UBC Mathematics Advice for PhD Programs

Not every top student should get a PhD in economics or finance. But if you are considering it, then some advanced preparation can make your life easier.

Reference Letters

Keep in mind that this advice is not sufficient to get into a top program. You could have perfect grades in all of your classes, but there are lots of students with high grades. The first-order concern for getting into graduate programs (both MA and PhD) is to get good letters of reference from research faculty. It does not matter how many math classes you have taken if you don't have an economist saying you would make a good researcher. Also keep in mind that good reference letters are more than just "so-and-so got a 90% in my class". Research experience (such as being a research assistant for a professor, or getting a pre-doctoral fellowship) is also much more useful than taking particular math classes.

Math Classes for MA Programs

The letters still matter, but if you think you would do a terminal MA (and not apply directly for a PhD), then there is less benefit in loading up on math courses. Regardless, take MATH 200 (Calculus 3) and MATH 221 (Linear Algebra). If you take more math classes, then do it for your interest or in order to make the option of getting a PhD in the future easier.

Math Classes on your Transcript for PhD Programs

One indicator for getting into top economics/finance PhD programs directly from an undergrad is whether you have done sufficiently well in a difficult math course such as real variables/analysis.  This filter is because of the giant leap in mathematical sophistication required for the first year of a PhD program. Advanced undergraduate math classes are proof that you can handle the difficulty, and signal your intelligence.

The converse is true as well: doing poorly on tough math courses is a terrible signal that would significantly hurt your chance of getting into top programs. You are better off not taking hard math classes unless you can do well in them.

Also, in many ways, our theoretical 400 level economics courses (described below) are a better direct technical preparation, and are much more useful for getting letter writers. Taking math classes should be done in addition to those courses, not instead of them. With that said, for many fields you will find the tools of advanced mathematics classes, and the rigor of doing proofs, directly useful.

To plan for getting into a top PhD program directly out of your undergrad, you could (1) try to get real analysis/variables is on your transcript (or a number of other courses from the Math department), and (2) use it as an indicator to yourself of whether you are well suited to graduate economics or finance.  This will require some early planning in your course selection

Ordered Course Selection (for students interested in a PhD)

  1. MATH 200: Calculus 3
  2. MATH 220: Mathematical Proofs
    • Need >80% in the class.  Math department curving means you need to work hard.
  3. MATH 221: Linear Algebra
    • While not a pre-requisite for Real Variables, strongly consider it prior to MATH 320 to build more mathematical sophistication, and because the tools are very useful in economics.
  4. (Optional) MATH 302:  Introduction to Probability
    • Another class to consider prior to starting Real Variables for math practice and to learn some useful tools.

Real Variables (for those directly considering a PhD, and already taking 400-level econ courses)

At UBC, the analysis course is MATH 320: Real Variables I

Risks in Taking MATH 320

The upside of getting a decent mark in MATH320 is that it is a strong signal to graduate schools of your technical rigor and intelligence. The downside risk is that you could get a terrible mark in the class, which both hurts your GPA and may serve as a bad signal on your ability to handle difficult material. For all but the most technical students, the downside risks outweigh the potential upside. Also, to repeat an important point: MATH320 is helpful, but is not a substitute for doing well in upper-year economics courses and getting good letters.

If you do very well in 220, 221, and 302, then it is probably worth the risk to take it for credit on your transcript.

Advanced Economics Courses

Math courses have their own focus on theory and proofs. You should also learn more on how to use these tools, which can be a very different experience.  Economics courses are suitable to bridge the gap between math and how we actually use it in graduate program and beyond.  In particular, for your 4th year economics courses make sure to take (in order of importance, but you should take all if offereed)
  • ECON 420: Optimization and Economic Theory
  • ECON 421: Introduction to Game Theory and Applications
  • ECON 425: Introduction to Econometrics
These should be taken even if you don't think you are interested in doing theory or microeconomics, as they will help you with graduate school much more than any field course.

An alternative strategy for most people to taking real variables may be to ensure that you do well in ECON 402, ECON 421, ECON 425, MATH 301, MATH 220, MATH 221, and MATH 302. But you are better off doing all of these as well as MATH 320 (which you would likely be well prepared for after taking those courses).