On this page, I am planning to upload some of my past applications in hopes that they may be useful to future applicants. If you're here because you'd like to apply to Waterloo (or you're already here), please have a look at:
Undergrads: Please reach out via email if you are interested in trying out research! And a funding opportunity. Also, I strongly recommend checking out the Directed Reading/Research Program.
PhD and MMath students: C&O grad applications (I don't accept applications via email) and Vanier CGS, a scholarship opportunity.
Post-docs:
Postdoc and tenure-track applications
These are far from perfect, and sometime, when I have time, I'll write more about this. For now, take these as examples, but not as templates for success.
Mathematical Sciences Postdoctoral Research Fellowship (NSF MSPRF, USA)
Project Description and References
Biographical Sketch (this was updated after I received the MSPRF, but the format is the same)
PhD program application
Advice (specific to North America):
This statement might be read by potential supervisors or by the admissions committee.
Mention who you'd like to work with. List around 3 names (not emeritus professors and not postdocs). This gets your application into the right hands.
List which area you want to work in. Describe your experience related to this. Don't repeat your transcript, but talk about research experiences or anything else that's not just "I did well in this class". Do highlight if you've taken grad classes.
For the research, it is useful to include some details, but at the level that another undergrad could easily understand.
You can include statements about why you want to work at this university in particular. You can briefly talk about career plans. You can talk about what brought you math and your area on particular.
Explain your contributions to joint projects; don't be humble. Mention if there is a paper, preprint, or plans for such.
Explain anything else you need to explain (I didn't take the GRE because... Or I got a low grade in this class related to my area because...) if you have a good explanation.
Miscellaneous
If you're writing applications in LaTeX: the font size (e.g. 12pt) you specify in LaTeX comes out smaller in PDFs. If your application needs a specific font size, scale it up by a factor of 1.00375.