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Essays On Mathematics
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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
Essay Title: Linear Transformation On Upper Triangular Matrix

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
Essay Title: Math Through the Ages, A Gentle History

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
Essay Title: Mathematical Errors in 7th Grade

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
Essay Title: Mathematician Leonhard Euler’s Refutation of Pierre de Fermat’s Conjecture

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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
Essay Title: Mathematics in Investment: A Review of Two Trade Textbooks

Mathematics in Music
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This 5 page paper considers the way that maths can be seen as present in the subject off music. The paper looks at notation, frequencies and accounting as relevant subjects in this field. The paper is written to demonstrates the wide use of mathematics in many subjects. The bibliography cites 4 sources.
Filename: TEmathmu.wps
Essay Title: Mathematics in Music

Mathematics in Sports
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An 11 page explanation of how mathematics are indeed an important tool in sports. Not only does an understanding of mathematics empower players by enabling them to use their body in the most effective manner to achieve optimum performance, mathematics are also useful in a diversity of other areas that are relevant to sports. Bibliography lists 10 sources.
Filename: PPmathSp.rtf
Essay Title: Mathematics in Sports

Mathematics Used in Accounting Practice
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This 3 page paper looks at the use of mathematics in accounting practice. Double entry bookkeeping is used as an example. Bibliography lists 3 sources.
Filename: SA344mth.rtf
Essay Title: Mathematics Used in Accounting Practice

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