What math classes should I take if I want to get an econ/finance【转载】

(The personal opinions of Anthony Lee Zhang. See below for a supplement directed at Chinese students by Lingxuan Wu. Comments, suggestions, and questions welcome, email [e-mail] and/or [e-mail]. For example if there’s a class we haven’t discussed here that you want our opinion about, just email us. Feel free to re-share, re-post, etc. This is a work in progress and we may add/change things over time

Some disclaimers:

• Anthony's part is most directly relevant for US undergrads -- experiences for international undergrads may differ substantially. Lingxuan's part below discusses Chinese undergrad programs.

• There are many ways to get into an econ PhD program besides taking advanced math classes, especially if you’re interested in doing less math-heavy fields. This document is purely directed at, if you’re in a position where you want to take hard math classes for their signal value, what is in my opinion the optimal way to do so.

• These suggestions are purely about my view on maximizing your admissions chances. This is of course not necessarily the optimal strategy for your education/future paper writing success/happiness and intellectual satisfaction/quality of life/etc. Those are separate questions!

• I haven’t yet been directly involved in making admissions decisions so you shouldn’t interpret this document as representing “insider information” in any sense

)

First of all: take undergrad real analysis. You may need to take some prerequisites for this, do those or skip those, your call, just try your best to get an A in this. Nowadays doing well in undergrad real analysis is basically a requirement for top 10 econ PhD programs. If you’re self-studying, the standard textbook is Rudin “Principles of mathematical analysis”, and I think an alternative is Pugh “Real Mathematical Analysis”

After undergrad real analysis, I think there are basically two undominated options:

1. "Hard" real analysis: Functional analysis or measure theoretic probability, basically math or stats PhD 1st year sequences. There are a lot of textbooks at this level, but for example, (analysis) Royden, Rudin real + complex analysis, Rudin functional analysis, (probability) Billingsley, Dudley, Durrett, etc.

1. Econ PhD 1st year micro/metrics

• 1 has higher signal value than 2 as it's standardized and slightly harder

• I think that getting an A on 1 in a good school puts you somewhat above the median math ability at the Harvard/MIT econ PhD programs -- I am not sure how far above, my guess would be somewhere between 60th and 80th percentiles

• However, you should take the hardest classes you can get an A in: a A on 2 is better than a B+ on 1.

• Between econ phd first year micro or metrics, just pick the one that suits your research interests better, I don’t think one systematically has better signal value than the other

• However if your school is much better known for either micro/metrics, probably pick that one

• If you don’t feel confident you can get an A or A- in 2, then it may not make sense to take these -- the next level down would probably be like, statistics without measure theory (at the level of e.g. Rice or Casella/Berger). But my belief is that there is unfortunately a discontinuous decline in signal value when you go downwards from 2.

• It would be ideal to do 2., econ PhD first-year classes, in a relatively high-ranked US/Europe PhD program. Of course this is not an option for everyone (though through, e.g. exchange programs or RA programs, may be possible). I’m not sure how effective PhD level classes at non-US/Europe institutions are.

I think that taking classes outside of 1 and 2 is riskier. Some examples:

• Other hard math classes (algebra, geometry, stats theory, complex analysis etc...): This is risky because they’re less common. one example would be grad 1st year theory of statistics -- this is a bit less commonly seen on (non-metrics) applicants' profiles

• I would especially lean away from “algebra-like” pure math classes (group theory, etc.) and “physics-like” math classes, e.g. differential geometry, complex analysis, etc. They’re sufficiently not relevant for econ that their signal value is lower controlling for their hardness, and they PROBABLY won’t be as useful for you in your econ career. Too bad! They are fun! Remember, I’m not saying not to take them -- just be aware of the tradeoffs and opportunity cost.

• In contrast, there are a few math classes that are more useful for econ: convex analysis, probability theory, diff eq’s, especially like Brownian motion/stochastic diff eq’s as used in micro theory and finance applications. May be others that don’t immediately come to mind. I probably wouldn’t take these over 1 and 2, but it’s a close call, and they’re good choices for next classes after you’ve done 1 and/or 2

• Other hard stats, physics, CS, etc. classes: This has a similar problem to hard math classes -- they’re nonstandard and many admissions committees will have a hard time evaluating these in relative terms, because they’re seen more rarely than 1 and 2 on applicants’ profiles.

• Things are a bit different if you want to do theoretical metrics, in which case, things like grad stats theory become more useful

• PhD 2nd year econ classes: This is risky because PhD 2nd year field classes are not standardized, often have no problem sets, and as a result some are actually really easy and thus have little signal value. Yours might be hard, but the admissions committee doesn’t know that!

• Numerical computation, linear algebra: These two are, I think, the classes that I put on this list most unhappily. These are two of the more useful classes you can take in undergrad (especially if you want to do anything structural, like macro/IO, or even theory with any calibration/simulation components) -- however as far as I can tell they don't count very much towards grad school admissions at present, unfortunately. So, learn it, but don't weight it above 1 or 2 above if your goal is optimizing for grad school admissions

• A relatively hard machine learning class: This is the one thing I would potentially recommend as an alternative to 1 or 2 above. It is slightly risky: classes and material are a lot less standardized than more classical subjects. But it has a "cool" factor which sets it apart from some of the other things in this bucket. Also, I think it is more useful than 1 or 2 above. Depending on what you want to do. So, this could be considered.

• Similar fancy things like NLP (natural language processing), deep learning, etc. also fall in this category.

Supplements for Chinese students from Lingxuan Wu ([e-mail])

(I did math and physics in college. When I got interested in econ, I started with micro theory but then got more attracted to macro and made the change. Now I work mostly on macro/finance theory and some applied micro theory topics like IO/behavioral.)

Getting into an econ/finance phd program from mainland China can be quite different. For better or for worse, econ as a field is highly concentrated in the English world especially in the US. Here are a few thoughts of mine:

1. Above all, talk to people who get into econ phd programs from similar backgrounds (education, interests, skill set, etc.). Figuring out whether to do an econ phd is the first thing. (And it is always an ongoing process. You may find some careers better for yourself during your phd or afterwards. Even one advisor of mine thought about taking up a government job when he had an assistant professor offer from Harvard. And we're all glad he stayed in the econ academia.) And you'll get useful information on how to prepare for econ phd from them as well on all aspects.

1. Overall, I believe in terms of importance: recommendation letters > grades >~ own research > TOEFL/GRE. For TOEFL/GRE I think as long as you pass some threshold there is not much added value. (But communication skills are very important at any stage.)

1. Many Chinese schools provide GPAs and rankings. Don't be shy to list them on your CV if they're good. Rankings are easier to evaluate than GPAs.

1. I suspect the "real analysis" in the English context actually means "mathematical analysis" or "calculus" in many mainland Chinese schools. What Chinese schools call "real analysis" is usually based on measure theory, not multivariable calculus. So I suppose in your application you can clarify and say you have taken real analysis. This is actually a broader point: I've seen similar guides written by prominent economists suggesting students should take more math courses, and I suspect they are very targeted at students in the US. My sense is the Chinese undergraduate curriculum in math/science/engineering covers all the math skills needed for phd courses, perhaps except for some field courses in theory. Even in that case, you can usually pick up the missing parts along the way.

1. In terms of own research, econ is very different from other science/engineering subjects in that it's very hard to make a good contribution before seeing the big picture, at least in macro. Also the production process of a paper is very lengthy and uncertain. The result is very few undergraduates will have substantial outputs for phd application. But it's important to think actively, ask questions, discuss with advisors, and in that process you find your interests and reveal them to your advisors, and they will write your recommendation letters based on their interactions with you. (I applied for econ and finance programs with a writing sample in game theory. Econ programs don't usually have interviews. The interviewers in the finance programs that interviewed me didn't seem to read it carefully beforehand. But I suppose it's just a mismatch of topics.)

1. On recommendation letters, those from influential economists carry more weights. You may also ask around about their placement records. I think it's very important to get chances to spend time in the US/Europe, get exposed to the frontier econ research, get to know and perhaps work for professors. There are many exchange/visit programs that provide such opportunities. Doing masters/full RA may take more years, but it's helpful similarly: they give the exposure, prepare you not only for phd application but also for your research afterwards.

1. Last, enjoy the process. There're good days and hard days - keep at it though. I often fail to appreciate how far I've gone. Keep in mind we're uncovering the mysteries of the world.

转载自：https://shimo.im/docs/1bf584d893934bfd/read/