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Some application materials from my job search of 2006-2007 (which ended successfully in an NSF Fellowship, Instructorship at MIT and one-year appointment at IAS):

Three cover letters, for MIT, Stanford, and AIM: They're mostly the same boilerplate; the only important differences are in the second paragraph. Hopefully I was right in thinking that cover letters aren't actually of great importance.

My research statement: In case any of you are wondering, no, I didn't do any of this research. Maybe next year. If any of you get brilliant ideas based on this stuff, give me an email, and we can write the paper ;)

My teaching statement: yes, it's kinda cheesy, but how could a teaching statement be otherwise?

My CV at the time: I used Ezra Miller's wonderful template, which I think is the most aesthetically pleasing I know of.