Computer Science 280: Homework 2

Important Note: In problems where the reasoning isn't totally obvious, EXPLAIN your reasoning. This is an important part of the thinking process (and also gives you a chance for partial credit). Note that there are solutions to some of the problems (but not any of the ones assigned for homework) at the back of the book. You may want to check them out to get ideas for the assigned problems. Also note that this problem set is a bit longer than usual. I want to get the first two chapters out of the way.

Homework 2:
2/5/00 (due 2/12/00) Read: 0.4 - 0.7, 1.1 - 1.6, Supplementary problems 4, 6 (read them; you don't have to do them for homework). 


Section   Number         Points    Comments
0.4: 	  6(b) 		 1
	  10(b),(d),(f)  6
	  14 	         3          Hint: use the formal definition of floor
	  28(b) 	 3          Note that for this  problem, congruence is 
                                    defined as a relation on integers, as I did in class,
                                    and not as a relation on the natural numbers.  
          29 		 3
          33 		 3
          35 		 3
	  39 		 3          List the expressions in increasing order
0.5: 	  3(c) 		 3
          4(a) 		 3
          6 		 6
	  8 		 3
0.6: 	  9(b) 		 3
0.7 	  4(b),(d) 	 2
	  5(b),(c),(e)	 3
 	  11(b),(c),(e)	 3         
1.3: 	  28(a) 	 5 	   The ideas in this exercise turn out to be really important in
				   cryptography, when you have to takenumbers to large powers
				   to do encoding. 
1.4 	  7 		 4 
1.5 	  17(d)          4
	  20 		 4

One more problem:

1.
[2 points] Compute the following matrix product:

\begin{displaymath} \left[ \begin{array} {cc} 2 &3\\ 5 &7\end{array}\right] \left[ \begin{array} {cc} 3 &7 \\ 4 &2\end{array}\right] \end{displaymath}