Seeking Coursework Advice | Early Undergrad

[piperpanama]

I'm an undergraduate student at Michigan State University and in a few years I want to apply for a PhD in either Applied/Computational Mathematics or Economics. I've been lurking on this forum for some time now, and see a lot of importance in choosing the right coursework, so I'm looking for suggestions on my coursework outline and for things that I may be unintentionally neglecting that are important, etc. My profile (GPA, research, etc.) is included in another post from this account.

 

 

1st year (19 - 20)

Partial Differential Equations (MTH 442), Discrete Mathematics I (MTH 481), C++ Programming (CSE 232), Intro Econometrics (EC 420), Behavioral Econ (EC 404), Honors Micro (EC 251H), Discrete Structures for CS (CSE 260), Honors Linalg (MTH 317H), and Intro Engineering (EGR 100).

2nd year (20 - 21)

FS20: Parallel Computing (CMSE 822), Stats & Prob I (STT 861), Econometrics IA (EC 820a), and Honors Abstract Algebra I (MTH 418H)

SS21: Numerical Linalg (CMSE 823), Stats & Prob II (STT 862), Econometrics IB (EC 820b), and Honors Abstract Algebra II (MTH 419H)

3rd year (21 - 22)

FS21: Microeconomics I (EC 812A), Macroeconomics I (EC 813A), Intro Analysis (327H, may skip this since I have Analysis credit from high school), and Selected Topics in Computational Math (CMSE 890).

SS22: Microeconomics II (EC 812B), Macroeconomics II (EC 813B), Real Analysis (429H, may elect to take graduate Complex Analysis (MTH 829) instead), and Selected Topics in Computational Math (CMSE 890).

4th year (22 - 23)

FS22: Time Series Econometrics I (EC 822A), Cross Section Econometrics I (EC 821A), Special Topics in Applied Math (MTH 994), and Numerical Analysis I (MTH 850), and Capstone in Mathematics (EC 496W).

SS23: International Trade: Theory and Commercial (EC 840), Applied Econometrics (EC 823), Special Topics in Applied Math (MTH 994), Partial Differential Equations (MTH 849), and Capstone in Mathematics (MTH 496W).

[Bayes]

That is hell of a schedule you got there! I don't think you would need the field PhD Economics courses (such as International Trade Theory, time series etc) and Macroeconomics (it does not have signalling value since the class differs greatly among schools); your time would be best spent RA'ing for a professor and spending a significant with that.

 

As for your math courses, abstract algebra carries little weight (since its not applicable to Economics). If you are taking it to fulfill a math major then it is reasonable. Graduate Real Analysis would be a better option if you are keen on taking a graduate level mathematics course.

 

For undergraduate math courses, my suggestion is: Analysis II, Metric and Topological Spaces.

[coloradoecon]

Bayes, given that the OP has not decided between Applied Mathematics PhD or Economics PhD (and has just finished freshman year, so they have lots of time), I would recommend they keep Abstract Algebra unless they decide to pursue an Economics PhD, as most graduate math programs want to see two semesters of Algebra (as well as two semesters of Analysis).

 

You have a very challenging courseload, good luck! You look like you are driven, which is good. I might consider moving the Abstract Algebra to your junior year, and take an analysis sequence during your sophomore year. This will prepare you well for the graduate micro courses you want to take during junior year. Given your school (T30), if you manage to get excellent grades with this course-load, and have good research experience, you should be competitive basically everywhere.

 

Edit: I'm realizing you are taking the entire first-year PhD sequence in your sophomore and junior years. That probably is not necessary (like Bayes says, drop Macro) and potentially has more risk than reward. The Metrics and Micro sequence is worth taking, but I would ask the professors whether it is okay to take Metrics I without any previous coursework in probability / statistics in a math department. I don't think I would have been able to succeed without my prior training in rigorous probability / stats courses.

 

Additionally, consider taking a lighter load your last year, and doing an independent thesis project. You will also be applying then, which will consume quite a bit of your time.

 

I think you'll learn, the more you RA and work more closely with professors, that an Economics PhD is not about coursework, but about producing research and developing research skills. The coursework is an means to that goal of producing research.

Edited July 13, 2020 by coloradoecon

[startz]

Both Bayes and coloradoecon have pointed you to being a research assistant or doing an independent thesis. They are right.

 

Past some point, getting experience doing research is much more important than more coursework both for learning the trade and for getting letters of recommendation.

[piperpanama]

Both Bayes and coloradoecon have pointed you to being a research assistant or doing an independent thesis. They are right.

 

Past some point, getting experience doing research is much more important than more coursework both for learning the trade and for getting letters of recommendation.

 

Absolutely agree. I haven't done any work as an RA for an Economics professor, but I've done separate research projects as an RA in Developmental Econ and Financial Math under a Statistics professor last semester. I'm continuing the RA work in Developmental Econ into this Summer by writing a manuscript to eventually be submit for publication. I'm also participating in an external research program through NSF XSEDE with work primarily in parallel computing, computer vision, and performance optimization.

 

I'm going to get more research experience under an Economics professor this coming year through a specialized program at my university which starts this Fall. I got admit as a rising Sophomore, so I should be able to squeeze quite a bit out of that.

 

I haven't considered doing an independent thesis before. I think there's something like that through my university's honors college, but that's a ways off. Is a thesis something that I could be starting this early on?

[coloradoecon]

A thesis in your sophomore year is a little early, but you should definitely be thinking about what you are interested in and perhaps read / attend seminars around those topics. Don't also feel the need to corner yourself in on your interests so early. People change all the time after they enter grad school.

 

Usually, people begin seriously researching during their junior year, often for a proposal and to receive funding, which leads to a two or three semester research and writing period for the thesis. It's not a dissertation, and it probably won't be great. But it is a good place to start writing and learning about the entire research process, as your first papers are almost always bad.

 

When it comes to RA positions, look to not only take on short-term projects, but long-term ones as well. Not only will you learn a lot and understand more about the research process, but the professor you have worked long-term with and taken a (preferably advanced) course from will write you the strongest letters.

[piperpanama]

Bayes, given that the OP has not decided between Applied Mathematics PhD or Economics PhD (and has just finished freshman year, so they have lots of time), I would recommend they keep Abstract Algebra unless they decide to pursue an Economics PhD, as most graduate math programs want to see two semesters of Algebra (as well as two semesters of Analysis).

 

You have a very challenging courseload, good luck! You look like you are driven, which is good. I might consider moving the Abstract Algebra to your junior year, and take an analysis sequence during your sophomore year. This will prepare you well for the graduate micro courses you want to take during junior year. Given your school (T30), if you manage to get excellent grades with this course-load, and have good research experience, you should be competitive basically everywhere.

 

Edit: I'm realizing you are taking the entire first-year PhD sequence in your sophomore and junior years. That probably is not necessary (like Bayes says, drop Macro) and potentially has more risk than reward. The Metrics and Micro sequence is worth taking, but I would ask the professors whether it is okay to take Metrics I without any previous coursework in probability / statistics in a math department. I don't think I would have been able to succeed without my prior training in rigorous probability / stats courses.

 

Additionally, consider taking a lighter load your last year, and doing an independent thesis project. You will also be applying then, which will consume quite a bit of your time.

 

I think you'll learn, the more you RA and work more closely with professors, that an Economics PhD is not about coursework, but about producing research and developing research skills. The coursework is an means to that goal of producing research.

 

Thank you for the very detailed response!

 

My background in probability/statistics was something that I was concerned about when choosing to enroll in the Econometrics sequence. I emailed the professor beforehand asking if I could enroll. He brought up a similar concern, but was satisfied when I told him that I had completed AP Statistics (got a 5, but that's probably irrelevant) and EC 420 (Intro Econometrics w/ STT 441 prereq) with a 4.0. I wanted to enroll in EC 421 (Advanced Econometrics) initially, but my advisor heavily advised me against doing so. In retrospect I wish I ignored that since I don't think I got very much out of EC 420. I'll also be enrolled in STT 861 (Probability & Statistics I, basically the harder version of STT 441) during the Fall, and STT 862 (Probability & Statistics II, harder version of STT 442) in the Spring.

[coloradoecon]

I would highly, highly recommend you do some studying in a Calculus-based probability text this summer on your own before you take that class. I am talking about something like the first part of Casella & Berger (Ch 1-4, 5.5) or Grimmett & Stirzaker's "Probability and Random Processes" (Chapters 1-5, 7). Brush up on your analysis as well, since elements of measure theory may be introduced.

 

Your goal in a graduate-level course is to place as high as possible (ideally in the top quartile). Most of the students in the course likely have taken a yearlong probability & statistics sequence, which places you at a disadvantage. You can make up for that by working hard and getting acquainted with key prerequisite material. Feel free to direct message me if you have questions.

Edited July 15, 2020 by coloradoecon