How important is Real Analysis for admission?

[Applegate]

I am a research assistant ("Junior Professional Associate") at the World Bank and I am considering applying for PhD programs next year (for fall 2010 admission). I attended Northwestern University, graduated with a 3.93, and took a number of economics courses (macro, micro, stats, econometrics, and upper-level development economics -- all As); as for math, I got an A in Linear Algebra. Calculus is on my transcript because I passed two AP tests in high school, but I did not take calculus in college.

 

I am considering taking a math class this year in order to improve my admission chances. If I don't take a math class, however, I think I'll have a better chance of publishing a paper (I'm working on several projects with colleagues, and taking a math class would mean less time for these independent research projects). While I've published a number of articles in the press (journalism), I don't have any academic publications.

 

So: would you recommend I take Real Analysis? Focus on publishing? Or maybe take an advanced Linear Algebra class? The latter option would allow me to continue with my own research, because it would be less demanding than RA, but it also might signal to admission committees that I have a good grasp of the basics.

 

Would very much appreciate your advice.

[pevdoki1]

I think it's quite important to know what writing a correct proof entails, and I would say you need some math courses. I don't know if anyone comes into PhD econ programs without college calculus, save for some "genius" examples. Of course, if you take real analysis and do well you don't need a course in Calc 2. I would suggest doing it.

 

P.S. From what I gather so far, linear algebra is not used much at all, so something like Analysis or Advanced Calc would be much better to take. If you're scared of doing too much work, you should do some research on what the first year of your PhD program will be like!

[paradox3696]

I can GUARANTEE you that you will need lots of "knowledge" from Linear Algebra and Differential Equation in Micro, Macro, Econometrics and perhaps some of your field course as well for Phd program in Econ.

 

If you are aiming for top schools, then it wouldnt hurt to have one proof-based Math course and it does NOT need to be Real Analysis (eg, Elementary Logic and Set Theory will do ).

[pevdoki1]

Here at Minnesota people basically shrugged their shoulders when I asked them how important linear algebra is. From what I understand, nothing in linear algebra is used that's not elementary or that you can't pick up in a couple of hours. And both here and in Washington St Louis people told me that a course in differential equations would be a waste of time.

 

On the other hand, everyone here is basically required to have an analysis course: if someone doesn't have it, they definitely take it their first year. You don't need it to get in, but you must be able to learn the stuff. Econometrics people say that the most useful course to take is a PhD level sequence in Probability and Measure (for which analysis is a prerequisite). Other math courses people suggest are things like functional analysis (for which real analysis is also a prerequisite).

[GymShorts]

If I remember correctly, there is no AP test for multivariable calculus, which is a prerequisite for pretty much every program. So at the very least, you should take that.

[Golden Rule]

I'd try to take multivariable calc and also real analysis if possible. I don't think it's all that likely that you'll get a quality-enough publication that would actually make a considerable difference in admissions. Just do enough on those projects to get an LOR that can vouch for your ability to do independent research.

[Legatus]

Take more math! I guess the lesson here is graduate economics does not equal undergraduate economics. There really is nothing in common except for maybe some intuition. At a minimum you should have multivariate calc. Most of the people in my class are math and physics majors and the review sessions we have been doing for micro (yes we have econ camp) are more advanced then my adv micro I took. The only thing that really helps me here is my math background.

 

And with the comments about being able to pick up stuff as you go. Although it's probably true because a lot of matrix algebra and ODE's is mechanical, with so much else going on when you enter first year, is this really the time you want to be learning this stuff? If you can, fill your schedule with math.

[YoungEconomist]

I'm confused that a lot of people are talking about multivariable calculus. At my school calculus 3 covers things like partial differentiation, double integration, etc. However, multivariable covers lots of high level vector calc, and other stuff I've been told is not very helpful in economics (but rather helpful for physics).

 

So when people say that multivariable calc is a required, I imagine you are talking about stuff like partial derivatives and double integrals, and not really vector calc, right?

[asianeconomist]

My only advice to you would be to not underestimate the difficulty of taking RA (especially without much prior math) and getting a good grade in it. You might want to check out the text-books that will be followed in your course and try to browse through a few chapters (not to actually solve the maths, but appreciate the level of difficulty that you might have to encounter).

[TruDog]

Differential equations is a waste of time, but linear algebra is quite useful in understanding econometrics.

[asianeconomist]

Differential equations is a waste of time, but linear algebra is quite useful in understanding econometrics.

 

Excuse my ignorance, but isn't DE utilized in dynamic macro models ?

[funkychinamen]

I think that might depend on each school's syllabus. I know at my school we did vector calculus and partial derivatives in the multivariable calc section and we did double and triple integrals in the vector calc section. Although, when I took the classes, I believe the school was transitioning to a new textbook, so that may have been the cause of the mislabeled classes.

 

And I believe what everybody is referring to is the fact that the AP tests does not go up to partial derivatives (I only took AB, so I can't say too much about the BC test, but the AP website states that the BC test tests calculus of a single variable), thus the original poster (who passed out of calc through the AP test) may not have learned partial derivatives or double integrals.

[YoungEconomist]

I'm just wondering if I will have met most (all?) programs calculus prereq's for admission as long as I've covered things like partial derivatives and multiple integrals?

[TruDog]

Excuse my ignorance, but isn't DE utilized in dynamic macro models ?

 

We used differential equations once in dynamic macro models (in conjunction with Hamiltonians). But DEs are still by far the least used math class here at Wisconsin.

[Palimpsest]

And I believe what everybody is referring to is the fact that the AP tests does not go up to partial derivatives (I only took AB, so I can't say too much about the BC test, but the AP website states that the BC test tests calculus of a single variable), thus the original poster (who passed out of calc through the AP test) may not have learned partial derivatives or double integrals.

 

I took BC Calc. Definitely no multivariate stuff -- I didn't see that until I took Calc III at a university. To quote wikipedia:

 

"AP Calculus BC includes all of the topics covered in AP Calculus AB, as well as convergence tests for series, Taylor and/or Maclaurin series, the use of parametric equations, polar functions, including arc length in polar coordinates, calculating curve length in parametric and function (y = f(x)) equations, L'Hôpital's rule, integration by parts, improper integrals, Euler's method, differential equations for logistic growth, and using partial fractions to integrate rational functions."

[YoungEconomist]

I took BC Calc. Definitely no multivariate stuff -- I didn't see that until I took Calc III at a university.

 

Yeah, this is spot on. When I took the calc series, I had some people in my class who took AP Calc in highschool. During Calc I and Calc II, they had already seen the material. Once we got to Calc III however, they had not seen any of it.

[Applegate]

Thanks everyone for your helpful advice. The consensus seems to be that I should take a multivariable calculus class and/or real analysis. I've copied a couple of course descriptions below ... would these be appropriate? Thanks again for your comments.

 

213 Analytic Geometry and Calculus III (3:3:0) Prerequisite: grade of C or better in MATH 114. Partial differentiation, multiple integrals, line and surface integrals, and three-dimensional analytic geometry.

 

290 Introduction to Advanced Mathematics (3:3:0) Prerequisite: MATH 114. Set theory; graphs; functions; equivalence relations and partitions; partially ordered sets; induction; construction of the natural, rational, real, and complex number systems; well-ordering principle; and cardinality. Primarily intended for mathematics majors.

[Palimpsest]

Thanks everyone for your helpful advice. The consensus seems to be that I should take a multivariable calculus class and/or real analysis.

 

As far as I've found, multivariate calc (esp. partial differentiation) is absolutely crucial to studying graduate economics, both as an explicit admission requirement and in terms of everyday practical use.

 

In contrast, I believe that while real analysis is very useful in some subfields and extremely valuable for learning how to think in a sophisticated mathematical fashion, it is usually suggested preparation.

 

So if it's a choice between the two, I think you almost have to take Calc III to even apply to most programs.

[GymShorts]

213 Analytic Geometry and Calculus III (3:3:0) Prerequisite: grade of C or better in MATH 114. Partial differentiation, multiple integrals, line and surface integrals, and three-dimensional analytic geometry.

 

290 Introduction to Advanced Mathematics (3:3:0) Prerequisite: MATH 114. Set theory; graphs; functions; equivalence relations and partitions; partially ordered sets; induction; construction of the natural, rational, real, and complex number systems; well-ordering principle; and cardinality. Primarily intended for mathematics majors.

 

 

I would argue that you need 213, and that 290 would be helpful, but you could get some decent admits without it.

[Thesus]

For what it's worth, I believe that 16 of 17 people at this year's class at Rochester have at least one course in analysis - and if you didn't have a course in analysis, getting through the math camp problem sets would have been nigh-impossible, given the pace at which lecture was proceeding.

[Golden Rule]

I agree with what others have said. Taking 213 multivariable calc. is priority #1. Real analysis is recommended.

 

However, 290 isn't what most of us are calling a real analysis course. I think 315 (which lists 213 & 290 as a prereq) is more like it.

 

315 Advanced Calculus I (3:3:0) Prerequisites: MATH 213 and 290. Number system, functions, sequences, limits, continuity, differentiation, integration, transcendental functions, and infinite series.

 

Or even a level above that.

 

431 Topology (3:3:0) Prerequisite: MATH 315. Metric spaces, topological spaces, compactness, and connectedness.

 

I don't think it'd be unreasonable to skip 290 and take 315. Stuff like continuity and sequences is important, stuff like constructions of the reals, not so much.

 

Here are the Harvard/MIT syllabi for real analysis, for example. It doesn't seem you have a course exactly like this though.

http://www.math.harvard.edu/~strain/06ma112/syllabus.pdf

MIT OpenCourseWare | Mathematics | 18.100B Analysis I, Fall 2006 | Syllabus

[Thesus]

Nod. I agree exactly with Golden Rule. I picture 315 as the typical first course in analysis and practically an absolute necessity, but 431 is exactly what we're doing here as preparation for the semester.

[pookie bear]

If Rudin is so hard, why do Harvard and MIT use it as their "intro" book?

 

Most schools have a baby analysis class that uses something like Ross's elementary analysis book. Is there a class like this at Harvard/MIT or are their students just immediately exposed to Rudin after multivariate calc?

[Golden Rule]

Most schools have a baby analysis class that uses something like Ross's elementary analysis book. Is there a class like this at Harvard/MIT or are their students just immediately exposed to Rudin after multivariate calc?

Harvard has a course called Math 101 which is partly a baby analysis class for people who don't have experience with proofs and want to take the Math 112 above or similar level courses. They also have harder freshmen math courses (23, 25, 55) that all cover the material in Math 112 in addition to multivariable calculus and linear algebra. (They're recently retitled these courses Linear Algebra and Real Analysis)

 

At MIT they have theoretical varieties of multivariable calc like 18.014 and 18.024 that I'd consider baby analysis courses. At least that's what I'd have taken if I'd gone there and wanted to continue with analysis.

[pookie bear]

Okay that makes sense, thanks for the clarification.