Numerical Analysis vs. Complex Analysis

[dogbones]

Which one, Numerical Analysis or Complex Analysis, would be more useful for Econ PhD admissions? I don't really understand the applications to Economics of either one... can someone fill me in?

[tutonic]

Numerical methods will help if you want to do structural work in macro.

[dogbones]

I see, thanks tutonic! Where does complex analysis come in? Maybe economic theory or micro?

[tutonic]

I don't think there's many applications of complex analysis in economics, but I could be wrong.

[laborsabre]

To expand on what tutonic mentioned, complex and numerical stuff shows up a little when using the log-linearization method (or other numerical algorithms) to solve rational expectations macro models, because you need to compute eigenvalues at one point, and in some situations these can be complex. See this nice write up from Notre Dame: https://www3.nd.edu/~esims1/linear_rational_expectations_sp12.pdf. The basic idea being that sometimes models get so complex that closed-form solutions take too long or are not known to exist.

 

But at least in my core sequence, the parts that involved numerical analysis or complex analysis were so brief/niche I can't imagine it is very helpful to take an entire class on them. The main gain from taking the class would probably be the practice doing proofs that you gain from such a math class, not the content itself. If you had to choose though, I would suggest numerical over complex.

[therealslimkt]

Are these the only two options?

[startz]

Perhaps remind us of your math background. How did you do in real analysis or other more advanced courses?

[dogbones]

I'm actually planning ahead for the master's program I will begin next fall. I plan to spend 3 years in the master's program and take courses not only in economics but also in math and political science. My research interests are game theory/mechanism design, network economics, health & development policy analysis, and theoretical economics. I feel that complex analysis is a more fundamental course than numerical analysis which to me seems more niche. This math course will be in my last semester of the third year, and prior to that I will take courses like probability/statistics, real analysis, econometrics 1 & 2, and the other core math classes that I've already taken like calculus and linear algebra...

[tutonic]

What startz meant is, give us a breakdown of the courses and grades obtained in previous math classes.

 

To add, if it wasn't sufficiently clear, there isn't anything 'fundamental' about complex analysis. You'll get much more use from numerical methods than complex analysis. Most of the work that deals with the complex domain merely draw from several key results in complex analysis. That's why it's not really worthwhile to take a whole course in it, unless you really really like math. Functional analysis will provide you with better mileage, comparatively.

 

Now, as to whether or not such a course is even necessary, most of the time, the answer is no. If you're bent on taking more math, you're better served doing a class that delves deeper into topology, since that's still moderately useful in micro theory.

 

Should you find yourself interested in some of the niche fields in economic theory, you will have sufficient time to pick up whatever is required during your 2nd and 3rd year. For example, if you find yourself really interested in networks, you'll need sound knowledge in combinatorics. However, outside of networks, there's not much use in economics, so it doesn't really make sense to take a class in it, when that time could've been better spent remedying other deficiencies in your profile.

 

The general advice espoused in this forum isn't that "more math is good" ; rather, it's "more math is good, if it doesn't take time away from remedying other aspects of your profile".

 

Let me just add one final thing. Most people seem to ignore, or pay less attention to, their statistical training. It is as important as your mathematical training. If you don't have it, you should look to do a course in measure theory. Stochastic calculus is another that's useful in macro, when expanding the agents models to infinity and econometrics (both 1 and 2).

[therealslimkt]

I've asked a lot of professors what the best math to take is, and neither complex analysis nor numerical analysis ever features very highly - stochastic processes, stochastic calculus, topology, functional analysis, measure theoretic probability are the go to. Since you're interested in networks and mechanism design, both of them use more discrete methods so a combinatorics class would be useful.

 

So if you have some of these as options it might be really better to consider them than either numerical or complex analysis.

[dogbones]

Thank you for these helpful pointers! So I could also choose between combinatorial mathematics and topology... which would be better to take with my research interests?

[dogbones]

Actually if I shave off intro to political science which may not be necessary, then I can take both combi math and topology... this is good right?

[EXP]

Actually if I shave off intro to political science which may not be necessary, then I can take both combi math and topology... this is good right?

 

If you're considering taking both in the last semester of your program, I don't believe they will matter much for admissions. However, the knowledge never hurts.

[tutonic]

As with any 3rd/4th year math course (past real analysis), doing well in them will only marginally help you in admissions, but doing poorly in them will really hurt you; by poor, I mean anything lower than an A-. That's why there's really little merit in taking those courses, unless all other aspects of your profile are already perfect.

 

If you provide a current profile, you'll be met with much more meaningful and specific suggestions.

[dogbones]

I'd been meaning to post my profile since startz mentioned it earlier too, it just took a while for me to complete it... so I'm a BA graduate and will begin my MA next fall (2020), and will do RA for two years after that, and then apply to PhD programs. I would appreciate any insights you all can provide. Thank you in advance!

 

Type of Undergrad: BA in Economics & BA in Psychology from best school in state (public university)

Undergrad GPA: 3.3 (graduated in December 2013 and I’ve been studying intensively for the past year as well as maturing as a person since graduating and entering the workforce)

Grad Concentration: likely admit for MA in Economics from Fall 2020 at the same school (I was admitted this year but had to defer because of financial and academic reasons – I thought everything would be significantly better if I had another year to prepare)

Grad GPA: unknown (aiming for 3.8+)

GRE: Q162 / V161 / AWA 5 (I will retake this and aim for perfect scores in five years when I’m applying for PhD programs)

 

Undergrad Econ Courses: Principles of Micro (A+), Intermediate Micro (A), Intermediate Macro (A), Games & Economic Behavior (A-), Financial Markets & Institutions ©, Mathematics for Economics (B), Introduction to Statistics (A-), Chinese Economy (B), Health Economics (A)

 

Undergrad Math Courses: Calculus II (C+), Elementary Probability Theory ©, Calculus III (B+), Calculus IV (B), Linear Algebra & Differential Equations (B-, the modal grade for the class was a D and I was in the top 15% of the class)

 

Graduate Econ Courses: planning to take Mathematics for Economics, Micro I, II, & III, Macro I & II, Econometrics I & II, Health Economics & Policy, Advanced Topics in Economics (seminar), and Master’s Thesis course

 

“Graduate” (Undergraduate) Math Courses: Calculus IV, Linear Algebra, Introduction to Advanced Mathematics, Elementary Probability & Statistics, Real Analysis, Topology, Combinatorial Mathematics

 

“Graduate” (Undergraduate/Graduate) Political Science Courses: Political Inquiry & Analysis, Scope & Methods of Political Science, Political Theory & Analysis

 

Programming: learning Stata, R, & Python, and also learning LaTeX

 

LORs: same three professors who will be on my Master’s Thesis defense committee (microeconomics & graduates of top PhD programs)

 

Research Experience: planning to be an RA during my second and third years in the MA program per the advice of my Master’s Thesis chair, planning an internship somewhere with the federal government during the first summer of MA program, have plans to collaborate with numerous academic economist contacts to publish papers in various fields and I hope to write a few of my own as well, after the MA program I’m planning to be an RA for two years prior to applying to the PhD programs

[tutonic]

You have a string of Cs and Bs for your undergraduate math courses. In my opinion, having no grade is better than a bad grade, during the admissions process. A bad grade is a definitive signal of inability to handle math, while having no real analysis in your transcript still provides some ambiguity, as they'll have to infer of your ability through other less-direct means(which can work to your favour, in this instance).

 

A few bad grades can be explained away, but a string of bad grades in math courses will cast considerable doubt on your ability to handle first year coursework. First-year coursework in Economics is very different than what you've encountered in undergrad. I honestly feel that first-year coursework is essentially applied math, and not so much Economics.

 

Unless you get an A for Real Analysis, I wouldn't advise taking anything beyond that.

[dogbones]

If you're considering taking both in the last semester of your program, I don't believe they will matter much for admissions. However, the knowledge never hurts.

 

Hi EXP, actually planning to take Topology in my fall of third year and Combi Math in the spring of that last year. And I would be taking two years off to be an RA while continuing to take a graduate class each semester/quarter, so anything I do during the MA probably would count heavily towards my admissions since my undergrad was so mediocre...

[dogbones]

You have a string of Cs and Bs for your undergraduate math courses. In my opinion, having no grade is better than a bad grade, during the admissions process. A few bad grades can be explained away, but a string of bad grades in math courses will cast considerable doubt in your ability to handle first year coursework.

 

Unless you get an A for Real Analysis, I wouldn't advise taking anything beyond that, if you're so inclined. Having no Real Analysis in your transcript is arguably better than a C in it.

 

Thanks tutonic for your feedback. The thing is, I came from arguably the best high school in the state and was a little too expecting of the educational quality at my home public university (naïve) and then I was personally not nearly as matured as I could've been so classes for me were almost like a casino game to a certain extent where what happened, just happened. I've been out of school for almost six years now, and I think I've caught up in my academic discipline, and am hoping to keep working to expand my understanding of economics, math, and general knowledge. My attitude towards the murkier classes in undergrad would be absolutely appalling to me now. And I'm just amazed that I pulled off such decent grades given my lack of resources (couldn't really buy books out of the blue because I wasn't working) and I can attribute it to my ambitious nature and as my workforce peers often say, my work ethic (when the casino is functioning towards my benefit, lol)...

[dogbones]

I've asked a lot of professors what the best math to take is, and neither complex analysis nor numerical analysis ever features very highly - stochastic processes, stochastic calculus, topology, functional analysis, measure theoretic probability are the go to. Since you're interested in networks and mechanism design, both of them use more discrete methods so a combinatorics class would be useful.

 

So if you have some of these as options it might be really better to consider them than either numerical or complex analysis.

 

Thanks therealslimkt, this post was so immeasurably helpful! I'm so very grateful for you sharing the fruit of your labor with us here!

[dogbones]

Unless you get an A for Real Analysis, I wouldn't advise taking anything beyond that.

 

That sounds fair enough, and if I don't get an A in Real Analysis (which would be really bad since I'd be preparing for it years in advance) I'd probably opt to retake it. I know how important writing proofs is for higher level economic research!

[startz]

Dogbones, it is certainly good that you are planning ahead. But you're going to learn a lot in the next couple of years about your strengths and preferences. Maybe you will excel at math and want to take more to present background to do theory as a strength. Or maybe you'll fall in love with the applied side and want to concentrate on that. So keep an open mind.

 

I know how important writing proofs is for higher level economic research!

Writing proofs is of little or no importance for 90% of higher level economic research. It is important for learning underlying material in graduate school.

[dogbones]

I really do appreciate your advice, startz! Thank you for your 2 cents, it is invaluable feedback. I've always loved math and hope to learn enough before I start the program to excel in it academically. With all the plethora of books, including the Kindle versions, on various topics exploding into the market these days, I feel like I can do well and get a handle on being where I need to be.