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Biological Evolution and Mathematical Development, 2005.
This paper discusses if biology, evolution and the development of mathematics have a connection.
675 words (approx. 2.7 pages), 3 sources, AU$ 42.95
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Abstract
The paper examines the possibility that biology, evolution and the development of mathematics are linked more closely than mathematicians would necessarily have us believe. The paper challenges the basic Platonist assumption that abstract mathematical concepts possess concrete being and are consequently fundamental parts of the universe. Instead, the paper discusses the possibility that mathematics is a construction of the human mind and an evolutionary development.
From the Paper
"Most often we take mathematical truth for granted. Rather than understand it as an historical construction - not so different from any other human production, such as language - most people fully believe that mathematics is natural and etched into the very fabric of the cosmos. This is a classic Platonist view of the universe in which even abstract concepts have physical reality. Twentieth century theorists, especially in linguistics, have repeatedly challenged the efficacy of abstract concepts. But mathematics is still, in some part, understood to be the realm of the gods with right-brains their unerring prophets."
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Mathematics and Universal Truths, 2005.
This paper discusses whether mathematical thought can lead to fundamental truths and highlights the use of metaphor in mathematical thought.
675 words (approx. 2.7 pages), 3 sources, AU$ 42.95
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Abstract
The paper argues that fundamental truths cannot be arrived at by math. The paper is of the opinion that this is insofar as the questions we ask, the processes we use and the assumptions we make are shaped by environmental, biological and contextual factors that have little - if anything - to do with "rational" and purely objective thought. The paper places great emphasis upon the place of metaphor in the construction of mathematical thought.
From the Paper
"The question of whether there are unquestionable truths in mathematics is indeed a puzzling one. This paper will examine the matter by looking a few readings from our class notes. As will soon become apparent, there is much doubt that mathematics leads irrevocably to universal truth; indeed, in the limited space available, this paper will suggest that, because so much of mathematics is metaphorical in nature, Euclidean mathematics and other "relational" branches of math may lead us into the realm of creative metaphor and no further. In fact, as Sawyer seems to suggest, mathematical "truth" - all truth - is essentially the product of cultural epistemology and ontology."
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High School Math, 2005.
This paper provides a lesson plan for the teaching of mathematics in high school.
3,825 words (approx. 15.3 pages), 10 sources, AU$ 245.95
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Abstract
In this article, the writer develops a lesson plan for teaching quadrilaterals in high school math and considers some of the underlying pedagogical theory and how it applies. The writer notes that quadrilaterals are defined as polygons with four sides, and while this encompasses any such figure, the more important of these are parallelograms, squares, and rectangles. Further the writer shows how the student can discover certain relationships by looking to the real world.
From the Paper
"Below is a lesson plan for the instruction of high school students in the mathematics, specifically on the subject of quadrilaterals. This lesson is found in the larger subject area of Geometry. Quadrilaterals are defined as polygons with four sides, and while this encompasses any such figure, the more important of these are parallelograms, squares, and rectangles. The lessons in this subject area define these figures and address different mathematical concepts applying to them, including ways of determining area, angles, and other ratios. This lesson should introduce the students to the area of quadrilaterals defining this area of Geometry by describing the elements that make up a quadrilateral and the mathematical relationships that define this type of figure, as well as the formulae that are used to calculate different characteristics."
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Biology, Evolution and Mathematics, 2005.
This paper studies the connections between biology, evolution and mathematics.
675 words (approx. 2.7 pages), 6 sources, AU$ 42.95
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Abstract
This paper examines the question of what mathematical premises would be dependent on the biological and physical evolution of a given species, assuming of course that we knew other intelligent species had evolved. The writer discusses that some critics suppose that language and mathematics by extension are dependent upon the physical parameters set out by the body. The writer explains: ten fingers and hence a decimated numerical system. This essay probes that assumption.
From the Paper
"There is almost certainly a connection between biology and the ability to conceptualize. The basic logical processes that we, as humans, often take for granted are in reality quite dependent upon our own physical evolution. How likely is it that we would have developed a base ten numerical system if we didn't just happen to have ten fingers? It would be perfectly plausible to have a base six system or base twelve, for example. But the question becomes how much of mathematics is a product of biological evolution and how much of it exists unto itself."
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Astronomy from Ptolemy to Galileo, 2005.
This paper studies science, in particular astronomy, making use of the book "Science without Limits" by James Perlman.
675 words (approx. 2.7 pages), 1 source, AU$ 42.95
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Abstract
This paper examines the history of science in terms of changes in astronomy from the time of Ptolemy to Galileo, based on the book "Science without Limits" by James Perlman. The writer notes how the ancients saw science as a form of philosophy, while by the time of Galileo, observation was being joined with experimentation to examine concepts and find the truth.
From the Paper
"The history of astronomy shows the development of science as a discipline from the ancient world to the Renaissance, from the time of Ptolemy to the time of Galileo. Over that period, astronomy began to shift from a philosophy to a science. Science in the ancient world was not created out of whole cloth and was based on observations and the application of reason. Mathematics were also used to develop ideas about the universe. Mathematics is itself an application of reason, though aspects of mathematics have also been developed through observation and testing. By the time of Galileo, however, science was gaining a more experimental structure, and Galileo himself tested many ideas directly. His astronomy was also based on observations, but he was able to observe more directly and closely with the telescope. Perlman notes that "science in large part . . . is a matter of testing assumptions"."
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Matrices, 2005.
This paper present a study of the theory of matrices that includes its history, development and uses.
900 words (approx. 3.6 pages), 2 sources, AU$ 57.95
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Abstract
This paper discusses the theory of matrices, how it was developed, how it changed, some of the applications for which it has been used, and other aspects of the issue. The writer notes how the underlying ideas are ancient and began with the Babylonians and Chinese and then resurfaced in the seventeenth century with the world of Cayley and others. Further the writer points out that the theory of matrices has led to uses in physics, chemistry, and economics as well as mathematics.
From the Paper
"Matrices are a means of visualizing mathematical concepts and relationships in graphic form. A matrix is a rectangular set of elements viewed as a single entity, identified by the number of rows and columns of which it is made. Matrices can be added or multiplied on the basis of an algebra of matrices, and one application of this sort of operation is seen in vector analysis and in the solving of systems of linear equations. The basis for the matrix is found in the Cartesian system of Rene Descartes, whose contribution to mathematics was in the development of analytical geometry, closely tied with the development of the Cartesian system of mapping on a grid or graph, for Descartes saw that a function or polynomial can be represented graphically by points."
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Mathematics Education Dissertations, 2005.
This paper describes two distinct mathematics education dissertations.
2,250 words (approx. 9.0 pages), 2 sources, AU$ 144.95
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Abstract
This paper explains that the field of mathematics education provides considerable support for a variety of perspectives, which include new and innovative ideas and concepts. The author points out that graduate-level mathematics students are typically required to develop and submit a comprehensive dissertation to demonstrate their knowledge and skills. The paper presents two distinct mathematics education dissertations in greater detail, emphasizing the key strengths and weaknesses of each argument and the supporting literature reviews.
From the Paper
"The field of mathematics education provides considerable support for a variety of perspectives, which include new and innovative ideas and concepts that provide valuable contributions to the subject. It is evident that today's mathematics educators provide valuable knowledge, information and skills to mathematics students of all ages, and that there is a wide body of research that exists regarding mathematics education that is critical to the field. Graduate-level mathematics students are typically required to develop and submit a comprehensive dissertation to their respective schools in order to demonstrate their knowledge and skills in order to earn a graduate degree. The following discussion evaluates two dissertations written in the field of mathematics education, promoting different concepts in unique ways. A comparison and contrast is introduced, along with an evaluation of the key strengths and weaknesses of each dissertation."
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Mathematics Pedagogy, 2005.
This paper discusses of teaching mathematics.
3,825 words (approx. 15.3 pages), 13 sources, AU$ 245.95
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Abstract
This paper examines issues of mathematics pedagogy and the degree of the contextualization of the subject matter in teaching mathematics. The author points out that mathematics is often presented more as a more abstract examination of numbers and measurements that appear, when mathematics really is always relevant and should be seen in the context of the real world. The paper states that mathematics pedagogy needs to develop a way present mathematics within this real world context.
From the Paper
"The issue of relevance in education is often a question of the contextualization of subject matter, meaning that the subject relates to the lives of the students because it can be seen in the context of their lives, with issues understandable because they are applicable to the real world. Mathematics is often presented more as a pure Mathematics has the dual character of being both a language (a symbol system) and an underlying model of relationships among actions with objects. As such, it fits closely with the Vygotskian description of sign-sign relationships and de-contextualized knowledge. At the same time, its development in relation to human actions on objects gives it a prominent place in Piagetian analysis. Furthermore, mathematics teaching requires the recognition of mathematics as a sociocultural achievement worthy of reproduction in new generations."
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Mathematics Education, 2005.
This paper analyzes if it is possible to test the understanding of mathematics.
3,600 words (approx. 14.4 pages), 10 sources, AU$ 230.95
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Abstract
This paper is a report on a questionnaire given out to students in college to test their understanding of mathematics. The author points out that this research investigates the difference between knowledge and understanding and seeks the way to assess understanding. The paper concludes that the questionnaire derived from the GED in mathematics is a way to test understanding of high school mathematics for students who have graduated from high school.
From the Paper
"The purpose of this analysis is to see if it is possible to test understanding, specifically the understanding of mathematics. Such an analysis tests both mathematics teaching and mathematics learning, though at this preliminary stage it is not clear whether the teaching method is what is most important or the learning style of the student. Testing understanding is different from testing knowledge, for the latter shows that the student has assimilated ideas and even processes, while the former shows that the student has learned the underlying theory and can apply it in different situations. In mathematics, testing understanding is perhaps more common in normal testing than would be the case in certain other disciplines where simple facts are more common. In mathematics, of necessity the student must show an understanding of theory in order to apply mathematical concepts to written problems and arrive at the correct answer."
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Natural Human Languages and Mathematics, 2005.
This paper discusses the similarities of human languages and mathematics.
675 words (approx. 2.7 pages), 1 source, AU$ 42.95
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Abstract
This paper relates that one often hears people say, "I am good with languages but useless at math" and vice versa as if the two were entirely opposite ways of thinking. The author points out that closer examination of human language and mathematics reveals a surprising number of similarities. The paper states that the most obvious similarity between the two is that both natural human languages and mathematics have a formal syntax i.e. a set of rules that governs them.
From the Paper
"Human languages and mathematics seem on the face of it to be very different things. One often hears people say "I am good with languages, but useless at math", and vice versa, as if the two were entirely opposite ways of thinking. However, closer examination reveals a surprising number of similarities. The most obvious similarity between the two is that both natural human languages and mathematics have a formal syntax, i.e. a set of rules that governs them. In the case of language, this is a set of rules that governs how the words may be put together. "
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Natural Human Languages and Mathematics, 2005.
This paper examines the similarities between natural human languages and mathematics.
675 words (approx. 2.7 pages), 1 source, AU$ 42.95
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Abstract
This paper relates that both natural human language and the language of mathematics have a precise formal syntax. The author points out that they both offer meaning in the form of semantics and rely upon a body of commonly held assumptions. The paper concludes that both language and mathematics formalizes the informal in order to facilitate the communication and comprehension of meaning.
From the Paper
"Upon considering the relationship between natural human language and mathematics, it becomes evident that a number of similarities exist, for both natural human language and the language of mathematics have a precise formal syntax, both offer meaning in the form of semantics, and both rely upon a body of commonly held assumptions. Each of them formalizes the informal in order to facilitate the communication and comprehension of meaning. Lewis Carroll offers examples of the relationship between natural human language and mathematics in his dialogue between the Tortoise and Achilles, for their conversation reveals how linguistic uses of logic are similar to mathematical equations."
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Language and Mathematics, 2005.
This paper explores the similarities that exist between language and mathematics.
675 words (approx. 2.7 pages), 4 sources, AU$ 42.95
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Abstract
This paper explains that obvious similarities conclude that human language may be reducible to mathematical formulation. The author points out that that mathematics consists of sets of axioms in which statements can be either true or not. The paper relates, while this does not necessarily seem very much like language, Godel's Incompleteness Theorem relates that meaning can exist outside of axiomatic sets, providing a new basis for similarity.
From the Paper
"It should not be surprising that mathematicians and linguists have drawn parallels between these two disciplines. There are obvious similarities that have made many believe that human language may be reducible to mathematical formulation. Some have even attempted to use the assumption to teach machines how to speak, constructing complex utterances based on a limited number of syntactical rules. However, these efforts and others to fully connect mathematics and language have proved largely unsuccessful. The following paper will briefly examine some of the similarities between language and mathematics. By its nature, language has a combinational structure, known as syntax or grammar, that permits the communication of complex ideas (Devlin "Born")."
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Language and Mathematics, 2005.
This paper discusses the similarities of language and mathematics.
675 words (approx. 2.7 pages), 3 sources, AU$ 42.95
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Abstract
This paper explains that language and mathematics are similar in that they both have rules. The author points out that people make assumptions when it comes to language and mathematics, which may not be proven and only are assumed to be correct. The paper relates that mathematics and language have many similarities such as syntax and semantics.
From the Paper
""Colorless green ideas sleep furiously," are words with specific meaning but put together in a sentence they clearly lack meaning (Devlin, Born). Does language and communication mean the same thing? Do the formulas for mathematics always have the same answers? Language and mathematics do not always make sense without the formal rules of syntax. People make assumptions when it comes to language and mathematics that may not be proven and only assumed to be correct. Mathematics and language have many similarities such as syntax and semantics."
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Soft Computing, 2004.
This paper reviews the development, applications, and future of soft computing.
1,125 words (approx. 4.5 pages), 5 sources, MLA, AU$ 64.95
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Abstract
In this article, the writer defines the term of soft computing as a collection of mathematical and reasoning disciplines that when incorporated into decision-making models provide a means for considering the effects of uncertainties on probably future outcomes. The writer reviews the development of soft computing and looks at applications. Further, the writer discusses the future of soft computing.
From the Paper
"Soft computing (S.C.) refers to a collection of mathematical and reasoning disciplines that when incorporated into decision-making models provide a means for considering the effects of uncertainties on probably future outcomes. The mathematical and reasoning disciplines typically included in the definition of S.C. are a probabilistic reasoning (P.R.) S.C. models allow analysts to include data characterized by imprecision uncertainty partial truth and approximation in decision analyses ... "
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Alan Lightman's "Einstein's Dreams", 2005.
Applies of theories of developmental psychology to Alan Lightman's book "Einstein's Dreams".
1,350 words (approx. 5.4 pages), 2 sources, APA, AU$ 77.95
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Abstract
This paper looks at the way Alan Lightman's novel, "Einstein' Dreams", handles Einstein's theory of the relativity of time, mainly the "elasticity" of time. The paper discusses this in terms of how it relates to adult cognitive development.
From the Paper
"Alan Lightman's book "Einstein's Dreams" is a novel that plays with Einstein's theory of the relativity of time. There is a proverb that says "a watched pot never boils". It requires some level of cognitive development to understand this proverb. It does not mean that the water in the pot will never boil. Depending on the level of heat applied to the pot, the water could boil in as quick a time as three minutes. However, for someone who stands over the pot and ..."
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Who is Rene Descartes?, 2004.
A biographical account of the life of philosopher Renee Descartes and a look at his basic philosophy.
1,125 words (approx. 4.5 pages), 3 sources, APA, AU$ 64.95
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Abstract
This paper provides a general biography of Rene Descartes, as well as a basic summary of his philosophical tenets. The paper also discusses Descartes' accomplishments in the field of mathematics as well as philosophy.
From the Paper
"Often considered the father of modern philosophy, Renee Descartes is one of the most influential ground-breaking thinkers in the history of human thought. Indeed his accomplishments go beyond the field of philosophy as he was an elite mathematician who is credited with inventing analytic geometry. However it is Descartes' work in laying the philosophic foundation for modern scientific thought that is his greatest achievement. Descartes' philosophy was deeply rooted in rationalism because he began his inquiry by questioning the very validity of the knowledge that man believes he possesses."
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