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Benjamin Banneker, 2002.
An introduction to "First African-American Scientist", Benjamin Banneker and his contribution to mathematics.
835 words (approx. 3.3 pages), 4 sources, MLA, $ 29.95
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Abstract
The paper introduces Benjamin Banneker, an African American born in 1731, who made enormous contributions to the study of mathematics. The paper discusses his spheres of interest in the field, including clock building, astronomy, tide and weather. It discusses, too, his widely publicized almanac that served as a contradiction to the American belief that blacks were inferior, and his contribution to the building of the city of Washington D.C.
From the Paper
"In addition to creating America's first clock, his studies in astronomy made a mathematical calculations of the stars and constellations, which he used to correctly predict a solar eclipse that took place on April 14, 1789. Furthermore, Banneker was not quiet about this contradiction. Infact, he was a social critic of slavery. Thus, it was this reason and an attempt to promote change; he sent a copy of his first Almanac to Thomas Jefferson."
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Calculus and its Application to Aerodynamics, 2002.
This paper explores some of the different applications of calculus to the field of aerodynamics.
2,525 words (approx. 10.1 pages), 5 sources, APA, $ 76.95
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Abstract
This paper states that the field of aerodynamics could not exist without calculus. The author discusses the most prevalent and widely used equations. The advent of the computer has greatly improved the use of these equations in the field and allowed the field of aerodynamics to become more precise.
Table of Contents
Introduction
The Myth about Bumblebee Flight
Turbulence
The Bermouli Equation
Continuity Equation
Navier-Stokes Equations
Conclusion
From the Paper
"Math is the language of science. The different disciplines of math relate to different areas of science. Science needs math in order to be understood. Algebra allows us to create sentences using numbers to describe an event. Geometry and Trigonometry help us to describe shapes, and Calculus is the tool for describing change. It can be a change in angles as in vector calculus, a change in rate, a change in speed, or almost any other change."
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Discoverers of the Physical Sciences, 2002.
A paper which discusses how the discoveries of 6 scientists overlapped and influenced one another.
1,800 words (approx. 7.2 pages), 9 sources, APA, $ 57.95
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Abstract
A paper which considers how the work of Kepler, Newton, Copernicus, Brahe, Ptolemy and Galileo overlapped, how one discovery influenced another and how the work of these scientists helped form the foundation of modern scientific knowledge of the physical sciences. The paper studies the life histories of each of these scientists.
From the Paper
"Galileo was appointed professor of mathematics at Padua, his duties included to teach the geometry of Elucid, and geocentric, astronomy to the medical students. However it is noted that he discussed more natural philosophy and forms of non standard astronomy, this was also carried out in a public lecture in reference to a New Star that had appeared, now known as Kepler's supernova. Galileo also wrote personally to Kepler stating that he was a follower of the Copernican theory, however there was no outward evidence of this until many years later (Field, 1995)."
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The Many Wonders of Archimedes, 1999.
This is a paper about the life and works of the phenomenal mathematician Archimedes.
1,725 words (approx. 6.9 pages), 7 sources, APA, $ 55.95
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Abstract
A look at the different discoveries by Archimedes focusing on what he is most greatly known for - discovering the solution of pi. His approximation of pi between 3-1/2 and 3-10/71 was the most accurate of his time, and with this discovery he devised a new way to approximate square roots.
From the Paper
"Little known details remain about the life of Archimedes who was one of antiquity's greatest mathematician, Archimedes. Most of the facts about Archimedes' life come from a biography written by the Roman biographer Plutarch. What is known, is that he was born in Syracuse, Sicily in the year 287 B.C., and died in 212 B.C. at the age of 75 in Syracuse. I was able to come up with an astonishing amount of information on Archimedes for this paper. It seems that there is no end to his accomplishments, and I tried not to leave out any of them. "
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The Impact of Newtonian Science, 2002.
A description of Newton's creation of calculus and its impact on the world, both socially and scientifically.
1,825 words (approx. 7.3 pages), 8 sources, MLA, $ 58.95
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Abstract
This paper helps to explain and justify the creation of calculus. Isaac Newton helped to solve some of the most perplexing problems the world has imagined, and the method he used in doing so is still used for the same purpose today. Newton's creation of calculus and ideas of using it to prove the universal laws of nature made human reason the most powerful method of thought and most definite route to seeking the truth.
From the Paper
"In mathematics, a certain surprising thing happens again and again. Someone poses a simple question, a question so simple that it seems no useful result can come from answering it. And yet it turns out that the answer opens the door to all kinds of interesting developments, and gives great power to the person who understands it." (Saywer 3) This quote from a prestigious professor of mathematics parallels the story of Isaac Newton and his development of calculus. Isaac Newton helped to solve some of the most perplexing problems the world has imagined, and the method he used in doing so is still used for the same purpose today. There is a popular myth that Newton was sitting under a tree when an apple fell from it, and he asked himself what force could pull the apple to the Earth. Whether this story is true or not is uncertain, but the image is clear of Newton getting hit on the head with the apple of epiphany. He used calculus to prove that gravity pulled objects to Earth and held the planets together, and also to prove his world-renowned three laws of motion. By forming this revolutionary method of problem solving, Newton not only paved the way for new roads in mathematics but also changed the way that people thought and sought out answers. Newton's creation of calculus and ideas of using it to prove the universal laws of nature made human reason the most powerful method of thought and most definite route to seeking the truth.
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Galileo Galilei, 2001.
This paper is about Galileo Galilei and his impact on history.
950 words (approx. 3.8 pages), 2 sources, MLA, $ 33.95
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Abstract
This paper details how Galileo Galilei affected history by discovering the potential of the telescope, pioneering new approaches to science, and challenging the authority of the Catholic Church.
From the Paper
"Galileo Galilei was a mathematician, an astronomer, and a physicist who made several significant contributions to modern scientific thought. During his life, he made many scientific discoveries, often in contradiction with the centuries-old ideas of the Greek philosopher Aristotle. These contradictions led to great conflict with the Catholic Church; however, he emerged as a symbol to others who oppose unyielding authority and champion scientific progress. As James Reston's biography Galileo makes clear, Galileo is a historical figure who affected history by discovering the potential of the telescope, pioneering new approaches to science, and challenging the authority of the Catholic Church."
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Mathematics: Fermat's Last Theorem, 2002.
This paper describes the interesting phenomenon called Fermat's Last Theorem, written in layman's terms.
613 words (approx. 2.5 pages), 5 sources, MLA, $ 21.95
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Abstract
Fermat's Last Theorem (FLT) has been one of the most fascinating theorems in mathematics. This paper looks at the conformities and the disparities of this statement. It assesses the theorem and the problem it comes to solve as well as the theorem's proof. It gives a detailed mathematical exercise which he solves using the theorem.
From the Paper
"Pierre de Fermat was born near Montauban in 1601. He was born in a family reared by a leather-merchant who was his father and was educated at home. He was essentially a lawyer and was an amateur mathematician. Throughout his life, Fermat published only one mathematical paper, which was written anonymously and appeared as an appendix to a book. He died in 1655."
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Oliver Kellogg, 2001.
This paper provides a biography of Oliver Kellogg, and his book, "Foundations of Potential Theory".
1,235 words (approx. 4.9 pages), 4 sources, MLA, $ 42.95
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Abstract
This paper looks at the life of Oliver Dimon Kellogg, who spent much of his time researching and advancing potential theory in the world of mathematics. The author discusses his contributions to math and physics, still used today.
From the Paper
"When the country no longer required his services, Kellogg was sent to Harvard University. Here he explored a few new mathematical venues before returning to his groundbreaking work in Potential theory. The 1920s were in many ways a decade of inspiration for artists, writers, mathematicians, scientists, and other thinkers across the globe. The war had dampened many spirits, but others saw its finale as a chance for new hope -- for a future without war. Others saw it as a future that was considerably grimmer, yet still full of the possibilities that only the realization of one's own finite nature can bring."
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Game Theory Applied to Corporate Finance, 2002.
How applications of game theory can be used to explain various observed phenomena in corporate finance.
1,955 words (approx. 7.8 pages), 7 sources, MLA, $ 62.95
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Abstract
This paper explains that traditional financial thinking relies on assumptions of certainty, complete knowledge and market efficiency and in this context, financial decisions should be relatively straightforward. In the real world though, many times what is observed deviates greatly from what would be expected using traditional financial thinking. This paper therefore uses different game theory models to more accurately explain observed financial decisions dealing with capital structure, corporate acquisitions and initial public offerings (IPOs).
From the Paper
"Game theory has made great strides in explaining many of the observed phenomena falling under corporate finance. One example is the capital structure decided upon by a firm's management. Capital structure deals with the firm's decision to raise funds through debt versus equity and what ratio of debt to equity should the firm maintain. Modigliani and Miller in 1958 showed that in perfect capital markets (i.e. no frictions and symmetric information) and no taxes a firm could not change its total value by altering its debt/equity ratio; thus capital structure is irrelevant. However in the real world, capital structure is carefully thought about by every company, and it is in fact not irrelevant because taxes do exist and capital markets are not perfect."
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Adding Binary Numbers, 2003.
This paper discusses and analyzes the process of binary addition.
600 words (approx. 2.4 pages), 4 sources, $ 21.95
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Abstract
The following paper analyzes the process of adding binary numbers by making reference to an addition algorithm as an example of this process. Background information to binaries is included.
From the paper:
"The binary number system was based on the decimal system, but uses only two digits, 1 and 0, instead of the 10 digits used by the decimal system. The system was developed for computer systems because they are more economical and precise when writing code. All digital computers use binary as their primary code. Each binary digit represents either "on" or "off" to the computer."
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Friedrich Bernhard Riemann, 2001.
This paper looks at the life and works of Friedrich Bernhard Riemann.
4,000 words (approx. 16.0 pages), 6 sources, $ 108.95
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Abstract
This paper examines the life and the work of the 19th century German mathematician Friedrich Bernhard Riemann, whose ideas concerning geometry of space had a profound effect on the development of modern theoretical physics, including providing the foundation for the concepts and methods used later in relativity theory.
From the paper:
"An examination of the facts of Riemann's family background would not have led one to suspect that he would have become the great mathematician that he would develoo into. He was the second of six children of a Lutheran pastor and it was this pastor/father who gave him his first formal education. Indeed, much of his early education was centered in his family, which was by all accounts both happy and deeply devout. He later attended the local high school, where he made quick and substantial progress in mathematics, soon moving beyond the ability of his teachers to educate him further (Laugwitz 38-41). He quickly mastered calculus and theory of numbers of Adrien-Marie Legendre. After graduating from the high school (or gymnasium), he studied at the universities of Gottingen and Berlin from 1846-51. It was at this point in his education that he became interested in problems concerning the theory of prime numbers, elliptic functions, and geometry, theoretical interests that would guide much of his later work."
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Why is Algebra so Important?, 2001.
This paper discusses the importance of learning algebra.
1,310 words (approx. 5.2 pages), 4 sources, $ 44.95
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Abstract
This paper examines why it is necessary to learn algebra. It shows its everyday uses and importance. It uses some basic examples such as calculating the miles per gallon of a car, and solving a calendar riddle.
From the paper:
"Algebra is simply the branch of mathematics in which the operations and procedures of addition and multiplication are applied to variables rather than specific numbers. It is also probably the subject about which schoolchildren are most likely to ask the question: What good will this ever do me when I get out of school. This paper puts forth three different answers to that eternal question of what good will algebra do me?"
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Albert Einstein, 1999.
This paper is a brief biography on Einstein's achievements.
1,050 words (approx. 4.2 pages), 3 sources, $ 36.95
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Abstract
This paper explains how if it were not for Albert Einstein the world would be a lot different today as his discoveries and theories lead the way for physicists.
From the Paper
"When ever the phrase great mind or genius is mentioned usually one name comes to mind, and this name is Albert Einstein. This is so, because Einstein may very well have been the greatest mind of the twentieth century. Einstein revolutionized modern scientific thinking and was a master of physics and mathematics. From an early age Einstein showed skills and interests rare among others his age. From the beginning Einstein was destined for something special."
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The Man Who Was Pythagoras, 2001.
This paper is a biography of the mathematician, his work outside mathematics, a description of the Pythagorean Theorem, and the Pythagorean Society.
815 words (approx. 3.3 pages), 2 sources, $ 29.95
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Abstract
This paper offers a biographical look at Pythagoras. The author discusses the many mysteries surrounding this man, in addition to his many contributions to mankind. Included are some explanations of some Pythagorean theorems, with pictures to highlight textual information.
From the Paper
"Numbers play a large part in our everyday lives, from the time we get up, how long we cook our food, the distances we travel, and other such aspects, many of which we take for granted. A scholar who played a large part in the way we view certain numbers and objects people use regularly is Pythagoras. Pythagoras was a philosopher, medical practitioner, astronomer, and mathematician. Although he contributed many thoughts and ideas to society, such as those of the Pythagorean Society, the Pythagorean Theory is by far the most practiced and well-known."
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Sir Isaac Newton's Mathematical Influence on Physics, 1997.
1,390 words (approx. 5.6 pages), 5 sources, $ 46.95
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Abstract
This essay discusses the life of Sir Issac Newton and the points of his life that brought forth his great advances in the realm of physics and mathematics.
From the Paper
"As a child Sir Isaac Newton took little interest in what was being taught to his classmates (Bixby 90). Instead, he found ways to fulfill his desire to learn. He marked where the shadows fell in his yard in order to keep time, thus producing his sundial (Rattansi 12). His interest in rushing water inspired Newton to build a windmill. He created the first horseless carriage. In addition to the pursuit of his numerous boyhood interests, Newton spent time with his landlord as the apothecary and concocted remedies for the illnesses of the locals (Christianson 16)."
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