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Philosophy of Mathematics, 2007.
An analysis of the universal nature of mathematics and developments in the philosophy of mathematics.
1,899 words (approx. 7.6 pages), 6 sources, APA, $ 60.95
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Abstract
This paper considers some of the major developments in the philosophy of mathematics regarding the capacity of mathematics to be universally valid and applicable. It presents some of the basic arguments and schools of thought of the philosophy of mathematics. The paper then analyzes whether, at its foundation, mathematics can have a legitimate claim to be universal.
Table of Contents:
The Problem Of The Ideal And The Real
Math As Logic
Math As Structure
Application And Universality
From the Paper
"This problem, Russell's paradox, proved to be an intractable problem for Frege which, after it was pointed out to him, he could not overcome. The impact upon the philosophy of math was major. An important attempt to boil math down to logical principles had proven unsuccessfully, and eventual efforts to rescue the project by Russell and others were unable to develop a logicism that showed math as both consistent and complete. Therefore math cannot be said to be universal by appeal to logic alone."
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The Lookback Option, 2007.
This paper discuses lookback options, an "exotic" nonstandard option type as compared to its opposite the usual "vanilla" standard options.
2,960 words (approx. 11.8 pages), 12 sources, MLA, $ 87.95
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Abstract
This paper explains that a lookback option is path dependent, based on the maximum or minimum underlying value reached during the entire life of the option. The author points out that, at the expiration date of these options, the holder may "look back" over the life of the option and exercise it, based on the optimal underlying value achieved during that period thus giving the holder the ability to buy an asset at its lowest price or sell it at its highest price achieved over the life of the option. The paper relates that, through the lookback option, the investor can achieve economic intelligence and value through the benefit of hindsight; however, lookback options carry risk and are more expensive than standard options. The paper includes several formulas.
Table of Contents
Definition of Options
Call and Put Options
Introduction to Lookback Options
Lookback Options in Greater Depth
The Model
Option Pricing
Discrete Lookback Options
Case Study of Lookback Options
From the Paper
"Put options conversely involve the investor aiming for a stock price decrease. The put option, as mentioned in the introduction, allows the holder to sell an asset by a particular date for a certain price. An example demonstrated by Hull (2006) involves a European option involving an investor who buys the option to sell 100 shares with IBM for a strike price of $70. If the current stock price is $65 and the expiration date is in three months, Hull supposes for example that the option to sell one IBM share is $7. The initial investment, therefore, will be $700."
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Manipulatives, 2007.
This paper researches the use of manipulatives in the field of mathematics.
3,446 words (approx. 13.8 pages), 37 sources, MLA, $ 97.95
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Abstract
In this article, the writer researches hands-on manipulatives use in mathematics. This work explores the historical perspective, the effects on education and the supporting theories. In addition, the writer looks at what research has been thus far conducted. Finally, this work researches the special benefits of using algebra tiles. The writer maintains that it is significant to note that algebraic functions are mathematical processes involving abstract or symbolic representation. The writer concludes that it is quite difficult for the beginning algebra student to conceptualize the processes and functions of algebra; however, the use of manipulatives has been shown to assist in this area, making their use in algebra instruction particularly effective in classroom instruction.
Outline:
Objective
Introduction
What are Math Manipulatives?
Why Use Math Manipulatives?
How Should a Teacher Use Math Munipulatives?
Summary
What
Why
How
From the Paper
"Today's mathematics teacher has many resources that are available in assisting the development of appropriate curricula that meets the content standards of the NCTM. Not only are standard tools available but the Internet also offers several web-based learning activities that assist mathematics learning and instruction. Before this development, the teacher often would contact businesses in the community in order to obtain 'real-world' manipulatives for use in the classroom. The work of Shield holds that web-based tools motivate students in learning mathematics content but also the delivery of the information is interesting to the student."
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Hands-On Manipulative in School, 2007.
An exploration of the use of the hands-on manipulatives in the middle school math classroom
3,876 words (approx. 15.5 pages), 25 sources, MLA, $ 106.95
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Abstract
This paper reviews findings in literature stating that hands-on manipulatives are effective in the middle school mathematics classroom. The paper then reports that the findings are of limitations in the use of manipulatives and, specifically, in the misuse of the manipulatives in the classroom. The paper further emphasizes that teachers must be well-educated and trained in the use of manipulatives, whether concrete material or virtual manipulatives for use on the computer and the Web. The paper concludes that it is clear that the use of manipulatives in mathematical instruction and learning in combination with cooperative learning is the best practice for instructional methods in today's mathematics classroom.
Outline:
Objective
Introduction
Historical Perspective
Theories
Research Studies
Virtual Manipulatives
Limitations
Static and Dynamic
Algebra Manipulatives
Summary
From the Paper
"The slide-rule is a manipulative that was used in early education in providing students with a hands-on application in mathematics. Hands-on manipulatives such as blocks, rods, bean sticks and other manipulatives have been historically used in the math classroom as an aid in teaching mathematics. The work of Clements (1999) entitled; 'Concrete Manipulatives, Concrete Ideas" published in the Journal of Contemporary Issues in Early Childhood states that: "The notion of 'concrete' from concrete manipulatives to pedagogical sequences such as 'concrete to abstract' is embedded in educational theories, research and practice, especially in mathematics education."
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George Polya, 2007.
A discussion of the life and career of mathematician George Polya.
1,234 words (approx. 4.9 pages), 3 sources, MLA, $ 42.95
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Abstract
The paper discusses the Hungarian mathematician, George Polya and relates that he is hailed by many as not only one of the greatest mathematicians, but also a great teacher of his time. The paper examines his schooling, his studies in university and the path to his career in mathematics. The paper details all his various accomplishments and promotions.
From the Paper
"Polya's parents, Anna and Jakab, were both Jewish. Jakab's original surname was in fact Pollak, but he changed this for the sake of his professional goals. After his law firm failed, he worked for an international insurance company. However, Jakab's dream was to obtain a research post at a university and pursue his true interests, economics and statistics. It appears therefore that George inherited not only his father's tenacity, but also his interest in numbers. In 1882 Jakab Polya was finally appointed as Privatdozent at the University of Budapest."
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William Gosset, 2007.
A description of th life and achievements of William Sealey Gosset in the realm of statistics.
863 words (approx. 3.5 pages), 2 sources, MLA, $ 30.95
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Abstract
This paper discusses the life and work of William Sealey Gosset, who was one of the leading statisticians of his time, particularly with his work on the concept of standard deviation in small samples. It gives examples of some of his achievements in the realm of statistics. The paper describes Gosset as both brilliant in his professional work as a chemist and statistician and as a loved and respected man.
From the Paper
"After Gosset had worked for many years developing the practical application of his theory, he was involved in a terrible car accident in 1934 which left him incapacitated for many months. During this time, he had the opportunity to continue to work on his statistical work. He recovered enough after a year to move to London where he became the head brewer and scientist of production at a new Guinness brewery. Gosset continued to publish the results of his statistical findings while working in London. He did not hold his position there long as he died in Beaconsfield, England, on October 16, 1937 (O'Connor and Robertson)."
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John Wilder Tukey, 2007.
An analysis of the important statistical contributions of John Wilder Tukey.
741 words (approx. 3.0 pages), 2 sources, MLA, $ 26.95
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Abstract
This paper discusses the life of John Wilder Tukey, who was a mathematician. It describes Tukey's upbringing and his introduction to mathematics. The paper discusses Tukey's most important statistical work, which was the way he presented his evaluation of "spectra time series". It then describes the three major contributions of Tukey according to Regents of the University of Minnesota.
From the Paper
"Tukey's first official school was at Brown University where he took both his Bachelor's Degree and the Master's Degree in Chemistry. Since he was interested in mathematics, he pursued his Ph.D. at Princeton University in 1937. Lefschetz supervised Tukey's research and Tukey eventually received his doctorate in 1939 with a dissertation in Denumerability in topology that was published in 1940 as Convergence and uniformity in topology (O'Connor and Robertson, 2004)."
"Tukey became a mathematics instructor at Princeton and joined other famous statisticians and mathematicians during the World War II to study the statistical mathematical problems of artilleries and weapons. This study covered the computations and calculations of how to accurately target traveling objects. In 1945, he was enlisted at AT&T Bell Laboratories in Murray Hill. By 1965, he wrote a manuscript entitled Mathematics in Computation with J. W. Cooley wherein he presented the Fourier transform algorithm."
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Regression Analysis, 2007.
A regression analysis used to explain whether police use different standards of severity when dealing with resident versus non-resident drivers in Florida.
1,080 words (approx. 4.3 pages), 2 sources, MLA, $ 37.95
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Abstract
This paper discusses whether police use different standards of severity when dealing with resident versus non-resident drivers in Florida. The paper uses the regression analysis, which estimates the significance of the variation of the dependant phenomenon with the independent and the influence of the latter on the former. The paper explains its analysis and shows that a relationship does exist.
From the Paper
"The hypothesis is tested with the confidence level of 95%, thus the allowed chance of rejecting no relationship between the variables when there is actually this relationship, is 5%. Decreasing the confidence level to 90% will give more errors in the model and the model did not result in better relationship. Having carried out this multifactor regression, the result revealed that there is no statistically significant relationship between the over speeding and the fact that the person is a resident or non resident and the gender of the person. The first problem with the model could be the very data set as out of the 536 observations in the population, only 136 were the cases when people were none residents. Thus, the results could be distorted. The R2 in the model is extremely low and reveals that very little variation in the severity of this crime could be explain by the factors in the model. P-values are low only for the intercept and none-residence factor."
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Math Achievement in African-American Males, 2007.
An analysis of the differences in mathematical achievement between African American males and White males.
5,741 words (approx. 23.0 pages), 44 sources, MLA, $ 138.95
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Abstract
This paper focuses on mathematical achievement in African-American boys versus their white counterparts. It addresses risk factors such as family income, mother's education, single-parent households and a non-English primary language. The paper discusses the works of theorists Lev Vygotsky, Jerome Bruner and John Dewey regarding this issue.
Table of Contents:
Objective
Introduction
Theoretical Framework
Limitations
Literature Review
Summary of The Literature Reviewed
From the Paper
"The African American male was not expected to achieve in educational areas of management and accounting studies evidenced in the statement related in the work of Dantley and Leonard (2006) who states that a participant related that: "I only indulged myself in my studies to the degree that I was satisfied that I could do math up to multiplication and division of fractions and decimals and it was good enough for me for what was I going to do. I wasn't going to be doing any math. To be a laborer, all it's going to require is to run a piece of machinery." (p. 42) additionally a participant stated: "We don't have no industry out there and the industry that is out there, they're not targeting the Black community and saying, "If you go and get more math, then I can guarantee you this." (p. 45) and finally: "I have hopes. My expectation is that (my son) will graduate from high school. If he doesn't, it's no big deal...My expectation for him is to probably be no worse than I was. Just to pass." (p.46) (Dantley and Leonard, 2006)"
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Hyperbolic Geometry, 2007.
An examination on using M.C. Escher' "Circle Limit III" to instruct students in hyperbolic geometry.
2,279 words (approx. 9.1 pages), 6 sources, MLA, $ 70.95
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Abstract
The paper examines how, though not always apparent, there are a number of significant connections between mathematics and art. The purpose of this paper is to demonstrate how the fundamental similarity between math and art can be exploited as a means to teach difficult mathematical concepts to students. To show how this could happen, a particularly complex--if intellectually intriguing--mathematical concept is explored: the concept of distance in hyperbolic geometry, specifically in a Poincare disk.
Outline:
Introduction
Context: What Is Hyperbolic Geometry?
Context: Who Is M.C. Escher?
Developing an Appropriate Class Project
Conclusions
Works Cited
From the Paper
"Since mathematics education produces singular anxiety for many students, this confluence with art presents significant possibilities for the imaginative educator (Granger 10). It is possible that we could, as educators, use art as a physical and visual means of explaining complex mathematical concepts in other than abstract terms. Over reliance on complex equations and difficult language can and will stymie many students. By endeavoring to ground mathematical theory in artistic reality, students can leans mathematical lessons in the process of seeing how math and art aren't really all that dissimilar."
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Zipf's Law and Benford's Law, 2007.
An analysis of the mathematical significance and applications of Zipf's Law and Benford's Law.
1,279 words (approx. 5.1 pages), 4 sources, MLA, $ 43.95
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Abstract
This paper addresses both Zipf's Law and Benford's Law. It describes the theories of each law in detail and discusses how they can be applied to various situations. It describes Zipf's Law as not a theoretical law, but rather an experimental law. The paper then discusses the significance of these two laws to the field of mathematics.
From the Paper
"However, there is some lack of precision where this is concerned. Most items have to occur a number of times that is actually an integer (Li, n.d.). In other words, a word that is seen within a document cannot appear in that document 2.5 number of times. It either must appear, in this example, 2 times or three times, since there cannot be an area of the document where only 1/2 of the word appears. Despite the fact that there is some variation and lack of precision, however, when wide ranges are examined and one only desires to have a relatively close approximation, many of the natural phenomena that are seen in this world do obey Zipf's law (Li, n.d.). This is seen to hold true as long as the individual examining the issue is not looking for scientific precision and will accept the slight variation that is seen."
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John von Neumann, 2007.
An analysis of the mathematical and scientific contributions of John von Neumann.
2,009 words (approx. 8.0 pages), 6 sources, MLA, $ 63.95
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Abstract
This paper discusses John von Neumann's contributions to the fields of quantum physics, functional analysis, set theory, economics, computer science, numerical analysis, hydrodynamics, statistics and other mathematical fields. The paper also discusses his contribution to the creation of the hydrogen bomb. It goes on to describe some of his most influential achievements.
From the Paper
"John Von Neumann inarguably contributed a wealth of knowledge to the development of computers, and without his contributions the face of technology today would be primitively underdeveloped. However, Neumann may have canceled out the "good" he did in an act of self-fulfilling equivalent exchange with his work in the realms of math and science with the contributions he made to warfare and massive weaponry. The name Von Neumann is associated as much with the Atomic Bomb as it is with computer programs (Wilson), and Neumann may have had even more devastating projects on the horizon at the time of his unexpected death from cancer. During the Second World War, von Neumann worked as a consulted to both armed forces and civilian agencies that were involved in wartime projects. Neumann's genius was in high demand, and he was able to design an implosion method for bringing nuclear fuel to explosion, as well as playing an integral part in the development of the hydrogen bomb. (Cabrera) According to one of Neumann's biographers, "It has been stated that von Neumann's electronic computer hastened the hydrogen bomb explosion on November 1, 1952." (Bochner)"
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The Statistical Lie, 2007.
This paper explores how statistics can often be misleading and delusional.
1,065 words (approx. 4.3 pages), 3 sources, MLA, $ 37.95
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Abstract
The paper relates that one of man's greatest fears is that of the power of numbers. The paper demonstrates how statistics are used to misrepresent, under-represent or over-represent an event, occurrence, situation or phenomenon. The paper defines statistics as a set of numeric values obtained by way of a measurement process. This process can be either one of observation or direct testing. The paper reveals that the most widely used means whereby researchers lie is with statistics, usually for increased profits and sensationalism. The paper illustrates how companies can use a self-selecting population for survey results, or they use obscure definitions and data sets that mislead consumers.
From the Paper
"For most people numbers are nothing more than a hodgepodge of digits that are bewildering and oftentimes meaningless. As a result individuals often prefer to judge events, occurrences, phenomena, and situations from a traditionalist point of view wherein reason, conclusion, and inferences are made on the basis of past experiences rather than on best practices policies. Justification for historical acceptance is usually based on a fear of numbers and a lack of willingness to extract meaningful information from them. For those accepting of the alternatives, statistical tools have been devised wherein it is possible to extract meaningful information from data and interpret whatever the data holds as its' secret."
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Josiah Willard Gibbs, 2007.
This paper looks at the life and achievements of American scientist, Josiah Willard Gibbs.
1,544 words (approx. 6.2 pages), 9 sources, MLA, $ 50.95
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Abstract
In this article, the writer studies the character of Josiah Willard Gibbs, a mathematician and physicist. The writer discusses that he managed to achieve great things during his lifetime and lead the world on to greater and better scientific discoveries. The writer points out that Josiah Willard Gibbs has been recognized as one of the greatest American scientists of the nineteenth century. Further the writer notes that it is Gibbs who managed to provide a sound thermodynamic foundation to physical chemistry, to America and to the entire world.
From the Paper
"The second work that Gibbons published in the same year was "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces". From the years from 1876 to 1878, Gibbs published two memoirs, which were later to be combined into one work, entitled, "On the Equilibrium of Heterogeneous Substances". Added to this, Josiah Willard Gibbs has contributed to various other spheres, like for example, crystallography, the determination of planetary and comet orbits, and also to electromagnetic theory. The most interesting phenomenon that Gibbs managed to achieve was that he made the practical side of science appealing and fascinating. Gibbs was also recognized as a 'theoretical physicist' of international stature, and he received a patent in the year 1866 for an improved type of railroad brake."
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Dyscalculia, 2006.
A discussion regarding the academic developmental disorder, dyscalculia.
1,683 words (approx. 6.7 pages), 11 sources, MLA, $ 54.95
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Abstract
This paper reviews dyscalculia, an academic developmental disorder that is believed to affect about 3 to 6 percent of the population. According to the paper, an individual with dyscalculia may struggle with a number of different issues such as, linguistic skills, perceptual skills, attention skills and mathematical skills.
From the Paper
"Dyscalculic individuals can usually learn the sequence of counting words, but can have trouble moving back and forth, especially in twos, threes or more. Estimating numbers is also more of an issue in comparison to others their age. With dyscalculia, the lack of understanding number magnitudes, which is typical of children in the age group of 7 to 11, is absent. Math vocabulary may also to lead to problems for students, especially when they have to use several different words at a time, such as "add," "plus," and "combine" that can be used interchangeably. Other terms, such as "hypotenuse" and "to factor" do not occur in normal discussions and must be learned specifically for mathematics. At times, an individual may understand the underlying concept but not how to use a specific term correctly."
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