New guy here, maths question

[luke77]

Hi guys,

I'm a 2007 graduate from a top 25 US school with a strong academic record and good test-taking skillls. I'm currently working in banking on wall street but am considering a PHD, probably in behavioral finance, though possibly Public Policy/Economics or Marketing. Like I said, I'm working in finance now, but I am a biology major without formal business training. I'm not quite sure that I will apply to PHD programs because of the math. Both because I don't have the math background required (I took through Calculus 2 and intro statistics but that's it), and because I'm not sure that I would "enjoy" the math enough to go through the math-intensive PHD process. So I guess I'm trying to get an idea of what the math required is "like", before I enroll in a masters program or something like that. Picking up a textbook and starting to read doesn't seem like a great option - are there any resources that I can read (either online or a book) that will give me an idea what the math will be like?

I'm also interested, anecdotally, how difficult you guys think the higher level math is, compared to intro calculus or stats.

Thanks for any help.

Luke

[oldprogrammer]

I think it really depends on what level of school you are trying to get into.

At a minimum, multivariable calculus, a course in linear/matrix algebra, and a course in calculus-based statistics seems to be expected for a top-50 program. Top 20 Finance and Economics programs seem to like Real Analysis, Advanced Calculus, or some other proof-based math course.

And since you're not from a business background, you would probably need to add Intermediate Microeconomics and Econometrics. In the end, it varies from school to school, and this kind of information can usually be found on their PhD FAQ.

I know that doesn't directly answer your question about what the math would be "like", but this information should be indicative of what will be expected of you from department to department. My understanding is that Econometrics is typical of the kind of math you would be doing.

[luke77]

Thanks, I appreciate the response. I'll probably be applying to a wide variety of programs - a few from the top 10, a few top 50, and a few top 100. I have a 3.8 undergrad GPA and scored a 1600 on my SAT in HS (haven't taken the GMAT but anticipate doing ok on it, based on this), so if I add the math I think my profile will be competitive, but I know how low the acceptance rate is and will not be crushed if I don't go to Harvard or top school - my goal is simply to get through a program which will get me a job at a "decent" school after graduation - I'm actually not sure I would want the (I'm sure) very intense atmosphere at some of the top programs.

To clarify my question, though, is there something you'd suggest I read to get an idea of what taking a course in econometrics, or upper level calculus will be like? In other words, what would you suggest to someone who wants to self-teach himself econometrics or calculus?

Thanks again,

Luke

[calchas]

I'm going to give you an indirect answer as well but perhaps it can help. I'm preparing for a PhD in finance and will be taking some math courses as well. It's almost guaranteed that I won't "enjoy" them as much as the topics covered in finance and economics ..

I grew up in a sports culture and I'm telling myself this: For all the glory and glamour of the 2-3 hours that athletes perform in a game, there's probably a similar amount or more of weight lifting, training, game film watching, etc... Many of these they don't enjoy but it's learning the tools of the trade ... and accepting these less-than enjoyable aspects for the passion and benefits of the career they have ..

In the academic field, I look at the next 12 months of math courses as the temporary price to pay to have an academic career and the individual freedoms that it affords ..

So, I'll just ask you why you want to do a PhD and what you see yourself doing after the PhD. If you crave that after-PhD life, then accept the less enjoyable parts of the journey to get there ...

[oldprogrammer]

I'm in agreement with Calchas. I think what is more important than your enjoyment of math (which is just a tool) is your enjoyment of the subject. You listed several different PhD fields, but you need to narrow that down. I kind of always knew I wanted to be a professor, but I did need to take some time to find out where my true interests are. If you don't love finance (and I mean really love it) you're not going to make it through the program. I know that sounds dramatic, but how do you force yourself to repeatedly do independent research in a subject that holds no interest for you? How do you find the inspiration to do so?

If you want to look into Econometrics and Advanced calculus, I would start with Wikipedia and WikiBooks. From there you should find all kinds of material. This would give you an overview, but I think you need to take a class to really appreciate these subjects. And I say that because unless you're the most dedicated person on the planet, I don't think you could approach these subjects with rigor you would get from the classroom. And without that rigor you probably won't sink your teeth in deep enough to really "get it". And besides, you'll need these courses on your transcripts if you really want to do this. Of course, unless you're set on a top 20 school you probably don't need the Real Analysis/Advanced Calculus. But it never hurts.

Econometrics - Wikipedia, the free encyclopedia
Econometric Theory - Wikibooks, collection of open-content textbooks
Real analysis - Wikibooks, collection of open-content textbooks


What would probably serve you better is to find out what areas of Finance might have an interest for you. To get ideas, check out the faculty pages at major universities and see what they're working on. Seems like NYU Stern's faculty pages are descriptive. You mentioned Behavioral Finance, which I'm not familiar with, but you might try seeking out journal articles on the subject. Sure, you probably won't understand what they're doing, but you can find out if the question was interesting.

[desimba]

Another good resource is the econphd.net site. Once you go to the site, you will see links for lecture notes. You can look at some of the microeconomics lecture notes to see the level of rigor. You might also look at some of the analysis material though I am afraid it will scare you unnecessarily especially if you were planning on a PhD in Public Policy.

[hvzw]

good answers