Algebr No Reasoning Without Algebra

Algebr No Reasoning Without Algebra
No Reasoning Without Algebra I am a math major, I love and excel at math, and I failed my first
algebra test. I know of many people who hate math, who struggled with math, who could not get
past algebra, no matter how hard they tried. Yet we cannot blame them–and we cannot blame
algebra either. I got past that test and I passed the class, and algebra has helped me in countless
ways, and it has made me a better student. It is the responsibility of schools to prepare students for
the working world, to prepare them to be a thoughtful, skillful, and knowledgeable member of our
society. Some people mistake a lack of technical, specific abilities as a weakness, but the focus on
general knowledge like algebra allows for a breadth of tools to be opened up for students to learn in
the future. Schools should teach students to reason abstractly, to acquire skills to be used in many
contexts, and to learn to solve practical problems. Algebra does this. Before we even consider the
benefits of algebra, and the benefits of abstract skills, there is an elephant in the room that must be
discussed: why is algebra so difficult for students? In "Is Algebra Necessary?" (2012), Andrew
Hacker claims "algebra is an onerous stumbling block for all kinds of students," saying that algebra
"blocks further attainment for much of our population" due to high dropout rates coupled with low
math scores on transcripts. He believes that forcing students to take algebra means that fail will be
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The Application of Algebraic Topology ot Data Analysis
The application of algebraic topology to data analysis is relatively new but promising. When
confronted with large volumes of high dimensional data we would like to identify significant
phenomena, and the persistence of topological features provides a new and potentially useful
measure of significance. A key promise of this method is the ability to identify features without a
model– truly unsupervised learning.
Unlike traditional statistical methods of data analysis which are primarily concerned parameter
estimation, topological data analysis regards the data as a sample from a manifold embedded in
euclidean space and attempts to recover topological features such as connectedness or the number of
holes. An advantage of considering topology is that it is stable under deformations, and can
therefore be said to be insensitive to errors introduced in the sampling [].
To see the utility of the topological approach, and in particular the utility of homology to
multidimensional data analysis, consider the following example, first describe by Scott (1992). Take
random samples in R3 from two different populations. Suppose that these sample points form data
clouds, similar to the shape of 2–dimensional spheres of with two different radii, with the smaller
one being from one population and the larger one from the other population. Moreover, the smaller
sphere sits inside the larger sphere.. Most multivariate and dimensionality reduction methods would
not be able to detect the

Phobe's Positive Effects On The House Of Seven Gables
Phobe is the niece of Hepzibah. She shows up at the house of Seven Gables. Phobe was looking for
a place to stay because of her father getting remarried. Phobe lived with her family in Maryland
before coming to the house of Gables. Hepzibah decided to take her in since Phobe was clearly
family and in needs of a place to stay. Phobe had a positive effect on the inhabitants of the house of
Seven Gables. She started looking after her aunt Hepzibah's shop. She also started looking after the
house of the Seven Gables. Phobe had an amazing spirit. She was a very loving cheerful girl. Phobe
usually had a positive attitude and was very respectful. She brought light into the house since
Hepzibah at one point was living by herself. Phobe also brightened up the lives of her aunt and
uncle Hepzibah and Clifford. ... Show more content on Helpwriting.net ...
The House of Seven Gables holds a family legacy which was relevant to Phobe. Being in that house
had very many traditions and legacies that were Phobe's ancestors even though the legacies and also
Phobe's family history was not cheerful and successful, it still was like home to Phobe. Since
Phobe's father was starting a new life in their home with somebody else, Phobe wanted to find
comfort in a home with her own family. People living in the house had positive effects on Phobe.
Her aunt and uncle Hepzibah and Clifford were very good to Phobe. Since Phobe took in the
responsibilities in the house, it gave a positive effect to Hepzibah and Clifford. Hepzibah had her
mental problems but in overall were very good to Phobe. She understood Phobe's reasons for
coming to stay in the House of Gables. They treated Phobe like family and respect just as Phobe did
to

Aggie Math Prep Essay
Proposed Course Title: Aggie Math Prep Purpose of Course: The Aggie Math Prep course is a non–
credit hour, on–line, self–paced tool aimed at providing incoming students the opportunity to review
basic math skills needed to be successful in college mathematics courses. Topics include (list
topics*). Those completing the course prior to the start of the semester are encouraged to take the
NCA&T Mathematics Placement Test if they wish to obtain a higher mathematics course placement.
Completing the Aggie Math Prep course does not guarantee a higher mathematics course placement.
Course Duration: The course will be opened for 6 weeks. The initial competency level of the student
will dictate the amount of time spent in the course. Considering ... Show more content on
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If not, the student will proceed to the o Student Engagement  Instruction materials (videos,
PowerPoints, animations, etc.) will provide the student with instruction on the content  Activities
will give the student the opportunity to practice the topic  Feedback – students will be able to pose
questions and/or post their work in Blackboard (via Discussion
Board/Collaborative/recommendation of online development team) in order to clarify any
misconceptions or misunderstandings. Note: This will be done during the 1st implementation of the
course. Upon repeat implementations, a Commonly Asked Questions page will be available for each
module.  Links – Will provide the web addresses to free, interactive sites that allow more practice
(Khan academy, MathSkills.com,

Mc Escher Research Paper
Carter Goebel Art History 3/7/18 Mrs. Wood Biography of M.C. Escher Growing up as the son of a
civil engineer is tough especially when you do not do well in school or like math, luckily some of
his fathers intelligence rubbed off on Escher because most of his work employs the help of complex
mathematical equations. All M.C. Escher painting use some form of complex mathematical
equation, he uses these equations so that his lines and proportions can be completely perfect. He was
actually quite popular with mathematicians before art critics because they appreciated the perfection
in his art. Although, Escher did not completely understand the equations he was using so when he
would speak with a mathematician he would just smile and nod, ... Show more content on
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In 1903 his family moved to a town named Arnheim where he grew up being called Mauk, a
nickname given to him because of his constant childhood sickness as he even attended a special
school starting in 1907. Growing up Escher took Piano lessons and even some Carpentry
apprenticeships until his early teens, he received very poor marks and even failed the second grade.
His exceptional art skills carried him through most of his academic career. He began college in 1918
where he first studied Architecture but as a result of a persistent skin infection he failed several key
classes and decided to begin decorative art school under the wing of another graphic artist. Early
college was not a complete waste of time for Escher as it turns out, this is where he first learned to
make woodcuts, a skill which is invaluable in the art of making Woodcuts, Lithographs, and
Mezzotints. Escher drew much of his influence from the time he spent touring Italy and falling in
love with the geometric architecture and buildings. Escher met, married and had a son with his first
wife, Jetta Umiker, during his 12 year stay in Rome. Escher became unhappy in Italy when Benito
Mussolini took power and the government ideals changed to largely nationalist and fascist ideas that
would later lead to Italy's involvement in WWII as they fought with the axis

Group Development Stages
Knowing and understanding the five stages of group development is extremely important. The first
step is called Forming. Forming is when the group first meet up and is getting to know each other.
During the forming stage members usually introduce themselves and give a brief introduction about
their likes dislikes and interest. The members usually discuss what role each person will perform, by
now the group should have a group leader who should be in attendance making sure the meeting is
running smoothly. The second stage is called storming, storming is when the group comes together
and bring their ideas to the table. Most groups don't get passed this stage because there tend to be
arguments when it comes to deciding which direction the group ... Show more content on
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At times the roles they play can they play can have a positive impact on the group and other times it
may have an extremly negative impact and set the group back in progress. An example of this would
be the Joker, the joker in the group serves as an distraction to the group and usually can't stay focus
and distract other members from staying focus, the devils advocate has a negative impact as well,
this member tend to disagree with almost every decision the group comes up with on the flip side
the devil advocate tends to have great ideas that are deep in thought. You also have the sniper who
can shoot down ideas that other group members come up with which can lead to them dismissing
good ideas that just need to be brainstormed on. You also have the dominator who intimidate the
other members from speaking up due to there dominate personalities. There's also the decision
maker of the group who tends to attempt to make all the decisions for the group and doesn't give
enough time for ideas to develop before making decisions. There's other roles which bring positive
attributes to the group like the mediator, the mediator serve a good purpose of bringing peace and
balance to the group the only issue with the mediator is that they are ofter relationship oriented
instead of task oriented. There's also the Listener who sits down and respectfully listens to everyone
opinion can come up with well

Definitions Of Vague Ideal And Vague Prime Ideal Of A Γ...
Vague Prime Ideals of a Γ–Semirings–II Y.Bhargavi Research Scholar, Department of Mathematics,
K.L.University, Guntur, India. yellabhargavi@gmail.com T.Eswarlal, Associate Professor,
Department of Mathematics, K.L.University, Guntur, India. eswarlal@kluniversity.in
Abstract The concepts of vague ideal and vague prime ideal of a Γ–semiring which is characterized
by a truth–membership function and a false membership function in a complete lattice satisfying
inﬁnite meet distributive law (i.e., CompleteBrouwerianLattice)areintroduced.
Furtherallvagueprimeideals of a Γ–semiring are determined by establishing a one–to–one
correspondence between vague prime ideals of a Γ–semiring and the pair (I,α), where I is
aprimeidealofaΓ–semiringand α isaprimeelementinthecompletelattice.
Key Words: Complete lattice, Brouwerian lattice, vague set, vague ideal, vague prime ideal.
Mathematics Subject Classiﬁcation: 08A72, 20N25, 03E72.
1.Introduction In 1965, Zadeh.L.A[16] introduced the study of fuzzy sets. Mathematically a fuzzy
set on a set X is a mapping µ into [0, 1] of real numbers; for x in X, µ(x) is called the membership of
x belonging to X. The membership function gives only an approximation for belonging but it does
not give any information of not belonging. To overcome this, Gau.W.L and Buehrer.D.J[7]
introduced the concept of vague sets. A vague set A of a set X is a pair of functions (tA,fA), where
tA and fA are fuzzy sets on X satisfying tA(x)+fA(x)≤1, ∀ x ∈ X. A fuzzy set tA of X

M. C. Escher Tessellations
Have you ever looked into the concepts behind what makes a tessellation? Tessellations are made
using a combination of artistic and mathematical abilities. M.C. Escher was a talented man from the
Netherlands who made tessellations. He made such interesting art pieces of various types by using
mathematical concepts and artistic details. M.C. Escher's techniques on his tessellations made them
stand out to viewers. M.C. Escher was born in 1898 as Maurits Cornelis Escher ("Biography"). He
was born in Leeuwarden, Netherlands ("Escher, Section 1"). As a student, Escher was not
particularly skilled in mathematics, even though, later in life, he used many mathematical concepts
to create his art ("Escher, Section 1"). Escher was a skilled artist at an early age, and both his family
and teachers recognized his remarkable abilities ("Escher, Section 1"). During his lifetime, M.C.
Escher lived in several countries in Europe, including the Netherlands, Italy, Switzerland, and
Belgium ("Escher, Section 1"). M.C. Escher died in 1972 ("Biography"). He was seventy–four years
old and he died in North Laren, Netherlands ("Escher, Section 1"). M.C. Escher was an influential ...
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Escher was also a skilled mathematician, since he applied his mathematical knowledge to his art in
order to make it pop. Though Escher was not an exemplary mathematics student during elementary
school, he improved and began to demonstrate mathematical concepts in his art ("M.C. Escher.").
Escher made his images lighter as they approached the edge of his canvas so the viewer's eye would
be drawn to the center of the piece of art ("M.C. Escher."). Some of Escher's artwork is symmetrical.
Escher also made images smaller as they approached the end of the canvas, or towards the middle
("M.C. Escher."). He made so many images in one piece of art that the viewer might think the
images would repeat infinitely. All in all, Escher employs multiple mathematical concepts to make
his art

Theories Of Tuckman's Stages Of Development
STAGES OF DEVELOPMENT the model presented by Tuckman and Jensen "studies "... theory
groups, human relations training or T–Groups, and natural and laboratory –task groups have two
realms–task and interpersonal" (Tuckman & Jensen p. 280). It suggests that team's growth occurs in
stages with each dissimilar through each level of development. Tuckman, identifies four stages of
team development referred to as, forming–which occurs when individuals are introduced and
brought together for a purpose. Storming members' strained relationships and conflict, about
disagreement about a task, vision and/or approach of a shared purpose, norming where
unconsciously or consciously working relationship members come to a consensus. Finally,
performing team expecting

Argumentative Essay On Golden Gate Bridge
Tyler Gershman English 005 Professor Schwartz May 8, 2015 Lock the Golden Gates "Everyone is
better off without this fat, disgusting, boring girl." –Suicide note by Marissa Imrie, age 14 "I thought
how unpleasant it is to be locked out, and I thought how it is worse perhaps to be locked in." –
Suicide note by Madison Holleran age 19 Marissa Imrie jumped from the bridge on December 17,
2001. Marissa was a straight–A student at Santa Rosa High School. Her grades were a source of
pride to her divorced parents. But, Marissa was more preoccupied with how she looked than how
she tested in school. Like many teenagers in the United States, she considered being popular a
higher priority than being smart. Although she appeared athletic and beautiful ... Show more content
on Helpwriting.net ...
"Suicide from the Golden Gate Bridge." Clinical Case Conference. Psychiatric Foundation of
Northern California, 10 Oct. 2009. Web. 12 May 2015. The Golden Gate Bridge is the number one
suicide site in the world. In this clinical case conference, the authors begin by presenting vignettes to
capture the diversity of bridge suicide. They then examine the demo–graphic characteristics of those
who commit suicide from the bridge as well as the fatal attraction of the Golden Gate Bridge.
Interviews with jump survivors and potential jumpers are presented, and the authors examine the
evidence for the efficacy of suicide barriers. Cabanatuan, Michael. "Golden Gate Bridge Board OKs
$76 Million for Suicide Barrier." SFGate. N.p., 28 June 2014. Web. 13 May 2015. Board of
Directors for district that operates the world–famous span unanimously OKs $76 million to fund a
device to deter any jumpers. Fagan, Kate. "Split Image." ESPN. ESPN Internet Ventures, 7 May
2015. Web. 13 May 2015. "Even people you think are perfect are going through something
difficult." The tragic story of Madison Holleran taking her own life. Friend, Tad. "Jumpers – The
New Yorker." The New Yorker. Letter From California, 13 Oct. 2003. Web. 13 May

Mc Escher Tessellation Essay
A tessellation is a pattern put together by identical shapes that fit together perfectly with no gaps or
overlaps. M.C. Escher is the man who created the idea of tessellations, who is a Dutch graphic
design artist. He had a very tough early life since he suffered from very common skin infections,
which in turn caused him to do very poor in his core curriculum. Although he was very bad in his
main subjects, he excelled in his music and art classes. As an artist, M.C. Escher began by drawing
landscapes primarily of nature. After a few years of this, he decided to go in a different variety of art
by using the dimensional planes to his advantage to create illusions and trick the eye. He would
sketch landscapes of Italy from very unique perspectives that alter reality, later he would sketch
artwork from his mind rather than looking at nature. His form of artwork is commonly referred to as
"impossible reality". He mainly worked with lithographs and woodcuts, lithograph is an ... Show
more content on Helpwriting.net ...
Escher tessellation is called, "reptiles" which is actually a tessellation inside of another drawing. In
this drawing, there is a tessellation drawn on the table, made up of lizards. Then, the lizards appear
to be coming out of the drawing and wrap around back into the tessellation. This tessellation is made
up of many geometric shapes; such as many circles, squares and triangles, but the main geometric
figures used to create this tessellation are thousands of dots and lines. This drawing is a mezzotint
which is made by hatching, layering lines and dots. The mathematics behind this certain tessellation
can get pretty complicated. Escher's work mainly involves the mathematics of the geometry of space
and planes. In this tessellation, it is evident how the planes change as the lizards go into the
tessellation and leave. "Lizards" would be classified as an irregular tessellation, something that
Escher was very interested in, where the tessellation interacts and often leaves the

Asclepius: A Narrative Fiction
Asclepius' hands, which now glowed the usual pinkish color, and any visual presence of the vibrant
blue color quickly disappears. The cold that was brought along with it, was quickly replaced by
Axel's normal heated feeling. Relaxing, he sat back down beside her, keeping one hand still gently
laid atop Rogue's whilst the other waves off her apology. "No... No please, don't... Don't be."
Asclepius starts in a tired, kind tone, before his eyes meet the other's. Giving her a confident smile,
Asclepius voice slowly echoes back into her head. "You couldn't of... Of known, and... And I was
unaware that... That seeing you would trigger... Trigger him to attempt to... To take control, so I... I
could not of warned you.." Axel reassured her in a knowing tone, patting her hand lightly with his
own had located on top. ... Show more content on Helpwriting.net ...
It was inevitable that it would. Listening to her confession, Axel's head shifted to a different
position, one that made him look towards an old, dying tree. The only one in the outline of rather
healthy trees that boxed–in this odd clearing. Looking on, to that particular tree with an absent mind,
Asclepius nods simply. It takes him a minute, staring at the dead piece of vegetation, to think of the
words he was to use to describe what it is that he could do for her. But eventually, the words quickly
poured out of his mind, and into

Derivative and Graph
CALCULATOR SECTION
1. For find at the point (3, 4) on the curve.
A. B. C. D. E.
2. Suppose silver is being extracted from a mine at a rate given by , A(t) is measured in tons of silver
and t in years from the opening of the mine.
Which is an expression for the amount of silver extracted from the mine in the first 5 years of its
opening?
A. B. C. D. E.
3. Joe Student 's calculus test grades (G) are changing at the rate of 2 points per month. Which is the
expression that says this?
A. B. C. D. E.
4. If f is a continuous and differentiable function, then approximate the ... Show more content on
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A. Points A and B B. Points A and D C. Points B and D D. Points B and C E. Points A and C
18.
The graph of is shown above, on the interval [ –5, 5] . Which is true?
A. The graph is continuous and differentiable. B. The graph is continuous but not differentiable. C.
The graph is not continuous but is differentiable. D. The graph is not continuous nor differentiable.
19. Graph in the plane above, over the window [–1, 8] X [–25, 25].
20. Give the x–interval(s) where the graph of g is increasing. GIVE A REASON for your answer.
21. Give the x–interval(s) where the graph of g is concave up. GIVE A REASON for your answer.

22. Give the x–coordinates of any critical points for the graph of g. For each tell if it is a relative
maximum, a relative minimum or neither. EXPLAIN.
23. Give the x–coordinate of any points of inflection of the graph of g.
24. If is the velocity function for a particle moving along the x–axis, for time seconds, tell ...
A. when the particle changes direction. for .
B. for what intervals of time () the particle is moving to the left.
C. for what intervals of time

Contemporary Transcendentalism Project Analysis
On April 6, 2018, Diorys, Emily, and I completed the task of living ten arduous hours without the
use of technology. Throughout the duration of this project we attempted to keep ourselves occupied
by accomplishing the assignments we had been given by our teachers, or the projects we had been
aiming to complete. We began the ten hours by working on our Contemporary Transcendentalism
Project. Previous to this time period we had gathered our supplies and printed our information,
however, we utilized this time to construct the poster. Diorys, Emily, and I then decided to partake in
the board game, Sorry, which we had not played in a lengthy amount of time, before moving on to
our other spring break homework. It should be noted, that throughout

Why I Use Sequence
Sequence: I use sequence first because, I like to take my time and do any assignments that my
instructor gives me. I don't like to rush through my work or have someone to tell me what to do,
when I am in the middle of my assignment. I like to get a clear understanding and also like to do
things step by step. When I am doing something for my teacher or just doing something for school I
like to ask am I meeting their expectations that they are excepting of me to do. I also like for people
to show me examples of what I should be doing, instead of just telling me the word from their
mouth. I stay focus mental and I like for my work to be accurate and correct and not half stepping.
When I work alone I can take my time and not rush. Sequence is used by asking directions, what is
the instructor expected me to do. When I get started on an assignment I do not like when the teacher
change the direction on me. ... Show more content on Helpwriting.net ...
When my instructor asked me about something, I can't give her a straight answer because my mind
goes blank when too much information in on my mind. I am a type that asks a lot of questions and
love to answer them as well. I have to make sure that I have all my information together but starting
a paper. When I have everything together, everything falls into place. I am a great note at taking
notes, because I don't miss any information that can help me with my assignments or research paper.
When I think people are trying to hide information from me I feel frustrated and think they won't
share with

me I and me
Ch. 1 Data Collection 1.1 Introduction to the Practice of Statistics 1 Define statistics and statistical
thinking. SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question. Provide an appropriate response. 1) What is statistics? MULTIPLE CHOICE.
Choose the one alternative that best completes the statement or answers the question. 2) Which of
the following is not true of statistics? A) Statistics is used to answer questions with 100% certainty.
B) Statistics involves collecting and summarizing data. C) Statistics can be used to organize and
analyze information. D) Statistics is used to draw conclusions using data. 2 Explain the process of
statistics. MULTIPLE CHOICE. Choose the one alternative ... Show more content on
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University administrators are interested in determining the average parking time (e.g. the time it
takes a student to find a parking spot) of its students. An administrator inconspicuously followed
180 students and carefully recorded their parking times. Identify the sample of interest to the
university administration. A) parking times of the 180 students B) parking time of a student C)
location of the parking spot D) type of car (import or domestic) 14) The legal profession conducted
a study to determine the percentage of cardiologists who had been sued for malpractice in the last
three years. The sample was randomly chosen from a national directory of doctors. Identify the
individuals in the study. A) each cardiologist selected from the directory B) the responses: have been
sued/have not been sued for malpractice in the last three years C) the doctorʹs area of expertise (i.e.,
cardiology, pediatrics, etc.) D) all cardiologists in the directory SHORT ANSWER. Write the word
or phrase that best completes each statement or answers the question. 15) Administrators at a large
university want to know the average debt incurred by their graduates. Surveys were mailed to 150
graduating seniors asking them to report their total student loan debt.

Tessellations: Maurits Cornelis Escher In Modern Art
Tessellations are are type of drawing that are formed when a shape is repeated over and over,
covering a plane without any spaces or overlaps. In modern day tessellations are also known as
tiling. M.C Escher is the main person and creator behind tessellations. Maurits Cornelis Escher was
born in 1898 on July 17 in Leeuwarden Netherlands. M.C Escher was born in the age of modern art.
Escher was known at a younger age, to visualize distinct spatial patterns. Escher was a very smart
man as well and attended Harlem's School for Architectural and Decorative Arts. Later Escher found
a wife, by the name of Jetta Umiker on his visit in spain and established his home in Rome. His
artistic side of him strated At Harlem's school, where he thrived

Leonard Euler And The Application Of The Graph Theory, (E....
DRAFT ONE
Mathematics IA
To investigate Leonard Euler and his application of the graph theory and 'e'
Caitlin McFarlane
10/14/2015
Table of Contents
Introduction
Leonhard Euler was a Swiss Mathematician and physicist during the 1700s. He was born in 1707 in
Basel, Switzerland. He is known to be a pioneer of mathematics contributing to trigonometry,
calculus and geometry. The principle that he came up with and investigated was the foundation of
modern day mathematics. His most famous was 'The Graph Theory', using mathematic to
investigate graphs. The aim of this Mathematics IA is to investigate Leonhard Euler and the
application of his 'graph theory and 'e' (Euler's identity) in real life situations. I ... Show more
content on Helpwriting.net ...
This question was the basis for Leonard Euler's investigation into graph theory. He observed when
answering the question that some graphs could be drawn in different way, and some with multiple
possibilities and other don't have any. Being able to answer this question is depends on the number
of vertices with the odd edges. In the example below display. When it refers to two odd veracities
refers to the connection between the line and the nodes. The example above is one that you are able
to draw without lifting your pencil off. This graph has two odd veracities what agrees with Euler's
observation.
However this example has 6 odd vertices making this graph impossible to solve. Knowing this rule
is important when solving the seven bridges of Konigsberg problem.
Seven bridge of Konigsberg problem
Leonard Euler used graph theory to solve the 18th century problem seven bridges of Konigsberg.
The problem states:
"Königsberg is divided into four parts by the river Pregel, and connected by seven bridges. Is it

possible to tour Königsberg along a path that crosses every bridge once, and at most once? You can
start and finish wherever you want, not necessarily in the same

Computer Science And Engineering Research Report
Department of Computer Science & Engineering
Independent Study & Research Report
On
Face Recognition
Submitted to
Amity University Uttar Pradesh in partial fulfillment of the requirements for the award of the degree
of
Masters of Technology
In
Computer Science and Engineering
By
Aqsa Zafar
A7600916005
Under the guidance of
Ms. Vandana Dubey
Sr. Lecturer
AMITY UNIVERSITY UTTAR PRADESH
NOIDA (U.P.)
2016
1
Chapter 1: Introduction
1.1 Background–
The Report presents a hybrid neural network solution, which compares favorably with other
methods and recognizes a person within a large database of faces. These neural systems typically
return a list of most likely people in the database. Often only one image is available per person. First
a database is created, which contains images of various persons. In the next stage, the available
images are trained and stored in the database. Finally it classifies the authorized person's face, which
is used in security monitoring system. Faces represent complex, multidimensional, meaningful
visual stimuli and developing a computational model for face recognition is difficult. Face has
certain distinguishable landmarks that are the peaks and valleys that sum up the different facial
features. There are about 80 peaks and valleys on a human face. The following are a few of the
peaks and valleys that are measured by the software:
*Distance between eyes
*Width of nose
*Depth of eye sockets

*Cheekbones
*Jaw line
*Chin
2.3 IMPROVING THE BASIC SOM
The

Reflection Paper
In the sixth grade, I was a part of the accelerated math program in my middle school; we moved
faster than the other classes so that by the time we completed 8th grade we would be finished with
Algebra 1 and ready to start freshman year in sophomore Math. Because we moved so much faster I
ran into more obstacles mastering the concepts than I might have at a slower pace and had to get
over them quickly. When I found myself beginning to fall behind on a topic, at first I panicked, but
then my natural response kicked in, I focused all of my efforts on the concept holding me back. This
has always been my response to a challenge, I bring all the mental force I have to bear on it until I
have completely mastered it, smashing the challenge into tiny bits that are easier to comprehend.
There is a quote from one of my favorite novels, A Wise Man's Fear, which sums up what I tend to
do: "The boy has a mind like an iron hammer." I tend to smash an offending obstacle into
manageable pieces. In Math, I overcame these struggles by delving deep into exactly how each
aspect of the topic worked and why, through asking more questions of more people and working to
understand the concept. I stayed after class, had my engineer dad teach the concept to me, and had
his co–workers reteach it to me. Now, I like to think that I have mostly mastered this technique, –
recently, when working with equations containing Euler's number I questioned three different
teachers, researched it online, and practiced logarithms until I was proficient enough to give a lesson
on the complete concept to my math team. By the time we moved on in class, the ideas that I
struggled with the most were the ones that I understood the best because I enjoyed overcoming the
challenge. Loving Math and its difficulties, it's not surprising I sought out a job as a Math instructor
at Mathnasium. I love the challenges that my job provides me. Each day is amazing and gives me an
incredible sense of fulfillment. I enjoy working to become a better teacher, but the much larger joy
comes from the fact that I lead my students to overcome their own obstacles. Typically they are
math related, but occasionally I end up teaching test–taking skills. I love this because I get to

Office Space And Bartleby Comparison
Office Space is a modern, Hollywood–driven adaptation of Herman Melville's 1853 short story
"Bartleby." It revives Melville's story by imagining modern equivalents for the major themes and
characters of the original. Whiling comparing the works of Office Space and "Bartleby", many
similarities and differences are shown.
Although years passed between the creation of the classic short story and the film, they both possess
similarities in plot, theme, and character development. "Bartleby" begins in an older office at the
start of the industrial age, and Office Space begins in an office during the compelling cubicle
employment days. In the beginning of "Bartleby", the narrator, whom is the lawyer in the book,
introduces the characters early to allow an understanding of the characters and what to expect during
the reading. Mirror this to Office Space as the characters are also introduced early on in the reading.
The working atmospheres for "Bartleby" and Office Space are occupied by employees who seem to
repeat the same work over and ... Show more content on Helpwriting.net ...
Melville chose to literate the reading in first person narrative by the lawyer, Bartleby's employer. His
choice of the lawyer allows the reader to feel close to Bartleby, but remain mystified by him. On the
contrary, Office Space is told through Peter's eyes.
Unlike Bartleby, Peter cares to interact with others and to take part in a social life. Upon one
morning of ignoring phone calls from Anne, who leaves him and admits she's been cheating, Peter
decides to skip work and ask Joanna, a waitress out to lunch. Along with lunch dates, Joana joins
Peter at his apartment to watch Kung Fu together. According to the narrator, Bartleby does not seem
to leave the office. He does not eat anything but ginger nuts, the cakes that Ginger Nut himself
delivers to the clerks. It is clear how both characters occupy different social lives from each

Summary Of The Simpsons And Their Mathematical Secrets By...
The Simpsons and Their Mathematical Secrets by Simon Singh is a trade book that talks about the
history of The Simpsons and Futurama and how mathematics is embedded into numerous episodes
in each series. Along the way Singh, in addition to the other main writers for The Simpsons, talk
about many of the subtle math jokes that are present. These jokes range from very simple jokes that
students in elementary school could understand to jokes that not even some mathematics professors
with doctorate degrees can decipher. Singh said that "everything that happens to us has some effect
on us, and I do suppose that the time I spent in grad school made me a better writer" at the end of
the book. He recalls when he was younger and he was working on numerous projects in
mathematics. In addition to being a bright student, he had the ability to make jokes. Eventually,
several famous people in television such as Johnny Carson and David Letterman noticed this and
gave him an "in" in the entertainment business. ... Show more content on Helpwriting.net ...
Over time, Fox wanted a spin–off show and Futurama was born. Futurama extends the jokes that
were used in the Simpsons to a higher–dimension. Many of the jokes in Futurama involve
sophisticated relationships learned in multivariable calculus such as surface integrals and Mobius
strips among other topics. The second half of the book focuses on these more advanced topics as
portrayed in

Essay about Alex Grothendiek
M. Hamilton
Honors Math II
2nd period
Honors Paper on Alex Grothendiek As stated in the book, "A Strange Wilderness" Alex
Grothendieck was born on March 28, 1928 in Berlin, Germany. He was one of the famous
mathematicians born in the 20th century. Alex began to love mathematics in 1942, when he attended
a secondary school in Chambon, France. When World War II ended, he went to University of
Montpellier, wanting to continue his fascination with math and become a mathematics teacher. He
received a scholarship after three years in 1948 and moved to Paris, to the University of Nancy and
worked on functional analysis. In 1957, he began to work on algebraic geometry and simple algebra.
(The Famous People)
The Institute of Advanced ... Show more content on Helpwriting.net ...
Grothendiecks' parents moved away from him in 1933 to fight in the Spanish civil war. That left him
in Wilham, Heydorn. He later found out his father was living in a concentration camp during World
War II, while he was attending school. He never heard anything more on his mother. (The Famous
People website.) In the mathematical years of Grothendiek, he did not face many challenges in his
life. One of the main reasons why he left IHES, was because of military funding problems. After all,
Grothendieck was the son of an antimilitarist anarchist and he grew up very poor. This is why he
grew up having compassion for the poor. He also left because he got so tired which led to the
problem of losing interest in what he was teaching at IHES. By the late 1960's, he became interested
in science. David Ruelle, a physician at IHES, claimed that Alex Grothendieck had come to him
later on asking him about the study of physics. (Astrology and Horoscope Website.) He was also
into talking about the war, politics, and the Military. He did agree to attend lectures given about
mathematics, but while he was there, he went into debates about the war. All of his followers
became irritated with him. He then wanted to destroy everything he had ever written about math.
(The Amazing Grothendiek.) After his last year at IHES, He applied to get a position at the College
De

A Study Of A Generalized Weak Kam And Aubry Mather Theory...
Here, we extend the weak KAM and Aubry–Mather theories to optimal switching problems. We
consider three issues: the analysis of the calculus of variations problem, the study of a generalized
weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations, and the
long–time behavior of time–dependent systems. We prove the existence and regularity of action
minimizers, obtain necessary conditions for minimality, extend Fathi's weak KAM theorem, and
describe the asymptotic limit of the generalized Lax–Oleinik semigroup.
Introduction
Overview. Dynamical systems given by Tonelli Lagrangians have been extensively studied in recent
years. The deep connections between the calculus of variations, the weak KAM theory, and the ...
Show more content on Helpwriting.net ...
Recently, several authors have investigated random switching problems, their weakly coupled
Hamilton–Jacobi equations [1], the corresponding extensions of the weak KAM and Aubry–Mather
theory [1], the long–time behavior of solutions [1], and homogenization questions [1]. In these
references, as in the present paper, the state of the systems has different modes. However, in those
problems, the switching between modes is driven by a random process. In contrast, here, the
switches occur at deterministic times as considered [1]. Our results complement the earlier research
in [1] and provide the counterpart of the aforementioned results for the optimal switching problem.
Setting of the problem. Let [1] be a compact, connected Riemannian manifold, [1] its tangent
bundle, and [1] a finite set of modes. The (multimodal) Lagrangian, [1], is, for each [1], a Tonelli
Lagrangian, [1], prescribing the running cost at the mode "[1]". The switching cost is given by the
function [1]. A trajectory, [1] determines both state and mode at each time. We denote by [1] the set
of all absolutely continuous curves from [1] into [1], and by [1] the set of all piecewise constant
functions on [1] taking values on [1]. More precisely, [1] if there exists a partition [1] of [1] such
that [1]. In other words, [1] can jump in the interval [1] only at the times [1] (note that [1] is allowed
to jump also at the initial and

Descriptive Essay About The Poison Room
The Crimson Room
The deep red blood coiled through my hands like snakes, ever changing, ever flowing. The crimson
drops soon fell between the fingers and puddled together on the floor. She was no more. Many a
times had I imagined this situation, however, I never imagined myself truly doing it. However, no
amount of remorse or regret can bring the lifeless chunk of flesh lying at my feet back to life. Her
eyes were still open in shock and awe, and her cold, stale face was still distorted into the grotesque
image of fear, a mask she never thought she would be wearing in her single last experience.
Her blood pooled itself quickly, almost as if trying to escape the terrible and single truth of life, that
all life must at some point or another ... Show more content on Helpwriting.net ...
One could have called me mad, if her death was so traumatic as for me to not be able to even accept
her loss, how could I ever have been able to feed her to a couple of starving hounds? As one could
expect, I neither have nor had an answer to this.
Within a few days the scratching on the door of the basement and the loud whimpering from it had
ceased, and the last hound had fallen victim to the terrible sickness one calls living. The dark, black
door easily slid open with the slightest push of my cold hands. The three hound lay silently by the
door, deep bloody cuts covering their bodies, not like that of claws, but like that of a long knife. In
the middle of the room, right where I had laid her, she laid, not a scratch on her body, aside from the
deep wound stabbing through her back and out her chest.
Her body was soaked in crimson, like the deep, red petals of an autumn rose. However, her face had,
instead of the pale mask shaped and twisted with fear, her face was calm. Her mouth was closed in a
slight smirk and her eyes were closed in peace. Not even a wrinkle on her face could even indicate
that she ever would have felt even a trace of the terror i knew she had felt in her moment of

Summary Of The Movie Hidden Figures
The movie Hidden Figures is based on the remarkable true story of African American women
working for NASA in Hampton, Virginia 1961. With all their hard work and determination, they did
the calculations and equations for the shuttle launches of Friendship 7, Apollo 11, and other Space
missions. One out of these women was a brilliant mathematician named Katherine Gobel– Johnson.
As a young child, Gobel she was recognized for her high intellect and was recommended to an
alternative school so they can see what she can really do. At first, Katherine's parents were hesitant
because of the cost to send an African–American child during that time but the teachers made a
collection and full scholarship for Katherine to go. During the movie, young Katherine was
presented to solve the equation Katherine solved the equation and the answer was x=1, –7, 3, and –
1/2. Katherine graduated high school at age 18, then went to West Virginia State College now called
West Virginia State University. She graduated summa cum laude with degree in Mathematics and
French in 1937. Next, she became the first female African–American to attend West Virginia
University Graduate School. With her superb mathematical intellect, Katherine became a
"computer" at NASA. On the article called Human Computers found on NASA, "The term
'computer' referred to people, not machines. It was a job title designating someone who performed
mathematical equations and calculations by hand. Over the next thirty years, hundreds

Pallet Observation
The four learning patterns, sequence, precision, technical, and confluence are used differently by
each of us. In everyday life, we definitely use them all. I use the area of sequencing daily. My job
requires of me to place automobile door frames in a pallet using sequence. The auto maker we
service makes two types of a certain vehicle. There is a panorama, and a standard, also left and right
side for each. The order, in which the car comes down the assembly line, is the manner I have to put
the part on the pallet. I have an assembly set up for each pallet, which is a paper that gives an
illustration of the cars on the assembly. Robots pick the parts off the pallets and place them directly
onto the car. Honestly, I also, use some of the other

M. C. Escher Research Paper
A tessellation is when a shape is repeated over and over again, using transformations such as
translations, reflections, rotations, and dilations. M. C. Escher was an artist and mathematician who
made many types of art, but is most known for his tessellations. He was born in 1898 in the
Netherlands, and died at age 73 in 1972. His full name is Marutis Cornelis Escher. As a kid, he got
bad grades, but he was very creative and great at drawing. He went to college to study architecture,
but didn't do very well so he switched to decorative arts. When Escher went on a trip to Italy and
Spain, he met Jetta Umiker, whom he ended up marrying. He then had 3 sons named Giorgio, Arthur
and Jan and lived in Italy. 11 years later, he decided to leave Italy and move to Switzerland, because
he wasn't interested in Italian politics, and he didn't like that his son was forced to wear a Ballila
uniform (an Italian fascist group). He didn't like the landscape of Switzerland, so 2 years later him
and his family moved to Belgium. 4 years later, they moved to Netherlands because of World War II.
He stayed in the Netherlands until he died in 1972. ... Show more content on Helpwriting.net ...
When he moved from Belgium to the Netherlands, most of his most famous works are from then
because the wet weather allowed him to work on them and he had a lot of time on his hands. When
he was a younger artist, he sketched things such as nature and landscapes. When he was in Italy, he
decided to draw things that didn't form naturally. 2 examples of his famous works during this period
were "Drawing Hands", where 2 hands are popping out of a paper and look like they are drawing
each other, and "Relativity", where there is a building with many different staircases which confuses
your brain because you don't know which way is up or

The Properties Of Soft Multi Sets
Abstract–In this paper we define some properties of soft multi sets. We also define soft multi set
topology, its interior exterior, boundary and their properties. We establish several important results
in mathematical modeling of spacial objects using fuzzy soft interior, fuzzy soft exterior, fuzzy soft
boundary.
Keywords–Fuzzy Sets, Soft Sets, Multi Sets, Fuzzy Topology.
I. INTRODUCTION (Heading 1)
We may have to face vagueness in most of the engineering, physics, computer sciences, economics,
social sciences, environmental science and medical sciences problems. These may be due to the
uncertainties of natural environmental phenomena, incompleteness of human knowledge about the
real world or due to the limitations of the means and methods used to take measurements. We can
see vagueness or uncertainty when we decide the boundary between the continents or between
different seas, when the growth rate of population in a country 's rural area is determined or when
we make decisions using database information. In all these cases classical set theory, which is based
on crisp concept will not furnish the exact information.
The mathematical ideas like probability theory, fuzzy sets [12], rough sets [10] are well known as
effective models for dealing with such uncertainties. However, each of them has distinguished
advantages as well as certain limitations. Fuzzy sets fail to parameterize a value.
Molodtsov [7] introduced a completely new approach for modeling vagueness and

Reflective Reflection : Reflective Thinking
This self–reflection will incorporate the 4R's model of reflective thinking in order for my reflections
to be properly structured. The overall group project was a good experience for me, and provided me
a great opportunity to work with people from different cultures. Although these people were from
different cultures, I knew each group member before this assignment and had worked with the
majority of them previously. Therefore, I respected all the group member's and the skills, strengths
and weaknesses they brought to our group. Because of my established relationship with all
members, I felt that I was able to be honest in my assessment of their work without being perceived
as bossy or creating conflict. The aim for all of us was to do very well in this assignment, so our
group established a clear idea of outcomes and quality of work.
While these positive experiences made the group project easier to complete. There are still
challenges that we faced as a group. One main issue was that several group members failed to meet
deadlines that the group had set. This is relevant because we as a group needed all involved to finish
their individual parts in order to for their work to be read to implemented into the report. Failing to
submit individual parts on time makes it more difficult for me to trust group members. This is a
common issue that has happened in almost every group assignment I have undertaken. I found that
communication with these group members was absolutely

The Theory Of Algebraic Semi Rings
ON BORNOLOGICAL SEMI RINGS
ANWAR N. IMRAN
Abstract. Our main focus in this work is to generalizes the theory of algebraic semi ring from the
algebraic setting to the framework of bornological set. More specifically, the concept of new
structure bornological semi ring BSR is introduced and the fundamental constructions in the class of
bornological semi rings are discussed. In particular, the existence of arbitrary projective limits and
arbitrary inductive limits of bornological semi ring is ensured. Additionally, the description of the
category of bornological semi rings is presented and we study the product, coproduct and fiber
product. Key words: Bornological Set, Bornological Ring.
1. Introduction
The notion of a bounded subset of (real or complex) topological vector space was introduces by von
Neamann. That motivated the definition and more general classes bounded sets and called
bornologies. A bornological space is a type of space in functional analysis and it is very useful to
solve problem of boundedness for set of elements and functions. That means, the main goal for
bornology is to determine the boundedness, location and sitting the boundary for any area. A
bornology on a set X is a family β of subsets of X, such that;
Every singleton set fxg is in β, that means, β covering X ;
If A ⊂ B, B 2 β then A 2 β;
β is stable under finite union.
The elements of β are called bounded subsets of X. Let X and Y be two bornological sets, a map f :
X ! Y is called bounded if

What Is Graph Theoretical Analysis
1.3.4. Introduction to graph theoretical analysis. The case of brain perfusion SPECT.
In the field of quantitative neuroimaging, graph theoretical analysis is one of the methods to study
brain connectivity [93–95, 100, 101]. A key concept of this method is the notion of topology. This
concept can be illustrated with a simple idea which is used when we travel in the subway of any
large city. In figure 3 two maps of the London subway appear, the first map shows a precise spatial
description of the railways (or lines) through which trains travel (i.e., the subway topography),
whereas the second one is only concerned with the relative locations of subway stations and
connecting lines (i.e., the subway topology). These two maps do not coincide with regards to the
relative position of the stations, neither in the distances nor in the location of the lines. However, the
topological map simplifies the problem for the traveler. For example, two stations may be physically
(topographically) ... Show more content on Helpwriting.net ...
By simply inspecting the topological maps, it is not easy to know if one subway is better organized
than the other (e.g., subway efficiency). One way to simplify this problem is to use metrics that
quantify or analyze the subway network using graph theory [94, 101]. Hence the name of graph
theoretical analysis.
A first aspect to measure could be how easy it is to travel between any two stations (e.g. the number
of stations on average, between the start and end of the trip). This aspect is relevant, especially if the
traveler wants to visit different parts of the city on the same day. This example illustrates the concept
of global efficiency of a graph [94, 101]. The metric of global efficiency is a way to quantify the
global connectivity (integration) of the network. In this example, it is assumed that the number of
stations (nodes) and lines (connectors) are the same in the two subways that are

Pediatric Fair Case Study
the complexity of the group dynamics in the current era which makes these groups difficult to
represent in a simple model. Furthermore, it fails to recognize that tasks benefiting the group and
contributing to the group's goal can and do happen at other stages than performing (Hall, 2010).
Nonetheless, the model offers a useful framework for the group development through its applied
perspective and common sense approach (Bonebright, 2010). The forming stage consists of
orientation to the task at hand, gathering information on differences and similarities with other
members of the group, desire for the acceptance, establishing communication methods and looking
for guidance from the group leader (Tuckman & Jensen, 1977). The pediatric fair

The Velveteen Rabbit Summary
"Does it hurt?" asked the Rabbit. "Sometimes," said the Skin Horse, for he was always truthful.
"When you are Real you don't mind being hurt." "Does it happen all at once, like being wound up,"
he asked, "or bit by bit?" "It doesn't happen all at once," said the Skin Horse. "You become. It takes
a long time. That's why it doesn't happen often to people who break easily, or have sharp edges, or
who have to be carefully kept. Generally, by the time you are Real, most of your hair has been loved
off, and your eyes drop out and you get loose in the joints and very shabby. But these things don't
matter at all, because once you are Real you can't be ugly, except to people who don't understand." –
The Velveteen Rabbit by Margery Williams (1922) This ... Show more content on Helpwriting.net ...
The word "anything" is obviously general – it could mean anything. Immediately, the reader will
imagine their own fears. I think that's the point, however. Leaving it general will allow the reader to
imagine the things they themselves are scared of, which makes the quote that much more powerful. I
also like the specific word "daylight." Millay isn't just speaking about light in general, like a
nightlight in a child's bedroom. She's speaking specifically about daylight – light from the sun. This
might seem unimportant, but it changes the way that I think about things for sure. Daylight makes
me think of outside exclusively, and forget about indoor lights and nightlights. Thinking about the
outdoors only makes the fears change. It also implies that the whole word is being affected by it, not
just you. If it said "light" in general, then I would have immediately thought of a nightlight. A
nightlight can't really protect you from monsters; but this statement is specific to you. "Daylight,"
instead, implies that everyone who no longer in daylight is in danger. You can't change it by turning
on your bedroom light, because it's still dark outside. This changes my point of view, and I like that,
because I would have thought of something completely different if it only said "light." Millay also
uses the phrase "bad things," which is extremely general. She could be talking about murder or
robbery; she could also be talking about

Nt1330 Unit 5 Exercise 1 Algorithm
In this section, we discuss the implementation of XXX and evaluate the performance of our
proposed algorithm with synthetic inputs in terms of 1) SFC request acceptance ratio, 2) backup
resource consumed by requests and 3) running time. For comparison, we implement a baseline
method, where for an SFC request which requires n VNF and has the availability requirement of _,
we keep increasing the number of backup for each VNF on all selected physical machines until each
VNF can have an availability of n p _. The statistics shown in this section are the average results.
A. Implementation
We implement XXX as a framework with both single core and multi–core versions in an objective–
oriented language. A topology can be built by declaring the connections ... Show more content on
Helpwriting.net ...
Since telecom networks must be always on, it is critical to guarantee network service availability
with the minimum amount of resources. In this paper, we presented XXX, our approach to
provisioning availability in NFV. XXX provides a suite for service providers to concisely describe a
data center topology and estimate the downtime distribution of a mapped SFC request. To reduce the
running time of XXX, we further proposed an optimization framework which estimates the
minimum amount of backup resources required to meet heterogeneous availability requirements and
showed an heuristic solution with a theoretical bound. Through evaluation with data from
production data centers, we demonstrated the effectiveness and efficiency of our solutions. For the
future work, we are expanding our optimization framework to enable expedited estimations of the
backup resource needed under other models of VNF. On the other hand, the downtime estimation
accuracy is heavily dependent on the accuracy of the failure and repair distribution of each layer,
including both hardware and software. Therefore it is important to analyze system log data, extract
and model them using appropriate general

The Pros And Disadvantages Of Modern Test Taking
Will Powers
Dr. Lenore
English 100
26 October, 2017
Modern Test Taking
There have been many studies done to figure out which of the many testing styles allow students to
both retain more information and help elevate some of the pre–exam stress, while at the same time
not putting too much work on the professor. Out of all the styles that have been tested, two of the
most common styles that constantly rival each other are the open book test vs. the closed book tests.
Many teachers still cling to the traditional closed books test.
A closed book test is a test where students are expected to study their note before a test is given and
try their very best to memorize everything that they can fit into their heads in order to successfully
pass the test, then go into the exam with nothing but the pencil in their hand and the test on their
desk.
An open book test, is a test that allows students to bring either their notes or something that can be
written on such as a sheet of paper or a note card that was given to the student before the exam.
Both of these exam types have a wide range of both advantages and disadvantages.
One of the most common disadvantages that is often mentioned for closed book exams is the fact
that as far as the real world is concerned, closed book test are unrealistic. For many subjects the idea
of doing a task with nothing but the sole information in someone's head would be seen as not only
absurd but actually careless. An example of this absurdity and

Beta Club Research Paper
Why I would like to join the Beta club
If I was given the opportunity to join the Beta club I would be the happiest person in the world! I
want to join the Beta club because I would meet new people, I would help a lot of people, and I
would be caring and have responsibility. If I was to join the Beta club I would take it very seriously.
So that way I can work hard. Before I make my decision on being in the Beta club I would think
carefully.
I would love to meet new people while I am in the Beta club. First of all they would show me how
to do things. Also, they would be respectful. The final reason why I would like to meet new people
is that then they might be able to tell me more about Beta club. So that's the first reason why I would
like

Personal Narrative: My First Semester At Husky Game...
As my first semester at Husky Game Development, it took a little bit to get the ball rolling. It was a
challenge figuring out exactly what team or teams I would be working with this semester, thanks to
me joining halfway through the year, and the team changes that occurred within HGD. I didn't know
what teams I was working for until around the 3rd week of the semester, so that was my first
obstacle. Another obstacle would be meeting with the teams and figuring out what I can do for them.
While one team met on a regular basis, another team had very irregular meeting times, if they even
had meeting time at all. This has made it difficult to connect with the team and figure out what they
want, and whether or not they like what I've already made

The Properties Of Multi Intuitionistic Fuzzy
ABSTRACT: In this paper, we study some of the properties of multi intuitionistic fuzzy rw–
continuous mappings and multi intuitionistic fuzzy rw–irresolute mappings in multi intuitionistic
fuzzy topological spaces and prove some results on these. 2000 AMS SUBJECT
CLASSIFICATION: 03F55, 08A72, 20N25. KEY WORDS: Fuzzy subset, multi fuzzy subset, multi
fuzzy topological spaces, multi fuzzy rw–closed, multi fuzzy rw–open, multi fuzzy rw–continuous
mapping, multi fuzzy rw–irresolute mapping, intuitionistic fuzzy subset, multi intuitionistic fuzzy
subset, multi intuitionistic fuzzy topological spaces, multi intuitionistic fuzzy rw–closed, multi
intuitionistic fuzzy rw–open, multi intuitionistic fuzzy rw–continuous mapping, multi intuitionistic
fuzzy rw–irresolute mapping. INTRODUCTION: The concept of a fuzzy subset was introduced and
studied by L.A.Zadeh [22] in the year 1965. The subsequent research activities in this area and
related areas have found applications in many branches of science and engineering. Intuitionistic
fuzzy set was introduced and studied by Atanassov.K.T.[2, 3]. The following papers have motivated
us to work on this paper. C.L.Chang [8] introduced and studied fuzzy topological spaces in 1968 as
a generalization of topological spaces. Many researchers like R.H.Warren [21], K.K.Azad [4],
G.Balasubramanian and P.Sundaram [5, 6], S.R.Malghan and S.S.Benchalli [14, 15] and many
others have contributed to the development of fuzzy topological

Algebr No Reasoning Without Algebra

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