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The Meaning of Resonance in Music, 2002.
Provides definitions of the term "resonance" for each of the different fields that it is used.
900 words (approx. 3.6 pages), 4 sources, $ 35.95
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Abstract
Resonance is a term belonging to the mathematics of sound, and to different fields of physics and applied physics. In music, resonance involves the cause of sound produced by musical instruments, in effects that affect standing waves of sound due to resonating strings and air columns that create different frequencies.
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Godel and the "Theorem on Incompleteness", 2002.
Review of R. Rucker's discussion of the concept of infinity and how it relates to Godel's "Theorem on Incompleteness".
650 words (approx. 2.6 pages), 4 sources, $ 26.95
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Abstract
R. Rucker helps us better understand Godel's "Theorem on Incompleteness" by discussing infinity and whether it can be seen as a real entity. In his view, infinity can be seen as a tangible reality. He argues that it is quite possible that time may actually continue forever - and that is precisely what infinity is. Rucker also sees the possibility of the potential infinite divisibility of space into smaller and smaller pieces.
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Question of Mathematical Truth, 2002.
Examines the concept of mathematical truth and whether it really exists.
900 words (approx. 3.6 pages), 4 sources, $ 35.95
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Abstract
In this essay, I will discuss the question of mathematical truth and attempt to decide whether there can be such a thing as an "absolute fact."
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Statistical Analysis as a Function of Time, 2002.
This paper is an overview of the field of statistical analysis as a discipline, which is a function of time.
5,963 words (approx. 23.9 pages), 27 sources, APA, $ 141.95
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Abstract
This paper discusses statistical analysis as a dynamic form of study that evolves over time to meet developing needs and to exploit developing capabilities and technologies. The author points out that statistical analysis is the process through which data becomes knowledge and is a science to assist one in making decisions under conditions of uncertainty. The paper relates that the most appropriate logic bases for the discipline of statistical analysis in the contemporary period are rational, quantitative, positivist and causality.
Table of Contents
Introduction: Reflections on Statistics
Reviewing Statistical Analysis
Defining Statistical Analysis
Alternative Logic Bases for Statistical Analysis
Rational Model versus Naturalistic Model.
Quantitative Model versus Qualitative Model.
Positivist Model versus Normative Model.
Causality Model versus Plausibility Model
Exploratory Model versus Confirmatory Model.
Randomization Model.
Conclusion: Reviewing Statistical Analysis.
Examining the Classical Model of Statistical Analysis
Descriptive Statistical Analysis
Exploratory Statistical Analysis
Inferential Statistical Analysis
Probability Theory and Classical Statistical Analysis
Conclusion: Classical Statistical Analysis
From the Paper
"Descriptive statistical analysis describes the performance or activity of one group or class, without attempting to generalize about other groups or classes. Classification, description, and measurement are activities applicable to variables associated with social research. The classification of variables is based on an assumption that social units are comparable within the context of specific definitional criteria. A social researcher attempts to control variation through the classification of variables. The description of variables is an effort to assign some degree of uniqueness to each variable, in order to provide a basis for the establishment of relationships among variables. The measurement of the extent of the uniqueness of variables generates the quantitative indicators of the strength of the relationships between variables. The process of classification, description, and measurement facilitates the development of causal explanations for both regularities and variations in empirical phenomena. Comparisons are made according to the degree of differentiation of structure in data in relation to a common and less differentiated point of origin. Such comparability is dependent upon both the classification of the social unit and the dimension of that social unit that is being measured. The dimension is the variable being measured."
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Diophantus - The Father of Algebra, 2002.
Examining the life and works of mathematician Diophantus and why he was called the "Father of Algebra".
3,014 words (approx. 12.1 pages), 12 sources, MLA, $ 88.95
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Abstract
Diophantus is referred to more often than not as the "Father of Algebra", although algebra predated Diophantus. His contributions to the study of algebra, however, have led to this attribution. This paper reviews his life, his mathematics, his place in the history of mathematics and the relevance of his work in the 21st century. The review is presented in discussions of his life, his work, his place in mathematics history and the contemporary relevance of his contributions.
From the Paper
"Diophantus lived in the third century A.D. The best estimates of his birth and death years are 200 A.D. and 284 A.D. Other conjectures of these data range from 150 B.C. to 350 A.D. Exactly when he lived, however, is not nearly as relevant to contemporary society as is what he accomplished while he lived. What is generally agreed upon about Diophantus is that he was a normal man who married, had children, and lived a normal but scholarly life. Not all of his work has survived, at least not in a recorded form that may be attributed directly to him. That work which has survived and which can be directly attributed to him, however, has established him as mathematics theoretician of worthy note (Heath (Vol. I) 15-16)."
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The Babylonian Zero, 2002.
An examination on how the figure "zero" evolved during the Babylonian times.
2,176 words (approx. 8.7 pages), 17 sources, APA, $ 67.95
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Abstract
This paper begins by providing a history of the evolution of zero and discusses the origin of the symbol. It then discusses the origins of the concept of "zero" and how this was perceived differently by various ancient cultures such as the Egyptians, the Mayans and the Babylonians. It then focuses specifically on the "Babylonian zero" and how this differed in concept from other figures at the time. The paper includes several diagrams and pictures.
From the Paper
"The symbol zero evolved into its present form after quite a number of transformations. The idea of how the symbol was devised also harbors a few contradictory ideas. Opinions range from it being a dot originally, replaced by a circle with a dot in the center and then maturing to the current form, an oval shape that we all are familiar with. (Pearce, I., 2002). The Egyptian zero that evolved has also been equated with the hieroglyph for beauty, and that of the human windpipe, heart and lungs. (Williams, S. W., 2002)"
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Albert Einstein, the Hero, 2002.
This paper sets out to prove that Albert Einstein was a modern-day hero.
1,280 words (approx. 5.1 pages), 5 sources, MLA, $ 43.95
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Abstract
This paper discusses what makes Albert Einstein a hero. The writer claims that according to the definitions in Webster's Dictionary, Einstein was indeed a hero of the world community. The paper gives examples from the life and work of Albert Einstein to show that, unlike heroes of legend, Einstein was a modern hero.
From the Paper
"Because of the anti-semitism he experienced and his dislike of the German military character, Einstein renounced his German citizenship in 1896 and was granted Swiss citizenship in 1901. He attended college in Zurich graduating in 1900 as a teacher of mathematics. In 1905 he earned a doctorate from the University of Zurich. It was also in 1905 that he wrote his revolutionary paper on the special theory of relativity. By 1909 he was recognized as a leading scientific thinker. In 1914 he returned to Germany to take up a prestigious research post. Einstein received the Nobel Prize in 1921 not for his theory of relativity but for his work on the photoelectric effect. He accepted a post at Princeton University and came to the United States in 1932, becoming a citizen in 1940 (Mathematicians/Einstein)."
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Kinematic Geometry, 2002.
An examination of Horace Barlow's paper on ?Exploitation of Regularities in the Environment by the Brain?.
1,465 words (approx. 5.9 pages), 10 sources, MLA, $ 48.95
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Abstract
This paper explores the general perceptions of Horace Barlow, reflected in his paper ?The Exploitation of Regularities in the Environment by the Brain?, pertaining to the role of evolutionary internalized regularities, especially as they occur in theories of vision. The focus lies principally on issues relevant to the ecological validity of Shepard's kinematic geometry constraint in ordinary motion perception perspective. This paper also establishes the thought for two individual sets of assertions; perception of apparent motion modeled as kinematic geometry theory and internalization of the like.
From the Paper
"The limitations of kinematic geometry proposed in Barlow?s paper have been recognized, however kinematic geometry being a model for perception of apparent motion in my opinion is an idea that can expand into new dimensions. However internalization of kinematic geometry does project reservations about being a possibility. As indicated by Barlow, internalized principle of object observation gives way to the perception of apparent motion. The human brain?s support for a percept is purged from an external stimulus. Conforming to the putative universals are the preferred perceptual solutions. "
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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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