What I wish I knew before applying to Grad school

Here's a brief wannabe one-pager answering key crucial elements:

Why doing a PhD?
The letter of motivation
Research experience and letters of references
Course selection

Why doing a PhD?

This is the first-order question. and the answer is straightforward: there are problems in the world that you would like to see fixed and a PhD offers you the time and the resources to answer these key questions. The perk is that, with the skills you developed, you will likely be able to keep doing so for the rest of your life. It could be on the same topic or on another with similar tools. Both the private, the public and the academic market will offer you such opportunities upon performing frontier policy-relevant research during your grad school.

Do you think homelessness is bad? Go talk to the local NGOs, find the issues that they face and then, think as a researcher. Question how you can help with the tools you have. Use your comparative advantage: UofT, for example, is a starling school for IO and Urban Economics, among others.

The ideal PhD student, to me, is deeply passionate about solving societal problems. They know the issues so well that they will find how to contribute to the literature. Everyone can do maths and solve regressions, what is odd, is a field expert. Let your curiosity feed you and the market will reward you.

Hence, if you would like to have your own project and make this world a better place, a PhD is for you.

Which story should you tell?

First and foremost, don't try to be liked by everyone. You only want to be loved by a handful of faculty members that will put your name into the hat, envisioning strong research potential in you. If you are passionate about environmental economics, don't hide it, in fact, demonstrate it. Make it your whole narrative. Your story. You want to show the faculty that you have Grit on a policy-relevant topic. That you will come to their university and have research ideas - the most valuable resource in academia, combined with the capabilities of finding data.

Examples of such topics are Climate Change, Inequalities, Financial Risks/Climate Risks, Homelessness, Crime, etc. You want to show that:

You have done research on the topic (and be technical to demonstrate your capability and experience, yet, concise);
That you found data on the topics and how - in a concise manner;
You've taken particular courses or jobs/RAs to deepen your understanding.

There are no dominant strategies (though there are strictly dominated ones such as being fuzzy and not demonstrating the required technical capabilities). You want to demonstrate that your whole higher education made you converge into performing a PhD to answer specific questions. Name drop professors name that you would like to work with and why (do your research). They might be on the selection committee. Again, clear and strong signal, not shy and fuzzy. It's a thresholds system and you want to be above it for certain universities. The application process is heterogeneous, so are the professor's preferences, makes this play at your advantage.

The intro should show why, personally, you consider a PhD. Then, the next paragraph should explain your research of interest and another one on how this particular university can help you (which prof and which resources), and then make distinct paragraphs on how you delve into this issue in previous research and professional experience. Also be technical, yet concise, regarding your past research experience. Finally, you should precise that you applied for grants such as FRQSC and SSHRC and why you might get it. Perhaps, by underlying your previous grants and social involvements. This might help you at the margin, and will also show that you understand the academic market.

Please, understand that this is the optimal scenario. You might not fulfill all of these criteria, hence, do backward induction and start working on it.

Research Experience

The most important thing to work on before applying to grad school is to have great research experience, ideally, in your field of interest, or at the very least, on skills you consider using. This is very important as you will likely become path dependent on these few research experiences as you will have a comparative advantage in these subjects and tools.

If you have not yet any research experience, quit this page, and look at the faculties in your University or even Province. Choose a handful and send an e-mail, once a week until one offers you a great research experience. Don't write to 5 in the same week as they might all say yes... It's ok to do research not paid, yet, there are often undergrad research grants if you start your process early enough.

Now the strategic side. Research experience matters -- A LOT --, but the admission committee put a hefty weight on the letters of reference as a signal of your capabilities.

Which course to take ?

Again, the goal is to craft your own narrative. Don't simply mimic others. If you believe that sociology and political science will significantly benefit your research agenda, pursue them (and let the committee know)! Most people drift in and have no clear focus; show that this is not your case, and that you have a clear and organized research agenda.

However, it's important to note that math courses adhere to Inada conditions: their marginal value is very high near zero and diminishes as x approaches infinity. Given this, here are the courses I recommend:

Multivariate calculus
Linear algebra
Discrete math (optional)
Real analysis
Probability (optional)

Believe it or not, I had a blast doing real analysis. I recommend tackling the topics in the order listed. Yes, constructing proofs is challenging, but that's precisely what you'll be doing in your first year of a PhD program.