percentile in the relevant math classes and 90th percentile in economics. Top 20 is unlikely, but I can see you landing on anywhere from #20 to #70 when you apply next year depending on the rest of your profile. Real analysis is hugely important for your career, but no single course is really going to limit your upper bound significantly.

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There's a handy rule of thumb: as an American undergrad, to get into a doctoral program at the same ranking as your undergrad institution, you should probably be around 90th percentile in aggregate performance in relevant coursework; this provides a rough conditional mean of your target with most of the rest of the variance (which is very high) coming from LORs. So if you're 90th percentile in a top 40 undergrad with an economics major and decent amount of math, you can probably land somewhere around #40 economics PhD.

 

Right now I'm guessing (depending on level of grade inflation at your university) you're sitting on something like a 75th percentile in the relevant math classes and 90th percentile in economics. Top 20 is unlikely, but I can see you landing on anywhere from #20 to #70 when you apply next year depending on the rest of your profile. Real analysis is hugely important for your career, but no single course is really going to limit your upper bound significantly.

 

What a ridiculous piece of advice. Someone with all as besides a b and b+ in advanced math courses at an elite university is not on the 75 percentile of any distribution. You will get in where you need to be based on your ideas. Are you sacrificing research and development on creativity in an attempt to be a perfect robot, when that may not be your strength. If that is the case you would be well served to invest equal effort in developing the qualities that make you excellent. Honestly the focus on being a perfect mathematician strikes me as a little absurd. You do realize Adam smith didn't even know what a regression was.

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Thanks for the advice chateauheart – I'd never heard that rule of thumb before, very interesting (though of course not fool proof).

 

publicaffairsny – T40 is hardly an elite university. A B or B+ probably is about the 70th or 75th percentile of my peers in the math department; maybe a little bit higher or lower depending on which courses they take. Additionally, my "ideas" require a strong foundation in mathematics – have you ever read an economics research paper? How can you explain fixed effects, IV estimation, etc. without at least basic calculus and linear algebra? Economics research requires mathematics, so of course admissions officers look for students that are strong in that subject! Additionally, math departments are more rigorous than economics departments, so it also solves the issue of signaling. For you to say that having some fantastic idea will get you into a good college, without having the necessary background to generate and then test that fantastic idea, is ridiculous. This isn't the 18th century.

 

I asked this question not because I want to be a "robot" – quite to the contrary. I want a PhD in economics because I love the subject, and because being in academia allows you a certain degree of intellectual integrity. It's a life choice that will make me very happy, regardless of which program I attend. All I wanted to know was the degree to which a poor grade (and YES, that is a poor grade considering the competition for the econ PhD) would hurt my chances at certain schools so I can apply within my range and get in somewhere.

 

I really don't know much about the economics PhD admissions process other than what I've gathered from talking to professors and reading this forum, so I don't comment on other people's threads. You would be well advised to do the same.

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I currently use fixed effect in my research with no calc background. Guess I'm just special. Anyways, we weren't talking about calc, were we. We were talking about perfection. if you got a B+ in the course you obviously understand the concept well enough to apply it to econ.

 

You don't need calc to type xtreg y x, fe into Stata, or similarly just to add a bunch of LSDV. So it doesn't make you special, it just means you know how to use a keyboard.

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What a ridiculous piece of advice. Someone with all as besides a b and b+ in advanced math courses at an elite university is not on the 75 percentile of any distribution. You will get in where you need to be based on your ideas. Are you sacrificing research and development on creativity in an attempt to be a perfect robot, when that may not be your strength. If that is the case you would be well served to invest equal effort in developing the qualities that make you excellent. Honestly the focus on being a perfect mathematician strikes me as a little absurd. You do realize Adam smith didn't even know what a regression was.

 

Given the purposes and objectives of this forum (to provide realistic advice to the less informed), I would urge the competent authorities to do something about this sort of comments, which are intentionally misleading and confusing for the people who come here to seek that sort of advice. The OP appears to be sensible enough to dismiss these ridiculous statements, but the same may not be true for other people who read this.

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I don't understand how you can do research involving regressions if you don't have calculus and linear algebra, at a minimum. Without calculus, how do you solve any minimization problem that is remotely complicated? Without linear algebra, are you restricting yourself to 2 dimensions with simple regressions? I am confused. Either that, or you are just typing in "reg y x," as yankeefan stated, and copying the results onto your paper, hoping they are somehow significant.

 

As to your claim that a B in a subject indicates understanding it well enough...sure, you'll understand it reasonably I imagine. However, using math in research requires more than passing knowledge. I'd venture a guess that mathematicians whose specialties lie tangent to calculus can still muster up an A in real analysis. Why shouldn't economists?

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You need good letters and research. Huge diminishing returns to mathematics knowledge.

 

You can check out my profile and see the grade I got in analysis (mediocre) and my final placement (excellent).

 

Ok, so how about this post that seconded what I said. Better censor them too. Censorship is great, especially when we have driven ourselves into an obsessive perfectionist rut. Who would want to even consider an alternative to such a stifling inhuman idea.

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Excellent. I'm glad you agree her point was spurious and I was correct.

 

I was being sarcastic. Any idiot can run a regression. It takes a solid understanding of econometrics/statistical methods in order to do them properly. Just because you are using fixed effects in your research doesn't mean you're using them properly or even fully grasp the conditions under which they are meant to be used.

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I was being sarcastic. Any idiot can run a regression. It takes a solid understanding of econometrics/statistical methods in order to do them properly. Just because you are using fixed effects in your research doesn't mean you're using them properly or even fully grasp the conditions under which they are meant to be used.

 

Sure, that's why I work with more advanced people who can direct me. I'm a second year MPA, not a nobel prize winner. End result though is a publication that demonstrates my competence in using the technique. The bottom line though, is that no argument, regardless of the extent to which you wish to underestimate my understanding of quantitative methods, disproves what I said about there being no difference between the understanding of the technique in question by someone who has an A rather than a B+ in the class in question (an argument born out by every other poster in this thread).

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no argument...disproves what I said about there being no difference between the understanding of the technique in question by someone who has an A rather than a B+ in the class in question

 

Emphasis is mine, of course. And jesus christ, if you seriously think that there is no difference in understanding material between a B+ and an A, then you are out of your mind. At most schools, this isn't the difference between 88% and 94% as you're likely inclined to believe. The reality is that in most math/stats courses (upper-division in particular), the average grade was around 40-50% at my undergrad. Someone that got a B+ in real analysis or abstract algebra likely had a weighted average of ~55% in the class. Meanwhile, someone that received an A had anywhere between an 80-100%. That is an extreme different in conceptual understanding.

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People are antagonistic towards you publicaffairsny because you express strong opinions on the admissions process without much credibility. chateauheart's rule of thumb is not something I agree with entirely but it is reasonable. A lateral placement into grad school involves competing with students worldwide while the undergrad mostly draws from the state.

 

For comparison, after grad school, a lateral placement would probably be top 5% or less of students on the market from the same school. That is, 1 job candidate out of 20 on average might receive a lateral placement.

 

Finally, for the B+/A argument, it really does depend. Some of my A students have near a 100% average. A top student most times would not even be close to the A/B+ cutoff. B+ students can have a poor understanding of the subject (barely satisfactory understanding to my standards) but most places grade on a curve so these students get B+ as long as they are 25-30%tile or so.

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The technique in question being fixed effects. I don't buy that there is any difference in the understanding of this technique by someone with an A vs B+ in the class in question. Honestly, are any of you actually interested in using the techniques you're learning to make the world a better place. If so, how do you expect to create a diverse community of scholars when you purport to screen out anyone who for whatever reason fails to live up to a superhuman standard in signal courses that have little bearing on actual econometric techniques.
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Perhaps a B+ and an A show the same level of understanding, but the admissions committees want to see the A, for whatever reason. This reason may or may not be justified; ie. grades may or may not be a poor/noisy signal of competency.

 

Let's just all agree that admission's committees want to see A's, and that is what one should aim to get (and also what any prospective PhD student should be able to achieve with some effort).

 

However, a B, or a few B's will NEVER rule a student out of contention. Good grades are neither necessary nor sufficient.

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An A is an important signal, but generally no single grade will break your profile.

 

Anecdotally, my final transcripts included B+'s in linear algebra and metrics, although linear algebra was taken as a high school student at my eventual undergrad liberal arts college. You will need to shine elsewhere to compensate for any shortcomings in your profile, but in general it is doable. I made the transition from a top 100 LAC to a top 10 with a few holes in my profile (no RAship or masters, but I did complete independent research. I was only #2 in gpa among math/econ double majors, but the other student is doing a finance masters at MIT.)

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I'm a junior at a USNews T40 American college. I have a near perfect GPA in the economics department, as well as a summer research project and TA experience. But, my math grades have left something to be desired: B+ in calc III, A in linear algebra, B in intro to proofs (ouch), A in differential equations, A in abstract algebra. It seems like to get into a T20 university you need A's in most math classes, so I don't have much room for subpar grades. I'm taking real analysis and probability theory this semester - probability looks like A or A-, but I ****ed up a real analysis midterm to the point that I probably can't get a better grade than a B in the course.

 

Have I completely shut myself out of the Top 20? What about Top 30, or Top 50? I still have next semester to take more math classes before applying next fall, but it seems like real analysis is one of the most important courses you can take to signal your intelligence.

 

Thanks for any advice, I just want to have a realistic understanding of what schools I can shoot for.

 

A few comments:

 

1. As others have said, no single grade will make or break any applicant. Despite the recurring meme on a certain other site, nobody is going to reject an otherwise perfect applicant with awesome grades (including in other advanced math classes) only due to a B+ in RA.

 

2. That said, that doesn't seem to be the case here. The problem isn't your RA grade, but your overall poor performance in mathematics. Is your current RA performance related to your performance in intro to proofs? That concerns me because it indicates that you didn't take the time to work on your proof skills prior to taking RA. Is that the case? If so, you may want to seriously consider dropping RA, working on improving your skills, then try again next semester. Keep in mind that RA is actually used extensively in many PhD programs--it isn't just a signal. And you absolutely must be comfortable with proofs.

 

3. That said, having mixed math grades doesn't inherently make a lateral or higher move impossible or anything. I came from a considerably lower ranked school than yours, had a fair amount of Bs in math classes, and got into a top-30. However, I had As in two semesters of RA (and other As too), and also had other strong aspects of my profile to compensate. You can see my profile and results for details.

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How can you explain fixed effects, IV estimation, etc. without at least basic calculus and linear algebra?

Actually, I wouldn't say that an understanding of calculus or linear algebra is required to perform research using canned estimation procedures. However, math is the language of economics research (including canned estimation procedures), and anyone who doesn't demonstrate the ability to do quite well in undergraduate math courses is immediately suspect for not being fluent. Additionally, there is practical value in calculus, linear algebra, and analysis for broad portions of economics.

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For comparison, after grad school, a lateral placement would probably be top 5% or less of students on the market from the same school. That is, 1 job candidate out of 20 on average might receive a lateral placement.

 

This was an interesting rule of thumb, so I ran the numbers on last year's job market candidates. Out of 24, we had 1 T5, 9 T10-30, 5 T50+, 8 Private, 1 Public. So one lateral, and most people in the next tier down.

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That is actually really good placement from a top 5 and an atypical year unless it is MIT. Only MIT consistently places that well - Harvard does it every other year or so. The rest of the top 5 (Yale, Princeton, Stanford, Chicago, Berkeley) would probably place five or less students at top 30s on average.
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If you compare the amount of undergrad majors, grad students and faculty in a department, then divide it by number of years they stay in that position, the ratio is probably something like 150:10:1. This gives you a rough idea of the size of their respective markets per year - and the immense difficulty of placing laterally, especially outside of the top few departments (with accumulating downward pressure from higher ranked departments). In the US there is international inflow for PhDs so the competition at that stage is even higher than otherwise.
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B+ in calc III, A in linear algebra, B in intro to proofs (ouch), A in differential equations, A in abstract algebra.

 

Well, I think you are at the stage in which the marginal effect of real analysis reaches its maximum. Be careful. For those get 10 As in math, a B or A in RA won't affect much, I guess. On the contrary if you get a few more Bs, your math will be considered 'poor' regardless of your RA grade.

 

That being said,

If you get an A, that means 'this guy can get As in upper-level math'.

If you get a B...probably people will think 'probably the abstract algebra prof gives everyone an A'

 

Good luck.

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