# CMPSCI 250: Introduction to Computation

### David Mix Barrington

### Spring, 2012

# Homework Assignment #4

#### Posted Friday 2 March 2012

#### Due on paper in lecture, Friday 9 March 2012.

There are eight questions for 60 total points plus 10 extra credit.
All but two are from
the textbook, *
Mathematical Foundation for Computer Science*. Note that the book has
both Exercises and Problems -- make sure you are doing a Problem and not the
Exercise with the same number. The number in parentheses following each problem
is its individual point value.

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

Correction in purple (to Problem D-1) added 5
March.

Correction in green (to Problem 3.6.2) added 6
March.

Correction in orange (again to D-1) added 9 March.

- Problem 3.5.1 (5)
- Problem 3.6.2 (5) Instead of "any number" it should say "any
positive
natural". You can't write zero or negative integers as products of
prime powers.
- Problem 4.1.3 (10)
- Problem 4.3.1 (10)
- Problem D-1 (10):
Let S(n) be the sum, for i from 1 through n, of (-1)
^{i}i^{2}.
For example, S(4) = -1 + 4 - 9 + 16 = 10. Find a polynomial whose value is
S(n) and prove by induction that your result is correct. (Your polynomial
may include a (-1)^{n}, for example.)
- Problem 4.4.4 (10)
- Problem 4.4.5 (10)
- Problem D-2 (10XC) Prove by induction that the number of possible
Hasse diagrams for the relation S in Problem 2.10.5 (d) is 2
^{n-2},
where n is the number of teams in the tournament.

Last modified 9 March 2012