STATS: ACTIVITY 4
Section 01
Wednesday, November 9, 2016
Directions: Complete the following problems in complete sentences with an answer
written within the context of the problem.
PART 1
Problem 1:
D
activity2
1 The College Boards, which are administered each year to many
thousands of high school students, are scored so as to yield a mean
of 513 and a standard deviation of 130. These scores are cl
STATS: ACTIVITY 3
Section 01
Wednesday, October 12, 2016
Directions: Complete the following problems in complete sentences with an answer
written within the context of the problem.
PART 1
Problem 1:
A
Active Listening Worksheet
PURPOSE:
Effective communication is a two-way street.it involves sending AND receiving messages. This
assignment provides students tools and practice using active listening
MATH 2520-01 Calculus II
Name:
Due date: 08/30/16
Instructions: You get extra 2 points if you do the following:
Print (two-sided) out the problems.
Do scratch work on scratch paper. When you are cer
The Man Who Saved Capitalism
Abbas P. Grammy
John Maynard Keynes (pronounced to rhyme with rains) was the most influential
economist of the twentieth century. His pioneering work, The General Theory o
Supplements to the Exercises in Chapters 1-7 of Walter Rudins
Principles of Mathematical Analysis, Third Edition
by George M. Bergman
This packet contains both additional exercises relating to the mat
ANALYSIS HW 11
ALEX GITTENS
Problems
Exercise 16, pg. 291. If k 2 and = [p0 , p1 , . . .] is an oriented ane k -simplex, prove that 2 = 0,
directly from the denition of the boundary operator . Deduce
ANALYSIS HW 6
ALEX GITTENS
Problems
Exercise 3, pg. 239. Assume A L(X, Y ) and Ax = 0 only when x = 0. Prove that A is then 1-1.
Proof. Let x, y X be such that A(x) = A(y ), then A(x y ) = A(x) A(y )
Math 118C Homework 5 Solutions
Charles Martin
May 12, 2009
1. Give an example of A, B R with A = B and d(A, B ) = 0.
Any sets A B where B \ A has measure zero will suce. For example, take A = R \ Q an
Math 118C Homework 6 Solutions
Charles Martin
May 20, 2009
Throughout the following, we use A to denote the characteristic function of A.
1. If f 0 and
E
f d = 0, prove that f = 0 almost everywhere on
Math 118C Homework 4 Solutions
Charles Martin
April 28, 2009
1. If is an additive set function, prove that () = 0.
Denote the underlying ring by G. Notice that, per our tacit assumptions on set functi
Math 118C Homework 7 Solutions
Charles Martin
May 20, 2009
1. If f L1 () and g is bounded and measurable on E , prove that f g L1 ().
Let M > 0 be such that |g | M . Then
|f g | d
X
M |f | d < .
X
2.
Math 118C Homework 3 Solutions
Charles Martin
April 21, 2009
9.19 Show that the system of equations
3x + y z + u2 = 0
x y + 2z + u = 0
2x + 2y 3z + 2u = 0
can be solved in terms of x, in terms of y ,
Math 118C Homework 2 Solutions
Charles Martin
April 16, 2009
9.11 If f and g are dierentiable functions on Rn , prove that
wherever f = 0.
(f g ) = f g + g f and that
(1/f ) = f 2 f
For i = 1, 2, . .
ANALYSIS HW 8
ALEX GITTENS
Problems
Exercise 16, pg. 240. Show that the continuity of f at the point a is needed in the inverse function
theorem, even in the case n = 1: If
1
f (t) = t + 2t2 sin
t
for
ANALYSIS HW 9
ALEX GITTENS
Problems
Exercise 9, pg. 290. Dene (x, y ) = T (r, ) on the rectangle
0 r a,
0 2
x = r cos ,
y = r sin .
by the equations
Show that T maps this rectangle onto the closed dis
ANALYSIS HW 6
ALEX GITTENS
Theorems from the Book
Theorem 1 (9.17). Suppose f maps an open set E Rn into Rm , and f is dierentiable at a point x E .
Then the partial derivatives (Dj fi )(x) exist, and
ANALYSIS HW 9
ALEX GITTENS
Problems
Exercise 5, pg. 289. Formulate and prove an analogue of Theorem 10.8, in which K is a compact subset
of an arbitrary metric space. (Replace the function i that occu
Chapter 6
Convexity and differentiability.
6.1 Convex functions of one variable.
Proposition 6.1 Let f be a real-valued function dened on (a, b) R. The following
are equivalent:
1. f is convex on (a,
MATH 618 (SPRING 2010, PHILLIPS): SOLUTIONS TO
HOMEWORK 3
1. Rudin Chapter 9 Problem 2
I have restated the problem in labelled parts for convenience.
(a) Compute the Fourier transform of the character
Self-Assessment Questions Math 118A, Fall
2009
1. Every rational number can be written in the form x = m/n, where
n > 0, and m and n are integers without any comon divisors. When
x = 0, we take n = 1.
Homework 2 Math 118B, Winter 2010
Due on Thursday, January 28, 2010
1. Suppose increases on [a, b], a x0 b, is continuous at x0 , f (x0 ) =
1, and f (x) = 0 if x = x0 . Prove that f R() and that f d =
Homework 5 Math 118B, Winter 2010
Due on Thursday, March 4th, 2010
1. Show that if f 0 and if f is monotonically decreasing, and if
n
n
cn =
k=1
f (k )
f (x) dx,
1
then
lim cn
n
exists.
2. Let n (x)
Self-Assessment Questions Math 118A, Fall
2009
1. Evaluate the limit
n
lim n
n
e
1
1+
n
n
.
without using LHospitals rule.
2. Prove that
n
1
1+
n
lim
n
exists using the following steps:
(a) Prove tha
Homework 1 Math 118B, Winter 2010
Due on Thursday, January 14, 2010
1. Let f be dened for all real x, and suppose that M > 0 and > 0
such that
|f (x) f (y )| M |x y |1+ , x, y R.
Prove that f is const
Homework 3 Math 118B, Winter 2010
Due on Thursday, February 4, 2010
1. Let be a xed increasing function on [a, b]. For u R(), dene
1/2
b
u
2
2
=
|u| d
.
a
Suppose f, g, h R(), and prove the triangle i
Self-Assessment Questions Math 118A, Fall
2009
1. For any sequence cfw_cn of positive numbers,
lim inf
n
cn+1
cn+1
lim inf n cn lim sup n cn lim sup
.
n
cn
cn
n
n
2. For any two real sequences cfw_a