Algebra College Essays Samples For Students

Application of Algebra in computing

Algebraic principles are used extensively in computing. In computer science, the computer algebra is called algebraic computation or symbolic computation. This is used mainly in software development and the associated algorithms that are used in the manipulation of mathematical expressions and objects. Kaltofen Erich (1982) noted that the long-known algorithms that were being used proved to be very long and this necessitated the revisiting of classical algebra with the intention of making them effective and efficient. In specific terms, algebra is used in the following fields of computing.
Encoding: in encoding, data that is arranged in arrays or ...

Solving Real-World Problems Using Algebra.

A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P= -25x2+300x . What number of clerks will maximize the profit, and what is the maximum possible profit?

Solution

The Quadratic equation P= -25x2+300x can be modified to the form y= -25x2+300x, where P= y.
Modifying the equation in this form enables us to plot the function y= -25x2+300x

For various values of x where x is a positive integer.

The general equation of a quadratic is given by y= ax2+bx+c where a, b and c are the ...

Kirchhoff’s Laws are fundamental in the analysis of electrical and electronic circuits. They describe the behavior of linear circuits accurately, and work well with approximations in other types of systems as well, making them extremely useful (“Electrical Principles”, 2013). Further, they are more popular and widely used than Maxwell’s equations, from which they can be derived. This is because Maxwell’s equations are very complex and involve brute Mathematics to solve even simple circuits, while the Kirchhoff’s laws are relatively much easier to use in most cases.

There are two laws which were given by Kirchhoff:

1) Kirchhoff’s Current law (KCL)
2) Kirchhoff’ ...

Given Traffic Scenario

Figure 1: The intersections of five one-way streets
1) There are five streets making six intersections. All the streets are one-way, that is, cars can move along only one direction on any street. The number of cars between intersections is the taken to be the traffic flows. For optimal flows, it is assumed that the number of cars entering an intersection in a given time must equal the number of cars leaving that intersection in that time. Also the number of cars entering and leaving any street per unit time is as mentioned in Figure 1. It is important ...

Mathematics and sciences gave me one of the biggest challenges in my early education life. Having studied in a private school in the US where I was introduced to Everyday Math, I realized that it was not as easy as the tutors would want us to believe. An s early as I can remember, the educators used old and ineffective teaching criteria. Having to count from 0 to 1000 and playing games seemed tedious at the moment but it was as much impractical as I would learn later on. Addition and subtraction facts were scanty, and less emphasized. Until 5th ...

A.1A single mom has to go back to work and needs day care for her baby. She is trying to decide between a baby sitter, who cares for children in her home,ora nearby day care center. The baby sitter charges a flat rate of $10 per hour, and the localday carecenter charges $325 per week, for 5 days per week, up to 40 hours. (Mon-Fri), plus $10 per hour for any time exceeding 40 hours.
A.2The baby’s mom will need day care services M-F from 7:30-5:30 (10 hours per day, or 50 hours per week).
A.3The baby ...

<Student’s name><Professor’s name><Course number>
<The date of the paper>

Part 1. Data collection.

Gather from credible sources the following data:

- The amount of calcium and iron (in milligrams) found in one 10 oz package of broccoli
- The amount of calcium and iron (in milligrams) found in a ½ cup of frozen corn
- The recommended daily values (in milligrams) of calcium and iron
We have found that in 10 oz broccoli there are 116.44 mg of calcium and 2.04 mg of iron.
Also we found, that in 1 cup of frozen corn there ...

Karl Theodor Wilhelm Weierstrass was a German mathematician who is often called as the "father of modern analysis".

Weierstrass was interested in the soundness of calculus, and also made significant advancements in the field of calculus of variations. Among the several significant axioms, Weierstrass established a necessary condition for the existence of strong extrema of variational problems.
As we know, Cauchy gave a form of the (ε, δ)-definition of limit, in the context of formally defining the derivative, in the 1820s, but did not correctly distinguish between continuity at a point versus uniform continuity on an interval, due to insufficient rigor. Notably, in his 1821 Cours d'analyse, Cauchy gave a famously incorrect proof that the (pointwise) limit of (pointwise) continuous functions was ...

According to Stanoyevitch (2010), cryptography refers to one of the oldest branches of pure mathematics that primarily deal with the study of integers. It deals with the prime numbers and also the properties of the objects which are made out of the integers like the algebraic integers. Cryptography is a very important tool for protecting information from unauthorized access in the computer systems. Currently, finite fields are becoming very vital in cryptography. Most cryptographic algorithms depend heavily on the properties of the finite fields especially the elliptic curve cryptography and the Advanced Encryption Standard (AES). The most important concepts of ...

Muhammad ben Musa al-Khwarizmi

Muhammad ben Musa al-Khwarizmi was a Persian astrophysicist, geometrician, and geographer. He was born in Persia at around 780 and died around 850. Though his name signifies that his family was originally from the region around Khwarizmi nearby the Aral Sea, historians trust that al-Khwarizmi was congenital in the town of Baghdad, which the current day Iraq. Though diminutive is identified about his cloistered life, al-Khwarizmi’s effort and participation have principally endured the ages discreetly intact. The exclusion is a volume of mathematics in which the novel cannot be established; there is, though, a Latin rendition of his effort as well ...

Introduction:

A linear equation is an algebraic equation in which the highest power of the unknown variable is a unit. Linear equation is in the form of where a, b and c are constants and x and y are the variables of the equation (PBS. Mathline). A linear equation produces a straight line graph when plotted to scale on a graph paper.

Solving a System of Linear Equations

A system of equations is the case when we have more than one linear equation. (When there are two or more equations). For elementary studies, the number of unknowns in the system is equal to the number of equations in the system. We ...

Question 1

R { 1,2,3,4 }
Z { 5,6,7,8 }
F is a subset of RZ
Where each element X ∈ R
and each element Y ∈ Z
(x, y) ∈ F

F subset { y ∈ Z| ( x, y) ∈ F for some x ∈ R}

R is the domain

Z is the codomain

, (4), ∈ Z

2.65 to 6.65

On the graph point 2.65 is (2.65, 4)

And point 6.65 is (6.65, 4)
x ∈ Z y ∈ R
( x, y ) ∈ F is a subset of RZ
Using = 4 Transforming R along itself

R ( 2.65, 4 )

F( 6.65, 4 )
R + Z defines a function since each element of R occurs only once among the ordered pairs.
Where set:
R is the ...

The paper analyzes and discusses different concepts related to Algebra. The paper talks

about Order of Operations, Linear equations and their application, linear inequalities,

Quadratic equations. It talks about and summarizes different methods of tackling and

simplifying such algebraic expressions. Finally the paper dwells into different functions and

their graphic representations.

Algebra and Functions

Order of Operations: Order of operations is a mathematical that determines the

correct order for solving any of math operations. Powers and roots are solved before

multiplication and division, which in turn are solved before addition and subtraction

(Toolingu, n.d.). The rule is used in calculation and simplification of a complex algebraic

expression involving many arithmetic operations. Order of operations ...

This discussion post or essay has basically been undertaken to understand some standard

results in Algebra in Mathematics. We would analyze the importance of using derived and

standard results and also about how they ease our calculations drastically. We would also

learn about some elementary but very important terms like Exponents, Integers etc. and

their usage with respect to solving questions in Algebra.

Here in the given questions we have got three variables namely a, b, c which have been

assigned values according to the problem statement (based on my date of birth). All three

variables are integers with ‘b’ being the lowest term and hold the following values:

a= 8
b=-2
c=87

Then we evaluate the algebraic equations based on the values of these three values.

...

Abstract. In recent time, connectomics which is filed aimed to construct wiring diagram of the brain at the level of synapses and their connections has gained an increasing interest and is very promising for neuroscience. Advance in technology allow to acquire huge volumes of data and the challenge for researchers and scientist now is storage, visualization, and processing of the data. Developing GPU technology provides effective solutions for computing on large datasets and its visualization. Moreover, several recent work propose techniques for optimized segmentation, reconstruction, proofreading, and visualization of connectome. However, existing solutions are still not efficient enough and ...

As I sit down to write a few lines on my experience related to mathematics, I find myself at a loss to describe mathematics, as I understand. I have read that mathematics is a science related to numbers and their operations, measurements, and abstractions. This evokes memories of childhood and how I dreaded numbers. How I hated memorizing multiplication tables. When I was in elementary school, I failed to recite the multiplication tables and my teacher punished me. This had profound effect on my young psyche. She forced me to write the tables ten times because she felt that ...

Al-Khwarizmi is the great mathematician, astronomer, geographer and the founder of classical algebra. Although the life of Al-Khwarizmi is little known, he left us his works that cover different areas of knowledge: mathematics, astronomy, geography.
Works of Al-Khwarizmi in mathematics are the most know. Two treatises such "The Book about the Indian account" and "Calculation by restoration and reduction" were translated into Latin and served for a long time the basic textbooks on mathematics. The arithmetic treatise of Al-Khwarizmi had an enormous influence on the development of science in the East and then in Europe. This work became the ...

Mathematics is the queen of sciences. It gives us a lot of things that successfully find their application in various scientific spheres but seem to be completely useless in ordinary daily life. One of such things is a matrix. Matrix helps us to solve differential equations, but one could say that its practical application looks rather vague. However, this statement is inaccurate. The aim of this paper is to discuss matrices and to observe their use in everyday life.
For a start, let’s make a brief overview of matrices and their scientific applications. According to the textbook, a ...

Modern technology has brought the revolution in the lifestyles of today human beings. It has turned the society into more casual and less hard working. It also has changed students` attitude towards attending classes. Because of such technological achievements, students feel less responsibility in attending them. However students` presence at regular classes should be mandatory if students want to score good grades, which results college performance, and socialize themselves.
For sure, student`s personality is shaped through attending classes on a regular basis. Responsibility – is what is trained among students by their teachers at classes (Kanar). Better responsibility for ...

Is being educated in all subjects necessary in every profession?

"You have to learn, young man. Philosophy. Theology. Literature. Poetry. Drama. History. Archeology. Anthropology. Mythology. Music. These are your tools as much as brush and pigment. You cannot be an artist until you are civilized. You cannot be civilized until you learn. To be civilized is to know where you belong in the continuum of your art and your world. To surmount the past, you must know the past." This particular statement by Mark Rothko to a budding artist from the play “Red” by John Logan notes that to be civilized, one must understand a variety of disciplines before he can ...

CRITIQUE OF “THE ALGEBRA OF INFINITE JUSTICE”

The Algebra of infinite justice is an article written by Arundhati Roy. Arundhati was born on Novemeber 24, 1961 in Shillong to a Bengali Hindu father and a Christian mother. She won a Booker Prize for her first novel-The God of Small Things in 1997. After that she wrote on many topics on politics, nuclear weapons s in India, corruption among others. One of her writing is “The algebra of infinite justice” where she criticizes the role of USA in the beginning, propagation, and methods to fight terrorist. She claims the USA is created terrorist and is attempting to destroy them. She ...

Abstract

Research into how individuals learn and the different stages of learning has been the focus of studies by various scholars. Based on the research that has been conducted so far, there are several theories that have been advanced. Notable among these theories are the theories that have been advanced by Piaget and Lev Vygotsky. They both concur on the role of the surrounding environment on the learner but differ on the effect. In spite of the differences that are evident in their theories they have been instrumental in shaping the teaching styles that are applies all over the world. ...

Narrative: Studying at UCA

During my life, growing up in Saudi Arabia, I worked for several different insurance companies and learned over time it was what I wanted to do with my life. From a young age, I loved it and wanted to pursue an education in the field. Today, I am only twenty-seven years old, and as an undergraduate, I have begun studying insurance and risk management in an effort to achieve this dream. There have been many obstacles along the way, but I have always proven to myself that if I stay dedicated and committed to my education and the plans ...

Application of Juvenile Delinquency Concepts

Introduction
The juvenile is a person who has not reached his or her eighteenth years of age and delinquency is the violation of law. Hence, the term “juvenile delinquency” refers to the violation of the law done by a minor that would be considered a crime if would have been done by an adult who have reached the age of eighteen or passed this age (Office of the United States of Attorney, n.d).

Summary of key aspects

The story of Barry Dale Loukaitis has been selected for examination. The key aspects of the story are that it shows the impact of wrong beliefs ...

For any person intending to take an engineering course, he or she must be willing to tackle mathematics units. The computation required for the engineering includes College Algebra, Trigonometry, Geometry, Statistics, Liner Algebra, Differential Equation, Calculus 1 and 2. (Nieße, Tröschel and Sonnenschein 37-51)
The study of mathematics in engineering is a process that requires continuous fundamental learning of things. It goes beyond just learning “order” and further emphasizes on the “design” process. The goal of studying engineering is to learn, understand, and use the concept of laws of science within the needs of the society and ...

The issue of gender disparity is commonly discussed with people raising a concern about how women and men do not have similar opportunities. The world continues to evolve and women today have broken barriers in a number of male-dominated fields. However, there are still issues of disparity in fields of science and engineering. Most women who have pursued a career in STEM-related fields have not joined the science and engineering fields. The following is a look at the statistics showing the existence of the problem, followed by recommendations on how the issues can be addressed.
Studies show that there ...

The word depression (/dɪˈprɛʃən/), a noun which was introduced to the English language by the turn of the fifteenth century, holds a wide range of meanings today. It can refer to an economic condition, an emotional one, or a physical one. The word even has a number of mathematical and scientific uses in the fields of algebra, geology, astronomy, and psychology. Depression originates from the Latin verb dēprimĕre, meaning “to press down.” Its current morphology is dated to 14th century French, depression (Oxford English Dictionary).
The word first enters the English language as an astronomical ...

Abbasid Caliphate

During the time that Europe was still grappling with the Dark Ages, civilization and knowledge revolution was being adopted in Baghdad. In this regard, Muslim scholars were gathered in the House of Wisdom under the leadership of the Abbasid Caliphate. The House of Wisdom was instituted with the focus of promoting the translation of scientific related texts and concepts. They endeavored to conserve information related to classical civilizations which lay a basis for the formation of academic disciplines which still maintain their relevance in the current society.
The Abbasid Caliphate sought to spread Islam through conquest and conversion in ...

Trigonometric computations are used in nearly all fields of geometry, physics and engineering. The triangulation technique has the great importance, which allows measuring the distance in astronomy and geography, monitoring the satellite navigation system. Also trigonometry is used in such areas as music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medicine and so on. Daniel Bernoulli, Fourier and Cauchy made a huge contribution to the involvement of trigonometry and developed the idea of trigonometric series.
In the middle of the XVIII century, appeared the most important in its consequences "argument of a string". Euler ...

James Baldwin wrote the short story Sonny’s Blues in 1957 and one of the main themes in it is music. The story is about the relationship between two brothers who lost their parents and the older one takes care about the younger one, Sonny. Music is about expressing feelings and Sonny is a person who is very emotional and prone to the feeling of sadness, which is why he finds comfort in music that takes away all the pain.
The narrator is the older brother and he is a serious man who teaches algebra in school. Sonny is ...

Abstract

The Sonny’s Blues story begins at the point when a narrator, who remains unnamed in the story, but was identified as an algebra teacher reads the arrest of his brother who had been charged with selling Heroine. The teacher is therefore deeply perturbed and the thought of his brother keeps reminding him of the students in his class who also face the realities and the possibilities of the hostile world. The narrator again fails to pay a visit to the brother for a very long period until the time of the tragic death of his daughter. At this ...

DeMorgan’s Theorem is one of the most important transformation rules in digital electronics. It is a pair of transformation rules which could be applied in propositional logic and are both valid for rules of inference. It was named after its developer Augustus De Morgan who is a British Mathematician. The simplest way to define DeMorgan’s Theorem is that the logical expressions remains unchanged when the inversion bar of the expression is broken and the operation is changed to its opposite.
DeMorgan’s Theorem come about in order to simplify logical expressions in mathematics. It was influenced by ...

Before the onset of the seventeenth century, the Middle East had dominated in the area of mathematical ideas. Many philosophers and scientists came up with compelling ideas in mathematics and proved many formulas in mathematics from the Middle East. Essentially, there were distinct factors that influenced scholars and philosophers from this region to be competent in mathematics and other scientific inventions as they were. However, in the onset of the seventeenth century, Europe replaced the Middle East, which had been vastly associated with mathematical discoveries. Europe thus became the new engine house of mathematical ideas from the seventeenth century . ...

Instructional leader

Abstract
This essay will discuss tools, which will assist the educational leader in promoting the learning outcome and assessment of students by guiding, encouraging, motivating and supporting the school culture and offering instructional programs in the area of mathematics, which are conducive to student learning and the professional growth of staff members. Mathematical tools are measured and structured to assist teachers who can examine distinct or various approaches to improve the mathematics performance of students in middle school. Students that are in elementary grades 3 through 9 accept the challenge and the desire to succeed. According to research, ...

Mid-Term

Cope
Bloom’s Taxonomy in Mathematics Teaching
Bloom’s and Anderson’s Taxonomy
This paper discusses a brief history and background of the original Bloom’s taxonomy established in 1956 and the revised Bloom’s taxonomy by Anderson et al. in 2002. It attempts to explore how the taxonomy of learning in the cognitive domain is applied in a specific teaching field such as Mathematics.
In 1956, Benjamin Bloom headed a committee of educators to establish a systematic hierarchy in classifying educational objectives. They published their findings in a book, Taxonomy of Educational Objectives: The Classification of Educational Goals (Bloom ...

Education is by far the most important activity in a person’s lifetime. It is said that education never ends and a person’s capacity to learn is only limited to his or her belief of the knowledge they possess. Educational institutions all over the world impart knowledge to young minds in various fields established by human kind throughout its existence. However, education is not only about gaining knowledge and certifying oneself (Hacker). It is about increasing one’s awareness, one’s own personality and one’s one perspective of the world around them. However, each individual has a different take on ...

Introduction to Electrical Engineering

Electronic gadgets are in great demands today because of the evolution of high technology and advancement of internet connection. People are always finding something new, so, many companies are giving funds for research. With the help of electrical engineers, companies are providing new gadgets every now and then to surpass the features of the previous gadgets that they have been produced.
In order for the students to solve complexities of a problem, electrical engineering program gives an opportunity to learn new things by experimentation and analytic solving. Therefore, this program mainly tackles mathematics and science. Because of experimentation and ...

There are several mathematical formulae that mathematicians and scientists have come up with over time. These mathematics formulae solve or address several issues or problems in the real world or mathematical and scientific field. One of the well-known mathematicians is Augustin Louis Cauchy. He is credited for coming up with the Cauchy sequence (the Cauchy sequence is named after him). This paper explores the Cauchy sequence, explaining its nature, form, application, and other related aspects of the sequence.
What is Cauchy sequence? This is a sequence whose elements become arbitrarily close to each other in the course of progression ...

Validity and Scope of Approximate Methods of Integration

Introduction
Addition of discrete numbers is pretty straightforward; more than 80% of the human population can make mental calculations instantly. So when integration was introduced as a kind of addition in a continuous domain, I was not very worried. However, it didn’t take me long to realize that understanding integration is more than solving a bunch of problems using well defined techniques. So in my pursuit to understand the topic well, I decided to research upon how some of these techniques (Trapezium Rule and Simpson’s Rule) came about, how they work, and what they really mean. With this intent, ...

The properties of real numbers is a fundamental concept of basic algebra. Any given individual should be aware of these concepts as we may face them in our everyday lives without even noticing. When you actually are doing simple math operations while buying groceries or calculating your monthly expenses, you are dealing with real numbers, and, therefore, you should be aware of their properties in order not to make a mistake in your calculations. The distributive law, simplification procedures and operations with removing parentheses are important to know anytime you are facing a problem which involves calculations. The knowledge of these properties ...

Before the age of Mohammed Muslims said that their people lived in the age of ignorance and the Arabian Peninsula was an archaic place that housed a myriad of religions and cultures – some sort of political wasteland (Basif, 2013). The Bedouins were the nomads that occupied the peninsula and provided the backbone for the social atmosphere. They were skilled travellers and controlled the commercial networks. While the peninsula housed a lot of towns and cities, Mecca stood out from them all. It was not a major trading city or a crossroad to one but it stood near an oasis marked by a black cube. ...

Personal Portfolio

During my studies at the university I have taken courses in algebra, statistics, English, history, wind energy, and pharmacology. This wide variety of courses has helped prepare me for interdisciplinary studies in that I am creating a wide base and background of basic knowledge in multiple areas. This variety will give me a basis well in the range of areas as they move into upper-level courses and become more specialized in certain areas during my studies in my later years of schooling.
The algebra course that I took builds on basic knowledge that is required of high school graduates. These ...

An Exploration of the American Dream as it is presented in Salinger’s “A Perfect Day for Bananafish”, Updike’s “A &P” and Baldwin’s “Sonny’s Blues”
The American Dream is often thought of as a defining national characteristic of the USA. The Dream is most frequently thought and spoken of as the opportunity for financial success and material prosperity, achieved through determination and hard work.
The three succeeding short stories show the authors’ critical standpoint towards the American dream. To begin with, Seymour Glass in “A Perfect day for Bananafish”, Sonny in “Sonny’s Blues” and ...

Summary

Bilal Haq, a scientist from the National Science Foundation Arlingtion, Virginia encountered foraminifera on his trip to Qingdao in China. Foraminifera are small creatures that grow shells on their bodies. Their shells are varied and very diverse, as if they are created by visionary artists. Haq thought the foraminifera would make beautiful pieces of art and should be put on display. Haq’s fellow colleague from China, Zheng, agreed and put things into action by involving local craft workers. It resulted in a park for foraminifera since the end of 2009 and already a million people have visited (Larkins, 2012).

It is ...

The science of numbers otherwise known as mathematics is various disciplines and principles that involve changes in structure, space, quantity and change. It has been a fundamental of many other sciences that rely on numbers for reasoning. Being said that, mathematics need to have learning standards. Because having standards in mathematical learning will give students realistic and clear expectations of what they are about to learn in math disciplines. Students will also have understanding of the reasons why learning math is detrimental in connecting concepts to their previous learning and how they apply in practical situations.

How do standards improve ...