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Language and Mathematics, 2006.
Discusses the similarities between natural human languages and mathematics.
1,350 words (approx. 5.4 pages), 3 sources, AU$ 76.95
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Abstract
Normally, natural human languages and mathematics are regarded as being diametrically opposed to one another. Mathematics is formal and is marked by precision; the objects of theory must be carefully defined so that the informal can be formalized. Natural human language on the other hand is flexible, and one term can denote not just multiple meanings but opposing ones as well. This paper explains that, in spite of these differences, human language and mathematics actually share common ground such as the fact that both human language and the language of mathematics actually have a precise formal structure.
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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$ 38.95
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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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Language and Mathematics, 2005.
This paper explores the similarities that exist between language and mathematics.
675 words (approx. 2.7 pages), 4 sources, AU$ 38.95
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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, 2002.
A comparison between mathematical statements and language structures.
650 words (approx. 2.6 pages), 3 sources, AU$ 38.95
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Abstract
This essay talks about the similarity between mathematical statements and language structures. What is essential to both is that there are fixed rules which determine what mathematical symbols have meaning and what do not. Language also functions in a similar way. As Keith Devlin states, all languages are variations on a single theme (Devlin 7). Thus, Both mathematics and language are governed by particular rules that are syntactically or structurally similar.
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Human Language and Mathematics, 2007.
This paper discuses that mathematics and human language are very similar in structure and form because they can both be broken down into ever smaller functional units.
1,520 words (approx. 6.1 pages), 2 sources, MLA, AU$ 73.95
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Abstract
This paper explains that regressions are preformed all the time in mathematics, which involve the division of numbers into innate and precise formal units; however, this is not a common practice in human language other than by theorists of deconstruction techniques. The author points out that the deconstruction of language, both verbal and non-verbal, has been a practice of linguists, philosophers and critical theorists for many years. The paper relates that verbal and non-verbal human communication is comprised of both signs and symbols,which together form a recognized code, or what laymen commonly refer to as a language. The author underscores that there is a significant problem in reaching some consensus on what constitutes a verbal sign or symbol because of significant confusion regarding both meaning and intent.
From the Paper
"The solution to developing a better understanding of the relationship between sign and symbol in order to make the case for a deep similarity between human language and mathematics is to develop a more pragmatic framework within which to develop a more complete paradigm of the communicative process of verbal and non-verbal communication. Devlin does this when he speaks of the grammar generated, deep structure strings in the text of the "Language in the Mind". Some theorists say this need is a distinction that must be better developed between components of a sign to define as the signified and the signifier."
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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$ 38.95
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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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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$ 38.95
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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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Mathematics and Language, 2002.
Compares and gives similarities of mathematics and language.
650 words (approx. 2.6 pages), 2 sources, AU$ 38.95
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Abstract
This paper discusses the similarity between mathematics and language. Human languages have certain structures that facilitate the expression of ideas. These structures operate by the same rules as mathematics.
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Programming Paradigms and Mathematics, 2008.
This paper looks at programming languages that are grounded in mathematical logic.
762 words (approx. 3.0 pages), 3 sources, MLA, AU$ 39.95
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Abstract
The paper outlines the paradigms within the programming arena that have a close link to mathematical logic and provides an explanation for that link. The paper points out that it is difficult to separate the mathematical logic from the programming paradigms, which highlights how connected each programming logic is to the mathematical concepts, functions, methods and logic.
From the Paper
"The procedural paradigm refers to the programming language that specifies steps it takes to reach a desired state. Within the language the operations contain a series of steps that are completed to finalize a desired action. The object-oriented paradigm is the programming language where each object is considered a separate entity that translates processes, receives and sends data throughout the process, (Hudak 360). The objects are collectively responsible for operations, but each object has its clearly defined role within the system. Functional programming paradigm uses mathematical functions for processing and evaluating data, and focuses on the application of functions as the avenue for programming languages. The logic paradigm is the mathematical concepts for computer programming, with the programming language utilizing logic for the problem solving and model development process."
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Educational Decrease in Language and Art, 2006.
Examines the change in high school students' interests in the arts and mathematics.
2,300 words (approx. 9.2 pages), 10 sources, APA, AU$ 114.95
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Abstract
This paper discusses the general problem of decreased achievement among high school students in language arts and mathematics. It looks at the significance and impact of the problem, the interests of high school students and presents a research design to investigate the problem.
From the Paper
"The general problem is that high school students demonstrate decreased achievement levels in mathematics and language arts literacy compared to middle school levels..."
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Mathematics Instruction in English in Bilingual Classrooms, 2005.
Research proposal for examining the effects of mathematics instruction in English in bilingual classrooms.
2,211 words (approx. 8.8 pages), 14 sources, APA, AU$ 99.95
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Abstract
This paper proposes a research project that would examine the effectiveness of English instruction of mathematics on Second Grade ELL (English language learners) students as compared to the effectiveness of instruction in their native language. The proposal is in response to the controversy surrounding the issue of how best to teach mathematics to children from non-English-speaking backgrounds, since it has been found that the best way for children to learn to use mathematics to organize, understand, compare, and interpret their experiences is by making a connection between mathematics and their everyday lives. The paper examines whether ELL students should be taught how to make this connection in their native language with gradual exposure to English in language classes, or whether they should be immersed in English as early as possible. The paper includes an annotated bibliography and an observation checklist of lessons taught in class.
Introduction
Setting
Problem/Issue
Research Question
Hypothesis
Methodology
Subjects
Instrumentation
Significance of the Study
From the Paper
"Mathematics is a powerful tool for interpreting the world. Research has shown that for children to learn how to use mathematics to organize, understand, compare, and interpret their experiences, mathematics must be connected to their lives. Such connections help students to make sense of mathematics and view it as relevant. There has, however, been controversy with regard to children from non-English backgrounds and the best ways to get them to make those connections. Questions are raised regarding how to instruct these children who are referred to as English language learners (ELL?s). Should they initially be taught in their native language with gradual exposure to English in language classes, or should they be immersed in English as early as possible."
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Philosophy of Mathematics, 2007.
An analysis of the universal nature of mathematics and developments in the philosophy of mathematics.
1,899 words (approx. 7.6 pages), 6 sources, APA, AU$ 87.95
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Abstract
This paper considers some of the major developments in the philosophy of mathematics regarding the capacity of mathematics to be universally valid and applicable. It presents some of the basic arguments and schools of thought of the philosophy of mathematics. The paper then analyzes whether, at its foundation, mathematics can have a legitimate claim to be universal.
Table of Contents:
The Problem Of The Ideal And The Real
Math As Logic
Math As Structure
Application And Universality
From the Paper
"This problem, Russell's paradox, proved to be an intractable problem for Frege which, after it was pointed out to him, he could not overcome. The impact upon the philosophy of math was major. An important attempt to boil math down to logical principles had proven unsuccessfully, and eventual efforts to rescue the project by Russell and others were unable to develop a logicism that showed math as both consistent and complete. Therefore math cannot be said to be universal by appeal to logic alone."
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A History of Mathematics, 2002.
This paper discusses some aspects of the history of mathematics from the earliest mathematical records to the modern era.
1,400 words (approx. 5.6 pages), 9 sources, AU$ 76.95
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Abstract
This paper only touches on some selected aspects of a broad and encompassing subject. The author begins by outlining some of the key developments as a whole before further subdividing into three sections: Greek mathematical developments; Chinese and Middle Eastern developments; and Western developments. The paper concludes by drawing attention to the enormous scope of the history of mathematics.
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Mathematics Pedagogy, 2005.
This paper discusses of teaching mathematics.
3,825 words (approx. 15.3 pages), 13 sources, AU$ 219.95
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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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Stephan Korner's "The Philosophy of Mathematics", 2004.
Summary and review of Stephan Korner's "The Philosophy of Mathematics: An Introductory Essay".
1,091 words (approx. 4.4 pages), 2 sources, MLA, AU$ 55.95
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Abstract
The first part of this paper expounds on Stephan Korner's discussion, in "The Philosophy of Mathematics, of the nature of mathematics, and the three main schools of thought relating mathematics to philosophy. The paper continues with a discussion on logicism and why it provides the clearest way to look at mathematical concepts and the best way to explain mathematical philosophy.
From the Paper
"Mathematics is an indispensable science that justifies and confirms many aspects of other scientific subject matter. Mathematics relies on conclusions not assumptions and evidence is required to confirm theoretical entities as true. Of course the debates exist as to which school of thought holds the most validity. Mathematical realism will always be different to each of these philosophical schools and arguments can be found to both support and reject each school of thought."
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Mathematics and Art, 2008.
A comparative analysis of the disciplines of mathematics and art.
2,332 words (approx. 9.3 pages), 10 sources, MLA, AU$ 103.95
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Abstract
This paper discusses how mathematics is often treated as a distant and very different discipline from the arts even though the arts make use of mathematics in a number of ways. In particular, the paper looks at how paintings, drawings, and designs can be analyzed according to mathematical principles to see ways in which the artist balances different shapes and forms according to mathematical principles or draws on mathematical theory for inspiration. The paper also examines how the art of different periods may reflect different mathematical ideas.
From the Paper
"The classical era was one in which mathematics was used quite consciously in developing artistic styles, and some of these styles have even been named with mathematical references. The artworks of a given era reflect the formalist, social, and economic realities of the period, exemplifying the prevailing artistic styles and the social and economic structures which influence the arts. In Greek art, the Geometric period was an era which produced a good deal of pottery and other geometrically regular works. The Geometric krater from the Dipylon cemetery from the eighth century B.C. (De La Croix, Tansey, and Kirkpatrick 130) exemplifies the style of the period. The Geometric period is the name given to the era between the end of the Mycenaean age and the beginning of the Classic age. "
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