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After discussing administrative aspects, I introduce some motivating examples for the course. We discuss three problems in linear algebra. graph theory, and matching theory which are superficially different, but are very closely related. Lecture notes at: http://math.sfsu.edu/federico/Clase/M... Sorry that the camera is so erratic. This was our very first try with an inexpensive, 100% DIY setup that we learned from figure skaters. Some heat sensors by the board tell the camera where I am, and it follows me automatically. With time I learned to move around less so the camera wouldn't get confused. We also improved the algorithm so that (hopefully) the camera won't follow me if I am just crossing the room to pickup the eraser. I think the videos mostly got better as time went on. (My colleague Arek Goetz set this up, a big thank you to him!!!) San Francisco State University (San Francisco, USA) Universidad de Los Andes (Bogota, Colombia) Spring 2007 Partially supported by: US National Science Foundation CAREER Award DMS-0956178 US National Science Foundation Grant DMS-0801075 SFSU-Colombia Combinatorics Initiative.