Abstract A paper that states that the use of math manipulative to teach math concepts in geometry increases the student's ability to grasp skills and concepts.
Abstract This paper provides an analysis of Stanley Kubrick's film, "Full Metal Jacket," and discusses how this film can be understood with relation to the Game Theory. The paper analyzes three characters from the film and considers how their choices in the film illustrate the viability of game theory. Game theory is described here as a mathematical formula that asseses outcomes of situations based on people's choices and the author of this paper sees Kubrick's film as an example of how outcomes are effected by particular choices.
Abstract .The author examines the influence Pythagoras had on ancient learning, the Pythagorean Theorem, and the Pythagorean School, and notes that that the Pythagorean School was inspired by Pythagoras's genius. It was half religious and half scientific, and followed a code of secrecy which served its purpose in ancient times, but which has prevented historians from obtaining much information about Pythagoras other than through later second-hand sources.
Abstract This essay analyzes the inspiration and creation of the calculator. It also discusses the positives and negatives of calculator use, emphasizing its use in classrooms. It also discusses how this invention has impacted society.
From the Paper "Blaise Pascal received credit for inventing the first digital calculator in 1642. After Pascal observed the tedious processes his father underwent in order to complete his taxes, he was determined to invent a helpful tool. Pascal invented the Pascaline, which was a numerical wheel calculator that consisted of eight movable dials that added up to eight figured long sums and used base ten. When the first dial (one's column) moved ten notches ? the second dial moved one notch to represent the ten's column reading of 10 ? and when the ten dial moved ten notches the third dial (hundred's column) moved one notch to represent one hundred, and so on. As technology progressed so did the calculating devices. The first electronic desktop calculator was invented in 1961 and the first handheld calculator was introduced to the world April of 1970. Ever since its creation, the calculator has significantly perpetuated our dependence on technology as well as alter our everyday lives on unimaginable levels."
Abstract This paper provides biographical information on famous women mathematicians and explains the contributions they made to the field of mathematics. The paper describes many of the contributions these women made, such as the Golden Mean Theory, Hypatia's work on conic sections, works on finite and infinitesimal analysis, and recursive function theory.
From the Paper "Women have played an important role in mathematics for more than two thousand years. Often overshadowed by their male counterparts, their contributions brought about the field of mathematics, as we know it today, nonetheless. Following you will find brief biographical compilations of some of history's most notable female mathematicians, who surely serve as role models for today's women in mathematics."
Abstract This paper explains that the mathematical formula known as "Pascal's Triangle" was simultaneously discovered centuries before Pascal by the Chinese and the Persians; it was even mentioned by Omar Khayyam centuries before Pascal. Pascal, however, one of the world's most famous mathematicians, was the first "modern" mathematician to realize the true potential of the formula and apply it. The author points out that Pascal's Triangle contributed to the understanding of probabilities, which led to the development of "average gain" or "probable gain" formulas that are still used extensively in business and industry. The paper relates that there is one problem with Pascal's formula: as the numbers increase, the triangle takes much longer to solve, and the formula becomes ungainly, but mathematicians have learned to cope with the formula and have created alternates that let them work with the numbers more effectively. Formula included.
From the Paper "The mathematical formula known as "Pascal's Triangle" has long been attributed to the great mathematician and philosopher, Blaise Pascal, who lived in France during the 17th century. Pascal only lived to be thirty-nine years old, but during his lifetime, he made significant achievements in mathematics and philosophy, and may be most well known for the mathematical formula of Pascal's Triangle, which he did not invent, but has long received credit for inventing. Pascal was a bright child, who created the first known type of automatic calculator at the age of nineteen, and invented the modern-day barometer before he turned thirty-one."
Tags: probabilities, persians, chinese, formula, problem
Abstract This paper describes how logical fallacies can affect us in academic and scientific research and even in the decisions we make in everyday life. The paper points out that a very valuable skill in making decisions is the ability to identify logical fallacies and to apply tools that help you identify them. Moreover, the paper describes some types of logical fallacies and some of the tools for identifying them, as well.
From the Paper "There is little question that logical or analytical fallacies can (and have) plagued data analysts in all major fields of knowledge from the beginning of recorded time. Not only can these fallacies of reason cause immense harm due to their capacity to mislead, but they can also ruin an otherwise sound argument or conclusion. For this reason, it is important to utilize varied "tools" designed to prevent or detect fallacies."
Abstract Statistics are a valuable aspect of scientific research. This paper demonstrates many different ways in which scientific data is used in everyday life. By the same token, statistics may also be abused to reach a false conclusion, and this is also illustrated through several cases.
From the Paper "Just as statistics help in prosecution and defense of cases, they may also be abused when different experts in the same field offer different evidence and conclusions from examining the same data. Another way in which statistics may be abused is through corruption; in this case the police investigators may take DNA sample from a suspect and introduce it to a crime scene."
Abstract This paper examines the history of science in terms of changes in astronomy from the time of Ptolemy to Galileo, based on the book "Science without Limits" by James Perlman. The writer notes how the ancients saw science as a form of philosophy, while by the time of Galileo, observation was being joined with experimentation to examine concepts and find the truth.
From the Paper "The history of astronomy shows the development of science as a discipline from the ancient world to the Renaissance, from the time of Ptolemy to the time of Galileo. Over that period, astronomy began to shift from a philosophy to a science. Science in the ancient world was not created out of whole cloth and was based on observations and the application of reason. Mathematics were also used to develop ideas about the universe. Mathematics is itself an application of reason, though aspects of mathematics have also been developed through observation and testing. By the time of Galileo, however, science was gaining a more experimental structure, and Galileo himself tested many ideas directly. His astronomy was also based on observations, but he was able to observe more directly and closely with the telescope. Perlman notes that "science in large part . . . is a matter of testing assumptions"."
Abstract This paper addresses the identification and understanding of a simple graph. This graph is a line graph as opposed to other types of graphs such as pie charts, bar graphs or scatter plot graphs, and shows how one occurrence is related to another. The variables measured on this graph are pulse rate, heart beats per minute and time measured in minutes. The rising and falling of the pulse rate is followed as time ticks by for a period of five minutes.
From the Paper "What is the point of this paper is to study what exactly a line graph consists of, what its best uses are, how it compares to other types of charts and graphs, and if it is indeed the correct sort of graph to use in such a situation as this. The line graph will be defined by what sort of data it best represents, what type of variables can and are used with it, and how these factors come into play with the example line graph to be shown and discussed. Finally, factors which alter or corrupt data that is shown on this or other graphs will be discussed."
From the Paper "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 ..."
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 .."
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..."
From the Paper "The purpose of this research is to examine "The History of Calculus" by Carl B. Boyer. The plan of the research will be to set forth the general ideas in the book, and then to explore details contained in the book that summarize the concepts of calculus that Boyer wants to emphasize.
Boyer's The History of the Calculus is put forward as one of the few histories of how the discipline of calculus evolved, apart from an explanation of how to use it mathematically. It is by positioning the ideas of mathematics and philosophy that influenced calculus that Boyer gradually moves toward an explanation of how calculus can actually be used and applied. The background of Boyer's approach appears to be the idea that a richer understanding of how calculus came to "be" in the world of ideas can lead to an understanding of how it can be employed in ... "
From the Paper "Application of Learning Theories in Early Childhood Mathematics
The major theories of learning which underlie curriculum planning in the schools are generally classified into three groups: behaviorism, cognitive development, and phenomenology or humanistic psychology. Each of these schools of thought arose from distinct philosophies and individuals who developed the theories within the philosophies. It is the purpose of this paper to discuss the major learning theories, the psychologists representing each group, the learning implications for each learning theory, and a representative mathematics curriculum for early childhood applying the various learning theories.
Behaviorism is the oldest learning theory, and it continues to be popular in the United States. Psychologists Thorndike..."
