The major ideals , beliefs , attitudes , music , and other societal factors , all make up popular
culture. Pop culture is a mix of all things mainstream, it's the trends and fads that shape a given
body of people. Usually pop culture affects people aged 3
New York, NY
Engineer Entry Level
Engineer Entry Level
San Francisco, CA
Virginia Beach, VA
Skills for Health
Skills for Health is a valuable, skills-based health education course designed for general education in grades 9 through 12.
Skills for Health helps students develop knowledge, attitudes, and essential skills in a variety of health-
Feedback to Learner
Billions of people use some sort of power, or electricity everyday. The majority of this power is
supplied by the depleting cash cow, fossil fuels. Fossil fuels impact on the atmosphere and
economy are both
De Leon 1
Domonique De Leon
9 Feb. 2016
Fossil Fueled Future
Everybody wants a clean world but nobody really realizes how hard it is to actually come
by. Energy is mainly made up of renewable resources being wind, water, and so
Lab # 8Purpose- The purpose of this lab is to investigate variables that influence
acceleration and affect Newtons 2nd Law.
Materials- Stopwatch, Skateboard, Test Subject, Observer, Spring Scale
Hypothesis- If the per
Domonique De Leon
April 23, 2016
Effects of the Vietnam War
Life during, before, and after the Vietnam war is very different then it is now. I conducted
this interview with my grandmother, Nancy Meza, who is now eighty-thre
Unit 1: Building Skills for Health
Lesson 1.1: What Is Health?
Activity 1.1.1: Discuss - Meeting Your Classmates
Introduce yourself to your classmates and read the introductions that
they post. Discuss your own health questions you
Purpose: The purpose of this lab is to identify the relationship between centripetal
force, mass and velocity.
Materials: Tube, Rubber Stopper, Stopwatch, Nylon Cord, & Paper Clip
Hypothesis: If the mass of a
WRC 1023 Hybrid
1 Apr. 2016
Semester Analysis: Matthew Readeaux
Whenever a professor assigns a written assignment, it feels like they are personally
punishing me. Writing has never been something that i have enjoyed o
If f t ( t is real, t 0 ) is a function-original, then the Laplace-transform of this function is
L f (t )( s) F ( s)
f (t )e
st dt ,
where s is a complex variable, s i
We will use the following notations between a function-original and its L-transfor
FALL 2015 Exam # 3 Name 501 ([5973: [323 g 8)
Each problem is worth 5 points. Solve each problem, then circle your answer and
carefully mark your scantron card.
For problems 1 & 2: On a summer day, the outdoor temperature varied according
Test 1 Review
This review is not exhaustive. It is a summary of the topics we have covered.
Test strategy and study plan
For the test . . .
Work those question that you know how to do rst.
Do not spend too much time on one question. If you
Exam 2 Review
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
1) True or false?
SHORT ANSWER. Write the word or phrase that best
Classication of Surfaces
Richard Koch November 20, 2005
We are going to prove the following theorem: Theorem 1 Let S be a compact connected 2-dimensional manifold, formed from a polygon in the plane by gluing corresponding sides of the boun
Solution Set 12
May 4, 2003
and is isomorphic when restricted to such a neighborhood,
so Y is a covering space. Now, the disk at the center of
Y can be deformation retracted to a point, yielding two
spheres joined at a point, whic
Solution Set 11
May 3, 2003
Let X be a M bius band. (a) Show that 1 (X ) = Z.
(b) Exhibit a cover p : Y X where Y is simply connected. (c) Show that there does not exist a retract of
X onto its boundary circle C.
(a) Consider th
Solution Set 10
April 15, 2003
is a bijection. We want to show that this is an isomorphism.
Let f , g be representative paths for two elements of
1 (T , b0 ). Let f and g be their liftings to paths in R2 .
If they have endpoints
(b) A star-convex set is clearly path connected, so it sufces to check triviality of the fundamental group at the star
center. At this point, however, star-convexity ensures that
the straight-line homotopy between an arbitrary loop and
the constant loop t
that for all x, x whenever d (x, x ) < , then d (x, x ) < .
Since (xi ) is Cauchy under d , there is an N such that
for i, j > N , d (xi , x j ) < . But under these same conditions, d (xi , x j ) < . Therefore (xi ) is Cauchy under d ,
so it converges (un
Solution Set 7
April 15, 2003
4 34 3 Let X be a compact Hausdorff space. Show that X is
metrizable if and only if X has a countable basis.
Assume X is metrizable. X is Lindel f because it
is compact, and metrizable Lindel f spaces
number of rst coordinates in I0 , and so there is some x
[0, 1] such that x y A for all y [0, 1]. This means that
x (0, 1) is an non-empty open subset disjoint from A, so
A cannot be dense in I0 .
Solution Set 6
March 11, 2
First, observe that a bijective order preserving map between ordered sets is a homeomorphism of topological
spaces. Also, note that half-open intervals of R all have
the same order type if theyre open on the same side.
(a) Forward, let f : [a, c) [0, 1).
2. Second, if x = a 0, but a = 0, then cfw_(a 1/n
0, a 1/n) | n > 1 forms a countable basis. Since
b = 0, c must be less than a. Thus there is some n
such that a 1/n > c. And as in the rst case, either
e > a and any basis element works or e = a and th
Math 131: Solution Set 3. By Dennis Clark
18 8 Let Y be an ordered set in the order topology. Let
f , g : X Y be continuous.
(a) Show that the set cfw_x| f (x) g(x) is closed in X.
(b) Let h : X Y be the function h(x) =
mincfw_ f (x), g(x). Show that h is
13 7 Consider the following topologies on R:
Solution Set 2
February 11, 2003
T1 = the standard topology,
T2 = the topology of RK ,
T3 = the nite complement topology,
13 1 Let X be topological space; let A be a subset of X.
Solution Set 1
February 6, 2003
A x A for at least one A A
True, because x A for ever A A . This is equivalent to
the converse above.
The converse is false, because x must be in every A A
in order to be in the intersec