Solving 7 of the 8 problems correctly will be considered a full submission. Solving the 8th correctly will be considered "extra credit".

1. Exercise 4.2
2. Exercise 5.1
3. Exercise 5.2
4. Exercise 5.4
5. Exercise 5.6

   [In 5.4 and 5.6 you may assume the fundamental theorem of algebra: For a field F, and element a of F, a polynomial f(x) in F[x] satisfies f(a) = 0 if and only if x-a divides f(x).]

6. Exercise 8.2
7. 1. Exercise 8.4
   2. Continuing 8.4, assume the ring supports the FFT. For which values of n = 2^k is the FFT operation count, namely (9/2)n log(n) + 3n - 2, less than the Karatsuba operation count?
8. 1. Exercise 8.14
   2. Exercise 8.32