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Stephan Korner's "The Philosophy of Mathematics", 2004.
Summary and review of Stephan Korner's "The Philosophy of Mathematics: An Introductory Essay".
1,091 words (approx. 4.4 pages), 2 sources, MLA, $ 38.95
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Abstract
The first part of this paper expounds on Stephan Korner's discussion, in "The Philosophy of Mathematics, of the nature of mathematics, and the three main schools of thought relating mathematics to philosophy. The paper continues with a discussion on logicism and why it provides the clearest way to look at mathematical concepts and the best way to explain mathematical philosophy.
From the Paper
"Mathematics is an indispensable science that justifies and confirms many aspects of other scientific subject matter. Mathematics relies on conclusions not assumptions and evidence is required to confirm theoretical entities as true. Of course the debates exist as to which school of thought holds the most validity. Mathematical realism will always be different to each of these philosophical schools and arguments can be found to both support and reject each school of thought."
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Rationality, 2004.
Discussion on the human ability to practice rational thinking.
1,701 words (approx. 6.8 pages), 4 sources, APA, $ 55.95
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Abstract
This paper examines two of the systematic mistakes that humans tend to make when they make decisions that they are likely to consider to be rational. These include mistakes or inclinations toward both pessimistic and optimistic biases.
From the Paper
"Except, of course, that we?re not. But it is true that humans are relatively bad at purely rational thinking. This should not perhaps be surprising to us: We are not, after all, computers, which are far better than are humans at making rational decisions and providing rational calculations about situations. This is not entirely a bad thing: Humans have apparently (though the process of evolution) sacrificed the ability to make perfectly rational calculations for the ability to excel at what those who are trying to teach computers to think like humans call fuzzy thinking. We are good, for example, at being able to read another person?s internal emotional state by the tilt of their eyebrows but we are relatively bad at calculating the odds of whether to take another card in blackjack ? to the unending enrichment of the Las Vegas casinos."
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, 2003.
Contends that the relationship between gender, math, and science achievement remains unclear.
1,800 words (approx. 7.2 pages), 7 sources, $ 63.95
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Abstract
The paper shows that the differences between math and science levels for males and females is not consistent across age groups. It cites factors for males performing better than females in math and science.
From the Paper
"The Relationship Between Gender and Math/Science Achievement
Introduction
Public schools have shifted to a racial and linguistic composition that includes Hispanics and other ethnic populations. Many students are English language learners and many have ..."
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History of Primality Testing, 2003.
Presents a non-linear analysis.
2,700 words (approx. 10.8 pages), 12 sources, $ 95.95
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Abstract
Discusses history from the Early Chinese remainder theorem to the recent AKS system. Discusses the concept behind the two postulates, the search for a method to efficiently test for prime numbers, and the classical definition of a prime number.
From the Paper
"History of Primality Testing from the Chinese Remainder Theorem to the Agrawal-Kayal-Saxena (AKS) Algorithm
Introduction
This paper will present a non-linear analysis of the historical concept of primality testing from the earliest days of mathematical ...."
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Statistical Analysis, 2003.
Considers the scientific method as the underlying basis.
6,075 words (approx. 24.3 pages), 25 sources, $ 135.95
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Abstract
Examines elements of the scientific method, including concepts, definition, hypotheses, and theory. Describes statistical analysis as the process through which data becomes knowledge. Cites alternative models for statistical analysis.
From the Paper
"The underlying basis of statistical analysis is the scientific method. The foundations of the scientific method are (1) concepts, (2) definition, (3) hypotheses, and (4) the..."
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Statistics, 2003.
Examines the uses of statistics.
6,975 words (approx. 27.9 pages), 4 sources, $ 135.95
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Abstract
Discusses collecting, organization, analyzing, and presenting data. Presents two basic types of data: categorical and quantitative. Discusses various approaches to organizing data and approaches to other tasks, averages and variations, and the theory of probability.
From the Paper
The term "statistics" to many (perhaps most) people implies a collection of numerical data about a topic. The extent to which most people have confidence in the validity of such a collection of data depends upon ..."
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Research Design and Statistical Analysis, 2003.
Reviews concepts and issues.
2,700 words (approx. 10.8 pages), 7 sources, $ 95.95
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Abstract
Discusses background and definitions, theory in scientific inquiry, applications of quantitative statistical methods, descriptive statistics, statistical inference techniques, internal validity, measuring instruments, and reliability.
From the Paper
"This paper reviewed concepts and issues involved in research design and statistical analysis. The discussions covered ..."
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Theory of Everything, 2003.
An overview of the theories that explain everything from the workings of the universe to the behavior of tiny vibrating strings.
1,155 words (approx. 4.6 pages), 3 sources, MLA, $ 39.95
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Abstract
This paper expounds the ?Theory of Everything,? starting with the pioneering theories of Newton?s ?Laws of Motion? and Einstein?s ?General Theory of Relativity,? developing right through to the cutting-edge ?string theory? research currently being conducted around the world today. It shows the importance of fields of study as seemingly diverse as calculus, differential geometry, electromagnetism, particle physics and quantum mechanics to the development of a ?Theory of Everything?.
From the Paper
"However, there is a fundamental discord between Einstein?s ?Theory of General Relativity? and quantum mechanics. Einstein saw the universe in four dimensions (the three dimensions of space plus time). The gravitational force that binds matter to the earth stems from this space-time continuum. Since quantum mechanic?s subatomic particles only exist theoretically, they cannot be located in space-time and their motion can only be hypothesized. Thus, we have two theories that work individually but not together. There are also many unanswered questions. Relativity cannot tell us how the big bang created the universe or what black holes consist of. Similarly, quantum theory is not able to make order or sense of the assortment of miniscule matter it describes."
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Why Are Statistics So Alluring?, 2002.
A description the different ways that statistics can be skewed to sway public opinion and also the ways that people misinterpret them.
1,576 words (approx. 6.3 pages), 6 sources, MLA, $ 51.95
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Abstract
This paper discusses how people, in general, like to get a visual picture of what they are hearing about and how, through the media and constant representation of statistical data as hard fact, numbers can control people's opinions on issues. It shows how one of the largest issues regarding statistics and their appealing nature is the fact that most of us are innumerate. It also shows how, in addition to innumeracy, the public?s opinion of ideas often leads to skewed views on issues; statistics can become so alluring to activists that they can say something that will change a large group of people's minds on an issue, and then they will get what they want.
From the Paper
"Although even though some statistics are wrong, people want to believe them so bad that they will ignore all logic just so that they will have a numerical view of the situation. Perhaps the biggest real life example of this is a social statistic that Joel Best-in his book Damned Lies and Statistics-describes as "The worst social statistic ever... Every year since 1950, the number American children gunned down has doubled" (Best 1). To anyone using this statistic to promote gun control, this statistic is gold, and it sounds believable too. But if you analyze it you'll find otherwise."
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The ?Theory of Everything? and Stock Markets, 2003.
The application of science's "Theory of Everything" to understanding stock markets.
2,066 words (approx. 8.3 pages), 6 sources, MLA, $ 65.95
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Abstract
This paper expounds the ?Theory of Everything,? starting with the pioneering theories of Newton?s ?Laws of Motion? and Einstein?s ?General Theory of Relativity,? developing right through to the cutting-edge ?string theory? research currently being conducted around the world today. It shows the importance of fields of study as seemingly diverse as calculus, differential geometry, electromagnetism, particle physics and quantum mechanics to the development of a ?Theory of Everything?. It also demonstrates how those with access to this theory can use the knowledge as power for anything, such as understanding stock markets using the premise that the stock market moving up over time means that these are not random movements and therefore should be explainable.
From the Paper
"Stock markets exist over time and space (the geographical markets) that we are able to quantify and understand to a degree. Therefore, as with Einstein, we are fairly comfortable with the stock market in its familiar four dimensions. We have become accustomed to inflation; the rising of prices of goods rise over time and this is obviously a major reason for at least part of the upward rise of share prices. However, what happens when we explore the smaller dimensions ? like the six unknown dimensions string theorists grapple with? Like the string theorists who know that subatomic matter exists but can?t explain or predict its behavior, we often know what influences the stock market but are usually unable to predict it."
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The Calculator, 2003.
An overview of the history of calculator use.
1,177 words (approx. 4.7 pages), 5 sources, MLA, $ 40.95
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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."
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Technology and Geometry, 2002.
A look at the way teaching geometry is affected by technology.
2,400 words (approx. 9.6 pages), 10 sources, $ 89.95
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Abstract
This ten-page undergraduate level paper that discusses the effects of technology on teaching geometry. It will reflect the current trends in mathematics education from grades six to twelve and will point out the concerns of teaching geometry with the help of technology.
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