This document contains notes corresponding to the material that has been or will be covered during the discussion sections of the spring 2009 iteration of the course BU CAS CS 332, taught by Professor Leonid Levin. These notes will contain intuitive exposition, as well as problems and examples that demonstrate how the definitions and theorems presented during lectures and in the official lectur...

A search engine can index a concept that appears entirely on a single page. But concepts can span several pages. For instance, a page on trees may be linked to a page on lecture notes for a data structures course. If the trees page does not specifically mention lecture notes, then a search engine search for lecture notes on trees will, at best, only partially match each page. In this paper we d...

Lecture notes concerning basic properties of the solutions to the semi-linear Schrödinger equation. Based on these notes a series of lectures were given at the summer school on Mathematical Physics in Sogang University, Seoul, July 20-23, 2010.