IMMIGRANTS, OLD AND NEW
I. Arrival of different Europeans after 1890 -Southern and Eastern (peak year 1908: nearly
1,000,000.
II. Push factors and Pull factors - why leave?
1. 'Push"
a. Economic: poverty, or threatened poverty
Southern Italy and Sicily; G
1919 year in review
I.
Confusion and disillusionment at end of WWI
a. Initial influence of W. Wilson
b. European interests conflict with idealism
c. American rejection of treaty and League of Nations
II.
Demobilization and Depression
III.
Domestic
a. Wint
0169424 YES 001 0001
LORENZO C SUKHDEO
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Account number ending in: 8759
Dear LORENZO C SUKHDEO,
We are pleased to provide the 2015 Annual Summary for your Chase Slate credit card.
We hope you find this documen
SOLUTION TO MATH 612, PROBLEM SET #4
c
SIMAN WONG. COPYRIGHT 2017
Comments: As you read this solution key, pay attention to the many different ways to apply the Fundamental Theorem
and regular representations to solve problems. Also, keep in mind the chan
SOLUTION TO MATH 612, PROBLEM SET #9
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SIMAN WONG. COPYRIGHT 2017
1. If Q( D ) is actually in Q, then = m/n with m, n Z, n > 0 and gcd(m, n) = 1, so it
satisfies the equation nx
m = 0. Then is monic if and only if n
= 1, i.e. Z.
Now, suppose
Q( D) Q. T
SOLUTION TO MATH 612, PROBLEM SET #8
c
SIMAN WONG. COPYRIGHT 2017
1(a) The Zariski open sets of X are U (a) := cfw_p Spec( A) : p 6 a where a is an ideal of A. Let cfw_ f i i
be a set of generators of a this need not be a finite set. Then U (a) = cfw_p X
SOLUTION TO MATH 612, OPTIONAL PROBLEM SET #10
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SIMAN WONG. COPYRIGHT 2017
1(a) Fix an element b + b of B/b. By hypothesis b is integral over A, so b satisfies a non-constant
monic polynomial f ( x ) A[ x ]. Denote by f the image of f in ( A/a)[ x ]. The
MATH 612, PROBLEM SET #3. DUE WEDNESDAY FEB 15
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SIMAN WONG. COPYRIGHT 2017
1. Let : G GL(V ) be the permutation representation associated to the action of a finite group G on a
finite set X. Show that for any g G,
trace( g) = number of elements of X fixe
MATH 612, PROBLEM SET #2. DUE WEDNESDAY FEB 8, 2017
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SIMAN WONG. COPYRIGHT 2017
Remarks. #5 and #6 require careful examination of various definitions and illustrate subtle features of tensor/exterior/symmetr
products. The rest are straight-forward yoga;
MATH 612, PROBLEM SET #4. DUE FRIDAY FEB 24
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SIMAN WONG. COPYRIGHT 2017
1. (Example of permutation representation)
Recall that the group of orientation-preserving symmetries of the regular cube is isomorphic to S4 .
It follows that there is a natural act
MATH 612, OPTIONAL, EXTRA CREDIT PROBLEM SET #10
DUE WEDNESDAY MAY 3, 2017 BY 12 NOON
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SIMAN WONG. COPYRIGHT 2017
Note:
(1) While this problem set is optional, its content is not!
(2) You can earn up to one additional point for the total course grade for
SOLUTION TO MATH 612, PROBLEM SET #3
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SIMAN WONG. COPYRIGHT 2017
1. Label the elements of X as x1 , . . . , xm , and denote by VX the complex vector space with basis
cfw_exi xi X . Then the permutation representation associated to a group action of G on
SOLUTION TO MATH 612, PROBLEM SET #5
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SIMAN WONG. COPYRIGHT 2017
1. Any fixed Q( p1 , p2 , . . .) involves only finitely many pi , so in fact Q( p1 , . . . , pn )
for some n (depending on ). Thus Q( p1 , p2 , . . .) =
pn ). To prove (a) it then
n =1
SOLUTION TO MATH 612, PROBLEM SET #7
c
SIMAN WONG. COPYRIGHT 2017
1. If L0 is another intermediate subfield, then L0 L if and only if Gal(K/L0 ) Gal(K/L), and that
L0 /k is normal if and only if Gal(K/L0 ) is normal. Thus the field F we want must correspo
SOLUTION TO MATH 612, PROBLEM SET #2
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SIMAN WONG. COPYRIGHT 2017
1(a) Let x1 , . . . , xn be a finite set of B-generators of N, so every element n N can be written as
n = i i ni for some i B. Next, fix a finite set b1 , . . . , bk of A-generator of B. Th
SOLUTION TO MATH 612, PROBLEM SET #6, PART I
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1. Since [K : k ] > 1, we can find an element u K k. Then 2 = [K : k] [k (u) : k ] > 1, so K = k(u).
Set f := mink (u) k [ x ], so deg f = [k (u) : k ] = 2. Thus f splits over K sin
MATH 612, PROBLEM SET #6
SIMAN WONG. COPYRIGHT 2017
This problem set has two parts:
Mandatory: Hand in all problems in Part I (due Friday March 24 )
Mandatory: Present the solution of one problem from Part II in my office before MT#2.
Part I. Hand in ev
SOLUTION TO MATH 612, PROBLEM SET #1
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SIMAN WONG. COPYRIGHT 2017
1. Preliminary comments. Before I write out the proof, let me try to explain the idea behind it; it is built upon the Z/2 Z Z/2
calculation we did in class. To simplify the notation we wri
MATH 612, PROBLEM SET #9. DUE WEDNESDAY APRIL 26, 2017
c
SIMAN WONG. COPYRIGHT 2017
1. Fix a square-free integer D different
from
0,
1.
Denote
by
O
the
integral
closure
of
Z
in
Q
(
D ),
D
i.e. the set of all elements Q( D ) which are integral over Z. Show
MATH 612, PROBLEM SET #8. DUE FRIDAY APRIL 14
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SIMAN WONG. COPYRIGHT 2017
1. (Zariski yoga) Let : A B be a ring homomorphism. To simplify the notation and to help make
the setup better resemble the usual topological situations, we set X = Spec( A), Y = S
MATH 612, PROBLEM SET #1. DUE WEDNESDAY FEB 1, 2017
c
SIMAN WONG. COPYRIGHT 2017
Note. This problem set is a bit longer than usual, but #1-#5 and #7 are pure yoga, and none requires a lengthy solution/massive calculation. #1-#3 are similar to examples we
MATH 612, PROBLEM SET #5. DUE FRIDAY MARCH 10
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SIMAN WONG. COPYRIGHT 2017
Note: Aside from #3, the rest of the problems are yoga. The hint for #1 is a useful technique, and #7
develops basic facts about finite fields (to be continued in PS#6). With the h
MATH 612, PROBLEM SET #7. DUE FRIDAY MARCH 31, 2017
SIMAN WONG
Note: This is the last problem set due before MT#2 (Wednesday April 5, 9-11am).
0. (FTGT yoga) Do not hand in the solution of this problem, but make sure you can do this (in a couple of senten
Bubble Sort
Description
The Bubble Sort is considered to be the simplest, yet not the most efficient sorting
algorithm. The process entails comparing adjacent elements and interchanging them if they are
not in the correct order. Starting at the beginning
What is the field? What areas might one study? In what fields might one find jobs?
Mathematics is one of the areas in which the areas of knowledge can accurately and objectively decipher
as true, and essentially beyond dispute. Its theorems are derived fr
SOLUTIONS FOR REVIEW FOR FINAL EXAM: MAT 132,
FALL 2015
Information: The mat 132 final exam is scheduled for Wednesday December 9 from 2:15pm to 5:00pm; room assignments for the exam will be
announced soon on your lecture website. The exam will focus on t
REVIEW FOR TEST I: FALL 2015
Test I is scheduled for Wednesday September 30 from 8:45pm to 10:15pm.
The room assignments are announced on your lecture website. The test will
cover material in sections 5.1-5.7 and in approximating areas by Riemann
sums a D
APPROXIMATING AREAS BY RIEMANN SUMS
Let f(x) denote a continuous, positive valued and increasing function on
the interval [a,b]; and let A denote the area under the graph of f(x) and over
the interval [a,b]. Divide this interval into n equal subintervals
Important Maclaurin Series
P
1
=
xn = 1 + x + x2 + x3 + . . .
1 x n=0
ex =
xn
P
x
x2 x3
=1+ +
+
+ .
1!
2!
3!
n=0 n!
ln(1 + x) =
(1 < x < 1)
(for all x)
(1)n+1
P
x2 x 3 x4
xn = x
+
+ .
n
2
3
4
n=1
( 1 < x 1)
x3 x5 x 7
(1)n
2n+1
sin x =
x
=x
+
+ .
3!
5!
INFORMATION
SYSTEMSANDCAUSES
ANDEFFECTSON
BUSINESS
JACLYNGARBARINO
SEPTEMBER04,2016
INFORMATION SYSTEMS CAUSES AND EFFECTS ON BUSINESS
2
Information systems, what are they? What do they do? How do they improve businesses?
Information systems can be define