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Hume?s Problem of Induction, 2004.
A discussion of David Hume's problem of induction, which posed the question about what evidence there was to support the instinctive understanding that the future would resemble the past.
3,343 words (approx. 13.4 pages), 6 sources, MLA, AU$ 115.95
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Abstract
This paper begins with an explanation of deductive and inductive reasoning and then goes on to analyze the questions raised by well-known skeptic and humanist, David Hume, about finding indisputable evidence that the future will resemble the past or that observed instances can predict new instances.
From the Paper
"For some reason, the traditional example of how inductive reasoning works is to ask how it can be known that the sun will rise tomorrow. It is certain that every day as far back as one can remember or research, the sun has risen every day. How does this prove, however, that it will rise tomorrow? Even barring a super nova or an asteroid hit that took Earth off its axis, how could we know that the so-called laws of physics will be still active tomorrow? Mere deduction cannot prove that the sun will rise, though it may be able to explain how it rises. One depends rather on past experience to predict the future. The sun will rise, we believe, because it has always risen in the past."
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Graph Theory and Road Redesign, 2004.
This paper explores the ways in which graph theory can be joined to computer simulation programs to make the planning stages of road redesign more efficient and more accurate.
5,240 words (approx. 21.0 pages), 31 sources, APA, AU$ 158.95
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Abstract
This paper explains that graphs allow for a simplification of the real world, doing away with extraneous details without sacrificing any information necessary for the task. The author points out that graph theory is the best tool to use to solve the problem of road conversion because it is the most parsimonious. The assumptions made by graph theory more closely than any other model or theory match the real-world conditions. The paper states that, in converting roads, the effect in the real world will be a disruption of what had been the shortest paths between different points, and urban planners will include some consideration of shortest path issues. Tables and figures.
Table of Contents
Introduction
Graph Theory as the Basis for Conversion of Two-Way Roads
Undirected Graphs to Digraphs
Reachability Problem
Shortest Path Problem
Importance of Simulation
Comment on Validity of Data
Conclusion
From the Paper
"The specific shortest path method that is most useful in this particular type of problem is Pallottino?s graph growth algorithm with two queues. It must be emphasized that the determination of the shortest path algorithms is perhaps the most important component of any network analysis. It is also quite often the first step in any network analysis as the determination of the shortest path is often needed as a key datum in making later choices."
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Statistical Education, 2004.
An examination of the importance of learning statistics and how it can help in every aspect of life.
3,102 words (approx. 12.4 pages), 7 sources, MLA, AU$ 109.95
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Abstract
This paper explains how, in schools, statistical education is primarily taught in mathematics, yet statistical ideas are used in other subjects, including science and economics. It discusses why teachers and researchers need to constantly work towards improving statistical education, leading to a great deal of research in the field. This paper examines existing research to determine how statistical education research can be improved in the future.
From the Paper
"Statistical education has become an important part of curriculums in all levels of education. At both the undergraduate and graduate levels, statistical literacy is now a key objective in many classrooms. As a result, statistics is now being taught across various disciplines and is rapidly becoming a prerequisite course for graduation, regardless of a student's major. The teaching and learning of statistics has recently increased dramatically in many schools. As a result, many U.S. states now emphasize and include statistical thinking in their statewide curriculum guidelines."
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Integrated Studies, 2004.
A discussion of the association between mathematics and science.
1,935 words (approx. 7.7 pages), 7 sources, MLA, AU$ 74.95
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Abstract
This paper examines how, for many who lack a strong grounding in math and science, the two are often associated as being the same. The purpose of this paper is to define mathematics and science, showing them as two distinct fields of inquiry and then to show how advances in theoretical mathematics contribute the framework needed for scientists in the study of quantum mechanics, a branch of physics, which in turn, is one of the many branches of science.
Outline
Introduction
Mathematics
Science
Quantum Mechanics
Mathematics and Quantum Mechanics
Science and Quantum Mechanics
From the Paper
"Finally, applied mathematics is a term loosely applied to a range of studies which have significant use in the sciences, specifically the empirical sciences, (branches of science open to practical or experiential experimenting). Applied mathematics makes use of numerical methods and computer science, seeking concrete solutions to explicit mathematical problems. In science and technology it has a major use as a way to model and/or simulate natural phenomenon or events. Examples include using mathematical models in computer generated wind tunnel tests to predict the behavior of a given shape of a prototype airplane wing without resorting to expensive actual wind tunnel testing."
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Co-integration, 2004.
A research study using co-integration analysis to study the relationship between the stock index cash and futures market in relation to price discovery.
3,752 words (approx. 15.0 pages), 27 sources, MLA, AU$ 125.95
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Abstract
Co-integration has come to represent an econometric data analysis method that has been utilized to determine the long-run equilibrium relationships among nonstationary economic variables. This paper uses co-integration analysis to determine the relationship between the stock index cash and futures market in relation to price discovery, market stability, and market efficiency. The data for the study was collected from the Athens Derivatives Exchange S.A. (ADEX), with the main data for the study being the returns of the FTSE/ASE-20 futures and spot index. In order to study the relationship between the ADEX stock index cash and futures market in this paper, daily closing price returns of the FTSE/ASE-20 Index are considered for the period from 3 January 2000 to 27 July 2003. The paper includes several graphs and tables.
Paper Outline:
Data
Methodology
OLS Results
Co-integration Results
References
From the Paper
"GARCH modeling represents an important data analyses procedure as it provides a means of further understanding and modeling volatility, taking into account excess kurtosis (i.e., fat tail behavior) and volatility clustering, two important characteristics of financial time series. It provides accurate forecasts of variances and covariances of asset returns through its ability to model time-varying conditional variances. As a consequence, the application of GARCH models has been identified as useful in risk management, portfolio management and asset allocation, option pricing, foreign exchange, and the term structure of interest rates."
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The Meaning of the Word "Implication", 2004.
Looks at John Corcoran's work on the true definition of the word "implications" in all its variations.
2,916 words (approx. 11.7 pages), 12 sources, APA, AU$ 104.95
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Abstract
This paper summarizes, analyzes, and critiques John Corcoran's work, in which he puts the different definitions of the word "implications" into distinct, well-defined, recognizable contexts. The paper reviews Corcoran's work from the perspectives of history, logic, philosophy, and linguistics.
From the Paper
"In his paper, Corcoran lists several ?implication? phrases in common English usage which presuppose that the premise ?A? is true and that validates the conclusion B. Corcoran also critiques the philosopher/mathematician Frege in that Frege?s thesis on logic is constrained by his instincts. Corcoran avers that Frege included pure logic in his thinking and did not make room for deduction as a major contributor to the concept of implication. ?Frege's strategy was to show that no appeal to intuition is required for the derivation of the theorems of number theory. This in turn required that he show that the latter are derivable using only rules of inference, axioms, and definitions that are purely analytic principles of logic(Ref)??which he did not."
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History of Women in Mathematics, 2004.
Looks at the contributions to the field of mathematics made by women in the last two thousand years.
1,163 words (approx. 4.7 pages), 9 sources, APA, AU$ 49.95
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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."
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Chinese Mathematics, 2002.
Examines the history of mathematical knowledge in China.
1,570 words (approx. 6.3 pages), 4 sources, MLA, AU$ 62.95
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Abstract
This paper looks at the early Chinese achievements in the field of mathematics, including the decimal system, calculation of pi, the use of counting aids and the application of mathematical principles to everyday life. It also examines the influence of Indian and later, European mathematical knowledge into Chinese mathematics.
Early China
Indian Influence
Tenth Century to Ming Period
Influence
From the Paper
"Suan chu was thus developed, which covered a wide array of practical and spiritual concerns. Subjects as diverse as religion and astronomy were tapped to devise ways to control the floods (Martzloff 21-22). The science of mathematics was an integral aspect to the of suan chu, particularly in the construction of dams strong enough to shore up the river banks and in the development of the Chinese calendar to record and predict the monsoon season."
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Earth's Diameter, 2002.
An insight in how to measure the diameter of the Earth.
915 words (approx. 3.7 pages), 2 sources, MLA, AU$ 39.95
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Abstract
This paper describes Eratosthenes' calculation of the Earth's diameter, based on one assumption and two measurements, that the Earth was a sphere and that the two measurements made are the degree of the Earth's shadow at noon at two points and the distance between those points. It outlines how this experiment can be repeated by measuring the degree of the shadows cast at two locations either directly north or south of each other at noon on the same day and details the equipment required, the measurements to be taken and the mathematical equations involved.
From the Paper
"Eratosthanes used the city of Syene in Egypt as the first point. This point was selected because it was known that on noon on the first day of summer the sun was directly overhead. This was known because people observed that at this time, the buildings cast no shadows (York University). Therefore, the degree of the shadow at Syene was 0o.
Eratosthanes then needed to know the degree of the shadow at another point either directly north or directly south, at the same time of day. Eratosthanes selected Alexandria as the second city. The degree of the sun's shadow was measured and found to be 7.2o (HEASARC)."
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Low Math Scores, 2002.
A discussion of the issues concerning the low math scores of American elementary students.
2,785 words (approx. 11.1 pages), 2 sources, MLA, AU$ 101.95
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Abstract
This paper considers the problem of low math scores for American elementary students and looks at how there are considerable differences between Chinese and American teachers and how these differences account for the poor performance of American students. It also analyzes how the problem goes beyond the teachers themselves, with the base cause being the American approach to mathematics.
Outline
Possible Explanations for Low Math Scores
Comparing Elementary Mathematics Teachers
The Problem with American Mathematics
Conclusion
From the Paper
"Ma argues that the American approach to teaching mathematics is based on teaching procedurally, not conceptually. According to Ma mathematics is approached as a collection of facts and rules where mathematics means following set procedures step-by-step to arrive at answers. This American approach appears to be a correct definition of how mathematics is seen. Unlike subjects like English and geography, the emphasis is not on understanding, but on remembering. Students do not have to know why a certain number is the area of a shape. Instead, all they have to do is remember the formula for calculating the area."
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Math Phobia, 2002.
The paper analyzes the phenomenon of Mathematics Disorder, and the ways teachers, administrators and parents can contribute to eradicating this phobia.
1,634 words (approx. 6.5 pages), 5 sources, MLA, AU$ 64.95
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Abstract
The paper discusses the nature of the phobia as being an irrational fear of being unable to acquire good mathematics skills. The paper explores ways to get rid of this phenomenon using curriculum material designed for weak students, multimedia and integrating parent cooperation, planning learning models, interacting with pedagogic experts and using workshops.
From the Paper
"Teachers, administrators as well as parents of children are becoming more aware of the deficiency in not meeting the challenge of change and adopting Math as part of the curricula [Reys et al 1999]. The focus of the standardized test is to achieve the purpose of dissemination of math knowledge to children and testing them based on the skills acquired. This model in the olden days was called the NCTM Standards in which all recommendations of implementation activities are provided while in the modern day the NSF Standards have replaced the NCTM and has been able to make significant improvement on the old."
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Math Education, 2002.
Examines the present method of math education at the high school level.
6,381 words (approx. 25.5 pages), 12 sources, MLA, AU$ 179.95
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Abstract
Details the current teaching and testing methodologies in high school mathematics classes. Also discusses some alternative strategies for teaching math that have been employed at the secondary school level.
Outline
Current Teaching and Testing Methodologies in High School Mathematics
Classes
Alternative Strategies for Teaching Math Employed at the Secondary
School Level
Learning Concepts and Mathematics Education
The High School Environment: Putting it all Together
Conclusion
From the Paper
"As I have stated, the perceived general needs of the high school can be seen as duo-fold: to provide an education that encourages excellence to exceptional students, and to provide an education that encourages competency to average students. Based on the size, location and level of heterogeneity at any particular school, these needs attract varying degrees of attention."
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Elementary Math Education, 2002.
Discusses educator Diane McCarty's approach to teaching math and the method she designed for using her approach.
774 words (approx. 3.1 pages), 1 source, MLA, AU$ 33.95
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Abstract
Reviews the article ?Morning, Noon, Night and Math? and its discussion of Diane McCarty?s approach to teaching the relevance of math in everyday life. As an educator, McCarty sought to dispel the myth that mathematics is not needed to perform daily tasks. McCarty designed a math unit with the following goals in mind: 1) experience the role of math in everyday life, 2) recognize relationships among different aspects of mathematical processes, 3) become more familiar with the use of mathematical precepts in various careers, 4) relate the use of math to common human activities, and 5) enhance students understanding of mathematics.
From the Paper
"The math unit created by McCarty was very effective in showing the students the importance of mathematics in everyday life. The children found that math was an instrumental part of all three environments?this was especially true in the work environment. The interviewees encouraged children to learn as much as they could about math even if math wasn?t their favorite subject. The interviewees were very effective in demonstrating to the students the relevance of math in the work environment."
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Practical Statistics, 2002.
A look at the development of statistics and how they are used.
1,328 words (approx. 5.3 pages), 9 sources, MLA, AU$ 53.95
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Abstract
This paper discusses the way the study of statistics has developed over time and how it is used in a practical manner today. It looks at the history of this topic and how scholars have helped it progress into an independent academic study. Examines some of the famous statistics that are used in everyday life - divorce rate, GDP, high school drop-out rate, poverty rate, literacy rate etc.
From the Paper
"Statistics is a branch of mathematics dealing with the collection, organization and analysis of numerical data the application of this information to make informed decisions in a variety of applications. Statistical results may be used to forecast business trends, define the extent of prevailing opinion throughout a given population, changes in availability of resources or assets, and provide quantifiable answers to questions in almost every type of business, social or political area. Professor Edwards of the Andover Theological Seminary defined statistics as ?the ascertaining and bringing together of those facts which are fitted to illustrate the conditions and prospects of society.? "
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Parental Guidance, 2002.
This paper looks at the cases of John Nash and Anais Nin who both grew up in troubled households and later developed severe emotional and psychological problems.
920 words (approx. 3.7 pages), 4 sources, MLA, AU$ 39.95
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Abstract
This paper examines the emotional scarring that children undergo as a result of abusive or neglectful parents. It follows with a look at their lives and it concludes with specific examples of parental abuse and its impact on the children's lives as adults.
From the Paper
"Anais Nin on the other hand went through different though equally disturbing experiences as a child, revealed in her book, Dairy of Anais Nin. She, like Nash, grew up in a family where father was the culprit. Her parents had an abusive relationship and fighting was a regular feature of their troubled marriage. He proved to be anything but a good father when he would openly make sexual advances to Anais and would regularly spank the children. Despite occasional periods of apparent tranquility, the family hardly ever felt harmony and real peace because Anais' parents would argue incessantly. This had a bad impact on Anais who it is believed developed psychological problems, as she often experienced bouts of depression, which she was able to overcome with the passage of time. Though her personal journals and dairies were received well by the public, she was nonetheless accused of lying in her diaries by some of her critics."
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Go Figure!, 2002.
A review of the math book, "Go Figure, Using Math to Answer Everyday Imponderables" by Clint Brookhart.
1,103 words (approx. 4.4 pages), 1 source, MLA, AU$ 46.95
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Abstract
This paper examines the bove book which discusses every imponderable imaginable right from the mundane ones such as lottery odds, predicting a child's height, baseball arithmetic, to more complex ones including Windchill equivalent temperature, carbon dating, Newton?s relativity theory and synchronous satellites. It shows how the book improves one?s problem solving skills by making them think about imponderables and also aids one?s understanding of mathematical concepts and sheds light on their useful application in our everyday lives. It evaluates how the book is also an attempt to improve numeracy among American public by making them more aware of the usefulness of mathematics in their lives.
From the Paper
"The book begins with calculation of distance between one particular point and the horizon. Brookhart gives a simple geometric formula to predict the approximate distance. A casual look at these formulas in the beginning of the book prepares the reader for what comes later. However the very simple tone of the book is what arouses skepticism in readers. Some have even pointed out the errors they found in the book. For example the rejection of Goldbach's well-known assumption that "no one has ever found a number greater than 2 that could not be expressed as the sum of two prime numbers" is one such error."
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