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The Fibonacci Sequence and the Golden Mean in Art
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A 6 page paper discussing the history and development of the Fibonacci sequence; the development of associated ratios; and their applicability to visual images. Fibonacci published his sequence in 1202, and da Vinci used the concept of "thirds" in much of his work as did some other artists of the period. The paper provides the mathematical basis as well as illustration. da Vinci's "The Annunciation" is used for example purposes. Bibliography lists 5 sources.
Filename: KSfibonacci.wps

The Future of Graph Theory in the Realm of Computer Science
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This 3 page paper defines and explores graph theory in mathematics. How it applies to computer science, and where it can take it in the future, is the focus of this paper. Bibliography lists 4 sources.
Filename: SA311grp .rtf

The Game Of Blackjack / Card Counting & Other Strategies
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This 5 page paper provides an overview of the game of Blackjack. A brief history and explanation of the game is included but the focus is on methods used to increase the odds of winning the game. Card counting, perecentages, & commonsense ratios are discussed and other strategies are explained in detail. Bibliography lists 5 sources.
Filename: Blakjack.wps

The Geometry of a Ship's Masts
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This 5 page paper provides an overview of the geometry of a ship's mast. Bibliography lists 2 sources.
Filename: MHGeoSh1.rtf

The History of Algebra
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This 3 page paper is a brief overview of the history of algebra. Bibliography lists 3 sources.
Filename: HValgbra.rtf

The History of Calculus
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This 6 page shows how calculus was derived from the studies in real analysis and lead to the development of calculus. The paper begins with the discoveries of Ancient Greece with thinkers such as Zeno of Elea and Archimedes and looks at many mathematicians such as Valerio, Cavalieri and Fermat finishing with Newton and Leibniz. The bibliography cites 3 sources.
Filename: TEcalhis.rtf

The History of Mathematics
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This 6 page paper examines three books on the history of math. Some quotes are included. Bibliography lists 3 sources.
Filename: SA712mth.rtf

The History of Numbers
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This 14 page report discusses the ways in which humanity has developed numerical systems corresponds to the ways that the human species also developed. As human thinking grew in complexity, so did the application of numbers and the understanding of numbers. And yet, little thought is given to why human beings came up with the idea of numbers or how it is possible to count. . Modern historians and social scientists have traced the processes associated in the history and development of numbers from Europe to China, via the Classical World, Mesopotamia, South America and, even more than any where else on Earth, India and Arab lands. Bibliography lists 3 sources.
Filename: BWhisnum.wps

The History of Quadratic Equations
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This 6 page paper takes a look at the quadratic formula through history. How the roots of it emerged in 2000 BC is traced to its current usage. Bibliography lists 4 sources.
Filename: SA744Q.rtf

The History of Real Analysis
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This 5 page paper delves into the concept of real analysis and looks at key people integral to the emergence of this mathematical field of study. Several mathematicians are named including Archimedes and Cauchy. Bibliography lists 4 sources.
Filename: SA228ra.rtf

The History of the “Zero”: The Influence of Geography and Culture on the Invention of the Number Zero.
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A 5 page review of the history of the manner in which the number zero came into common mathematical usage. Traces its development to Mesopotamia and through the various other regions of the world. Distinguishes between the mathematical concept and the philosophy of nothingness. Bibliography lists 3 sources.
Filename: PPzero.rtf

The History of the Pythagorean Theorem
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5 pages. An interesting research paper on the background of the Pythagorean Theorem that is used in algebra and geometry. Details the history of the theorem. This is actually a fascinating history and one that is not often discussed in the classroom. The Pythagorean Theorem was founded by a cult that actually worshipped numbers and felt that everything in the Universe was number-related. A very interesting history for a well-known math theory to say the least! Bibliography lists 2 sources.
Filename: JApythag.rtf

The Importance of Mathematics in Early Greek Culture
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A 12 page comprehensive study of early Greek mathematicians and their cultural significance. Included in the discussion are Ptolemy, Pythagoras, Aristotle, Plato, and others. Bibliography lists 9 sources. (also related to Astronomy)
Filename: Greekmat.wps

The Life and Works of Euclid of Alexandria
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This 10 page paper gives a brief overview of the Greek mathematician, Euclid. He was the chief architect of the concept and science of geometry. Bibliography lists five sources.
Filename: Euclid.wps

The Nature of Math Assessment: Assessment Inconsistencies, Priority of Math Assessment and the Use of Authentic and International Programs
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This is a 10 page paper discussing the interpretative and inconsistent nature of math assessment and possible authentic assessment programs. Several issues relate to the inconsistent and interpretative nature of math assessment within the educational curricula today. Firstly, on a national basis, studies reveal the range in attitudes in regards to importance math assessment has in the overall educational curriculum. While math assessment is often mentioned, its importance does not seem as highly weighted as other aspects of assessment of school performance. Secondly, within the school systems themselves, teachers in mathematics vary a great deal in their teaching practices which can affect assessment; perception of their students’ abilities based on social factors and past performance; perception of the importance of national and consistent assessment; and desired learning outcomes. There are many educational assessment tools which are available. However, assessment tools vary in regards to their expense, time, and curriculum considerations which can affect whether or not the tool can be usefully applied. One of the goals of the U.S. educational system is be “the first in the world in mathematics and science achievement” and some educational programs are trying to fulfill this goal by not only developing consistent national education and assessment programs but programs which are comparative on an international scale, such as that found within the International Baccalaureate Program (IB). Bibliography lists 10 sources.
Filename: TJmaths1.rtf

The Problems of Multicollinearity, Heteroskedasticity, Outlying and Influential Cases and Non-normally Distributed Errors When using Ordinary Least Squares (OLS) Regression
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Multicollinearity, heteroskedasticity, outlying and influential cases, and non-normally distributed errors all present problems for ordinary least squares (OLS) regression. This 8 pager paper explains why each is a problem for OLS, how it can be detected and looks at steps can be taken to deal with each of them. The bibliography cites 5 sources.
Filename: TEOSLerror.rtf

The Science of Escher / Symmetry and Metaphor
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A 10 page paper that provides an overview of the elements of science in the works of Escher, with a focus on symmetry and metaphor based in his mathematical approach. Bibliography lists 8 sources.
Filename: Escher.doc

The Subjectivity of Probability Distributions and Tools for Collecting Qualitative Data
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A three page address of two specific questions. The first questions regards the usefulness of probability distributions in terms of statistical analysis. The second question asks for the delineation of three specific tools that are useful in the collection of qualitative data. Bibliography lists 2 sources.
Filename: PPresrc2.rtf

The Turing Test of Intelligence: What Does it Suggest about the Nature of Human Reasoning
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This 5 page paper provides an overivew of the Turing Test and the views of Alan Turing in regards to the nature of human reasoning. Bibliography lists 2 sources.
Filename: MHTuring.rtf

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