Abstract This paper is a biographical description of the work of Georg Cantor and his work in the development of set theory. In his time, these hypotheses were considered greatly controversial by other mathematicians. However, now they are an integral part of the study of mathematics.
From the Paper "Georg attended several private schools in Frankfurt, and in 1859, entered the distinguished Grossherzoglich Hessiche Provinzialrealschule in Darmstadt. He left this institution in 1860 with high recommendations in mathematics. His father discouraged the study of math due to the fact that he wished him to become an engineer, a job that paid considerably more than mathematics. He originally attended Grossherzogliche Hoehere Gewerbeschule (Grand-Ducal Higher Polytechnic, later changed to Technische Hochschule) at Darmstadt following his father's wishes and studying Engineering. Later, when Georg convinced his father that his heart was truly in math, his father relented and he began the study of Mathematics in 1862 (Johnson, 1997). "
Abstract The Object Oriented Hypermedia Design Model uses an object oriented framework to allow a concise description of complex information items, and allow the specification of complex navigation patterns and interface transformations. This paper provides an explanation for each step in the process and discusses. The past, present and future business uses of the model.
From the Paper "A well-designed application is important because business owners understand that how a website functions will either create repeat customers or discourage customers from visiting the site. It is essential that a website is easy to navigate and that it functions in an efficient manner. It is also important for a business to be able to correct problems with the system quickly, which will prevent the loss of customers and profits. As a result of the demands that are placed on business to have an efficient website a precise software production process is needed. (Abrah?o, Fons, Pastor 2000, 2) The OOHDM process provides the stability needed to accommodate an e-commerce site."
From the Paper "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.."
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..."
From the Paper "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 ..."
From the Paper "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..."
From the Paper "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 ..."
From the Paper "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..."
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 pages), 8 sources, 1996, $ 79.95
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 ..."
From the Paper "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 .."
From the Paper "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.."
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, 1999, $ 111.95
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 ..."
From the Paper "Higher mathematics is a subject that has always seemed completely inaccessible to all but the select few who could breathe in the rarefied atmosphere of the intellectual plane where it lives. Just as mathematics seems to be beyond most people's intellectual grasp, however, it also seemed to make absolutely no difference to the great majority of the population. Number theory, probability theory, mathematical modeling, the mysterious math used in computer technology, and even statistics and mathematical reasoning seemed to have little to do with daily life, work, or anything that was of much interest to the average man, woman, or child. When a mathematician somewhere in Great Britain announced a few years ago that he had solved the problem of Fermat's Last Theorem the news made no difference to the vast majority of people, while a few, vaguely remembering the story of..."
Abstract This paper examines a crucial problem in American education, poor student performance, specifically in math and science. The paper focuses on the method of tracking or grouping, and provides arguments against this method. The paper proposes a study in order to find a successful solution to the problem. The proposed study is outlined, including the desired outcome.
From the Paper "Poor student performance is one of the most pressing problems in American education today. In particular, math and science scores lag behind those of other developed nations. Without a proper understanding of math, and mathematical concepts, today's students will find themselves unable to compete in an increasingly technological world. They will not be able to find jobs, nor will American industry be able to compete successfully against its foreign counterparts. Though an essential part of the educational process, the how-to of improving students? mathematical skills remains problematic. Numerous approaches have been tried, but not all have been successful. It is for this reason, that the following study is being proposed."
An analysis of an article by Davison, McCarthy, and Jensen, ?Component Probability and Component Reinforcer Rate as Biasers of Free ? Operant Detection", focusing on the issue of behavior analysis.
Abstract This paper is a written summary, including a discussion of the article ?Component Probability and Component Reinforcer Rate as Biasers of Free ? Operant Detection? by Michael Davison, Diane McCarthy, and Chris Jensen. The paper outlines the article, which is a series of experiments relating to behavior analysis in general, specifically the matching law and signal detection theory. The paper presents and summarizes the series of experiments designed by McCarthy et al., including all observations, results, and conclusions.
From the Paper "This series of experiments was designed to test the applicability of the signal ? detection model of Davison and Tustin (1978) in free operant detection under two biasing manipulations. The first was variation of component frequency (The probability of presenting S1, a bright light, over S2, a dim light), which was varied in experiments 1a and 2a. The second manipulation was variation of the within-component reinforcer rates (reinforcement schedules one each key) in experiments 1b and 2b. Each variable was varied while holding the others constant."
Tags: critical, design, experiment, learning, motivation, psychology, research, skinner, theory
