6 856 Randomized Algorithms
David Karger
Handout #9, October 2, 2002 Homework 5, Due 10/9
M. R. refers to this text:
Motwani, Rajeez, and Prabhakar Raghavan. Randomized Algorithms. Cambridge: Cambridge University Press, 1995.
1. MR Section 3.3. Evaluate t
z
~
z
z C 9p
%wtV
y v x u 9p
Fr Sqv G1V YtsdH
z CV T
| y v x u 9p V v V T
%FYgqv w13q 5rH rrv u
z y v x
I~
z
y v v V T
r 5 rH
~
~
z y v v V T
rr5 5 rdH
9p
w1V
x e D V Q D R v VE v R q D A 9p q 9p h TEE Tg D C A x 9 D C
lW1S1YwY6r1swc%Gw
18.781 Problem Set 3
Thursday, March 1.
Collaboration is allowed and encouraged. However, your writeups should be your own, and you
must note on the front the names of the students you worked with.
Extensions will only be given for extenuating circumstanc
Subject 24.242. Logic 11. Answers to the April 8 homework.
Define the restricted sentential calculus (RSC) as follows: The atomic RSC sentences are "A,"
"A," "A,", and so on, and the RSC sentences are the atomic sentences and expressions formed
kom RSC se
18.305 Fall 2004/05
Solutions to Assignment 5: The Stationary Phase Method
Provided by Mustafa Sabri Kilic
1. Find the leading term for each of the integrals below for > 1.
R1
3
(a) 1 eit dt
R
2
(b) 1 eit dt
R
(c) 0 ei cos t dt
2. Find the leading term fo
Homework 2
18.086
Spring 2006
for FRIDAY 3/3/06
Combine numerical experiments with analysis for *ONE* of these PDEs:
1. ut = c ux + d uxx Create the Figure 5.12 described in the notes and
test implicit diusion with d2 U at time n + 1.
2. ut = i uxx (Schrd