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Incorporating Fairness into Game Theory and Economics, 2002.
A referee report on Matthew Rabin's intention driven model of fairness.
2,340 words (approx. 9.4 pages), 6 sources, APA, $ 71.95
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Abstract
Matthew Rabin?s model of fairness is based on Geanakoplos, Pearce and Stacchetti's (1989) notion of ?psychological game?, in which payoffs depend on actions and on beliefs about actions. The paper describes how Rabin?s model shows how fairness expectations lead to different results than standard theory and demonstrates some general implications of fairness on game theory and economics. This paper contains a short description of Rabin?s model, gives some examples, propositions, proofs and critique.
From the Paper
"Suppose that (a1,a2) is a mutual-max outcome. Then both f1 and f2 must be nonnegative, thus reflect a positive regard for each other.
If each player chooses a strategy which maximizes both his own material well-being and the well-being of the other player this must maximize his own utility. In a case of mutual min outcome the f1 and f2 is non positive, thus, f~j(bj,ci)[1+fi(a1,bj)] is non negative. If each player is choosing a strategy which maximizes his own material well-being , this must maximize his utility."
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Encryption and Hash Algorithms, 2002.
A discussion of the differences between a code and a cipher.
2,025 words (approx. 8.1 pages), 7 sources, $ 71.95
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Abstract
Discusses differences between a code and a cipher. Requirements of each; how each works. History of encryption. Enigma machine of World War II. Pre-computer encrption. Development of computer program to encrypt data. Function of a "hash" (a number generated from text & smaller than the text itself). Privacy issues. Future of algorithms.
From the Paper
"Encryption and Hash Algorithms
Introduction
Stephen Levy (2001), reporting on the latest ?unbreakable code? begins his report by quoting Edgar Allan Poe. ?It may roundly be asserted that human ingenuity cannot concoct a cipher which human ingenuity cannot resolve? (Levy, 2001, 45). This article was selected to lead off this discussion of encryption because of two elements of confusion.
First, the headline read ?An Unbreakable Code?? and the article was about enciphering and deciphering, also called ?encryption? and ?decryption.? This is a common, and often-repeated mistake, one which can confuse the very field of study. A ?code? is not a ?cipher? anymore than a ?tennis ball? is a ?cabbage.?
A code is a..."
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Leonhard Euler, 1995.
Examines the life, career and major ideas of this 18th Century Swiss mathematician.
1,350 words (approx. 5.4 pages), 6 sources, $ 47.95
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From the Paper
"Leonhard Euler (1707-1783) published his first mathematical work in 1726, one year before Isaac Newton's death. Euler's enormous gifts and broad interests were ideally suited to this slot in history. In pure mathematics and mathematical physics, his work elaborated that of his predecessors, such as Newton and Leibniz, and exerted an enormous influence on those who followed him. Euler also systematized, standardized, and generally cleared the way for mathematical applications in numerous fields. In the course of his long and productive career, Euler "worthily united the ages of Newton and Gauss" (Morgan 133).
Euler was the most prolific mathematician in history. During his career, he published around 560 books and articles, and still left a backlog of over 300 works at his death. The St. Petersburg Academy did not finish publishing his "literary ..."
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Music and Mathematics, 1995.
Examines the inter-relations between music and mathematics. Discusses the theory and philosophy of music and focuses on the mathematical foundations of such composers as Mozart, Schoenberg, and Cage.
1,575 words (approx. 6.3 pages), 9 sources, $ 55.95
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From the Paper
"Music and mathematics are closely linked, and musical rhythm serves as an example of the practical use of different mathematical principles. It has recently been noted in fact that the mathematical regularity of certain music, such as that of Mozart, can be a spur to clearer thinking, at least for a short period of time after listening to a piece of music. Music has a psychological effect that is partly explained by its mathematical regularity, seen in the way music is divided into regular bars, beats, and different note lengths. Psychologists have discovered the importance of patterns in music and in aspects of human behavior. Music satisfies certain human needs for order and rhythm, and mathematics both explains and empowers this process.
Edward Rothstein writes about the relationship between music ..."
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Correlation and Regression Analysis, 1995.
This paper examines an application of the statistical procedures of correlation and regression analysis.
1,350 words (approx. 5.4 pages), 5 sources, $ 47.95
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From the Paper
"This research examines an application of the statistical procedures of correlation and regression analysis. The initial part of the examination describes correlation and regression procedures, and illustrates the use of the procedures in an application. Following the description and illustration, the accuracy and appropriateness of the application is discussed.
Description of the Procedure, and An Illustration of the Use of the Procedure in An Application
Correlation and regression procedures are described in this section. This description is followed by an illustration of the use of the procedures in an application."
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Sampling, 1995.
This paper examines an application of the statistical procedure of population sampling: Describes theory and techniques and assesses validity of application in population sampling.
1,350 words (approx. 5.4 pages), 5 sources, $ 47.95
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From the Paper
"This research examines an application of the statistical procedure of population sampling. The initial part of the examination describes sampling procedures, and illustrates the use of the procedures in an application. Following the description and illustration, the accuracy and appropriateness of the application is discussed.
Description of the Procedure, and An Illustration of the Use of the Procedure in An Application
Population sampling procedures are described in this section. This description is followed by an illustration of the use of the procedures in an application.
Description of Procedures ... "
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Normal Curve, 1994.
This paper defines and examines the normal distribution curve and its role in statistical analysis. Tables and graph.
1,350 words (approx. 5.4 pages), 6 sources, $ 47.95
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From the Paper
"Statisticians work with large masses of data. Before any conclusions can be drawn from such data, it must be condensed and arranged in a usable form. One of the most common ways to summarize and describe a mass of data is to arrange a frequency distribution table. These tables can then be graphed with the frequency scale on the y-axis and the interval being graphed on the x-axis. Above each interval a horizontal line is drawn which corresponds to the frequency of the interval, resulting in a stair-step histogram pattern. Connecting the midpoints of these class intervals produces a frequency polygon and an interval curve. Distribution curves which can be "folded" vertically so that the two halves of the curve are essentially the same are said to be bilaterally symmetrical. Perfectly symmetrical curves which have a bell shape are said to be normal curves, or Gaussian curve ... "
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Mathematics and Business, 1994.
This paper discusses that mathematics is at the core of understanding business and social sciences: Financial statements, supply and demand, forecasts, linear regression, equilibrium and elasticity.
1,350 words (approx. 5.4 pages), 5 sources, $ 47.95
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From the Paper
"Mathematics is at the core of understanding business and social sciences. Both disciplines make use of arithmetic, quantitative methods, statistics, linear regression and calculus as they seek to describe, predict and analyze the vast array of numerical data available in the fields. This research examines the application of math in these areas with a particular emphasis on math with regard to the supply and demand function.
Anyone selling a product or providing a service uses basic arithmetic to determine how much money they take in and how much money they pay out. When the expenses are less than the revenues, they make a profit. This simple accounting principle becomes more complex as the items associated with the various components increases in complexity. Revenues can be based on cash received, or they may be placed on accounts receivable."
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Evolution of Mathematics, 1993.
Ancient Greece to 1990s. Major figures & discoveries of mathematics. Looks at principles, calculus, physics, specialization and algebra. Compares the attitude differences between U.S and Japan.
3,600 words (approx. 14.4 pages), 16 sources, $ 127.95
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From the Paper
" The Evolution of Mathematics:
The American and Japanese Perspectives
Elementary forms of mathematics have probably been with man throughout his evolution. As human societies advanced, so too did mathematics. From the 1500s to the present, a long lineage of mathematicians have revolutionized the field. These men were often of European origin. Only in the last century has the United States and Japan emerged as dominant mathematical forces. At present, either of these nations could lead the field into the future.
The first systems of numeration were invented by the Greeks and the Romans (Struik, 1987, p. 80.81). Later, the Western merchant, Leonardo of Pisa, introduced the Hindu.Arabic system of numeration into Western Europe. Europeans came to accept these.."
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Learning Theories and Math, 1993.
A description of behaviorist, cognitive and humanistic approaches and the application to teaching math to children.
3,375 words (approx. 13.5 pages), 16 sources, $ 119.95
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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..."
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"How To Lie With Statistics", 1993.
A summary of this work on biases, averaging, graphs, figures and their abuse.
1,575 words (approx. 6.3 pages), 2 sources, $ 55.95
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From the Paper
"The purpose of this research is to examine the nonfiction book How to Lie with Statistics by Darrell Huff. The plan of the research will be to set forth the main ideas of the book as a chapter-by-chapter summary of the important ideas, including examples of misleading uses of statistics of the type presented.
The Sample with the Built-In Bias. Statistical measurement begins with assembling a credible sample of respondents on which to base conclusions that can be generalized from the sample to the population. There are two factors to consider: whether the respondents are truly representative of what is being measured, and whether the respondents tell the truth when they are asked questions. Both features of a sample may contribute to bias in the reporting of information. Huff cites a survey in which voters in 1936 were asked over the phone predict election ..."
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Teaching Mathematics in Saudi Arabia, 1993.
Research proposal for teaching math skills in Saudi Arabia to children at the same grade level, but at variable degrees of proficiency, using individualized instruction.
2,700 words (approx. 10.8 pages), 11 sources, $ 95.95
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From the Paper
"Teaching Mathematics to Elementary Children in Saudi Arabia With the Use of Individualized Instruction
Background of the Problem
While Christian Europe was slumbering through the darkness of the Middle Ages, the Middle East experienced its own renaissance of the arts and sciences, including mathematics. It is, after all, the Arabs who invented the concept of zero, along with Arabic numerals, and developed a sophisticated system of mathematics before the scientific revolution entered the European continent. This scientific outpouring did not last, however, and much of the Middle Eastern civilization that developed during the early Islamic period declined into quiescence (Nyrop, 1977)."
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"A History of Mathematics in America before 1900" (David Smith and Jekuthiel Ginsburg), 1992.
Summarizes and reviews the work on the uses, development and leading figures of math in the U.S.
1,350 words (approx. 5.4 pages), 1 source, $ 47.95
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From the Paper
"A History of Mathematics in America before 1900
A History of Mathematics in America before 1900 was written by David Eugene Smith and Jekuthiel Ginsburg and published by The Mathematical Association of America in cooperation with The Open Court Publishing Company in 1934. It is one of a series of monographs entitled, The Carus Mathematical Monographs.
The book is organized historically, covering the uses of mathematics, the development of mathematics instruction and research, and discussion of the important names in mathematics in America from the earliest settlement to the year 1900. The book is divided into four chapters, each chapter dealing with a particular time period in chronological order. The authors closely relate the development of mathematics in this country to the development of education and instruction of math, with ..."
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Babylonian Theory of Polynomials, 1992.
A look at the ancient civilization's contributions to the evolution of mathematical theory.
2,250 words (approx. 9.0 pages), 5 sources, $ 79.95
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From the Paper
"The purpose of this research is to examine the Babylonian theory of polynomials. The plan of the research will be to set forth the historical and cultural context in which the Babylonian approach to developing equation theory emerged, and then to discuss the ways in which the theory could have evolved across ancient cultures toward modern interpretations of the authentic character and importance of equations. As appropriate, reference will be made to the assessments of the Babylonian contribution to the body of mathematical thought as it may have impacted upon subsequent mathematical theory.
One may begin a discussion of the authentic nature of Babylonian theory of polynomials--not by saying what it is but by suggesting what it is not, which is an equivalent of purely theoretical explorations of the mathematical universe that were..."
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Content Analysis, 1991.
The use of statistical methods to analyze documents. Includes development, applications, techniques and positive and negative references.
1,800 words (approx. 7.2 pages), 4 sources, $ 63.95
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From the Paper
"A constant goal of sociologists and other social-science researchers is to determine objective, or relatively objective, ways of measuring something that is inherently very far from "objective," namely human (individual or social) attitudes and actions. One such technique is content analysis, or the use of statistical methods to analyze the contents of documents--usually written documents of one sort or another, though transcripts of speech, television shows, and other nonpaper "documents" can also be subjected to content analysis. In the simplest instance, content analysis may be performed by counting and tabulating the occurrence of particular words in a document. If, for example, a given document has frequent references to "God," "Christ," and "salvation," as compared to other documents, we might reasonably infer that the document is somehow concerned with Christian..."
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John Paolos' "Innumeracy: Mathematical Illiteracy and Its Consequences", 1991.
This paper is a critical review of John Paolos' "Innumeracy: Mathematical Illiteracy and Its Consequences".
1,350 words (approx. 5.4 pages), 1 source, $ 47.95
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From the Paper
"In his book, Innumeracy: Mathematical Illiteracy and Its Consequences, John Allen Paulos uses the term, "innumeracy" in the same way that the term illiteracy is used: to represent an unfamiliarity and ignorance in terms of numbers and mathematics. Besides being well written and entertaining, the book is also informative in explaining common instances of mathematics in everyday life.
Paulos does not confine his discussion only to one aspect of numbers and mathematics. His book is replete with examples of statistics, probability and mathematics. He suggests, for example, that we develop a "safety index" for certain activities or events which would provide the populace as a whole with a quantitative way to evaluate their activities. While such an idea may seem farfetched, it illustrates an idea which occurs .. "
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"The History of Calculus" by Carl B. Boyer, 1991.
This paper reviews "The History of Calculus" by Carl B. Boyer, the evolution and philosophy of this mathematical discipline.
2,925 words (approx. 11.7 pages), 1 source, $ 103.95
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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 ... "
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Statistical Analysis Applied to Unemployment Problems, 1990.
This paper explains the application of statistical procedures to the solution of a realistic problem; in this paper, the U.S. unemployment problem.
1,800 words (approx. 7.2 pages), 6 sources, $ 63.95
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From the Paper
'The purpose of this research is to explain the application of statistical procedures to the solution of a realistic problem. In this instance, the problem is related to the domestic economy of the United States.
THE PROBLEM
The level of unemployment is a matter of significant concern to both the general public and political leaders. In order to develop effective policies to address the unemployment issue, it is necessary to understand how the unemployment rate is related to other factors. It is this problem which is addressed in this research.
HYPOTHESES
A total of six hypotheses were formulated for, and tested in ... "
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