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

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 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

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

Mathematics; Anxiety And Commutative, Associative, And Distributive Laws
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This 3 page paper discusses with two issues. The first part of the paper considers how to help mature students that have a mathematics anxiety may be helped before undertaking a learning course containing maths when they have not tackled the subject for many years. The second part of the paper looks at three laws that are used in algebra; commutative, associative, and distributive and considers which is the most important.
Filename: TEanxilaws.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

National Statistics And Local Decisions
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A 3 page paper that begins by briefly explaining what statistics is and the purpose of statistics. The essay discusses how easily it is to misuse statistics, using the example of national teacher salary averages. Bibliography lists 4 sources.
Filename: PGstsnt.RTF

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

Newton’s Calculus
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A 6 page paper discussing events and conditions leading to Sir Isaac Newton’s development of calculus in the mid-17th century. An expansion of “Sir Isaac Newton” (PGnewton.rtf) that provides background information on Newton’s life and the dispute with Leibniz, this paper focuses on calculus and its significance during and after the time of its invention. Bibliography lists 7 sources.
Filename: KSnewtonCalc.rtf

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

Pascal’s Triangle
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This 4 page paper provides an overview of the central elements of Pascal's triangle. Bibliography lists 4 sources
Filename: MHPascal.rtf

Pascal’s Triangle
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This 4 page paper provides an overview of the central elements of Pascal's triangle. Bibliography lists 4 sources
Filename: MHPasca2.rtf

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

Piggy Bank Cash Back Promotion
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A 3 page memo to Piggy Bank's product development team explaining the process of selecting hypotheses and the rationale of including a null hypothesis. Bibliography lists 3 sources.
Filename: KSstatPigBnk.rtf

Predicting the Advertising Budget for Blues, Inc.
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This 3 page paper uses various statistical methods to predict an advertising budget for Blues, Inc., a company that sells denim wear. Bibliography lists 1 source.
Filename: HVBluBud.rtf

Probability
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This 7 page gives a comprehensive view of probability, explaining how to calculate probabilities, looks at the basic concepts and how probabilities are used giving examples such as decision making, marketing and medical research. The bibliography cites 4 sources.
Filename: TEprobab.rtf

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

Probability Case Study
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This 3 page paper examines a probability cases presented by the student. A couple are convicted of a crime based on their description and the statistical probability of the couple being a 1 in 12 million chance, calculated with independent variables. The paper looks at how and why the conviction may have been overturned at appeal, considering the way the probability was calculated and the way that probabilities were determined in the first place.
Filename: TEprobcase.rtf

Probability in Practice
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A 3 page paper addressing the fact that probability analysis often goes awry. This paper explores the potential problems that could have led to the failure of all of the engines on a three engine aircraft. Bibliography lists 1 source.
Filename: PPprobab.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

Pythagoras / The Philosopher, The Mathematician
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A 15 page account of what is known of the life and scientific and mathematical contributions of Pythagoras. Particular attention is paid to the religious beliefs of his Pythagorean Order and how their beliefs has made it difficult to get a true understanding of Pythagoras' contributions to science and mathematics. A summary of the contributions which have been attributed to Pythagoras is included. Emphasis is placed on the Pythagorean Theorem, the principles which determine the concordant scale, and musical spheres. Information is also provided regarding current thought regarding Pythagoras' beliefs concerning vegetarianism, the human and animal soul and reincarnation. A brief overview of his ethnic origins, his birthplace, his studies, and travels is also included. Bibliography lists six sources.
Filename: Pyth.wps

Pythagoras Theorem and Pythagoras Triples
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This 10 page paper explain these theories, giving examples of the formulas as well as the way in which they can be used and proven. The paper includes different illustrations to prove the theories. The bibliography cites 6 sources.
Filename: TEpytago.wps

Quantitative Measures at Carstab
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A 7 page paper discussing how the use of statistics and probability can be applied in making business decisions that affect the bottom line. The example used is a chemical manufacturer (Carstab) that produces a product needed by many customers but needed by one in higher grade. Most of the lots of product that Carstab makes is acceptable to this single customer, but nearly half are not. Carstab develops a pretest resulting in indicating that 90% of what the company sends the customer will be acceptable. The paper discusses this scenario, along with a "what if" discussion of a different set of probability values. Bibliography lists 8 sources.
Filename: KSprobCarstab.rtf

Questions and Prompts Mathematical Thinking
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This 3 page paper looks at the value and use of prompts and questions in the teaching of mathematics in post compulsory education. The paper considers why questions and prompts can be important in developing mathematical thinking and considers the ideas of theorists including Zygfryd Dyrszlag. The bibliography cites 4 sources.
Filename: TEqprompt.rtf

Regression Analysis
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This 3 page paper uses data already supplied to undertake a regression analysis looking at the level of fatalities that may be excepted in future years as a result of driving with different blood alcohol levels. The bibliography cites 2 sources.
Filename: TEalcoholreg.rtf

Regression Analysis Using Health Statistics
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This 4 page paper uses health data on live expectancy for males over a period of time to demonstrate the use of regression analysis. The data is presented, the method of analysis and results are discussed and presented in graph form. The paper ends by looking at the potential of model breakdown. The bibliography cites 2 sources.
Filename: TEreghealth.rtf

Reliability and Validity in Statistical Studies
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A 5 page paper discussing reliability and validity. The paper begins with defining the terms; how they relate to each other; and why they are important in statistics. It then identifies statistical tests, and concludes with an example. Bibliography lists 4 sources.
Filename: KSresReliabVal.rtf

Reliability In The Context Of Measurement Error
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5 pages in length. The writer discusses reliability in the context of measurement error, as well as addresses the notion of statistical significance as it applies to the evaluation of correlation coefficients used as measures of reliability. Bibliography lists 5 sources.
Filename: TLCrelia.wps

Research Methods And Statistics
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This 32 page paper looks at the subject of research in detail. The paper is written in eight sections as follows; the relationship between theory and research, the different ways in which knowledge is gained, scientific method, systematic inquiry, the use of statistics, including descriptive and inferential statistics and how they may be used, experimental, historical and statistical methods of research, null hypothesis and the way in which quantitative research may be undertaken from the selection of the sample and design of the questionnaires, to the final correlation of the data gathered in. The bibliography cites 10 sources.
Filename: TEstatre.wps

Research Outlines
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A collection of five one-page outlines addressing mathematics education history and how the learning disabled have been accommodated in the past century, but also the changes in technology and society that have made the teaching and learning of mathematics increasingly important in today's world. The final outline addresses these issues in an international context; the one before it addresses the same information focusing on the US. Bibliography lists 11 sources.
Filename: KSposOutlin.wps

Results of a Survey on Child Welfare
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This 6 page paper uses results generated by SPSS following a survey undertaken by the student and gives an analysis of the results, giving figures such as mean, median, mode, range and standard deviation, and looks at frequencies and then interprets the figures. The survey concerned child welfare, specifically poverty and abuse. The bibliography cites 6 sources.
Filename: TEcwelfareq.rtf

Review of "An Alternative Approach: The Unfolding Model of Voluntary Employee Turnover"
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A 6 page paper reviewing and discussing this study of why nurses chose to leave their jobs in the mid-1990s. The paper discusses the general focus of the study but concentrates on assessing the authors' use of statistical analyses for appropriate tests, reliability and validity. Bibliography lists 4 sources.
Filename: KSstatArtRevEmp.rtf

Roman and Mayan Maths
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A five page paper which looks at some of the differences between the Roman and Mayan mathematical systems, and the relative advantages and disadvantages of both. Bibliography lists 3 sources.
Filename: JLalgor.rtf

SALARIES AND STATISTICS
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This 3-page paper offers some calculations to determine mean figures for starting salaries between accountants and financial planners. Also discussed in this paper is the Mann-Whitney-Wilcoxon Test.
Filename: MTsalsta.rtf

Science and rationality: the Greeks
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A paper which looks at the common perception in Western civilisation that the Greeks were responsible for the origins of science and rationality, with reference to pre-Hellenistic theories and the ways in which science can be defined. Bibliography lists 10 sources
Filename: JLgreksci.rtf

Setting Alpha Level
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A 6 page paper discussing the origins and use of alpha in statistical analysis. Alpha is defined as the probability of incurring a Type I error, which is that of rejecting H0 when it is true. It is also found used virtually interchangeably with p-level, which is statistical significance and the exact probability of a Type I error. Bibliography lists 7 sources.
Filename: KSstatsAlpha.rtf