# Thread: Numerical Analysis vs. Complex Analysis

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## Numerical Analysis vs. Complex Analysis

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?

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## Re: Numerical Analysis vs. Complex Analysis

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

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## Re: Numerical Analysis vs. Complex Analysis

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

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## Re: Numerical Analysis vs. Complex Analysis

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

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## Re: Numerical Analysis vs. Complex Analysis

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_r...tions_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.

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## Re: Numerical Analysis vs. Complex Analysis

Are these the only two options?

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## Re: Numerical Analysis vs. Complex Analysis

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

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## Re: Numerical Analysis vs. Complex Analysis

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...

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## Re: Numerical Analysis vs. Complex Analysis

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).

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## Re: Numerical Analysis vs. Complex Analysis

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.