I'm a developer, but don't have the foggiest idea of how to prove something by induction. Is this the kind of book I should look at? Or is there something that should be taken as a prerequisite?
Former Illinois student here. There was another course called CS173 Discrete Structures that we took as a prereq to this class. You can find the textbook here http://mfleck.cs.illinois.edu/building-blocks/index.html with a chapter dedicated to induction