MATH 302 Discrete Mathematics
Assignment 8.
Due on Wednesday, April 6, 2016
Read: Sections 8.2,
Definition: Write down the definitions for the following terms.
[5 points]
linear homogeneous recurrence relation of degree k with constant coefficients
linear nonhomogeneous recurrence relation with constant coefficients
the characteristic equation of an recurrence relation
Theorem 3 on page 518: the general result about the solution of
linear homogeneous recurrence relations with constant coefficients
Problems to be graded:
[10 points total]
§8.2/ 1, 4 (a–d, each counts half point), 12, 14, 22,
§8.3/ 21, 22,
Please also do these. (This problem counts 2 points)
Use the Master Theorem to give an asymptotic bound for the sequence f (n)
where f (n) satisfies the following recurrences:
1. f (n) = 4f (n/2) + n
2. f (n) = 4f (n/2) + n2 .
3. f (n) = f (9n/10) + n
4. f (n) = 7f (n/3) + n2 log n.
Practice problems:
§8.2/ 2, 3, 6, 7, 13, 15, 19, 21,