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Analysis of Algorithms Math Review

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					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
       http://rkelley.wordpress.com
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!

				
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posted:10/13/2012
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