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Papers On Mathematics
Page 6 of 11
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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 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
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
METHODOLOGY, MATH AND THE SIXTH GRADE STUDENT
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This 4 page paper discusses the application and use of various curriculum for the sixth grade math student. Specific lesson plans discussed. Bibliography lists 4 sources.
Filename: MBmath1.rtf
Napier's Life & Works
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A short, 3 page overview of the life & works of John Napier containing brief descriptions of his major works and other people also associated with the development of logarithms.
Filename: Napier3.wps
Newton and Leibniz
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In this 7 page paper we look at how both of these men can be seen as the founders of calculus. The paper considers their ideas and the ways in which they were similar was well as the controversy over the publishing of these ideas. The bibliography cites 6 sources.
Filename: TEcalcul.wps
Number Theory / Chaos Theory
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A 10 page paper that presents the basics of chaos theory, including mathematical information in a historical context (theorists). The paper covers Lorenz, Ruelle and Takens, Benoit Mandelbrot, Einstein, Shaw and the Santa Cruz collaborative, and modern submissions. The paper concludes with a look at the possibilities of application of chaos theory to neural nets. Bibliography lists 8 sources.
Filename: Chaosthy.wps
Pierre de Fermat
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A 5 page research paper that looks at the life and contributions of Pierre de Fermat, the founder of modern number theory and probability theory. The writer also looks at Fermat's last theorem, the world's 'most famous unsolved mathematical puzzle.' Bibliography lists 5 sources.
Filename: 99fermat.wps
Probability and Sampling
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This is a 5 page paper discussing probability sampling. To properly understand inferences within a population, researchers have developed methods of sampling which combine with the concept of probability to acquire the desired results. There are various types of probability sampling each of which has its own advantages in regards to capturing a specific trend within the population. Sampling sizes are based on several factors as well which include level of confidence, population size, and sampling error among other factors.
Bibliography lists 6 sources.
Filename: TJprobs1.rtf
Pythagoras & Morality In Greek Philosophy
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A 9 page paper on theories of morality in Greek philosophy focusing upon the works of Pythagoras. Pythagoreanism is seen only as a theory of the universe but also as a way of salvation. Bibliography lists 5 sources.
Filename: Pythagor.wps
