Lights Out Lab Report

Lights Out Lab Report
The purpose of this project is to solve the game of Light's Out! by using basic knowledge of Linear
algebra including matrix addition, vector spaces, linear combinations, and row reducing to reduced
echelon form. | Lights Out! is an electronic game that was released by Tiger Toys in 1995. It is also
now a flash game online. The game consists of a 5x5 grid of lights. When the game stats a set of
lights are switched to on randomly or in a pattern. Pressing one light will toggle it and the lights
adjacent to it on and off. The goal of the game is to switch all the lights off in as few button presses
as possible. In the folling examples, 1 will represent a "on" light and 0 will represent an "off" light.
Yellow represents a button pressed ... Show more content on Helpwriting.net ...
To solve for the scalars matrix A is augmented with the original vector. This augmented matrix is
then row reduced to reduced echelon form. This will result in the number of times each vector
should be pressed, either zero or once. Matrix after augmenting and row reducing to reduced
echelon form. 100000000000000000000000010100000000000000000000000000100000
000000000000000001000100000000000000000000000000100000000000
000000000000000100000000000000000000000000100000000000000000
01000000010000000000000000000000000010000000000000000000 00000001000000000000000
1&&&000000000010000000000000010000000000010000000000000000000000
000010000000000000000000000000010000000000010000000000000010
000000000100000000000000010000000001000000000000000010000000
00000000000000000001000000010000000000000000001000000100
000000000000000001000000000000000000000000001000000000000000
000000000001000100000000000000000000001001000000000000000000
0000010000000000000000000000000010&&& This tells us that buttons 1, 3, 7, 10,
11, 14, 15, 16, 18, 19, 22, and 23 should be pressed. Remember these buttons can be pressed in any
order. This shows us that even the most elementary linear algebra skills can be useful for real world
problems. Resources Lights Out! – www.2flashgames.com/f/f–35.htm Jaap's Puzzle Page –
http://www.jaapsch.net/puzzles/lomath.htm Lights's Out puzzle Wolfram Mathworld –
... Get more on HelpWriting.net ...

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

Sample Resume : My Husband And I Have Had Have Mentored (...
Debbie I have answers to some of your questions. On Wed, Sep 16, 2015 at 5:19 PM, Deborah
Heiser wrote: Nancy, The questions I ask are broad – and the gyst is that I am looking for you
thoughts about mentors you have had – and of those you have mentored (or are currently
mentoring). Based on your answers, I will follow up with additional questions in order to get a clear
story. 1. Please tell me about yourself. What do you do for a living, and how did you become
involved in your line of work? My husband and I have done well enough financially that I now
devote my attention on ways we can improve the world. As a student in middle and high school, I
was fortunate to have a father who enjoyed pondering interesting math problems ... Show more
content on Helpwriting.net ...
With this in mind, Josh proposed that we create a festival rather than a contest that incorporated the
features we appreciated in the Saint Mary 's Math Contest: the ability to work on problems with
others in a non–competitive environment, and a range of problems that started off easy and rose to a
level that would challenge advanced students. I wanted to provide students with engaging, thought–
provoking problems that they are likely to find more interesting and challenging problems than
those they are assigned in school. We chose to name the Festival after Julia Robinson because she
contributed to solving a very difficult math problem, she lived in the San Francisco Bay Area, and
we knew her sister Constance Reid. Julia Robinson died July 30, 1985 so we weren 't able to ask her
directly, but her sister was delighted to have us use her sister 's name. We suspect that the name Julia
Robinson is one of the factors that has contributed to the popularity of Festivals with girls; about a
third to half festival attendees are female. We were fortunate that Google offered to host several
Festivals, as did Pixar. The first Festival was at Google in 2007; today most Festivals are hosted by
schools and universities. Wildly popular, Festivals fill up rapidly and expose tens of thousands of
students to fun and engaging math problems. JRMF 's vision is to inspire a lifelong curiosity for
mathematics by instilling a genuine interest in creative problem–solving from an early

Calculus As A Part Of Modern Mathematics Education
Calculus (from Latin calculus, literally "small pebble used for counting")[1] is the mathematical
study of change, in the same way that geometry is the study of shape and algebra is the study of
operations and their application to solving equations. It has two major branches, differential calculus
(concerning rates of change and slopes of curves),[2] and integral calculus (concerning
accumulation of quantities and the areas under and between curves);[3] these two branches are
related to each other by the fundamental theorem of calculus. Both branches make use of the
fundamental notions of convergence of infinite sequences and infinite series to a well–defined limit.
Generally, modern calculus is considered to have been developed in the 17th century by Isaac
Newton and Gottfried Leibniz. Today, calculus has widespread uses in science, engineering and
economics[4] and can solve many problems that elementary algebra alone cannot.
Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more
advanced courses in mathematics devoted to the study of functions and limits, broadly called
mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or
"infinitesimal calculus". Calculus (plural calculi) is also used for naming some methods of
calculation or theories of computation, such as propositional calculus, calculus of variations, lambda
calculus, and process calculus.
Contents [hide]
1 History
1.1

What I Learned As Well As My Career Essay
The Ninja Watch This paper describes my field experience and what I learned as well as my career. I
was placed in Sharpstown International School, in which I was with Mr. O 'Heron. He taught both
Pre–calculus and Calculus classes. Those two classes are for seniors and there may have been a few
juniors in the pre–calculus class. There are in total four classes that I observed, one calculus and the
rest pre–calculus.
Activities
Throughout the field, I barely engaged in any different activities, mainly observe the students.
Though they did ask a few questions. Although I mainly observed, I did enjoy listening to Mr. O
'Heron 's jokes and stories. Observation is my specialty, I felt a bit odd being there at first, but
eventually I got used to it. I would come in the class, usually, Mr. O 'Heron is explaining something
to the students and I sit in the back. I would sometimes sit with the students, but that 's with the pre–
calculus class. I kept this routine for the rest of the time. There are some points when the students
would ask me a few questions. In the beginning, they asked me some questions about college, since
Mr. O 'Heron explained some things about college. The other class, keeping in mind I saw four
different classes, they asked for some help with their math. I ask for them to refer to their notes and
point at their mistake. I do wish that I would have engaged in a variety of activities, but since it 's a
high school level class there wasn 't much I could do.

Who Is Leonhard Euler?
Leonhard Euler was born on April 15, 1707, in Basel, Switzerland, Leonhard Euler was one of
math's most pioneering thinkers, establishing a career as an academy scholar and contributing
greatly to the fields of geometry, trigonometry and calculus. He released hundreds of articles and
publications during his lifetime, and continued to publish after losing his sight.
Euler showed an early aptitude and propensity for mathematics, and thus, after studying with Johan
Bernoulli, he attended the University of Basel and earned his master's during his teens. Euler served
in the navy before joining the St. Petersburg Academy as a professor of physics and later heading its
mathematics division. In the mid–1740s, Euler was appointed the mathematics director

Leonhard Euler's Life And Accomplishments
Leonhard Euler was an 18th century physicist and scholar who was responsible for developing many
concepts that are an integral part of modern mathematics. Leonhard Euler is considered one of the
most renowned and respected mathematician of all times. Euler is known for the tremendous
contributions he made to the field of mathematicians. Many concepts of today's mathematics
originated from the works of this phenomenal mathematician. Euler works spanned many fields
including mechanics, fluid dynamics, optics, astronomy, and music theory. His interest in
mathematics began in his childhood from the teachings of his father, Paul Euler. Johann Bernoulli,
another great mathematician in his time, was a friend of Leonard's father was a major influence in
Euler. According to Gottschling, Leonard works covered many areas such as algebra, geometry,
calculus. Trigonometry, and number theory. Two numbers are named after Euler which are Euler's
Number in calculus, ... Show more content on Helpwriting.net ...
He began his study of theology in 1723 but after gaining his father 's friend, Johann Bernoulli, he
changed his study to mathematics. He completed his studies at the University of Basel. Around the
same time, Johann Bernoulli two sons, Daniel and Nicholaus were working at the Imperial Russian
Academy of Sciences in Saint Petersburg. On July 31, 1726, Nicholaus died of appendicitis and at
that point Daniel assumed his brother's position. He recommended his previous now vacant position
to be filled by his friend Euler. Euler arrived in Saint Petersburg on May 17,1727. He was promoted
to a position in the mathematics department. He stayed with Daniel Bernoulli whom he also worked
with. After the death of Peter II, Euler rose through the ranks of the academy and became professor
of physics in 1731. Daniel Bernoulli left the academy to return to Basel. Euler was appointed to the
vacated position of senior chair mathematics. This new post improved his financial

The Case Of Ikea
Ikea is a multinational group of companies operating on a global scale in the furniture industry,
offering a wide range of ready to assemble (Do It Yourself) furniture, appliances, and accessories
worldwide. The company is well known and recognized for its modern designs, functionality of
their products, quality services, and their eco–friendliness. Within the competitive market, Ikea aims
at being better than its competitors in the market, and offers the best standards of services to its
customers, as well as a wider range of products for low prices. As a system practitioner, it is
important to be able to differentiate between a difficulty and a mess. A mess may be regarded as a
problem or situation that is perceived and understood in different terms by different people. With a
mess, external settings are what cause dissatisfaction. A difficulty on the other hand is a problem or
situation that is perceived on the same basis by everyone examining it. To improve a difficulty, all ...
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Different stakeholders involved in the situation may study and analyze the situation in their own
way, and they come up with their own methods of overcoming the problem and reaching a
conclusion. In the soft system method, the situation has no clearly defined structured, and that the
solution comes from a person's own creativity and learning after further study of the case, and does
not need a computerized system like that in the hard system

Pre Calculus: Student Analysis
The greatest academic challenge I have faced to this day was Pre Calculus my Junior year. Math has
always been my weakest subject and the one that I need the most help in. Unfortunately, help was
something I struggled to find. The friends that I had in the class also struggled to understand the
subject matter just as much as I did and were unable to help me themselves. For a long time, I used
online resources to try and review the subject matter at home. While I could struggle through my
homework by comparing the problem step–by–step with an example, tests and quizzes felt
impossible. Eventually, I was able to gain some assistance in the Math Lab at school, a resource set
up for those who needed assistance. The one–on–one attention that I received gave me an
understanding that I did not achieve when just sitting in the lecture. However, while I was able to
better understand my homework, I still consistently earned a C on the tests and quizzes. Because
these parts of the class were weighed so heavily, I was unable to pull my grade up very far. What
helped my grade the most was the large extra credit project available in fourth quarter. Along with
two friends, I built a ... Show more content on Helpwriting.net ...
I found that being able to find a way to apply the concepts of the class to the real world helped my
understanding. It was unfortunate that the solar project did not fall earlier in the year, or that there
were not more of its kind. Using a more creative outlet, like the cooker, was a hands–on experience
that helped to cement my understanding. In addition, my learning type seems to be more visual than
auditory. I always needed to do a problem myself before I could even attempt to understand it. The
help that I received in the Math Lab was a great example of such. Being walked through a problem
as I completed it was extremely beneficial. It was through the help and patience of the teachers in
the Lab that I was able to do as well as I

The Discovery Of Calculus : Newton And Gottfried Von...
Throughout history, there have been numerous mathematical discoveries, but perhaps none of these
were met with the controversy of the discovery of Calculus. In the 1600s, two men, Isaac Newton
and Gottfried von Leibniz both began the study of differential and integral Calculus. During the 17th
century, plagiarism was an extremely serious offense and second inventors were often put in the
position to defend their right to the topic and against suspicion. Newton and Leibniz spent many
years with their respective supporters defending their claim to the discovery of Calculus although
today historians and mathematicians agree that Newton and Leibniz independently and without
knowledge of the other's work discovered the basis and methods for differential and integral
Calculus.
Gottfried Leibniz was born on July 1, 1646, in Germany to a wealthy family; his father was a
professor of moral philosophy. When young, Leibniz attended the Nicolai School, but mostly taught
himself out of his father's library. [1] He later went on to study at the University of Leipzig where he
focused on law. While studying at university he came in contact with many great philosophers such
as Bacon, Hobbes, and Descartes. [1] In 1666, Leibniz was denied his Doctorate of Law due to his
youth causing him to leave Leipzig, this same year he wrote his first book on philosophy. [2] Upon
leaving Leipzig, he met Johann Christian von Boyneburg and was hired as his assistant and used this
position to gain

Why Math Is Important For Teaching Mathematics And How...
Math Philosophy Paper Math is developing concepts or standards that's important for teaching
mathematics to students from Pre–K to high school. In our changing world, those who understand
and can do mathematics will have significant opportunities and options for shaping their future.
(NCTM 2000, p.50). The two important tools to be an effective teacher is knowledge of
mathematics and how students learn mathematics. The purposes of math education effect our life
since the time we were able to walk. We were taught how to count on our fingers to being able to
write our numbers to ten. Then as we got older, concepts were more challenging and involved
critical thinking to solve the problems. In society today, math is being utilized in simple to complex
avenues such as grocery shopping, measuring, budgeting, investments, architecture, science and
technology to name a few. If we take a look around our environment signs, buildings, bridges,
streets and just the different patterns and shapes all relate back to mathematics. My role as a math
teacher in the classroom would be creating an inviting math environment for my students, being able
to explain math to all my students in ways that they understand and model math in an effective way.
I want to be a leader, share my knowledge, engage and challenge my students, support them, respect
them, be positive and keep them interested in math. The qualities I would have as an effective
teacher is the knowledge and skills and the

Ap Calculus Ab Topic Is Solving Limits
My favorite AP Calculus AB topic is solving limits. This is because limits are fairly simple to solve.
AP Calculus AB was extremely difficult for me, so I was happy to find a topic that was somewhat
easy for me to understand. I know that a limit is the value that a function or sequence approaches as
the input or index approaches some x–value. To solve most limits, I had to use six basic properties
of limits: the sum rule, the difference rule, the product rule, the constant multiple rule, the quotient
rule, and power rule. Sometimes I had to use substitution, factor the limit first, use the conjugate
method, or simplify the complex fraction in the limit. To solve limits involving infinity, I had to look
at the highest degree of the numerator and denominator. If the degree of the numerator is equal to
the degree of the denominator, the limit is the lead coefficient ratio. If the degree of the numerator is
greater than the degree of the denominator, the limit does not exist (DNE), ± ∞. If the degree of the
numerator is less than the degree of the denominator. Understanding how to solve limits pleased me.
I liked solving limits because I did not have much difficulty doing it.
My least favorite AP Calculus AB topic is Riemann sums. This is because I had a hard time
remembering how to do them. Riemann sums are used to estimate the answer to an integral or
estimate the area under a curve. There are three different types of Riemann sums: left Riemann
sums, (LRAM), right Riemann

Lee Stiff To Math
History Lee Stiff is an African American Math education professor in the Department of
Mathematics at North Carolina State University. Lee Vernon Stiff was born in 1949. His father
provided for the family by working in a factory with a third– grade education level. While
researching Stiff, no information was found about his mother or siblings (if he had any). This essay
will provide information about the life of Lee Stiff and how he contributes to mathematics.
Education
In the year of 1971, Stiff received his Bachelor's degree in Mathematics from The University of
North Carolina at Chapel Hill additionally, He received his Master's Degree from Duke University
(1974) and his PH. D from North Carolina University (1978). (Lee V. Stiff (852), ... Show more
He has many publications, including the authorship, co–authorship, or editorship of textbooks in
middle grades and high school mathematics, six professional books and eight book chapters. Dr.
Stiff is a textbook author for the Houghton Mifflin Harcourt Publishing Company and McDougal
Littell. ''Houghton Mifflin Math'' is an elementary textbook series, K–6; and McDougal Littell's
titles, such as Math Course 1Algebra 1, Geometry, and Algebra 2 which is usually middle and high
school math textbooks. (Lee V. Stiff (8301), 1999) This is a list of some current textbooks that was
credited by Lee Stiff: Developing Mathematical Reasoning in Grades K–12, Geometry: Reasoning,
Applying and Measuring and Heath Algebra1: An Integrated

New York State Penal Law V. Newton Case Analysis
While on the surface the facts in the Newton case and in the variation may look very similar there is
one difference that could lead to the cases being decided differently. In the original case Newton is
flying from the Bahamas to Luxembourg. The captain of the flight made an unscheduled stop in
New York City at JFK International Airport. Shortly after two officers boarded the plane and asked
Newton if he had a weapon on him. When Newton answered yes he was arrested and charged with a
violation of section 265.05(2) of the New York State Penal Law. In this case Newton did not commit
voluntarily act because it was the decision of the captain to land in New York. Newton could not
have possibly known that he would be subjected to New York

Improving Students Entering Higher Education
For many students entering higher education, the hard sciences and advanced mathematics courses
are often avoided. As attrition rates in the fields of science, technology, engineering, and
mathematics (STEM) increase, the projected need for professions in these fields in the upcoming
years is increasing. Increasing success and retention in the STEM subjects has become a focus of
much recent educational research (Tsui, 2007). To avoid falling short of educated scientists and
engineers to fill the expected positions, intervention strategies and new teaching methods such as,
summer bridge programs (Ackermann, 1991), learning centers (Sullivan, 1980), career counseling
(Hill, Pettus, & Hedin, 1990) and others have been implemented (Seymour & Hewitt, 1997). Of
particular interest to this project is advanced mathematics achievement, specifically in calculus, in
hopes of increasing retention. Many higher institutions are seeing a strong avoidance of enrollment
in calculus courses and similarly any majors with calculus as a prerequisite. High failure and drop
rates in calculus have led instructors, policy makers, and administrators to investigate solutions to
improve the development of calculus curriculum as well as effective placement procedures (Edge &
Friedberg, 1984). Variables that are frequently considered predictors of mathematics achievement
include the SAT, ACT, and GPA scores. As the calculus instructor cannot influence those variables
for their incoming students

Jacqueline Gandara
The Math Autobiography of Jacqueline Gandara Mathematics is the study of the sciences of
numbers, quantities, geometry and forms. ("Mathematics dictionary definition | mathematics
defined", 2016) It is a subject that is simple as well as complex. Over the years I have learned that
math is not my cup of tea. I think I liked it more when I was younger, when it was simple, and
easier. I guess you could say that I liked basic math, like adding, subtracting, and multiplying.
Growing up, I actually had no problem with basic math. It was easier when I was in elementary
school. It was until I arrived to middle school and high school that I realized that math wasn't as
simple as I thought it was. Math did not really influence my life until I reached ... Show more
I use math to shop for things at the store, to cook, bake, and to keep track of my expenses. Math will
also be used in the career I have chosen. According to CFNC.org, math is a necessary skill for a
career in Customs and Border Protection, but it is not as important as reading comprehension,
writing and speaking skills. Level 2 math is used in this career and it is most likely not used on a
daily basis. (Corporation, 2016) However, basic math is necessary to get through some of the rules
and regulations. For example, let's say someone attempts to cross the border with 39, 12 oz. cans of
beer and 6, 12 oz. cans of ale. This is legal by law if the person meets the legal drinking age of 21.
However, there is a limit of 40 oz. of liquor, wine or 24, 12 oz. cans or bottles of beer or ale. This
person has passed the limit so, he has to pay a fine of 94 cents for every can that he has gone over.
You have to use your basic math skill to figure out how much money this man owes for bringing
extra liquor. 45 cans (what this guy is bringing) minus 24 (the limit) equals 21 cans. 21 multiplied
by $0.94 cents is $19.74. This man owes a total of $19.74 for his extra liquor. (Corporation, 2016)
The math class I plan to take for my major is college Algebra. Even though I probably will not use it
in my career, I have chosen to take it because I am pretty good at it and it is also essential for a
bachelor's

Csc200 Week 3
Taylor Shuler CSCI 36200 HW1 Report with Run Time Analysis Selection Sort: Pseudocode: n =
A.length for j = 1 to n – 1 c1: n smallest = j c2: n–1 for i = j + 1 c3: ∑_(j=1)^(n–1)▒〖(j+1)〗 if
A[i] < A[smallest] c4: ∑_(j=1)^(n–1)▒j smallest = i c5: ∑_(j=1)^(n–1)▒〖jt_(i,j) 〗 exchange A[j]
with A[smallest] c6: n–1 Best Case: Already Sorted; tij = 0 Worst Case: Sorted Backwards; tij = 1
T(n)=c_1 n+ c_2 (n–1)+ c_3 (∑_(j=1)^(n–1)▒(j+1) )+ c_4 (∑_(j=1)^(n–1)▒j)+ c_5 (∑_(j=1)^(n–
1)▒〖jt_(i,j) 〗)+ c_6 (n–1) ... Show more content on Helpwriting.net ...
In insertion sort, the best case is not quadratic because it only has to verify each entry once since it
would have nothing to insert. The algorithm would just read through the array once and see that it is
already sorted. Selection sort must check each entry twice to verify that the array is correctly sorted
in the best

Critical Reflection
"Anyone can turn his weaknesses into strengths", I was reading the book David and Goliath by
Malcolm Gladwell, and the book was about a battle between David, the underdog, and Goliath, the
giant, and it explains how David defeated a giant by using his unconventional strategies. It also talks
about how some underdogs can overcome their weaknesses; in addition, it also explains how power
comes in different forms. Malcolm Gladwell proved his arguments by providing some real–life
experiences of different underdogs. According to Gladwell, an underdog is a person who is
underestimated by everyone to perform any task successfully. Malcolm Gladwell also explains
many other terms to prove his argument. I have experiences in my student life where I felt like an
underdog. I felt disempowered because of my weaknesses. I still remember the first day of my
English 838 class at College of San Mateo, and I felt so unconfident in the classroom because I was
not a native speaker. There were also moments in my college classes where I felt empowered
because of my strengths; for example, I felt empowered in my Math–120 and pre–calculus class
because I already knew the concepts of these classes. I had a lot of moments in my life where I felt
empowered and disempowered as a student, but learning from those moments helped me to succeed
in my college classes.
I felt disempowered in my English 838 classroom because English was not my native language. I
have been in the United States for a year now. Earlier I was at the University of North Texas for a
semester, then I transferred to College of San Mateo because of some financial issues in spring
2017. I registered for my English 838 class for the spring semester, but I was really worried about
this class. I was so nervous for taking English class because It was my first time taking an English
class in the United States. I came from a country where English is not a native language. Even
though I was from an English medium high school in India, I was so nervous because I wasn't sure
that if I am ready to take a college–level English Class. I was so nervous on the first day of my
English class. There were a lot of thoughts going through my mind because I wasn't sure if I would
be able to

AP Calculus A: A Short Story
Growing up, I was always one of those students who never got anything less than an A. From
proudly receiving stickers and praise notes in elementary school to non–stop studying for an algebra
test, I've always expected an A on my assignments. But then came junior year of high school. I had
signed up for one of my school's most demanding courses, AP Calculus AB. On the first day of
class, the teacher explained the depth of the material we would be learning, telling us that it would
cover a wide range of math, and showed us a brief introduction to it. He also mentioned that it was a
course where we would have to take time and learn the material on our own. Having gotten straight
A's since the day I started attending school, I had no worries towards these statements. ... Show
more content on Helpwriting.net ...
Everyone in the classroom sat quietly in their desk, waiting with for the teacher to call out our name
to see our scores. Name after name was called. I could see the faces of disappointment cross my
classmates' faces as they saw their grades. My teacher finally called my name. I nervously made my
way up to the front of the room and took the test as my teacher handed it to me. As soon as I saw my
grade, I felt my stomach drop and my mind go into panic. I had absolutely bombed the first test of
the year. I wasn't the only one, but I couldn't believe the grade that I had gotten which was far off
what I expected. After receiving the horrendous scores from the test, students began to drop the
class. In just two weeks, the once filled class was reduced to a small classroom of only fifteen
students. Everyone in the class was overwhelmed and stressed by the amount of work load that we
were being given. As for me, I was doing worse and worse as the class progressed. For the first time
in my life, I was on the verge of receiving a failing grade on my progress report. I had two clear
options: give it my all and make it through or drop and save my

Essay On Geometry
Is Geometry the Most Fundamental Area of Math?
As the very name implies, Geometry means measuring earth ('Geo' meaning earth and
'metron'meaning measurement). Hence, one can understand how old this branch of Math is and what
importance it should hold among the branches of Math.
What is Geometry?
Geometry is the branch of Math which deals with shapes, sizes, figures and their various properties,
relations and measurements. Doing Geometry with seriousness helps a Math student develop good
mathematical abilities and a precise power of perception.
Origin of Geometry (How old is Geometry?)
Geometry was given importance right from the age of Greeks and most of its concepts were found
in measuring lengths, volumes and areas in their early culture. ... Show more content on
Helpwriting.net ...
The concepts of Geometry have given rise to Trigonometry with its angles, side angles, right angled
triangles and non–right triangles. Algebraic Geometry is also popular today with its concepts like
coordinates.
You have the emergence of Calculus from the aspects of Geometry. One can find the root of modern
integral Calculus in Archimedes' ingenuous techniques for calculating areas and volumes. You find
geometric figures like plane curves represented analytically in the form of functions and equations
leading to the emergence of infinitesimal Calculus. Today, you have Topology and differential
Geometry as well.
Overtones of Geometry in various areas of learning
Since Geometry is interlinked with Astronomy and is useful for calculating spatial distances, both
these subjects were learnt together in olden days. Not only that, Geometry has sprinkled its
influence upon various other areas like art, land survey, civil engineering and architecture. You can
find the overtones of Geometry in Science subjects like Physics also. Hence, Geometry has a vast
role to play in the contour of Math learning and makes for successful understanding of related topics
in Trigonometry and

AP Calculus Lessons Of My Life
It was December and near the end of the first semester of my senior year. I sat next to my close
friend Adrian as I helped him understand the last few AP Calculus lessons. The time had reached
4:30 P.M., and we'd been sitting together in Mr. Brink's room after school for almost two hours. Mr.
Brink sat at his desk while Adrian and I were at a different table. Only the three of us remained in
the room. Eventually, Adrian started to pack up. I gave him a hug as he left, then sat back down. As I
looked up, I made eye contact with my favorite teacher and best friend.
"Thank you for helping Adrian today." He said to me.
"Of course!" I smiled in return.
As strange as it may have sounded, calculus was important to me. Mr. Brink showed me how easy ...
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My life has been dramatically changed by the teachers in my life. From Mr. Brink, to my 8th grade
science teacher Coach Bradley, the love, service, and patience I've seen reflected in my favorite
teachers astounded me every time.
As a teacher one day, I can only hope to open up my arms with acceptance and love the way my old
teachers opened up to me. My past experiences have taught me not only how difficult life can be for
certain students, but also that there is beauty in diversity. I hope to show all of my different students
both appreciation and respect, regardless of their background, the way my teachers have for

Pt1420 Unit 1 Assignment
One of the assignment I chose for math was a test. I chose this assignment because one of the
hardest test †hey I have ever done. Even though received a C I am still proud of it because for me it
was a challenge. The assignment was about "Linear Equations, Getting m & b and Scatter Plots. The
problems that are in the test is for number seven which is about how the given data represents a
linear function and to complete the table of solutions and write equation. That is part of the test
questions that I had for this test which at first did not know what to at first so it came back to my
head and got the answer correct. The point of this assignment was to get it done at the time it was
giving in which I did not completed. Even though

Everything That Rises Must Converge Flannery O Connor
Everything That Rises Must Converge" "
By: Flannery O'Connor Fatmeh Tatour ID: 208864702
The relationship between different characters, cultures, and races in Everything that Rises Must
Converge" by Flannery O'Connor .
Flannery O'Connor story " Everything that Rises Must Converge " consists of different relations
between two different nations, customs, traditions and thoughts. The story talks about the
relationship between two different nations in the same country which every nation has her own
traditions, cultures, and thoughts. The writer presents the story Julian and his mother's, how they're
both have dissimilar ideas and personality and how both of them has dissimilar thoughts. The story
reveals how these two kinds of cultures coexist with each other, and how they thoughts about each
other. In my essay, I will discuss the relations between different characters according to the story.
One of these relations is between Julian mother's and her son. Julian's mother is a white American
citizen, believes that whites and black people must live separately also she believes that what we
wear is what will judge us, and the ... Show more content on Helpwriting.net ...
Carvers mother is a black woman, the mother of a young Carver. She seems as Julian mother wears
the same foolish purple and green hat, travels alone with her son as Julian mothers and upset by
having to sit with someone else's son on the bus. Although they have identical thoughts about each
culture and both of them want's to live separate and to rejoice all their rights, Julian's mother was
different she sees Carver's mother as an animal who stole her hat. Such a reaction shows that racism
is such a strong and a dark force that it leads people to dehumanize and alienate each other in even
the panelists circumstances, according to the LitCharts website of the article Everything that Rises
Must Converge summary &

College Classes Expand the Mind
After my early 9:00 a.m. Philosophy recitation I headed towards the elevators to head back down to
the first floor. I slowly drug my sleep–deprived body to the 10A bus that took me to my dormitory
hall up the hill. Once I finally arrived at my room, I sat down at my desk to start on my schoolwork
that would surely take hours to complete. Looking into my pages of notes, I started to question
myself on why I am doing all of this repetitive, seemingly unnecessary work. My homework
consisted of Calculus problems that required me to find the derivative of extremely long functions,
and I realized I am not benefiting anything from completing these tedious equations. Some of the
answers to the problems required a whole page to write the answer ... Show more content on
Helpwriting.net ...
Or is my path strictly limited to the careers that are related to the classes in which I succeed? It
seems that my "endless" career possibilities are suddenly narrowed down drastically when you look
at how I performed in certain courses in the past. This indication of my uncertain, almost
predetermined future makes it difficult to set goals that will help me achieve a career that best suits
me. It is very challenging to set goals for myself if I do not know the direction I am striving for.
Some of the previous goals I have set for myself include the basic ones: getting good grades, getting
into college, and not getting into any type of trouble. However, the only thing that these goals will
help accomplish is to give myself more options to choose from. For example, getting good grades in
high school allowed me to have many options in choosing the college that was right for me.
However, if my future is predetermined, what good is having all of these options to choose from? In
the end, I will ultimately pick only one of the options and never know what the options could have
been like. This way of thinking makes it extremely difficult to spend hours completing math
equations I know I will never see outside of a Calculus textbook. However, if I had not gotten good
grades in high school I would not be at the University of Pittsburgh right now. So this
"predetermined" future that many philosophers believe to exist

Calculus C Are Largely Defined By Derivatives Of Vector...
The major topics explored in Calculus C are largely defined by derivatives of vector–valued and
parametrically defined functions, integration by partial fractions, improper integrals, series
convergence (Taylor and Maclaurin), L'Hopitals Rule, and numerous applications. All of the
following topics require a solid foundation in not only Calculus A but also Calculus B.
Vector–valued functions include mathematical functions of one or more variables whose range is
defined as a set of both multidimensional vectors and infinite dimensional vectors. Much of this was
expanded on by Newton and Descartes during the Enlightenment in Europe. Newton largely defined
calculus in his book Principia Mathematica whereas Descartes was the founder of analytic ... Show
more content on Helpwriting.net ...
The derivative of a three–dimensional vector function can be differentiated by using standard
differentiating rules, taught in a standard Calculus A course, as it breaks up the components in the
Cartesian coordinate system.
Integration by partial fractions, or in other words commonly known as the partial derivative of a
vector function, is defined with a commonly used variable a, with respect to the frequently used
scalar variable q. A sub I is the scalar component of a in the direction of e sub i. Sometimes, it is
also called the direction cosine of a and e sub i, but it is also frequently known in most math classes
as the dot product. The vectors e1,e2,e3 form what is known as an orthonormal basis that is
commonly fixed in the reference frame in which the derivative of the partial is being taken. This was
also further expanded on by Newton in the 17th century in his famous book Principia Mathematica
and he often used the notation from Gottfried Leibniz, another 17th century mathematician.
Defined by Isaac Newton and Descartes, in calculus C, another frequently taught topic is what is
known as an improper integral. It is defined as the limit of a definite integral as an endpoint of the
interval or intervals of integration approach either a specified definite real number or infinity or
even in some cases negative infinity. In other cases both endpoints approach limits. Such an integral
is often written symbolically just like a standard definite integral,

My AP Calculus Class
When I was growing up I always did well in my math classes in comparison to my other classes.
Students have said "He only does well because he's Asian."; others said "He's just naturally smart
compared to the other students" . In reality, I was just extremely interested in math and spent most of
my time wanting to study and understand the subject compared to science and reading. Whenever I
am in a math class, whether it was my Algebra I class or my AP Calculus class, I am constantly
thinking to myself "How were these mathematicians able to correlate how certain numbers had
some type of relationship with a figure or equation such as the Pythagorean Theorem"? When I am
in another class, like my English or AP Government class, my mind tends to stray away from taking
notes or doing my assignment because I am always thinking about numbers and certain equations
and how they are able to be applied into the real world.
Math is engaging because of how difficult every new concept you learn is and how I had to struggle
so much in order to fully understand the concept. When I first walked into my AP Calculus class, I
expected nothing but straight forward problems. This was not the case when I learned about
derivatives and integrals because I struggled for ... Show more content on Helpwriting.net ...
In addition to this, math is captivating because of the various ways I am able to apply it in real life.
Construction workers use a mixture of algebra and trigonometry when creating building. The size of
a building and the area it covers is important for construction workers to keep note of when
designing new buildings. In addition to this, chemist manipulate algebra when finding the weight of
an element based on the conditions around the element, as well as how many atoms it contains.
Math applications used by chemist increase their understanding of elements or molecules they are
trying to

Teaching and Learning 'Rate of Change'' (Slope) in Senior...
Analysing understanding is an essay which will discuss the researched issue of Teaching and
Learning of 'rate of change (slope)' in Senior Secondary Schools in Australia. Students require a
contextual knowledge of slope "so that they come to see slope as a graphical representation of the
relationship between two quantities' (Center for Algebraic Thinking (CAT), 2014). Without the
multiple understandings required to master 'rate of change' and algebra many students are ill
equipped to go on to levels of higher mathematics. It is necessary to engage students at level where
they utilise the skills of enquiry, collaboration, hypothesis, deductive reasoning, and
experimentation in real–world examples so that misconceptions are be identified ... Show more
Explore the relationship between graphs and equations corresponding to simple rate problems). It is
year 10 (ACMNA237)) before the solving and graphical representation of linear functions
introduces the linear function of y = mx + c (where m is the slope or gradient of the graph) being the
algebraic representation of a linear relationship (Solve linear simultaneous equations, using
algebraic and graphical techniques including using digital technology. The ACARA (2014)
Mathematics Curriculum also specifies proficiency strands of Understanding, Fluency, Problem
Solving and Reasoning. These are an integral part of mathematics content across the three content
strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The
proficiencies reinforce the significance of working mathematically within the content and describe
how the content is explored or developed. They provide the language to build in the developmental
aspects of the learning of mathematics The chosen texts for this essay are the MathsQuest series for
Years 9 and 10A. These texts are designed for the current Australian Mathematics Curriculum and
provide many added advantages to the teacher and students. There is e–Text access available, online
class homework and assignment setting by teacher, on–line revision options, and many extra lesson
activities

History of Calculus Essay
History of Calculus
The history of calculus falls into several distinct time periods, most notably the ancient, medieval,
and modern periods. The ancient period introduced some of the ideas of integral calculus, but does
not seem to have developed these ideas in a rigorous or systematic way. Calculating volumes and
areas, the basic function of integral calculus, can be traced back to the Egyptian Moscow papyrus (c.
1800 BC), in which an Egyptian successfully calculated the volume of a pyramidal frustum.[1][2]
From the school of Greek mathematics, Eudoxus (c. 408−355 BC) used the method of
exhaustion, which prefigures the concept of the limit, to calculate areas and volumes while
Archimedes (c. 287−212 BC) developed this idea ... Show more content on Helpwriting.net
...
In Europe, the second half of the 17th century was a time of major innovation. Calculus provided a
new opportunity in mathematical physics to solve long–standing problems. Several mathematicians
contributed to these breakthroughs, notably John Wallis and Isaac Barrow. James Gregory proved a
special case of the second fundamental theorem of calculus in AD 1668.
Gottfried Wilhelm Leibniz was originally accused of plagiarism of Sir Isaac Newton's unpublished
works, but is now regarded as an independent inventor and contributor towards calculus.
Gottfried Wilhelm Leibniz was originally accused of plagiarism of Sir Isaac Newton's unpublished
works, but is now regarded as an independent inventor and contributor towards calculus.
Leibniz and Newton pulled these ideas together into a coherent whole and they are usually credited
with the independent and nearly simultaneous invention of calculus. Newton was the first to apply
calculus to general physics and Leibniz developed much of the notation used in calculus today; he
often spent days determining appropriate symbols for concepts. The basic insight that both Newton
and Leibniz had was the fundamental theorem of calculus.
When Newton and Leibniz first published their results, there was great

Newton's Negative Neglect
Newton's Negative Neglect Isaac Newton faced many hardships in his lifetime, yet managed to be
internationally famous for his genius mathematical and physical discoveries, and remarkable
inventions. Newton was extraordinary in the sense that he was able to endure complications in life
and still be an enormous success. The majority of individuals would have cracked under the
predicaments Newton faced. Newton overcame neglect by suppressing his emotions, defeating
limitations of his time, and becoming one of the most noteworthy mathematicians and physicists in
history. Isaac Newton had a tragic and unfortunate life ever since he was born. Three months prior to
Newton's birth, his father died. Then, when Newton was three years old, his ... Show more content
on Helpwriting.net ...
The time limitations imposed on Newton seemed to be no match to his genius, besides the fact of
the general public and others denying his new discoveries. Additionally, Newton overcame his time
limitations by contributing new inventions and technology to the world. One of his most well known
inventions is the pet door, which he created to end the problem of pets constantly scratching or
standing and waiting at a door. His other popular invention is a greatly improved telescope. His
telescope was more advanced than previous telescopes, due to his proprietary use of mirrors to look
at objects at a distance ("Sir Isaac Newton;" Ball). This advancement in telescopes opened up
numerous possibilities for astronomers. Newton's inventions further proved how he overcame even
technological barriers of his time. Another issue Newton faced was false accusations. Newton had a
dislike for publishing his works, until it seemed as if others were beginning to reveal the same things
he did. For example, a man named Gottfried Leibniz began uncovering things in the field of
calculus, a field Newton claimed to discover well before Leibniz had. Newton was then inclined to
publish his work in calculus, just before Leibniz did, which led to major controversy to who actually
uncovered the secrets of calculus. It is still in controversy today as to whether Newton plagiarized
Leibniz's works, but Newton is widely known as the original father of calculus

My Dialectical Journal
Journal # 3 6/11
In high school, I struggled with both math and physics. Between the two, physics was more
challenging for me than math. When my father realized I was failing both subjects (with flying
colors) he immediately hired a tutor for me. Prior to getting help, I spent a lot of time in circles
trying to figure out one question after another. For some reason I could not get the hang of physics. I
started to feel embarrassed about not know how to solve my math and physics problems when I
realized that one of my closest girlfriend was doing well in both subjects. After taking a quiz, I
would hide my grade from my classmates because I was so embarrassed about it. When my father
received my first quarter report card he was very disappointed

Pre-Calculus Research Paper
Prior to taking Pre – Calculus I had taken College Algebra which has helped me tremendously with
the objectives of Pre – Calculus. I learned basic algebra skills that helped me advance in solving the
objectives needed for the advancement of the course. I am currently working for a construction
framing business in which some math skills are required. I plan on obtaining a major in structural
engineering and a minor in mechanical. The College Algebra class thought me how to add, subtract,
divide, and multiply fractions which I had always had difficulty with. I have yet to master the skill,
but because of Pre – Calculus I am receiving a lot of practice, which has helped me comprehend
how to solve the math. College Algebra helped me understand that math is basically a puzzle that
needs to be solved with steps, because of this understanding the math has become fun to solve. After
solving a problem in class that my other classmates have ... Show more content on Helpwriting.net
...
Before deciding that I wanted to become an engineer, the thought of needing math in the future was
never important to me. Since deciding my future I obtained a job in construction framing to have a
hands on feeling of how buildings should be built. That is when I was truly enlighten in the need to
understand math. To build a building two of the hardest things to accomplish is the roof of the
building which has to have a slope, and an arc if the building were to have any luxury. The roof
requires a downward slope to get rid of water and debris, but to find the slope a basic knowledge if
trigonometry must be obtained first, which is where Pre – Calculus helped me understand the math
to create the roof of a building. The arcs within the building are used to dress up the building and
make it look luxurious. The arcs would have never been possible without learning the angle and arc
length which were learned how to be obtained when taking Pre –

Why Is Algebra Important
Algebra
When I decided to return to school to get my degree I did not think that much about which courses I
would be required to take. I knew there were basic classes such as English, Science, History and
Math, and then the courses that would be required for my degree. I knew I would be taking Algebra
at some point but was not expecting it to be so early on. I am not sure I see a lot of need for Algebra
itself in Human Resources, but I do know that I need it to graduate. I do not feel I am being forced
to take Algebra, it is just another required course, like Intro to Computers, or Student Success, or
English. Math has never been my favorite subject, but more out of fear of not being able to figure all
the problems out, than just a general dislike for the subject.
When I hear the term liberal arts, I think of general education classes not degree specific classes. A
liberal arts degree gives students an education in all the major areas of study such as History,
English, Math, Science and the Arts. Students with degrees in the liberal arts can find employment
in a lot of job fields, as they are educated in various areas. STEM, or Science, Technology,
Engineering and Math degrees and programs are popular today with the rise of ... Show more
Students attending universities and colleges are receiving a higher education. I believe the purpose
of higher education can vary based on the students needs or what they are hoping to achieve. For
some, a higher education degree is required for their choice of profession, such as a teacher or a
nurse. For others, a higher education degree is needed to help further them in a specific career field,
such as the dairy manager of a grocery store earning his Bachelor of Business Administration to one
day be the Store or Regional Manager. And others, such as myself, earn a higher education degree to
help with a career change or even for a feeling of personal

Eudoxus' Contribution to Calculus
Eudoxus was a notable mathematician and astronomer of ancient times, particularly 408 – 355 BC.
He lived in Greece and studied under Plato, one of the most notable philosophers ever. In Calculus,
Eudoxus is known for advancing Antiphon's ideas on the method of exhaustion. The method of
exhaustion is very important to calculus because one of the fundamental themes of calculus is
sending variables (or whatever it happens to be) to infinity, which is a branch of the method of
exhaustion. This is known as taking the limit. Eudoxus used the method of exhaustion to calculate
volume and area. One example of this is his work with the area of a circle. At the time they hadn't
established this yet. If you didn't know the formula for finding the area of a circle, you would need
to approximate it, just like how we have learned to approximate the area under a curve with Rieman
Sums. First, you could inscribe a circle in a triangle, and use the area of the triangle to approximate
the area of the circle. But that would not give you a very accurate answer, so next you would draw a
square around your circle. Still, this is not very accurate, so you would keep adding to the number of
sides of your polygon until you approached infinity, giving you the most accurate answer possible
without the formula. This is how Eudoxus would have figured out the area of a circle – with limits.
It seems thus that Eudoxus was the first person to develop the definition of a limit. This definition
has

Mathematics Is That Of Pi ( Π )
PI (π) One of the oldest and most commonly known and used concepts in mathematics is that of Pi
(π). In the earliest of know human civilizations, people realized the importance of finding the exact
value of π for practical reasons. Even by todays standards, we still only need to know the exact
value of π to a few decimal place values, although that hasn't stopped mathematicians from pursuing
a more accurate representation for its value throughout time.
The earliest know approximations for the value of π have been identified on ancient clay tablets,
dated 1900–1650 BC, from the Babylonian civilization which states the value of π as (25/8) = 3.125.
and from the Egyptian civilization, from the Rhind Papyrus(1650BC), which approximates the value
of π to be (16/9)^2 = 3.1605. Although these earliest of approximations have been proven to be
within 1 percent of todays actual know value, it marks the point of obsession for mathematicians to
find an exact value for π.
The next advancement in determining a more accurate value didn't occur for more than another 1000
years. Around 250 BC, the Greek mathematician Archimedes developed an approach using
circumscribed and inscribed polygons to prove that the value of pi to be between (223/71) < π <
(22/7) (3.1408 < π < 3.1429). This geometrical approach was predominantly used by
mathematicians for the next 1000 years, were in 1630 an exact value of π was found to 39 decimal
palaces.
Sometime around the year 1425, a new approach

Solving The Process Of Creating The Tool Essay
3.0 Problems In the Process of Creating the Tool We encountered a lot of problems during the
process of doing the project, mainly in three perspectives. First is the lack of coding ability, none of
us had prior coding experience before and the only Excel knowledge we know is what TAs taught us
in the lab. This problem branched off into many other problems such as disrupting the efficiency of
the team because the critical path was delayed at times. All these problems also related back to the
original plan because of our infinite view of the problem in the beginning. The big mistake was not
taking into account the constraints in the very beginning of the project. Instead of focusing on the
constraints, we focused on the basic needs and we focused too much on what we wanted the final
product to look like assuming that we all had the capability to code whatever we wanted to. In the
beginning, we only need to use simple Excel functions to create our tool which was within our
capabilities; however, with the increase of the requirement, we had to use more complex functions
and create our own function by VBA to satisfy the higher requirement for our tool. This problem
roots back to the original plan. Due to the fact that we planned the functions of the tool without
researching and analysing our constraints in coding. In the beginning we thought that the functions
planned were realistic and within our abilities because there were enough resources online to help
us. However as time

I Have The Pleasure Of Teaching Maiyuki Druen Essay
I have had the pleasure of teaching Maiyuki Druen for three years; as an 8th grader in Advanced
Geometry, as a sophomore in Math 174 Dual Credit Pre–Calculus through Morehead State
University, and currently as a junior in AP Calculus. In 8th grade, Maiyuki chose to arrive at school
an hour earlier in order to take Advanced Geometry at the high school. She was by far the best
student in the class, even though she was in a class of extremely bright freshmen and sophomore
high school students. Constantly pursuing opportunities for herself, as a sophomore, she chose to
take a dual credit class designed for juniors and seniors. She requested special permission in order to
take this college level class as a sophomore, and it was granted based on her stellar academic record.
She continues to push herself academically in my AP Calculus class. She accepts the challenging
problems I assign to the class as an opportunity to further develop her understanding of the
mathematics we are studying. She often spends time analyzing the different approaches to a problem
in order to determine the best course of action, and will diligently work the solution discussing her
results with her peers. Often I will observe her having a discussion about the problem solving
process with a fellow student rather than just conferring about her solution.
While actively engaging in class discussions, she will articulate beautiful solutions in such detail
that even the most struggling students can

The Contributions of Isaac Newton Essays
Isaac Newton was born in Lincolnshire, on December 25, 1642. He was educated at Trinity College
in Cambridge, and resided there from 1661 to 1696 during which time he produced the majority of
his work in mathematics. During this time New ton developed several theories, such as his
fundamental principles of gravitation, his theory on optics otherwise known as the Lectiones
Opticae, and his work with the Binomial Theorem. This is only a few theories that that Isaac
Newton contributed to the world of mathematics. Newton contributed to all aspects of mathematics
including geometry, algebra, and physics. Isaac Newton was born into a poor farming family in
1642 with no father. Newton's father had passed away just a few months before ... Show more
Later he read and mastered Oughtred's Clavis, and Descartes' Geometry, which led him to take up
mathematics rather than chemistry as a serious study.
As a result of the Plague, from 1665 threw 1666 Newton had spent a great deal of time at home.
During this time it seems evident that a great deal of his best work was accomplished. He thought
out the fundamental principles of his theory of gravitation. He determined that every particle of
matter attracts every other particle. Yet he suspected that the attraction varied depending on the
product of their masses. He suspected that the force, which retained the moon in its orbit around the
earth, was the same as the terrestrial gravity. And to prove this hypothesis he proceeded by doing
this. He knew that if a stone wall were allowed to fall near the surface of the earth, the attraction of
the earth caused the stone wall to move though sixteen feet in one second.
The moon's orbit relative to the earth is nearly a circle, and as a rough approximation assuming so,
he knew the distance of the moon, and therefore the length of its path. He also knew the time it took
the moon to go around the earth once, a month. Therefore Newton could find its veloisty at any
point such as M. Then he could find the distance MT through which it would move in the next
second if it were not pulled by the earth's attraction. At the end of the second it was at

The Creation Of Calculus, Gottfried Leibniz And Isaac Newton
Today, Calculus is one of the most important branches of mathematics with applications in science,
engineering and economics. But who invented this wonderful tool? As with many questions of
invention, the answer is a little complicated. Most mathematicians will tell you that two men
deserve the credit for the development of modern calculus, Gottfried Leibniz and Isaac Newton. Of
course, Newton and Leibniz were merely the next links in a long chain of discoveries that led to the
creation of modern calculus. The ancient Greeks had first dipped their feet into the field with the
famous mathematician Archimedes being the first to find the tangent to a curve and Antiphon of
Athens developing the method of exhaustion, an early technique to compute the area of a region.
Then the Indians added their own discoveries with the astronomer Aryabhata expressing an
astronomical problem in the form of a differential equation and Parameshvara of Kerala developing
an early version of the mean value theorem in the fifteen hundreds.
Finally, during the European enlightenment, men like Fermat, Pascal, and Isaac Barrow further
pursued the emerging new field developing the concept of the derivative. Barrow even offered the
first proof of the fundamental theorem of calculus linking the concepts of differentiation and
integration; however, it was one of Barrow's young students, Isaac Newton who would make the
next big splash in the creation of the art of calculus. In Isaac's eighty–four years, he

Diana Gu Passion
True Passion: Diana Gu's Experience of Success Mathematics is not for one type of person: not only
for the nerdy and weird outcasts, not only for the white male, not only for those who are not targeted
by the stereotypes prevalent in the field. Mathematics is not dry, nor boring, nor focused on inane
solutions never to be used after the discovery. Mathematics is not what people think it is; it is not
one field, one theme, one subject. Mathematics is everything. Look around, with clear eyes, and you
will see the art of mathematics everywhere. Dr. Diana Gu, the founder of MTY Academy, an
extremely successful institute in the Austin community, and long–time, inspirational professor at the
Texas State University, looks at the world and sees numbers. She sees passion and dedication and
motivation. She sees intensity and zeal and excitement. Explaining that mathematics is essential for
everyone, she emphasizes an idea: innate skill matters little, while practice is what defines you. The
belief originates from her experiences in her youth: her parents were extremely supportive,
providing her with the ... Show more content on Helpwriting.net ...
Mathematics is essential. She likens mathematics to a computer: it's indispensable, it's a tool, it's an
instrument to be used. She explains that everyone has misconceptions about math, and explains that
as a community, the face of mathematics can be changed. Mathematics is for everyone: not only for
the nerdy and weird outcasts, not only for the white male, not only for those who are not targeted by
the stereotypes prevalent in the field. Mathematics is lively, and exciting, and focused on solutions
to change the world. Mathematics is what Dr. Gu is guiding students to see; it is not one field, one
theme, one subject. Dr. Gu, the teacher I look up to the most, shows her students that mathematics is
beautiful. Mathematics is everywhere. Mathematics is our past, present, and

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