CMPSCI 250: Introduction to Computation

David Mix Barrington

Fall, 2007

Homework Assignment #7

Posted Tuesday 27 November 2007

Due on paper in class, Friday 14 December 2007

There are eleven questions for 100 total points plus 10 points extra credit. All are from the textbook, A Mathematical Foundation for Computer Science, the third (purple) course packet. "Problem 1.1.2", for example, is at the end of Section 1.1 and is labeled "P1.1.2". The number after each problem is its individual point value. Make sure you don't do an Exercise when a Problem is assigned! (Though the Exercises should be good practice and the answers to them are in the back of the book for Chapter 6, at least.)

Students are responsible for understanding and following the academic honesty policies indicated on this page.

All the questions in this assignment are group questions -- please hand on one paper per group. The groups are the same as those for HW#5 -- please email me with any questions or concerns.

• Pages 6-14 and 6-15: Problem 6.2.5 (10)
• Pages 6-18 and 6-19: Problem 6.3.2 (10)
• Pages 6-23 and 6-24: Problems 6.4.7 parts a,b, and c (10), 6.4.7 part d (10 XC). Please note the corrections on this problem and a different hint: "You may find it easier to prove the formula S(n,k) = k(S(n-1,k) + S(n-1,k-1)) and then use this formula to prove a formula for S(n,n-1) by induction. To prove the formula, first count the functions f from A to B where f(1) is needed to make f onto, then count the functions where it is not."
• Pages 6-33 and 6-34: Problem 6.6.3 (10)
• Pages 6-38 and 6-39: Problems 6.7.2 (10), 6.7.4 part a (10), and 6.7.4 part b (10).
• Pages P-5 and P-6: Problems P.1.3 (10) and P.1.4 (10)
• Pages P-13 and P-14: Problem P.2.5 part c (10)

Last modified 27 November 2007