Papers On Mathematics
Page 9 of 9


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
Paper Title: The History of the “Zero”: The Influence of Geography and Culture on the Invention of the Number Zero.
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 numberrelated. A very interesting history for a wellknown math theory to say the least! Bibliography lists 2 sources.
Filename: JApythag.rtf
Paper Title: The History of the Pythagorean Theorem
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
Paper Title: The Importance of Mathematics in Early Greek Culture
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
Paper Title: The Life and Works of Euclid of Alexandria
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
Paper Title: The Nature of Math Assessment: Assessment Inconsistencies, Priority of Math Assessment and the Use of Authentic and International Programs
The Problems of Multicollinearity, Heteroskedasticity, Outlying and Influential Cases and Nonnormally Distributed Errors When using Ordinary Least Squares (OLS) Regression
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Multicollinearity, heteroskedasticity, outlying and influential cases, and nonnormally 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
Paper Title: The Problems of Multicollinearity, Heteroskedasticity, Outlying and Influential Cases and Nonnormally Distributed Errors When using Ordinary Least Squares (OLS) Regression
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
Paper Title: The Science of Escher / Symmetry and Metaphor
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
Paper Title: The Subjectivity of Probability Distributions and Tools for Collecting Qualitative Data
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
Paper Title: The Turing Test of Intelligence: What Does it Suggest about the Nature of Human Reasoning
The Use and Misuse of Figures and Statistical Analysis
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This 20 page paper is written in four parts. Part one looks at a business proposal carries pout forecasts for the proposal of a new restaurant, showing how weekly, monthly and yearly forecasts can be made using excel. This section also shows the formula tables used for the projections. This section also considers the aspects which may not be including in financial proposals, such as stakeholder analysis and also the different between the flat rate and the annual percentage rate also known as the APR. The second part of the paper looks at time series data, what it is, how it can be used and presented using excel, and also the problems when using monetary time series data, explaining the difference between current and constant prices. Examples are given on this section. The third part of the paper looks at cross sectional data, what it is an how it can be used, an example is given. The example given is then analysed and the potential problems with this analysis are discussed. The last part of the paper explores correlation coefficients. Looking at what they are and how they may be used, as well as the way in which they maybe misused or misinterpreted. Examples are given to illustrate points raised. The bibliography cites 7 sources.
Filename: TEfigstat.rtf
Paper Title: The Use and Misuse of Figures and Statistical Analysis
The Use of Anova for Statistical Analysis
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This 8 page paper provides an overview of the statistical analysis using an anova. This paper integrates a view of assessments of nonverbal communication as a basis for the anova comparison. Bibliography lists 6 sources.
Filename: MHAnova.rtf
Paper Title: The Use of Anova for Statistical Analysis
The Use of Prime Numbers in Cryptography
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This 6 page paper examines the role and importance of prime numbers, or prime factors, in cryptology. The paper looks at public key cryptography (PKC) and the RSA algorithm demonstrating the way in which public and private keys are calculated with the use of prime numbers. The bibliography cites 5 sources.
Filename: TEprimecyp.rtf
Paper Title: The Use of Prime Numbers in Cryptography
The Use of Zero in Teaching Children's Mathematics
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This 4 page paper examines the use of zero historically and how it presents problems when teaching arithmetic and algebra. Examples of why zero is problematic is presented as well as how it is viewed by experts in the field. Bibliography lists 6 sources.
Filename: SA6030.rtf
Paper Title: The Use of Zero in Teaching Children's Mathematics
TITANIC AND STATISTICS
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This 5page paper discusses the doomed ship, the S.S. Titanic in terms of stastical analysis of passengers. Conclusions to be drawn were that those saved on the lifeboats tended to be of the wealthy, more privileged class. Bibliography lists 1 source. (available in French translation).
Filename: MTtitsta.rtf
Paper Title: TITANIC AND STATISTICS
Transportation Problem In Linear Programming;
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This 10 page paper (plus 2 page appendix) considers the transportation problem in linear programming. The problem is explain in general terms, and then examine more closely by working though a practical example. This include the definition of the problem and the parameters verbally and mathematically and then the minimisation of the problem in terms of an equation. The appendices is an example of coding the problem and also give the solution. The paper also includes an graphical network presentation of the same problem to enhance the students understanding. The bibliography cite 3 sources.
Filename: TElptran.wps
Paper Title: Transportation Problem In Linear Programming;
Understanding the Basics of Statistics
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This 3 page report discusses the practical
application of certain statistical concepts: Mean, mode, and median; frequency
distribution, and; sampling. Bibliography lists 3 sources.
Filename: BWstat01.rtf
Paper Title: Understanding the Basics of Statistics
Understanding the Transition for GCSE to A’ Level Maths; Geometry and Calculus
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This 9 page paper looks at the difference way in which the A’ level mathematics in the UK education system may be seen as a development and expansion of the GCSE level subject. The writer looks at the syllabus and consider how the transition between the two levels is made, and how it may best be understood by the student. The bibliography cites 8 Sources.
Filename: TEalevel.rtf
Paper Title: Understanding the Transition for GCSE to A’ Level Maths; Geometry and Calculus
Using Charts and Graphs
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This 5 page paper looks at how and why different types and charts should and can be used. The paper gives a broad overview of the use of graphical tools in communication and the discusses the use of different types of charts including pie charts, vertical and horizontal bar charts, line charts, Gantt charts and scatter graphs. The bibliography cites 2 sources.
Filename: TEcharts.rtf
Paper Title: Using Charts and Graphs
Using Scientific Method
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This page paper is an example of how to use scientific method to prove or disprove a theory or hypothesis. The paper uses the example of proving that grass which is watered will grow more rapidly that grass which is not watered. The paper demonstrated the use of an hypothesis test using a Chi Squared test. The calculation is also shown. The bibliography cites 2 sources.
Filename: TEgrass.rtf
Paper Title: Using Scientific Method
Variables and Clusters in Research
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This 4 page paper uses a article examining the influences on obesity to look at the way variables are used, identifying the dependant and independent variables and looking at the way the variables are clustered together. The paper also presents a conceptual map of the different variables. The bibliography cites 4 sources.
Filename: TEstatobese.rtf
Paper Title: Variables and Clusters in Research
Venn Diagrams and their Use of Boole's Algebra
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This 5 page paper examines the simple Venn diagrams represented by overlapping circles and considers how these may be seen as a visual representation of some of the logical ideas of Boole. The bibliography cites 2 sources.
Filename: TEvenbol.wps
Paper Title: Venn Diagrams and their Use of Boole's Algebra
Wages for Women in Different Industries; an Hypothesis Test
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This 3 page paper uses data supplied by the student concerning women wages and the industry that they work in to perform an hypothesis test to assess if there is any difference in wage based on the industry that the women are employed within. The bibliography cites 1 source.
Filename: TEwomwage.rtf
Paper Title: Wages for Women in Different Industries; an Hypothesis Test
Why Do People Hate Math?
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A 3 page paper which examines why people have a tendency to hate math. No sources cited.
Filename: RAmathno.rtf
Paper Title: Why Do People Hate Math?
Willard V. Quine’s “Indeterminacy of Translation” Theory
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This is a 15 page paper discussing Quine’s theory of indeterminacy of translation. Willard V. Quine was a mathematician and philosopher who lived from 19082000. During the last half of the 20th century, Quine developed several theories, one of which was the theory of indeterminacy of translation, which challenged some of the former assumptions used in the fields of psychology, linguists and anthropology. Quine asserted that accurate translations between languages could not be made for a number of reasons. Firstly, linguists could not get basic terms of references, or starting elements, because from a holistic perspective, sentences are the basic form of meaning and all sentences are semantically linked by the native speaker. Secondly, “meaning” could not be considered as an absolute element. In addition to some of these basic changes in the construct of translations, Quine also discussed the idea that not only were correct translations into English not possible but also two translation manuals given the same observational stimuli could also not be interchangeable because of the assumptions and the linguist’s imposition of his own beliefs and patterns onto the native language. Obviously, Quine’s theories were criticized as linguists made the case that several translations were considered successful because smooth negotiation and conversation could take place between native speakers and foreign speakers. However Quine’s dissection of the linguist’s process into one of a mathematical and scientific process is considered one of the most significant within the last fifty years in linguistic philosophy.
Bibliography lists 6 sources.
Filename: TJQuine1.rtf
Paper Title: Willard V. Quine’s “Indeterminacy of Translation” Theory
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