MA-351 Homework 3

Due at 9:00am , Wednesday October 15, 2003


Calculations necessary for these problems may be done either by hand or with Maple. Handwritten solutions may be submitted to me or put in my mailbox in HA 245 before Wednesday, or handed to Brenda Currin before 9am on Wednesday. Or you may email before the deadline an ASCII text, Maple Worksheet (.mws), html, or postscipt/pdf-formatted document to me (kaltofen@math.ncsu.edu).
Note my office hours on my schedule.

  1. Consider Stirling 's formula for approximating n!:


    		n
    		( 2*pi*n )1/2 * (
    		)n


    		e
    1. Using the binary operators + (plus), - (minus), * (times), / (divides), and ^ (exponentiation), all of which have exactly 2 operands, draw the expression tree corresponding to this expression.
    2. Convert the expression tree into a fully parenthesized linear infix expression string.
    3. Write the prefix and postfix expression string equivalent to the expression tree.
  2. DMM §3.3, Problem 8, page 107. Note: in order to have a unique DFS tree, assume that the order of the neighboring vertices of each vertex is alphabetical and that you start at vertex labeled a.