This page collects some of my advice on mathematics courses for undergraduates at UBC. It’s just my advice! It’s not a formal recommendation or official advice, and it’s only based on my experiences and other guidance online. Take this with a grain of salt; if you’re not sure, reach out to the director of graduate programs you are interested to get their opinion. You may also find my colleague Jesse Perla’s very good summary useful (and more concise!). The American Economic Association also has a set of recommendations you can check out.

Questions regarding mathematics are some of the most common ones I get when I advise students. There are three reasons for this:

- The standard economics curriculum (at UBC, and most schools) does not require more than the basic introductory calculus sequence…
- …but intermediate and advanced economics courses tend to use a great deal of math, as do readings and many textbooks…
- …and people have persistently heard that you need “more math” for graduate school or to be competitive on the job market.

These reasons are all interrelated, and largely correct, for for two key points: (i) economics, as a discipline, highly values logical, analytical, and organized reasoning with an emphasis on identifying assumptions and processes (i.e. “thinking like an economist”), and (ii) the most natural language for expressing this reasoning in a formal setting is mathematics and statistics. Modern economics (since the 1950s) uses mathematical and statistical models extensively, more than any other social science. This leads to a simple conclusion: more mathematics is beneficial *in general* – but some topics are more helpful than others.

## What’s the Point?

The point of taking math courses (in terms of graduate school applications) is to demonstrate to a program that (i) you are an academically robust student, and (ii) you will be likely to succeed in a graduate program. Graduate programs want to choose students who will be successful and do impactful research. The reason to take *math* courses (in particular) is because graduate economics involves a lot more mathematics than undergraduate economics. Taking math courses and doing well in them tells a program you will be likely to succeed – but doing poorly tells them the opposite! Some important points to consider:

- This is particularly true if you are intending on doing a PhD in economics; the benefits of math for Master’s level courses are still present, but are less essential. You can see below for a guide to the suggestions for each level.
- Reference letters are still the most important piece of information for graduate school; you can see my guide here.
- You can demonstrate your suitability for graduate school in other ways: advanced economics courses which are mathematical or technical in nature (e.g. ECON 420, 421, 425) are just as good or better.

In general, you should view your math courses are *electives* that strengthen your CV by showing your abilities and teaching you some new skills. If you are keen on graduate school, you should still focus on excelling in your economics courses, taking impactful and high-value electives, and getting good letters of reference.

### PhD Level Mathematics

If you want to get a **sense of the level of mathematics** expected for a top PhD program, consider this set of “challenge exams” from UPenn’s PhD Math Summer Camp, which is designed to prepare students to start their PhD program. In my opinion, this is fairly representative of the more difficult mathematics typical in a PhD economics program; Master’s programs are (usually) less intense.

## General Recommendations for UBC Math Courses

While math in general is useful, most economics relies heavily on a couple areas: (i) calculus, (ii) linear algebra, (iii) proof, and (iv) statistics. This gives some recommendations for the most important and useful courses to take at UBC:

**MATH 200 – Calculus III (link)**: this is advanced multivariable calculus, and is probably the most important course to take. Economics at all levels involves lots of optimization problems, and optimization often requires calculus.**MATH 221 – Matrix Algebra (link)**: this course studies the use, manipulation, and solution of problems using matrices. This is helpful for both solving complicated systems of equations (like in an optimization problem) but is essential to modern econometrics, which relies on linear algebra.**MATH 220 – Mathematical Proof (link)**: this course is about mathematical proof techniques and logic, usually in a number theory setting. This is surprisingly important for economics, since proving things about models is how economists understand them.- Be careful! The math department uses this course as a key indicator for their major, and aggressively scales (plus, it’s hard anyways). Aim for an A- or better.
- You may find the book “How to Prove It” by Daniel Velleman a useful counterpart or substitute for this course.

These are the three most important courses; if you are planning to do a Master’s degree in Economics, these would make you relatively well-prepared for the material being taught at that level.

### Other Suggestions?

Some less important, but potentially valuable courses to consider are:

**MATH 302 – Introduction to Probability (link)**: this is a mathematical introduction to probability, which is very useful for econometrics but also helpful for economic models that involve randomness (like stochastic equilibrium models). There are also some equivalencies for this course, which are probably just as useful (e.g. STAT 302).**MATH 256 – Differential Equations (link)**: differential equations come up somewhat often, and it can be valuable to be familiar with this branch of mathematics for some applications (e.g. evolutionary games) particularly including dynamics. There are a bunch of different courses on the subject, but this course gives an overview of the most important topics.- There’s probably no issue if you take any of the equivalent differential equations courses (e.g. MATH 215); I think MATH 256 is “the best” because it covers partial differential equations, but to be honest any course that covers ordinary differential equations in detail is fine.

## The Real Analysis Question (MATH 320)

One of the most important decisions to make concerns real analysis (**MATH 320 Real Variables I: link**), which is an important topic in many economic fields. You will often find advice for students online that they should take this course if they are interested in graduate school. However, it is not as clear-cut as it might seem:

- This course is very difficult: it is used as a key indicator for mathematics graduate school and is aggressively scaled (and the class is full of smart people). It can be hard to do well in this class, and doing poorly would be a bad indicator for graduate schools.
- This course is also not super
*directly*relevant in terms of the tools it teaches: it’s more an indicator of your overall mathematical maturity and capability rather than a demonstration of specific skills you will find useful.

For most students (and nearly all people who only want to do a Master’s degree) it’s probably not worth it; however, if you’re good at math and want to be really well prepared, it can be worth a shot.

### Update: Introduction to Real Analysis (MATH 319)

Recently, the UBC Math department has introduced another version of real analysis, which is intended for non-honours students. This course (**MATH 319: Introduction to Real Analysis: link**) is likely to be a better option for students who want exposure to real analysis but are not comfortable with the more intense version of real analysis that MATH 320 offers. However, this course and structure is still new, so we don’t really know exactly how this will play out.

## General Program Recommendations

My suggestion for students who are interested in being very well prepared for graduate school from a mathematical point of view are listed in Table 1. I have used a “tier-list” ranking system: courses listed with an A are very important or essential (A*), B are important but not absolutely essential, and C/D are optional. If you have any questions, don’t hesitate to send me an email and ask!

Course | MA Program? | PhD Program? |

MATH 200 | A | A* |

MATH 221 | A | A* |

MATH 220 | A | A* |

MATH 256 | C | B |

MATH 302 | C | A |

MATH 320 | D | B |

ECON 420 | B | A |

ECON 421 | B | A |

ECON 425 | B | A |

## Frequently Asked Questions

**Do I***really*need all that math?*Reallllllyyyyy?*- Yes. Don’t believe me? Check out that UPenn exam above. That’s not a joke, and they’re not trying to scare you off.
- If you want to do a graduate degree related to economics that’s less mathematical, something like public policy might be more appealing. You can also inquire about specific graduate programs – there’s a fair amount of variation, particularly at the Master’s level.

**I think group theory is interesting; should I take it?**- I mean, I agree – I think group theory is interesting. Is it useful for economics? To be honest, I have literally seen exactly one paper that uses group theory in my entire career in economics, so it’s definitely not that essential. It gets a D or F on the tier list (sorry group theorists – prove me wrong!).

**What if I did really badly in first year math? What can I do?**- If you got into the major, you didn’t do that badly. I still think taking some math courses is valuable, especially if you do better on harder courses. One thing graduate programs like (and your letter writers can highlight) is an upward trajectory. If you get a B in MATH 100 but an A+ in MATH 200, that’s probably fine. If anything, it shows you can recover from setbacks and work hard.

**What about computer science? Should I take CPSC courses?**- Maybe? It’s definitely valuable in economics to know how to write code… but that’s not the same as learning computer science. Understanding data structures and how to write in a programming language (even one like R) is useful, but it’s not the most important skill. C or D-tier.
- You can probably learn this on your own, by the way, for much less money. Go take an online “Introduction to Python” course for free!

**What about <random course X>?**- Shoot me an email if you’re not sure; I’m not familiar with every course, but if you have a course outline or past syllabus, I can probably give you a sense of its value.

*(Last update: 2023-08-04)*