Name (please print):
Math 213, Spring 2006
HW Assignment 2
Instructions
•Write your name on the cover sheet and staple the sheet to the assignment.
Do the problems in order, and make sure that each problem is clearly labelled.
•Write-up: For full credit it is essential that you write up your solution in a clear,
logical manner, and explain any key steps.
•Deadline: The assignment is due in class on Friday; late homework, or homework
dropped off in mailboxes, will not be accepted. (You can, of course, turn in the
homework early, in my office, any time before the due date).
•Tips: The problems are taken from the even-numbered problems in the Rosen text.
Most are similar to odd-numbered problems from the day-to-day non-graded assign-
ments, for which there are answers in the back of the Rosen text and detailed solutions
in the “Student Solution Guide”. Think of the non-graded assignments as a warmup
or practice for the graded HW assignments. If you have been diligent in doing these
non-graded assignments, as well as the daily reading assignments, you should have no
difficulty with the graded assignment (and the same goes for exams).
•Open House: I will have an “Open House” Thursday, Feb. 2, 5 - 6 pm, in 147
Altgeld. Feel free to stop by with questions about the homework or anything else
relating to this course!
Problems
•Section 2.2: 2(a)(c)(e), 4, 8(a)(d), 10, 14(a)(c)(e), 18, 20(a)(b)(c).
About these problems. All are from Section 2.2. In Problems 1–14 of 2.2, you have
to prove a Big-Oh estimate “explicitly” by (i) providing two “witnesses” Cand kfor
the estimate and (ii) showing that these witnesses work, i.e., that the relevant inequality
actually holds with these choices of Cand k. Part (ii) is an essential ingredient of a complete
solution; this part isn’t included in the answers in back of the book, but it can be found in
the Student Solution Guide. For the remaining problems (i.e., 18 and 20), explicit values
of Cand kare not required. You can refer to general results about sums and products of
Big-oh estimates, but state clearly which result you are using in each case.
Almost all problems in this assignment have an odd-numbered “companion” problem that
is of the same type and for which you can look up the answer/solution in the back of
the book or the Student Solution Guide. These companion problems are part of the non-
graded/non-collected assignment. I trust you are diligent in doing all of these non-graded
problems...; in any case, if you get stuck on or are uncertain about a problem on the graded
assignment, try the corresponding odd-numbered problem first, check your answer, and
look up the solution if necessary.