Lecture 1: FindMax, Permutations, Harmonic and Stirling Numbers

Background Material

• Summation notation, big Oh notation
• Natural logarithm, factorial function
• Recurrence relations, discrete probability,
• Lists and tables.

Reading

• Graham, Knuth, Patashnik, sec. 6-1 and 6-4.
• (maple online tutorial and help).
• New users tour
• Introduction to worksheets
• Help guide

Topics

• Maple programming, lists, and tables.
• Maple arithmetic (fractions, floating point)
• Names vs. values and evaluation
• permutations
• factorial function and growth rate
• cycle type and partitions
• Stirling numbers
• Harmonic numbers
• Analysis of FindMax program.
  • average number of updates
  • probability distribution.

Maple worksheets and programs

• max.mw - Maple worksheet for lecture 1

Assignments

• Install Maple 10 and peruse documentation and tutorials.
• Review Maple syntax and data structures.