Note: Exercises that are in bold underline (typed
like this) are to be handed in. Do the others (typed like this) on
separate paper so that you hand in only those exercises in bold
underline. This 1st assignment can be handed in as a group on a trial basis. Make sure all
names are on the front sheet. People should do equal or all work. All get the same grade. _________________________________________________________________________
Section 2.4, pages 81-82: 1, 2, 4, all parts are good exercises,
but I will
;
collect: 1(b,c), 2(c,d), 4(c,e).
Section 2.4, pages 81-82: 5, 7, 8. All are good
exercises, but I will
;
collect: 5(b,c), 7(a, b, d), 8(b, c, d)
Section 2.4, Page 81: 6a, 6c
***
Reading:
Exercises:
and:
Section 2.7, page 96: Prove the statement in #9a is TRUE.
Note: This proof is not in the book, but is covered in
class. Do this now without your notes. If you need to peek, that's ok, but
then do it again without your notes. This will be a fair test question. Recall
the definitions of evenand odd:
An integer n is even if there
exists an integer k such that n = 2k.
An integer n is odd
if there exists an integer k such
that n = 2k +1.
**Extra Credit**
You are walking on a road and come to a fork in the road. You have to decide whether
to take the left road or the right road. One of the roads leads to treasure, and the
leads to a horrible death. Two guards stand before the fork in the road. They
are identical in every respect except one: one of the guards always tells the
truth and the other one always lies. You may ask only one question to only
one of the guards, and the answer must be a YES or NO. If it is
not a YES/NO question, the guard will not answer. What question do you ask?
****Do NOT get any help from others in the class or books or the
web, and do not give your answer away to others.
Reading:
Section 2.8 (pages 96-99).
Exercises:
Section 2.8, page 102: 1a, 1b, 1c, 1d, 2, 3, 4
Note: For all of these exercises, if the argument is invalid,
then you must provide a truth assignment to the variables that causes all
the predicates to evaluate to TRUE, and the conclusion to evaluate to FALSE. (Such
an assignment proves the argument is invalid.)
(not collected)Prove by induction: For all n in
the natural numbers, 2^{n} > n.
(not collected) Prove by induction: For all n in the natural
numbers,
1
+ 2 + 3 + . . . + n = n(n + 1)/2.
to be collected: Prove by
induction: For all n in the natural numbers,
1^{2}
+ 2^{2} + 3^{2} + . . . + n^{2} =
n(n + 1)(2n + 1)/6.
to be collected: Prove by
induction: For all n in the natural numbers,
1
+ 3 + 5 + 7 + . . . + (2n - 1) = n^{2}.
Reading:
Sections 3.2, 3.3.
Section 3.4
Exercises:
Section 3.3, pages 138-139: All are good exercises to
practice. I will collect: 2, 4, 6, 8, 9, 10, 12.
Section 3.4 pages 143-144: Do 1-8, 11-13. I will collect:
2, 5, 6, 8, 12, 13, plus generate by hand rows 0 through 9 of Pascal's
triangle.
Describe your intended project for assignment 5. Every one of your team mates should have an assigned
portion. Need approval to go ahead. Need also a projected date for presentation.
Final student project:
This will be a team project you should work on throughout the semester as you learn new features and
discover what you'd like to do. Part of your assignment 3 would be to describe what you intend to do in this project, and get approval from me.
Find some team mates you'd like to work with or
work on your own. The last few classes will be devoted to presenting your project to the class.