Math 255 Final Exam (Take-Home)
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ID# LL77 Hiog
Department : lath
o The exam consists of 8 questions.
0 Please read the questions carefully.
0 Show all your work in legibly written, well-organized mathematical
sentences.
0 Simplify as far as p
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54
CHAPTER 1
Exercise 1.8.12. Consider once again the problem discussed in the previous example. (1)
Assuming that
IR> = fll x>
has a solution
I x(t)> = u(t)I x(0)>
find the differential equation satisfied by U(t). Use the fact that I x(0)> is arbitrary.
Math 236H Fall 2016HW 6Due Friday March 4 by 3 pm
Hand in to Hazel in Hylan 915
Make sure to tell her it is for Math 236H!
1a) What is the largest order of a cyclic subgroup of Z75 Z105?
b) Fipnd an element of maximal order in Z147 Z49 Z70.
c) How many el
Math 236H Homework 1Due Friday January 29 by 4 pm
Hand HW in to Hazel McKnight in Hylan 915
1) Let A = cfw_0, 1 and B = cfw_2, 3, 4, 5.
a) Interpret the identity 2 + 4 = 6 in terms of the sets A and B. What is the natural
set-theoretic representation of t
Math 236H Fall 2016HW 2Due Friday February 5 by 4 pm
1a) On last weeks homework, you showed that the set S = cfw_x R|x 1 was a
group under the operation defined by a b = a b a b + 2. Show that this group
is isomorphic to the group R of nonzero real number
Math 236H Fall 2016HW 4Due Friday February 19 by 3 pm
Hand in to Hazel in Hylan 915
Make sure to tell her it is for Math 236H!
!
"
!
"
1 2 3 4 5 6 7
1 2 3 4 5 6 7
1ai) Let =
and =
. Find ,
2 3 1 4 6 7 5
4 2 1 6 3 7 5
2 3, and 1000. What is the order of t
Math 236H Homework 1Due Friday January 29 by 4 pm
Hand HW in to Hazel McKnight in Hylan 915
1) Let A = cfw_0, 1 and B = cfw_2, 3, 4, 5.
a) Interpret the identity 2 + 4 = 6 in terms of the sets A and B. What is the natural
set-theoretic representation of t
Statement of Purpose
Haoran liu, hliu32@u.rochester.edu
University of Rochester, Class of 2016
Mathematics has always been my passion. I chose mathematics as my major on
the first day of classes at University of Rochester, and my passion [You might want a
Statement of Purpose
Haoran liu, hliu32@u.rochester.edu
University of Rochester, Class of 2016
Mathematics has always been my passion. I chose mathematics as my major on
the first day of classes at University of Rochester, and my passion for mathematics h
Ridiculogram:
They are very pretty.
They contain little to no useful information
They are perfectly appropriate for publication
in Nature or Science
Number of nodes: N
Number of edges: m
Simple, Undirected graph
Adjacency Matrix
1
1
1
3
2
2
6
4
3
4
5
5
PHY 525: Complex Networks
Gourab Ghoshal
Department of Physics & Astronomy, Computer Science and
Mathematics
Network: Any thing reticulated
or decussated, at equal distances,
with interstices between the
intersections.
Reticulated: Made of network; wi
PHY 525: Complex Networks
Gourab Ghoshal
Department of Physics & Astronomy, Computer Science and
Mathematics
Structural Measures
Paths
Number of Paths of length r
(3)
Nij
=
n
X
Aik Akl Alj = A
k=1
(r)
Nij = [Ar ]ij
l
k
i
3
ij
Loops of length r
j
Lr =
n
X
PHY 525: Complex Networks
Gourab Ghoshal
Department of Physics & Astronomy, Computer Science and
Mathematics
Jacob Moreno
Data from
AddHealth via
James Moody
Jim Moody
Social Networks
How does one actually measure a social network?
Direct observation
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PHY 122 HW 1 Solutions
2
1. We have seen that Coulombs Law (k Qr1 Q
, k = 9 109
2
m2
2
Gravitation (G Mr1 M
, G = 6.67 1011 Nkg
2
2 ).
N m2
C2 )
appears to be very similar to Newtons Law of
(a) Approximately how many times larger is k than G?
(b) Take 2 e
PHY 122 HW 2 Solutions
1. For a spherical surface centered around a point charge, the formula for electric flux E = E dA simplifies to
E = EA. Why? If our spherical surface is surrounding an electric dipole rather than a point charge, this simplification
PHY 122 HW 5
1. A square parallel plate capacitor has sides with a length of 1cm and a separation
between the plates of 1 m. If we fill the capacitor with a dielectric in order to
achieve a capacitance of 0.1 F, what does the dielectric constant need to b
PHY 122 HW 12
1. For the circuit below, draw phasors for I1 , I2 with Vab . Hint: start with Vab and I1 . Write an expression relating I1 and
I2 .
2. You are being held hostage on a jungle island by guerillas, not gorillas (bonus points if you know what m
PHY 122 HW 4 Solutions
1. If we multiply 1 Coulomb by 1 Volt, what type of quantity are we left with (i.e.
force, power, distance, etc)? How does this quantity relate to an electron volt?
Concepts
Units
Electric Potential
Electric Potential Energy
Ta
PHY 122 HW 2
1. For a spherical surface centered around a point charge, the formula for electric flux E = E dA simplifies to
E = EA. Why? If our spherical surface is surrounding an electric dipole rather than a point charge, this simplification
does not w
PHY 122 HW 7
~ which is perpendicular to the particles velocity, ~v . Will its
1. An electron enters a region of uniform magnetic field, B,
kinetic energy increase, decrease, or stay the same? Explain.
Solution: Since the particle is in circular motion,
PHY 122 HW 6 Solutions
1. Explain the difference between EMF and terminal voltage in an ideal battery.
Give an example where the difference between the two might matter.
Solution: The EMF () is the potential difference between the terminals
when no curre
PHY 122 HW 9
1. Describe the difference (in any) in the induced current in a wire loop when a magnet goes through the loop north side
first, south side first, and sideways.
2. A long straight wire oriented in the z direction carries a current I. A square
PHY 122 HW 7
~ which is perpendicular to the particles velocity, ~v . Will its
1. An electron enters a region of uniform magnetic field, B,
kinetic energy increase, decrease, or stay the same? Explain.
2. The same electron as above spends a time of t in t
PHY 122 HW 8 Solutions
1. For each of the following pairs of vectors ~a and ~b:
(a) What is the direction of the vector ~a ~b ( means a vector pointing out of the page)?
(b) Taking the magnitudes of ~a and ~b to be equal, rank their cross products in orde
Physics 122 Homework # 3
1. What do we mean by:
V (~r) =
U (~r)
q
and how is it analogous to the electric field and the electrostatic force?
Solution: If charge Q is the source of an electric potential V (r), and a charge q is within that electric potent
PHY 122 HW 11 Solutions
1. Youre in your lab, when the machine you are using breaks down! You manage to figure out that the inductor in one
of the circuits fried. You dont know the inductance it had, but you know it produced a peak emf of 150 mV from a
cu