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How much actual math in PhD programs - (once you're there, not to get in)


econdude

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I understand Linear Algebra and Real Analysis are pre-req's for the good PhD programs- but how much do you actually need it once you get in? Is it just a filtering mechnaism that is helpful, but not essential because you are studying along anyway, or will you basically fail if you have to learn the math as you go along?

 

Thanks.

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It's somewhere between the two -- and depends on what school you attend.

 

Linear algebra is used a lot, particularly in statistics/econometrics. You need to be comfortable with matrix notation, functions on matrices, inversion, etc. If you have to think about the notation or matrix operations, it will be really hard to keep up with the actual content.

 

Real analysis is a part of much of the first year sequence, especially micro. You will prove that there exists a utility function that represents preferences. You will prove that function is continuous, LNS, etc. You will use direct proofs and proofs by contradiction. You will use concepts like "open balls," and constructs like, given delta, there exists and epsilon such that... There's a lot of notation (symbols for things like "for each" and "there exists" that isn't difficult, but will make it hard to follow the professor on the board if you don't know the symbols being used.)

 

Now, some of this material will be covered in "math camp" or a math class during your first year. But typically that class is just a quick overview or refresher -- if it was your first time seeing the material, you'd probably need to do quite a bit of work outside of class to actually learn it on your own. And that will be time you just don't have first year. Real analysis and linear algebra are both tools that are supposed to make the intuition clearer. If you don't understand the math, then instead of focusing on the economics, you'll be stuck paying too much attention to the math.

 

(Note: this all pertains to top 20 or top 30 schools. I don't know as much about the first year classes at other schools. Also, I'm not advocating taking tons of extra math above and beyond those classes, but I do think they are useful in the first year as well as important for admissions. And it's a great question, because the focus should be on how to do well, not just how to get in.)

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Now, some of this material will be covered in "math camp" or a math class during your first year. But typically that class is just a quick overview or refresher -- if it was your first time seeing the material, you'd probably need to do quite a bit of work outside of class to actually learn it on your own. And that will be time you just don't have first year.

 

 

This statement cannot be over-emphasized, in my opinion. I'm taking the PhD "Math for Economists" course as a Master's student. I have not had Real Analysis (at the Roydin level, I'm currently taking a class using Rudin).

 

This "Math for Economists" course moves incredibly fast, so fast that I typically spend the class writing notes and then 3 hours that night trying to understand what was actually said in class. Real Analysis (probably even an introductory level) would have been infinitely useful.

 

On that note, if you can afford to take a general Topology class it will be very useful in the more advanced econometric courses.

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I didn't take real analysis as an undergrad, but i've heard how helpful it is for phd econ. I am currently attempting a self-study at rudin's book, and to my shock, i actually am understanding most of it. if not to please the adcoms, i think this will help me succeed once i get to grad school. however, it would be nice to signal to the adcoms somehow that I have this proof abililty. is this a good idea, and if so, in what medium should i attempt to convey this information. perhaps through LORs? mention in statement of purpose?
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Caprone, it's great that you are getting a handle on the material before starting a PhD! It really will be useful in your first year -- admissions is a huge hurdle, but that's only the beginning and it is really good to think a step further down the line.

 

If your professors are aware of your progress with real analysis, it would certainly be worthwhile to ask them to mention it in their letters. That will add more credibility to any mention you make in your SOP, and in addition to helping to demonstrate competency to the adcom, will also show motivation and dicipline. It would be a clearer and more useful signal to actually have a grade in the course, but an endorsement of your self study from one or more of your professors would probably be helpful.

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Thanks for all the input- I am taking Linear Algebra at a local college after work- it is pretty tough to keep up. I plan to take RA next semester. If I were to apply to programs and tell them somehow that I am enrolled- would that be good enough to get respect from the admissions committees, or do you actually need to show them you got an A? Anyone with concrete info on this would be appreciated.
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If you're applying this fall for 2007 admissions...

 

You can submit fall grades, and they'll affect admissions decisions.

 

However, you can tell them in your application that you plan to take RA, but they won't give it much credit until you have a grade (which won't happen if you're taking it in the spring). It likely won't make you more competitive with applicants who have a grade in RA; however, it may help somewhat against other applicants who have no intention of taking RA.

 

Really, you should take RA to make life easier in your first year anyway. Yeah, it sucks that it won't help you much for admissions purposes, but it's a useful course to take.

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How do you let adcoms know your fall grades. When you submit apps, usually grades for fall have not been posted. Since you send the transcript before the grades appear, how can they see these? Does one typically send an unnoficial transcript after the semester is over say after admissions deadline? Or do you just postpone sending your transcripts all together?

 

I would just like to know from someone who has done this before.

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How do you let adcoms know your fall grades. When you submit apps, usually grades for fall have not been posted. Since you send the transcript before the grades appear, how can they see these? Does one typically send an unnoficial transcript after the semester is over say after admissions deadline? Or do you just postpone sending your transcripts all together?

 

I would just like to know from someone who has done this before.

 

I have basically the same question: Do adcoms look at a transcript sent after the deadline is passed?

 

Some departments have early deadlines on 12/01 or 12/15, so I'll have to send in my transcripts without the first term's grade. But the transcript with those grades will be available by late December (around 12/20), should I send them my newly updated transcripts as well?

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You send a transcript with your application. When you get your fall grades, you send an updated transcript.

 

I'm guessing applications haven't been opened up yet, but several schools will ask you on the application to submit fall grades when you get them.

 

Oh, and don't worry... nobody will be reading your application in January, so there's plenty of time to get the updated transcript to them. :D

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Now if we start modelling the situation, registration for real analysis should improve one`s chances as exposure to a grad-like course should scare some students away from applying, working for those who still submit their forms.

Now who`s to collect the data? ;)

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Now if we start modelling the situation, registration for real analysis should improve one`s chances as exposure to a grad-like course should scare some students away from applying, working for those who still submit their forms.

One can register and then drop. So the registration alone is probably not enough. But if one has taken other similar math courses and got good grades, it's reasonable to presume that one would not drop the course and would probably get a decent grade.

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Isn't the point of taking these math courses to be "framiliar" with the material? I would think that the admissions committee would be ok with a student with good math grades in previous courses and being currently enrolled in RA or linear.

 

If this is not the case, one would have to wait an entire year before applying again. Is that the basic situation someone is in if they havn't taken the math courses and realize they want to apply for the next September? Dosn't seem right.

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You should be "familiar" in the sense that you comprehend the content of the course. Many people have problems with analysis and the abstract nature of the topic. That's why grades matter, especially with regard to analysis. I said this on another thread, but analysis is the first course that really tells math professors whether a student has the potential to study math at a higher level (i.e. MA/PhD in math). Before that, everything is plug-&-chug.

 

gredow, the question is somewhat tough. The issue isn't whether or not you could do the material; it's whether or not the courses are offered. You could definitely do Calc 2-3 and linear algebra in two semesters (since 2 is an obvious pre-req for 3). That probably leaves analysis for the summer, and most schools probably won't teach it then (though you can find some, as this came up a few months ago on TM). The main problem you'll face with PhD admissions this year is that you'll only have grades for Calc 2 and maybe linear algebra, and many other applicants (at say top 30 or 40 schools) will have grades for more math courses. And the Stewart book you asked about on another thread is the one I used for Calc 1-3.

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For first year core courses, they don't use much math actually. What u need is: Linear algebra+calculus+intro probablity+intro stats+a little analysis+a little ODE+comfortable working with math/logic things+economis intuition then you're ok. And the absolute difficulty level is lower than the typical real analysis course(I mean the content, not the test. real analysis tests are always easy. Prof cant fail the whole class:p ). Not sure about high level courses, but if you want to concentrate on finance. I think high level probability like brownian motion is necessary which means u have to be familar with measure and PDE.

 

this is the situation i am in. do you think that in the space of 11 months i can take cal. 2-3, linear algebra & analysis? (while working the whole time)

 

if u'r not feeling tired after work now, I think you can do it. And u don't need to study calculus first in order to study analysis. Analysis course will build everything from axioms.

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I am currently taking the econ phd courses (Micro, Macro, Math for Econ). A solid understanding of basic real analysis is great, but a solid understanding of logic is absolutely essential. For example, you need to know how to work with quantifers: if you need to prove that for all x in R and all L>=1, f(Lx)
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For first year core courses, they don't use much math actually. What u need is: Linear algebra+calculus+intro probablity+intro stats+a little analysis+a little ODE+comfortable working with math/logic things+economis intuition then you're ok.

 

Which school are we talking about?

 

Ram

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My 1.5 cents:

 

From what I understand, the analysis is helpful to formalize rigor in proof theory, etc. Epsilon/delta arguments, dealing with sequences/series, and understanding basic topological ideas like open/closed balls, etc come in handy in the heavy proof courses. For some people this may come naturally, but for us mere mortals it is difficult to pick these things up as econ phd courses tend to move quickly. Keep in mind that this is second hand info, and that I have yet to take a PhD level econ course (all my grad work is in math).

 

I have also heard that some top 50-30 schools will accept people without real analysis in the hope that they can pick up the ideas as they move along (placing the student in an uphill battle from the start).

 

With all of this said, I would suggest taking RA even if it comes too late for the admissions process. I really don't believe a person can be over-prepared in mathematics. The best voices on this subject are those already in programs. Zavera, Ramlau?, Snappy, etc

 

hope this is somewhat helpful, or at least entertaining.

 

Roger

 

this is the situation i am in. do you think that in the space of 11 months i can take cal. 2-3, linear algebra & analysis? (while working the whole time)

 

With all do respect, 11 months is impossible. This may be possible in 3-4 semesters, however, depending on your universities prerequisites. In my program, linear requires cal III , and analysis requires cal III and a introductory proof course called foundations of mathematics or possibly discrete math.

 

Roger

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this is the situation i am in. do you think that in the space of 11 months i can take cal. 2-3, linear algebra & analysis? (while working the whole time)

 

Actually if you're on a trimester system, then this is "theoretically" possible. You can take cal 2, 3, and analysis in term I, II, III respectively. You can take linear algebra in any term, but most likely it'll be term III. The problem is I think you'll have schedule conflicts because calculus and real analysis are usually intended for students of different years.

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I use almost all the math I took, all of the time right now. I took one semester of real analysis (Rudin) and one semester of Topology (Munkres). Those two courses have been very valuable. The only thing I wish I had taken in addition would be a course in optimization theory (not available at many schools) and a stronger course in Linear Algebra (or perhaps taken it seriously when I did have it).

 

In short, take analysis. If you can, take something just beyond analysis as well.

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this is the situation i am in. do you think that in the space of 11 months i can take cal. 2-3, linear algebra & analysis? (while working the whole time)

 

Although it may be listed as a prereq for analysis, I don't see why you would need Calculus III to understand Real Analysis. It's usually thought that the whole calc sequence would give you more maturity to take RA, but if you are really constrained by time you could try Calc II+Linear Algebra, then Calc III+Analysis.

But this course load may be incompatible with work. Anyway, you should be aware that it's a difficult task.

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With all of this said, I would suggest taking RA even if it comes too late for the admissions process. I really don't believe a person can be over-prepared in mathematics. The best voices on this subject are those already in programs. Zavera, Ramlau?, Snappy, etc

 

I'll agree with this. No such thing as too much math prep. Taking RA, anywhere along the lines will help. Taking any sort of analysis course will help, or really, any serious proof-based mathematics course. RA is still the most desired because it has the most direct application.

 

I'm starting in on my fourth week here today, and I use RA, measure, and even my Matrix Analysis, material on just about a daily basis. If nothing else, picking up a solid foundation on how to write proofs - esp. knowing when you've actually proved something, - seems to be very, very important. And the material is quite important too.

 

A good grade in Analysis seems to be a signal of three things:

 

1) being able to write proofs

2) being able to read/write at a high technical & high level

3) knowing analysis

 

1 and 2 are imperative. 3 is very important.

 

as far as being able to pick up mathematics when you're in grad school...I don't know how anybody can do it, or do it well. in grad school, you're pretty much expected to learn more than you can really handle - I figure we cover 6-8 chapters a week. that's a struggle in and of itself without trying to pick up a course like RA, which makes even some of the best math majors squirm. Get it done ASAP.

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as far as being able to pick up mathematics when you're in grad school...I don't know how anybody can do it, or do it well. in grad school, you're pretty much expected to learn more than you can really handle - I figure we cover 6-8 chapters a week. that's a struggle in and of itself without trying to pick up a course like RA, which makes even some of the best math majors squirm. Get it done ASAP.

This is absolutely true. I'll add that in an econ PhD program, math is supposed to be a tool -- something that helps explain and organize economic concepts. But if you aren't comfortable with the math before starting the program, then your first year classes become about the math more than the economics. It turns something that's already difficult into a very frustrating experience where you're struggling to keep up and not developing strong intuition for the foundational material of the field.

 

There are some people who do fine in their PhD without ever having written a proof before graduate school. But for most, it's a lot easier to really get a handle on the material -- to learn it in a solid enough way that it becomes the basis for your own future research -- if you speak the "language" in which it is being taught.

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