Lecture 3: Sequences, Recurrences and Limits
Background Material
 Fibonacci Numbers
 Recurrence Relations
 Full binary trees  all internal nodes have two children (number of
internal nodes is one less than the number of leaf nodes)
 Limits
 Asymptotic Computing Time Analysis
Reading
 Maple Help  rsolve, time,

Topics
 Programming in Maple.
 Maple procedures
 Recursion and "option remember"
 Timing maple commands
 Fibonacci numbers and dominoes  how many ways are there to
fill a 2 X n rectangle with 1 X 2 dominoes (placed vertically or
two stacked horizontally)?
 The golden ratio and solving the Fibonacci recurrence
 Empirical investigation of asymptotic computing times.
 Computing time of two algorithms to compute the Fibonacci numbers
Maple worksheets and documentation
 fib.mw  Maple worksheet investigating the Fibonacci
numbers. Also contains a recursive function to generate all configurations
of dominoes that fill a 2 X n rectangle.
Resources
Assignments
 assign1.mw  first assignment
to be handed in.
Created: Oct. 20, 2005 by jjohnson@cs.drexel.edu