<p>It's very personal and no right answer, but I would go for Complex Analysis - it doesn't come up explicitly but it will be behind a lot of the time series results in econometrics and macro sequences if you want to learn the proofs properly. It also underlies a lot of continuous time stochastic analysis if you go into that area.</p>
<p>Tom Sargent was of the opinion that knowing complex analysis was an arbitrage opportunity as an academic economist - as an undergrad he told me to take it, but I took numerical optimisation instead and I still regret that decision.</p>

CC BY-SA 4.0
2023-11-27T07:46:00.543Z
My economics background is only from self-study ( of macro ) but, As Debreu mentioned, complex analysis comes up a decent amount of time in advanced macro because solutions to differential equations ( and models in general ) sometimes involve it. I've never seen a macro application that required differential geometry but I'm not sure that I'd recognize it if I saw it. I'd go with complex analysis.
mark leeds
CC BY-SA 4.0
2023-11-22T07:31:15.457Z
2023-11-22T07:31:15.457Z
Debreu
<p>I am an undergrad (in math and econ) interested in pursuing a PhD in the latter. I can afford a pure math elective this semester and I am torn between diff geom and complex analysis. Which one is more useful for econ research (and for grad school apps)?</p>
<p>I am aware of sporadic but celebrated applications of diff geom (<a href="https://economics.mit.edu/sites/default/files/publications/ecta12030-%20final%20version.pdf" rel="nofollow noreferrer">nonlinear estimators</a>, <a href="https://www.ams.jhu.edu/%7Eabasu9/AMS_550-465/farkas-arbitrage.pdf" rel="nofollow noreferrer">arbitrage cones</a>, for example), but I am struggling to find any for complex analysis.</p>
<p>PS: I took the usually recommended math classes— analyses 1 and 2, calc up to PDEs, etc— so 'neither is useful take X' isn't useful either :').</p>

<mathematical-economics><reference-request>
Complex Analysis VS Differential Geometry as signals/preparation for grad school?
keynesian geometer
# Complex Analysis VS Differential Geometry as signals/preparation for grad school?

(Asked by: username_0 on 2023-11-17)

I am an undergrad (in math and econ) interested in pursuing a PhD in the latter. I can afford a pure math elective this semester and I am torn between diff geom and complex analysis. Which one is more useful for econ research (and for grad school apps)?

I am aware of sporadic but celebrated applications of diff geom ([nonlinear estimators](https://economics.mit.edu/sites/default/files/publications/ecta12030-%20final%20version.pdf), [arbitrage cones](https://www.ams.jhu.edu/%7Eabasu9/AMS_550-465/farkas-arbitrage.pdf), for example), but I am struggling to find any for complex analysis.

PS: I took the usually recommended math classes— analyses 1 and 2, calc up to PDEs, etc— so 'neither is useful take X' isn't useful either :').

**Tags:** mathematical-economics, reference-request

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## 1 answers

### Answer by username_1 on 2023-11-22. Score: 1

It's very personal and no right answer, but I would go for Complex Analysis - it doesn't come up explicitly but it will be behind a lot of the time series results in econometrics and macro sequences if you want to learn the proofs properly. It also underlies a lot of continuous time stochastic analysis if you go into that area.

Tom Sargent was of the opinion that knowing complex analysis was an arbitrage opportunity as an academic economist - as an undergrad he told me to take it, but I took numerical optimisation instead and I still regret that decision.

> **Comments:**
> **username_2**: My economics background is only from self-study ( of macro ) but, As Debreu mentioned, complex analysis comes up a decent amount of time in advanced macro because solutions to differential equations ( and models in general ) sometimes involve it. I've never seen a macro application that required differential geometry but I'm not sure that I'd recognize it if I saw it. I'd go with complex analysis.  

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