Analysis of Algorithms: Math Review Richard Kelley, Lecture 2
last time administrative stuff course webpage definition of “good” algorithm fun with C++ assignment 0 discussed but not assigned
“good” algorithms we agreed on the following we want to augment our statistical analysis of algorithms (i.e. profiling) with analytical analysis analytical analysis lets us make better predictions ( as close to science as you’re going to get in a CS program). we have to (get to?) do math we want to focus on the worst case performance of our algorithms. online notes
this time questions & points of clarification roadmap of math topics math motivation – harmonic numbers & approximation notation proofs the “friendly skeptic” induction proofs summation – probably not… assignment 0 “assigned” assignment 1 announced
the schedule: main topics basics mathematical foundations basic analysis easy problems graph algorithms (discrete) optimization – dynamic programming & greedy hard problems intractability randomness and approximation concurrency
mathematical foundations why are we doing this stuff? we get why we need math what math do we need? harmonic numbers show up in the analysis of quicksort the key idea is approximation
notation we talked about notation for input size and run time in lecture 1. this time numbers sets functions propositions
proofs what are they? what kinds are there? direct proof proof by contradiction induction most proofs in computer science use induction of some kind. how do we write “good” proofs? full sentences. I’ll accept English and Latin. you have to persuade the “friendly skeptic.”
induction what do we know already? what is it? when does it work? example why does it work? to the board!
assignments 0 & 1 assignment 0 out today but you don’t have to turn it in. assignment 1 out tomorrow by 8pm if not, bug me due on Wednesday, start of class all math, but not too hard I’ll write up my paper notes and put them on the blog. enjoy the long weekend!