Math 255 Final Exam (Take-Home)
Name Haom AM,
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

Math '25:") Final Exmn ('Iakamm'
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0 Tim exam consists of 8 quvstimm
o Pit-215v road ([19 (am-Minus (awfully.
I Show all your work in legibly written. wellorganized mathematical
sentences.
I Simplify

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