MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2003
Practice Exam #3
Problem 1 (35 points) Impurities in a Film
Small self-organized structures of macromolecules, micelles, can exist as impurities in
free-
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
pril 26, 2005
Problem Set 10 Solutions
ue: Monday, May 2 at 9 PM
Problem 1. Justify your answers to the following questions about independence.
(a) Suppose that you roll a fair d
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
February 22, 2005
Problem Set 4 Solutions
ue: Monday, February 28 at 9 PM
Problem 1. Prove all of the following statements except for the two that are false; for
those, provide c
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
March 15, 2005
Problem Set 6 Solutions
ue: Monday, March 28 at 9 PM
Problem 1. Sammy the Shark is a nancial service provider who offers loans on the following terms.
Sammy loans
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2004
Exam #4
Problem 1 (35 points) Flatland
FLATLAND, Edwin A. Abbot, 1884
Consider world, perhaps Abbots Flatland, where electromagnetic waves can only
propa
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2004
Exam #3
Problem 1 (30 points) Weakly Interacting Bose Gas
At low temperatures the entropy and isothermal compressibility of a weakly interacting Bose gas
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
pril 5, 2005
Problem Set 8 Solutions
Due: Monday,
pril 11 at 9 PM
Problem 1. n electronic toy displays a 44 grid of colored squares. t all times, four are
red, four are green, fo
uiz 1
2
Problem 1. [20 points]
(a) Consider the proposition:
R = For all x 2 S, P x) implies Q x).
For each statement below:
If R implies that statement, then circle ).
If R is implied by that statement, then circle (.
Thus, you might circle zero, one,
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2003
Exam #4
Problem 1 (35 points) Cooling of a White Dwarf Star
1
2
3
4
5
Just after a white dwarf star is formed it begins a long slow radiational cooling p
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6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
February 1, 2005
Problem Set 1 Solutions
Due: Monday, February 7 at 9 PM
Problem 1. The connectives ^ (and), _ (or), and ) (implies) come often not only in computer programs, but
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
pril 14, 2005
Problem Set 9 Solutions
ue: Monday,
pril 25 at 9 PM
Problem 1. There are three coins: a penny, a nickel, and a quarter. When these coins are
ipped:
The penny comes
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
February 15, 2005
Problem Set 3 Solutions
ue: Tuesday, February 22 at 9 PM
Problem 1. n urn contains 75 white balls and 150 black balls. While there are at least
2 balls remainin
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
February 8, 2005
Problem Set 2 Solutions
Due: Monday, February 14 at 9 PM
Problem 1. Use induction to prove that
1
1
1
1
1
2
3
for all n
1
4
1
1
n
=
1
n
2.
Solution. The proof i
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
March 29, 2005
Problem Set 7 Solutions
ue: Monday,
pril 4 at 9 PM
Problem 1. Every function has some subset of these properties:
injective
surjective
bijective
Determine the prop
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2003
Practice Exam #4
Problem 1: Ripplons (35 points)
(k)
k
We have seen that the bulk motion of a solid or liquid can be described by harmonic
normal modes (
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
March 1, 2005
Problem Set 5 Solutions
ue: Monday, March 7 at 9 PM
Problem 1.
quence
n undirected graph G has width w if the vertices can be arranged in a sev 1 , v 2 , v3 ,
, vn
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Physics Department
8.044 Statistical Physics I
Spring Term 2003
Exam #3
Problem 1 (45 points) Guiding Neutral Atoms on a Chip
We demonstrate the guiding of neutral atoms by the magnetic elds due to microfabricated cur
6.042/18.062J Mathematics for Computer Science
Srini Devadas and Eric Lehman
May 3, 2005
Problem Set 11 Solutions
ue: 5PM on Friday, May 6
This is a mini-problem set. The rst problem reviews basic facts about expectation.
The second and third are typical
uiz 2
2
NOTE: For this exam, a closed form is a mathematical expression without summation notation, product notation, or the
symbol. Factorials and binomial coefcients may appear in
a closed form. Some examples are shown below.
Closed Forms
NOT Closed For
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