I recently gave a pair of talks in the Math Department’s Applied Math Seminar on basics of TCS. It was intended for a mathematically mature audience with no background in TCS. The slides for the talk are available here; they are far from perfect — but I will happily take suggestions on things that should be dropped or added. Interest in the talk was pleasantly high. High enough that I plan on doing this again and advertising more broadly — to graduate students in physics, engineering, etc. I also think it acts as a list of topics about which students should be able to answer questions during a comprehensive exam.