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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, £ 24.95
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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, £ 30.95
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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, £ 19.95
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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, £ 50.95
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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, £ 31.95
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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, £ 89.95
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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, £ 16.95
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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, £ 26.95
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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, £ 19.95
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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, £ 22.95
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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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Cryptography, 2002.
An insight into the use of cryptography in data security.
724 words (approx. 2.9 pages), 3 sources, MLA, £ 15.95
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Abstract
This paper analyzes cryptography, the encryption or transformation of data into some unreadable form in order to ensure privacy by keeping the information hidden from anyone for whom it is not intended. It provides a brief overview of cryptography, discusses methods of encryption and description and examines cryptographic protection in Microsoft Windows 2000 as an example of cryptography utilization.
From the Paper
"Cryptography is the study of mathematical techniques related to aspects of information security such as confidentiality, data integrity, entity authentication, and data origin authentication. It is defined as the science of protecting data. Cryptographic mechanisms help organizations provide a complete suite of security services. The fundamental goal of cryptography is to adequately address systems and information security in the prevention and detection of cheating and malicious activities."
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Mathematics Curriculum Review, 2002.
A comprehensive analysis of the problems in the elementary school's mathematics curriculum.
3,545 words (approx. 14.2 pages), 6 sources, APA, £ 59.95
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Abstract
This paper examines the question of how to reverse the trend of lack of educational progress, specifically in the world of mathematics. This is considered through an evaluation of three elementary schools' stated mathematics curriculum, and how they compare to the standards of the National Council of Teachers of Mathematics published standards. The process of this evaluation is a point by point comparison between the NCTM standards and the printed curriculum guidelines for these schools. Specific points which are supportive, and which may fail to reach the guidelines are identified and discussed for each school. The purpose of this evaluation is not to approve or reject these curricula, but rather to identify specific applications which can be either improved through change, or strengthened by building upon existing positive initiatives.
Introduction
Discussion of the NCTM Standards
West New York Public Schools, West MY
Bogota Public Schools, Bogota, NJ
North Bergen Public School System, North Bergen, NJ
Bibliography
From the Paper
"According to national statistics, the mathematical educational progress of American elementary students has failed to keep progress with the rest of the world. This stinging indictment of the educational system of the most technologically advanced culture in the world has caused a serious evaluation of the standards and goals of the elementary system. According to the National Council of Teachers of Mathematics, there are knowledgeable teachers in the system. The teaching staff has adequate support and resources. In a society which depends daily on mathematics, there is opportunity for students to learn and apply math principles and facts. There also is an abundance of access to technology to support the educational process. Finally, if students are considering careers, those in math related fields, such as engineering, financial planning, accounting and many others are some of the highest paying positions in our current job market."
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Isaac Newton, 2002.
A look at the scientific discoveries of Isaac Newton.
606 words (approx. 2.4 pages), 3 sources, APA, £ 12.95
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Abstract
This paper begins by providing a brief biographical overview of Isaac Newton, from his birth in England in 1642 to his groundbreaking scientific theories and discoveries. The paper covers Newton's scientific achievements, starting with the fact that he established a unified theory of approach to modern science. It discusses his discoveries relating to the white light, the telescope and to the field of optics in general. The paper also covers Newton's mathematical achievements in the form of calculus and his most famous discovery of all - gravity.
From the Paper
"Newton?s discoveries in optics were offset by his even more groundbreaking discoveries in pure mathematics and the science of mechanics. One of the most important modern mathematical tools ?The Integral Calculus? was the brainchild of Newton. It need not be mentioned that without this mathematical tool the progress that the scientific community achieved in many disciplines would have been significantly delayed. However Newton?s discoveries in the field of mechanics outweigh all his other accomplishments. Though Galileo had already discovered the first law of motion his theory was based on the movement of objects without any external influence or attraction between them. Newton?s three laws of motion explained the hitherto inexplicable behavior of all physical bodies in motion. Still more astounding was Newton?s discovery of gravity. All these four laws put together explained the mechanical motion of all earthly and heavenly bodies. Newton not only proposed these laws but also ratified them by using the integral calculus."
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Euclid's Fifth Postulate, 2002.
A paper which discusses the philosophical and logical problems contained in Euclid's 'Fifth Postulate' on planar geometry.
1,622 words (approx. 6.5 pages), 3 sources, APA, £ 31.95
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Abstract
Euclid gave the world much of the information it has on planar geometry in his five postulates. The paper shows that while the first four are relatively easy to understand, the fifth one is very difficult in relation to the others. It is this fifth postulate that many people feel can never be proven. The paper discusses how there are those that say it is simply incorrect, those that say it's both true and false and others that say there is no possible way to prove it, and Euclid himself may have realized that the task was impossible. The author of the paper surmizes that if someday the fifth postulate is proven to be either true or false, and the decision is agreed upon, then it could change the way mathematics are done and the way geometry is looked at.
From the Paper
"Theoretically it would be possible for the lines to move toward one another so slowly, because of the low degree of angle, that they take a huge amount of space to come together at the end. But is it possible to have such a slight angle that the lines are almost parallel? They would be so close to parallel at that point that the impression that they are drawing closer together wouldn't be noticed unless they were looked at over miles at one time. That must be possible, but they still must meet somewhere in infinity.
Perhaps Euclid was right and the lines do meet somewhere, but the angles can be so minute that the lines go on almost to infinity, and we don't have the capabilities to calculate just how far that is yet. Perhaps Euclid is wrong and lines will go on into infinity still never touching, but only being a hair's width apart. Mathematicians may never know, since they haven't discovered any way to prove Euclid's fifth postulate by now."
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