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

• www.maplesoft.com (Maplesoft Web site)
• www.mapleapps.com (Maple Application Center Web site)
• www.maple4students.com (Maple Student Center Web site)
  

Assignments

1. assign1.mw - first assignment to be handed in.
   Created: Oct. 20, 2005 by jjohnson@cs.drexel.edu