Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
November 14
revised November 19, 2005, 1141 minutes
Solutions to Quiz 2
Problem 1 (10 points). True/False. Circ
Massachusetts Institute of Technology
6.042J/18.062J, Spring 02: Mathematics for Computer Science
Professor lbert Meyer and Dr. Radhika Nagpal
March 1
revised
pril 28, 2002, 855 minutes
Solutions to Quiz 1
Problem 1 (25 points). Consider the following sys
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2003
Exam #1
Problem 1 (35 points) Isotopic Abundance
p(A)
1/2
1/3
1/6
n
n+1
n+2
A
A certain element has three stable isotopes with atomic weights A = n, n +
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
November 9
revised November 3, 2005, 1273 minutes
Solutions to roblem Set 7
roblem 1. There are 20 books arrang
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 12
revised October 10, 2005, 616 minutes
Solutions to Problem Set 4
Problem 1. For functions f : A ! B
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 28
revised October 12, 2005, 909 minutes
Solutions to roblem Set 5
roblem 1. Suppose that one domino ca
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 3
revised October 8, 2005, 979 minutes
Solutions to Problem Set 3
Problem 1. (a) List all the different
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2003
Exam #2
Problem 1 (25 points) Bose Gas
In a weakly interacting gas of Bose particles at low temperature the expansion coefcient and the isothermal compre
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2003
Practice Exam #1
Problem 1 (35 points) Clearing Impurities
p(x)
1/3
0
a
x
In an eort to clear impurities from a fabricated nanowire a laser beam is swep
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2003
Practice Exam #2
Problem 1 (25 points) Elastic Rod
For a certain elastic rod of length L, tension F , and temperature T the following
facts are known.
i)
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 26
revised November 5, 2005, 1389 minutes
Solutions to Problem Set 6
Problem 1. Youve seen how the RS e
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 21
revised September 21, 2005, 1076 minutes
Solutions to Problem Set 1
Problem 1.
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2004
Exam #1
Problem 1 (30 points) Doping a Semiconductor
p(x)2
0.2
02
l d
x2
When diusing impurities into a particular semiconductor the probability density
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
December 2
revised November 20, 2005, 1182 minutes
Solutions to roblem Set 9
roblem 1. Professor Plum, Mr. Gree
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
December 21
revised December 22, 2005, 1118 minutes
Solutions to the Final Examination
Problem 1 (15 points). I
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
October 17
revised October 18, 2005, 125 minutes
Solutions to Quiz 1
Problem 1 (15 points). Let G be an undirec
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
December 9
revised December 2, 2005, 1086 minutes
Solutions to roblem Set 10
roblem 1. MIT students sometimes d
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
November 21
revised November 27, 2005, 858 minutes
Solutions to Problem Set 8
Problem 1. Find the coefcients of
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2004
Exam
2
Problem 1 (25 points) Polar Molecules
E
+
+
+
+



+
+
+




In a particular situation polar molecules (molecules possessing a permanent el
Massachusetts Institute of Technology
6.042J/18.062J, Fall 05: Mathematics for Computer Science
Prof. lbert R. Meyer and Prof. Ronitt Rubinfeld
September 26
revised September 20, 2005, 1388 minutes
Solutions to Problem Set 2
Problem 1. Use induction to pr