1. Analysis of Algorithms: Math Review Richard Kelley, Lecture 2

2. last time  administrative stuff  course webpage  definition of “good” algorithm  fun with C++  assignment 0 discussed  but not assigned

3. “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  http://rkelley.wordpress.com

4. 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

5. 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

6. 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

7. notation  we talked about notation for input size and run time in lecture 1.  this time  numbers  sets  functions  propositions

8. 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.”

9. induction  what do we know already?  what is it?  when does it work?  example  why does it work?  to the board!

10. 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!