# Analysis of Algorithms Math Review

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```					Analysis of Algorithms:
Math Review
Richard Kelley, Lecture 2
last time
   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
   http://rkelley.wordpress.com
this time
   questions & points of clarification
   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
   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!

```
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 views: 8 posted: 10/13/2012 language: English pages: 10
Jun Wang Dr
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