Homework Assignments

1. Due 9/30
   • 1.3-3, p. 15
   • 1-1, p. 17
   • 2.1-4, p. 31
   • 2-2, p. 38
   
   
2. Due 10/7
   • Express (z + z^3 + z^5 + z^7 + ...) with |z|<1, in closed form
   • 3.2-4, p. 52
   • 3-1 b, p. 52
   • Express Sum_{k=0 to n} log ( (n^2)/(2^k) ) in a closed form
   
   
3. Due 10/14
   • Use iteration to solve T(n)=2T(n/3) + n^2, with T(1)=1
   • 4-1 c, p. 72
   • 4-4 a, p. 73
   • 4-4 c, p.73
   • Find a closed form for T(n)= ((log n)/(log (n-1))) T(n-1) + n log n, with T(2)=1
   
   
4. Due 10/21
   • 7.4-1, p. 149
   • 7.4-2, p. 149
   • 5.1-4, p. 81
   • 5.2-3, p. 83
   
   
5. Due 11/4
   • 8.1-2, p. 155
   • 8.2-1, p. 160
   • 8.3-2, p. 163
   • 8-3, p. 169
   
   
6. Due 11/11
   • 16.1-1, p. 308
   • Explain why (including finding counter-example) the following algorithm for the matrix chain problem does not work: Suppose n>2 and that p_i is smallest of p_1 .. p_n-1. Break the product after A_i, and recursively apply this procedure to the products A_1..A_i and A_i+1..A_n.
   • 16.2-3, p. 314
   • 16.3-1, p. 319
   • 16-2, p. 325
   
   
7. Due 11/18
   • 17.1-3, p. 333
   • 17.2-5, p. 337
   • 17.3-2, p. 344
   • 5.4-4, p. 90
   
   
8. Due 11/25
   • 23.1-3, p. 468
   • 23.3-6, p. 484
   • 23.4-1, p. 487
   • 24.2-4, p. 510
   • 24.2-5, p. 510