SPRING 2006 : CS 1050D (Understanding & Constructing
Proofs) -- P. Tetali
Office hrs: MWF 2-3pm (Skiles 234) ph. 894-9238
Teaching Assistant : Brooks Van Horn III
(vanhorn@cc.gatech.edu)
office hrs at CoC Commons : Mon, Wed. 4:35-5:35 and Thurs. 1-2pm.
* Click
here for an outline
* Click
here for a brief handout on ``Writing Proofs"
by Chris Heil, Prof. in School of Math, Ga Tech
* Notes from a
similar class at UC Berkeley
``Why do CS students need (discrete) Math?"
Check out the special issue of Communications of the ACM (Sept.
2003, CACM)
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SOLUTIONS TO ALL GRADED HWs ARE POSTED HERE
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* HW 1 (due in class on Friday, Jan. 20th, 2006):
Section
0.1 : Problems 4 (j), 5 (f, i, m, p), 6 (c, d, i), 7(h, n)
and 8
Section
0.2 : Problems 17, 23, 25
Section
1.1 : Problems 6, 10
* HW 2 pdf
file of HW 2 (Due: Friday, Jan. 27th)
* HW 3 (No need to submit this hw; some will be done in class):
Section
2.4 : Problems 4, 6, 10, 17
Section 5.1 :
Problems 6(a,b), 8(a), 9(a), 12, 15, 18, 27
* HW 4 (due in class on Monday, Feb. 20th, 2006):
Section
3.1 : Problems 10, 18(b,c), 25(a,c), 29
Section
3.3 : Problems 12(b), 19(a,c), 21, 30
Section
4.2 : Problems 12 (d,e,j), 17 (b,d), 20
*** QUIZ 1 happened in class on FEBRUARY 27th (Monday)
* HW 5 (due in class on Monday, Mar. 6th, 2006):
Section
4.3 : Problems 7, 28(b,c), 34(c,d)
Section
4.4 : Problems 7(a), 9(g,i), 14(c,d)
Section
4.5 : Problems 18(e,g), 21(d), 25(b)
*** TEST 2 will be in class on MARCH 8th (Wednesday)!!
*** REVIEW SESSION for Test 2 on March 6th (Skiles 270) :
6:10--7:10pm
*** Sample Test Questions HERE
* HOME WORK 6 (Due: Wednesday, March 29th) : see problems on recursion
below:
1. Prove, using induction, that 2^(2n) -1 is divisible by 3 for all
n>=1.
(Note that the recursive tiling procedure for the chessboard problem
mentioned in class gives an indirect proof of this fact.)
2. The factorial of a positive integer n is defined as the product of
the
integers 1 through n.
Give a recursive definition of the factorial, and write a recursive
function
factorial(n) that evaluates the factorial of n for any positive
integer n.
3. Section 5.2, problem 52 (Hint: Guess the answer, and then prove it by
induction.)
4. Consider the variant of the Towers of Hanoi problem mentioned in
class
(see Section 5.3, problem 24). Describe a recursive procedure to
transfer a
stack of n disks from one peg to an adjacent one. Give a recurrence
relation
for the number of transfers used by the procedure.
5. Given the arithmetic expression 3 + 9/(2 + 5 - 2 * 5), draw the
expression tree for it. If you evaluate it using the recursive function
eval(e), how many recursive calls to eval are made?
6. Extra Credit Problem: The positions of n ghosts and n ghostbusters
are
given
by 2n distinct points in the plane, such that no three of the points are
collinear. All the ghostbusters are equipped with a proton gun each.
Give a
recursive procedure to match the n ghostbusters with the n ghosts such
that
no two of the proton beams cross each other.
* HOME WORK 7 (Due: Friday, April 7th):
Section 5.2: Problems 44, 49
Section 5.3: Problems 9, 13, 16, 18, 22
OPTIONAL: Section 5.2: 17, 42, 51, Section 5.3: 11, 12, 15
******** REMINDER : TEST 3 (MONDAY, APRIL 10th) *********
REVIEW SESSION : FRIDAY, April 7th, 4:30 -- 5:30 Skiles 270.
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