ESSAYS -
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Life and works of Euler
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A paper which looks at the life and works of the mathematician Leonhard Euler, and his contribution to the different fields of science, technology and mathematics in Europe in the eighteenth century. Bibliography lists 4 sources.
Filename: JLeuler.rtf

Linear Algebra
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A 15 page research paper on various concepts in linear algebra. The writer details multivariables, vectors, determinants, gaussian elimination, and other elements of linear algebra. Bibliography lists 6 sources.
Filename: Linalgeb.wps

Linear Algebra; Linear Models, the Wassily Leontief Input Output Models
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This 5 page paper examines the Wassily Leontief Input Output Models, looks at the assumption and the way in this is calculated with example calculations throughout. The bibliography cites 4 sources.
Filename: TEwassleo.rtf

LINEAR REGRESSION AND CORRELATION
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This 5 page paper gives a brief overview of linear regression, then details the correlation of the regression to independent variables. One graph included. Bibliography lists 3 sources.
Filename: MBstatlin.rtf

Linear Transformation On Upper Triangular Matrix
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This 6 page paper considers this complex subject, first defining both linear transformation and upper triangular matrices, going on to look at the preserving elements with sub sections on inertia-preservers, idempotent preservers and commutativity preservers. The bibliography cites 6 sources.
Filename: TElintrn.wps

Math Through the Ages, A Gentle History
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A 4 page book review. William Berlinghoff and Fernando Gouvea offer a fascinating and insightful view of the history of mathematics in their text Math Through the Ages: A Gentle History For Teachers and Others. The authors' intention in this work is to give their readers "a general feel for the lay of the land perhaps to help you become familiar with the significant landmarks" (Berlinghoff and Gouvea 5). In short, this is an overview of math history, a "brief survey" of what is in a gigantic topic (Berlinghoff and Gouvea 5). However, the appeal of this book goes deeper than this, as the authors often offer insight into the topic that helps to explain historical details, helping the reader see how math concepts developed and evolved. No additional sources cited.
Filename: khmtta.rtf

Mathematical Errors in 7th Grade
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This 3 page paper provides an overview of common mistakes made in seventh grade mathematics problems. This paper relates the reasons for these mistakes and their impacts for learning. Bibliography lists 1 source.
Filename: MH7GrMat.rtf

Mathematician Leonhard Euler’s Refutation of Pierre de Fermat’s Conjecture
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This is a 3 page paper discussing Euler’s refutation of Fermat’s conjecture. In 1637, French lawyer Pierre de Fermat wrote that he had “discovered a truly marvelous proof which this margin is too narrow to contain” in regards to a mathematical statement which had been unproven for over 1000 years. The basis of Fermat’s (“Last”) theorem or conjecture began with that of the Pythagoras equation [x.sup.2] + [y.sup.2] = [z.sup.2] which he proved “had an infinite set of whole number solutions” which related to the lengths of the sides of a right-angled triangle. Pythagoras did not know “how many solutions existed if the exponent in his equation were a number greater than 2”. Fermat claimed that “for any exponent greater than 2, there were no solutions at all”. During his lifetime however, Fermat often did not supply “proofs” of many of his theorems but many mathematicians since his time have been able to prove his claims to be correct except for that in relation to the Pythagoras equation. Swiss mathematician Leonard Euler (1707-1783) did however work further on many of Fermat’s theorems and “later proved that there are no solutions when the exponent is 3” and “unfortunately, an infinite number of cases remained and the case-by-case method was doomed to fail”. While Fermat’s Last Theorem proved to be difficult to prove, Euler managed to disprove and refute other assertions such as “2^(2^n) = p, where p is a prime number” and found that it is only true for the first four cases provided by Fermat. Bibliography lists 4 sources.
Filename: TJEuler1.rtf

MATHEMATICS AND THE ART OF WAR
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This 8-page paper examines how mathematic applications have been used to help analyze and calcluate wars. Bibliography lists 3 sources.
Filename: MTmatwar.rtf

Mathematics in Investment: A Review of Two Trade Textbooks
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A 3 page overview of Nicholas Dunbar's "Inventing Money: The Story of Long-Term Capital Management and the Legends Behind It" and Roger Lowenstein's "When Genius Failed: The Rise and Fall of Long-Term Capital Management". Each of these books detail specific mathematical applications in the finance trade. The author of this paper explores their coverage of the Black-Scholes Formula and its role in the collapse of the massive hedge fund Long-Term Capital Management. Bibliography lists 3 sources.
Filename: PPmathTx.rtf