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Sir Isaac Newton, 2000.
The impact of the discoveries and writings of the English mathematician on the evolution of scientific thought and practice.
1,575 words (approx. 6.3 pages), 8 sources, $ 55.95
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From the Paper
" Sir Isaac Newton (1642-1727) was one of the greatest scientists in history and, after an initial period of resistance, his discoveries, theories, and methods proved to be a major force in the emergence of modern science. Newton became the best-known scientist in the world and, even though most of the eighteenth-century public understood little of his work, his fame eventually provided the impetus to elevate scientific research to a new level of respectability. Other seventeenth- and eighteenth-century scientists participated in the general move away from the Aristotelian paradigm of science that had dominated the Western world for two millennia. But Newton's inspired work resulted in what has justly been called the Newtonian Revolution in science. Ironically, however, Newton's progress in mathematizing science and opening it up to the full play of scientific method meant..."
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Teaching Math, 1999.
Examines problems, evolving theories and techniques, examples, problem-centered instruction, curriculum, measuring performance, teaching standards and proposes a field trip to encourage problem solving.
3,150 words (approx. 12.6 pages), 15 sources, $ 111.95
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Abstract
In response to unacceptable levels of mathematics achievement in the United States many groups with an interest in the teaching of mathematics have called for reform (Niemi, 1996). The calls for reform are based on recent advances in cognitive theory that call for a more constructivist view of learning (Wood & Sellers, 1996).
From the Paper
"In response to unacceptable levels of mathematics achievement in the United States many groups with an interest in the teaching of mathematics have called for reform (Niemi, 1996). The calls for reform are based on recent advances in cognitive theory that call for a more constructivist view of learning (Wood & Sellers, 1996). Traditionally, mathematics instruction in the primary grades has consisted of teaching computational skills, drills, and simple word problems. Concepts now included in mathematics curricula are being changed to stress problem-solving skills, but the resources and teaching methods available to primary grade teachers are not keeping current with the new standards. In 1989, the National Council of Teachers of Mathematics (NCTM) began emphasizing the teaching of mathematical concepts and problem solving at all grade levels. In the years ..."
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Airline Competition & Game Theory, 1999.
Applies game theory to airlines' fare-setting. Description of economic & mathematical theory, modeling & strategies, yield management, zero-sum.
2,925 words (approx. 11.7 pages), 11 sources, $ 103.95
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"ABSTRACT
One research question was addressed in this study. That question is as follows: ?Can the competitive behavior of air transportation companies in the United States market in relation to setting fares be explained as an application of game theory??
Game theory, as applied in the airfare wars. forecasts how competitors will respond when confronted with certain competitive situations. When formulating business strategy, no company can afford to ignore how competitors will behave. Game theory is based on the premise that in any competitive situation there are factors at work which lend themselves to mathematical representation and analysis. In turn, these representations and analyses will help explain how a result will occur.
The findings of this research indicate that the airfares competition gives the appear.."
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Math and Achievement of Girls, 1997.
Examines causes & effects of gender gap in learning math, social sterotypes & teacher bias, anxiety & self-image, examples, cultural support and solutions.
3,150 words (approx. 12.6 pages), 20 sources, $ 111.95
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From the Paper
"The purpose of this review of literature is to examine factors that contribute to the under-achievement of girls in mathematics and projects and programs which have been used to remediate the situation. The review begins with a brief description of the problem, and ends with the formulation of conclusions regarding factors producing the problem and interventions that will reduce and or eradicate the problem.
Description of the Problem
In general, at both elementary and high school levels, boys tend to have higher achievement levels in mathematics than do girls; moreover, girls tend to have significantly more negative attitudes toward mathematics than boys (Froebe, 1996). In ..."
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Chaos Theory & Art, 1997.
Describes scientific theory of unpredictability of life & its relation to modern art (Picasso, Pollock, computer effects).
2,700 words (approx. 10.8 pages), 11 sources, $ 95.95
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"This paper is a study of the relationship between the relatively recent scientific development of chaos theory and art. Chaos theory recognizes and attempts to analyze the points at which regularity becomes unpredictable, form turns into formlessness, Euclidean geometry yields to pandemonium. This apparent abandonment of established order also describes the dramatic changes that inspired impressionistic art and most of what are now termed modern arts - wild breaks with traditional approaches to the representation of human beings and nature, even to the point of choosing nontraditional subject matter or no apparent subject matter at all. Just as the chaos scientists upset the establishment by ignoring disciplinary boundaries and ways of examining a problem, so too did .."
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Goals in Math Education, 1997.
Examines five goals of National Council of Teachers of Mathematics & ways to achieve them.
1,125 words (approx. 4.5 pages), 6 sources, $ 39.95
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From the Paper
"The National Council of Teachers of Mathematics has produced a list of five goals which students in a well-taught classroom should achieve. This paper will outline how these five goals can be attained by students in a fourth-grade classroom using the Saxon text, Math 54: An Incremental Development (Hake & Saxon, 1996). Examples of how to incorporate each goal individually into the class's lessons will follow.
A good mathematics curriculum will help a teacher instill these goals in students. The best method of disseminating these goals to students is within the context of mathematics study and through opportunities for cross-disciplinary teaching; the five goals cannot be effectively taught in isolation from one another or from other subjects.
The five goals can be summarized as follows: .."
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Quantitative Decision Making, 1997.
Examines process of decision making about probable future occurrences based on objective data & subjective insight, using Bayesian statical analysis.
2,250 words (approx. 9.0 pages), 8 sources, $ 79.95
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From the Paper
"INTUITION, EXPERIENCE, AND QUANTITATIVE DECISION-MAKING
Introduction
Quantitative decision-making is thought of most often as an objective exercise based only on the cold analysis of verifiable hard facts. Intuition and even experience tends to be excluded from quantitative decision-making on the grounds that such information is subjective in character, and, thus, has no role in quantitative analysis.
Quantitative decision-making is based in large part on the ability of decision-makers to make inferences about the probabilities of occurrence of future events from the analyses of objective data (Markowitz and Xu 60-69). One means of improving probability estimates in such predictions, however, is the application of Bayes? Theorem (Peebles 17-19). Classical .."
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Econometrics, 1997.
A mathematical analysis of economic problems. Discusses advantages, goals, methods, models, applications and limitations.
1,350 words (approx. 5.4 pages), 5 sources, $ 47.95
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"APPLICATION OF MATHEMATICAL METHODS IN ECONOMIC ANALYSIS
When mathematical methods and statistical techniques are applied to the analysis of economic problems and issues, the term usually applied to the process of applied economics is econometrics (Ekelund & H?bert, 1991, p. 372). The goal of econometrics is the development of valid, reliable, and value free predictive models of economic phenomena.
Alan Greenspan (1991, p. 52), Chairman of the Federal Reserve Board, stressed the importance of econometric models as a means of providing a clear understanding of economic events. He argued that the greatest advantage of a "fully articulated model is that it helps the forecaster keep track of the interrelationships among the primary variables of interest" (Greenspan, 1991, p. 53). Within the context of this argument, he ..."
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Pi, 1996.
Examines mathematical theorem that ratio of circle's circumference to diameter is 3.14159. History, impact on science, search for extraterrestrial life, symbols.
2,250 words (approx. 9.0 pages), 8 sources, $ 79.95
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From the Paper
"This research examines the mathematical theorem that the ratio of the circumference of any circle to its diameter is 3.14159 . . ., an irrational number, describing a relationship that is irreducable to a whole number, and which is referred to as ?, hereinafter referred to as [Pi]. The primary focus of this research is on the wider societal impact of [Pi], as opposed to the theorem's mathematical properties.
History
Motz and Weaver (1993, p. 4) stated that no evidence is known that supports a contention that Archimedes deduced the value of [Pi] in geometric terms to support technology. Nevertheless, they ..."
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Fuzzy System Analysis, 1996.
Describes & analyzes techniques & advantages of imprecise mathematical system & application to stock market trading.
1,350 words (approx. 5.4 pages), 5 sources, $ 47.95
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"Traditional sorts of mathematical analysis generally yield hard yes or no answers. A number is, say, greater than 7 or it is not. There is another type of commonly asked question, however, which cannot readily be answered in this way. Suppose, for example, we wish to ask whether a given number is "a lot" less than 7, or "a lot" more, or is "rather close" to 7? Such questions cannot be properly answered by a simple yes or no. Suppose that we say that 6 and 8 are close to 7. Does that mean, however, that 5.9 and 8.1 are no longer "close" to 7? Intuitively, we may sense that this is not what we intend, but the conventional mathematics of set theory, and computer programs applying such mathematics, compel us to set such artificial boundaries.
Yet in a great many practical situations, however, we are..."
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Factor & Multivariate Analyses, 1996.
Describes & compares theories & techniques of two approaches to analyzing research data.
1,575 words (approx. 6.3 pages), 7 sources, $ 55.95
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"This research presents an overview of factor analysis and multivariate analysis procedures. Additionally, the advantages and disadvantages of each set of procedure are identified.
Factor Analysis
Many research studies generate vast quantities of data. These data more often than not are multidimensional and are characterized by multicollinearity (Summers, Peters, and Armstrong, 1993, p. 555). In most instances, if the data are to be used effectively, it is necessary to reduce the number of explanatory variables to more manageable proportions.
Factor analysis is a general descriptor for a group of specific computational procedures (Emory, 1992, p. 559). Each of the ..."
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Plane Projective Geometry, 1996.
Technical analysis of mathematical process involved in producing Reuleaux triangle from equilateral triangle.
2,250 words (approx. 9.0 pages), 4 sources, $ 79.95
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"The Reuleaux triangle is derived from an equilateral triangle. It is produced by replacing each side of the equilateral triangle with the arc of a circle. These two-dimensional triangles can be used to create somatocharts. Three-numeral somatotype data can additionally be plotted within a standard rectangular coordinate axis system. Geometric figures may be analyzed according to their component parts. Perhaps the most basic components of the Reuleaux triangle consist of those points which comprise it. The position of a point in a plane can be given by means of two numbers. For example, x, y can be the distances of a point, P, from two given perpendicular lines. Given this information, the position of P can be determined when the values of both x and y..."
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Mathematics in Business, 1996.
Uses of math, quantitative methods & intuition in financial statements, aggressive accounting, rate of return.
2,250 words (approx. 9.0 pages), 7 sources, $ 79.95
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"Much emphasis is placed on using quantitative methods and mathematical techniques in business and economics. Such approaches, it is considered, give additional credence to business decisions and help managers and executives justify their actions. However, objective information must be tempered with intuition and experience in order for companies to realize their full potential, and excellent managers are separate from their average peers by the use of their experience when considering quantitative data. This is particularly true when trying to determine what products to manufacture, or what price to charge, but is also true when making more mundane decisions in business. This research considers the use of quantitative methods and mathematics in business and explores how intuition and experience come into play in the ..."
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Mathematics & Literature, 1996.
Use of poetry & stories to foster children's reasoning & performance in math.
1,350 words (approx. 5.4 pages), 6 sources, $ 47.95
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From the Paper
"Can literature be used to foster mathematical reasoning and performance? The answer, according to Curcio, Zarnowski and Vigliarolo (1995) is "yes." Indeed, the authors feel that poetry dealing with numbers is a particularly good literary mode for sparking mathematical interest and facilitating comprehension.
An example of how poetry dealing with numbers can facilitate math learning is provided by Curcio et. al (1995) in their description and discussion of children's responses to a poem entitled, "Overdues." In the book, a character owes the library a fine for a book he has not returned in 42 years. Based on their discussion of the poem, children became interested in determining just how much money was owed to the library.
With respect to learning, in their attempts to compute the..."
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Florence Nightingale, 2002.
This paper highlights Florence Nightingale's life not only as a nurse but also as a mathematician.
555 words (approx. 2.2 pages), 5 sources, MLA, $ 19.95
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Abstract
This paper discusses Florence Nightingale?s work as a statistician upon which the reform of the sanitary conditions in military field hospitals was based. The author points out that Nightingale was the first woman to be a Fellow of the Royal Statistical Society, the first woman to receive the Order of Merit and author of the first nursing textbook.
From the Paper
"In 1840, Florence begged her parents to let her study mathematics instead of, ?worsted work and practicing quadrilles.? Her mother did not agree with this idea. Although Mr. Nightingale loved mathematics and had passed this love along to his daughter, he urged her to study subjects more appropriate for a woman. After a long battle with her parents, they finally gave her permission to be tutored in mathematics. This included Sylvester, who developed the theory of invariants with Cayley. She was said to be his most distinguished pupil."
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Construction of Pyramids, 2001.
Reviews application of mathematics by ancient Egyptians in design and construction of Pyramids. 2 Exhibits.
1,125 words (approx. 4.5 pages), 6 sources, $ 39.95
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"This research reviews the application of mathematics by the ancient Egyptians in the construction of pyramids. This research focuses on two issues. The first issue involves the mathematical principles that, of necessity, were applied in the construction of the pyramids. The second issue concerns the contention by some people that alien civilizations from outer space were the source of mathematical knowledge required for the construction of the pyramids in Egypt, as the Egyptians of that era had not developed the knowledge of mathematics required for such an undertaking.
A pyramid is a polyhedron whose base is a polygon and whose sides are triangles having a common vertex. The pyramids at Giza..."
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Creation of Horoscopes, 2001.
Hand mathematical calculations vs computer math. Brief history.
1,125 words (approx. 4.5 pages), 5 sources, $ 39.95
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"The process through which astrologers cast charts seems to be a mysterious one -? at least to the lay public. The arcane knowledge and the mathematical calculations required to construct a horoscope have made astrology the field of the professional rather than the amateur.
However, the time has come to divulge a trade secret of astrology: While there is certainly a body of knowledge required to create a horoscope -? and both intuition and intelligence are certainly called for -? the mathematical abilities required to construct a horoscope are in fact relatively minimal. The relative simplicity of the technical skills involved in creating a horoscope, and the benefits of personal, hand mathematical calculations over computer-derived ones have become increasingly important as an issue as more and more computer programs are developed.."
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Routing Algorithms, 2002.
An insight to the mathematical algorithms of routing processes in network environments.
2,314 words (approx. 9.3 pages), 7 sources, MLA, $ 71.95
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Abstract
A router is used to manage network traffic and to find the best route for packets to be sent. This paper discusses the algorithms available in order to find the best route to destination for these packets in the network environment. The two main algorithms are "Global routing algorithms" and "Decentralized routing algorithms". The paper evaluates in detail these two methodologies together with their bottlenecks and illustrates examples with diagrams, graphs, tables and code.
From the Paper
"In this step, routers should choose the best route for packets to every node. They do it by using an algorithm such as "Dijkstra Shortest Path Algorithm?. In this algorithm, router, based on information that has been collected from other routers, build a graph of network. This graph shows the location of routers in network and their links. Also every link will be labeled with a number that is called weight of link and is also known as cost of link. This number is a function of delay time, average traffic and sometimes simply, it is the number of hops between nodes. For example if there were two links between a node to destination, the router chooses the link with the least weight."
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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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