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Measures of Central Tendency, 2008.
Discusses measures of central tendency and their respective applications.
1,475 words (approx. 5.9 pages), 5 sources, APA, $ 48.95
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Abstract
This paper first explains that measures of central tendency are those descriptive statistics that describe the point or points about which a distribution centers. The paper then provides a description of the three measures which are used to describe central tendency and identify the advantages and disadvantages of each, as well as describing a situation in which each of these measures might be used. A summary of the research and salient findings are presented in the conclusion.
Table of Contents:
Review and Discussion
Introduction
Mean
Median
Mode
Summary and Recapitulation
Table:Summary of the Three Measures of Central Tendency
Conclusion
From the Paper
"This measure of central tendency is sometimes referred to as the arithmetic mean or "average". According to Cai, Lo and Watanabe (2002), seven properties of the arithmetic average are as follows: (a) the average is located between the extreme values; (b) the sum of the deviations from the average is zero; (c) the average is influenced by values other than the average; (d) the average does not necessarily equal one of the values that was summed; (e) the average can be a fraction that has no counterpart in physical reality; (f) a value of zero."
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Science and Math, 2008.
This paper discusses the teaching of math and science and looks at both traditional and more innovative ways of teaching.
943 words (approx. 3.8 pages), 4 sources, APA, $ 33.95
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Abstract
In this article, the writer discusses how the reform movements impacted the teaching of math and science. In addition, the writer looks at the differences between traditional teaching and current practices in mathematics and science. The writer notes that the absence of a national curriculum means that how children learn varies greatly, yet the increased demand for accountability through frequent national standardized assessment limits curricular innovation on the part of teachers, as more conceptual learning may be more time-consuming and take longer to show immediate results. Additionally, the writer points out that current educators may not be familiar in the ways to teach such subjects. The writer concludes that when contemplating educational reform in math and science, America seems to be caught in a paradox--America demands quick, demonstrable improvement but is unwilling to relinquish local control, current testing standards, or different ways to fund and teach scientific and mathematical concepts.
From the Paper
"Ever since Horace Mann began his innovative educational reforms in the public schools programs of the 19th century, American education has tended to stress practical skills in its curricular approach and local control of schools. These two impulses have often existed in tension, as Americans have strived to remain competitive in math and science education and wish to see gains in the performance on standardized tests by its nation's youth. However, there is often great resistance to changes in the ways that such subjects are taught and standards are set by government agencies.
"Math and science education is seen as vital for the nation, economically, and also in terms of its national security. The resolve to put a man on the moon was accompanied by a new emphasis in technical education. "
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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, $ 71.95
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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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Strategy/Implicit Instruction, 2008.
This paper explores the strategy/implicit instructional strategy as suitable for a middle school mathematics class.
1,117 words (approx. 4.5 pages), 3 sources, APA, $ 38.95
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Abstract
The paper explains that strategy/implicit instruction is a student-centered approach, which focuses on the general skills, rules and processes required for learning a particular concept. The paper highlights the advantages of using this method and refers to several literary sources on the strategy/implicit instruction. The paper presents the conclusion that the combination of strategy/implicit instruction and direct instruction is the ideal method for teaching mathematics in the classroom.
From the Paper
"In order to make the right decision concerning the choice of instructional strategy for middle school mathematics class it appears necessary to take into consideration the general school mathematics standards and the peculiar needs, behaviors and interests of middle school students. Besides complying with the standards, an efficient strategy should promote successful and productive learning. When it comes to middle school, the instructional elements, which could be extremely useful, are the following: clear routines, integrated curriculum, cooperative groups, combination of challenge and support, resorting to real-life connections. All of the above can provide valuable assistance to the teacher. The environment in the class should promote inquiry- and project-based, cooperative instruction. Engaging activities and connections with real life are sure to increase students' motivation and involvement. Thus, the challenging material will be easily tackled by them."
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Contextual Factors in the Classroom, 2008.
This paper explores how contextual factors affect the teaching/learning process in the mathematical classroom.
1,637 words (approx. 6.5 pages), 2 sources, APA, $ 53.95
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Abstract
The paper discusses community, classroom and student characteristics that include geographic factors, community and school population, socio-economics, race/ethnicity, community stability and classroom rules and routines, grouping patterns, scheduling and arrangement and how they affect the teaching/learning process. The paper explains that contextual factors also acknowledge the impact of aspects like attitudes, perceptions, expectations, abilities, gender, socio-cultural background and maturity on every learning experience. The paper also looks at how community, classroom and student characteristics influence instructional planning and assessment.
From the Paper
"It generally goes without saying that contextual factors play an important role in mathematical classroom via the way they affect the teaching/learning process. Among these factors are environmental (geographic location), community and school population, socio-economics, race/ethnicity, community stability, political climate and community support for education as well as classroom factors represented by rules and routines, grouping patterns, scheduling and classroom arrangement. Student characteristics should also be examined when designing instruction and assessing learning, such as age, gender, race/ethnicity, special needs, achievement/developmental levels, culture, language, interests, learning styles/modalities and skill levels."
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Student Groups and Achievement, 2008.
This paper presents a study to determine whether tracking of students in math increases state standardized testing achievements.
2,494 words (approx. 10.0 pages), 18 sources, APA, $ 75.95
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Abstract
The paper explores whether tracking groups for students according to non-biased indicators will allow the students to increase their state testing scores in math. The paper defines the relevant terms, provides a literature review, outlines the methodology and research designs and explains the anticipated outcomes.
Outline:
Introduction
Statement of the Problem and Purpose of the Study
Background and Significance of the Problem
Definitions and Terms
Literature Review
Research Questions
Brief Description of the Methodology and Research Design
Anticipated Outcomes
From the Paper
"The work entitled: "Equitable Practices" states that "...despite prevailing practices, research over the last two decades has demonstrated the negative results of sorting students according to perceived motivation or ability." (NWREL, 2001) Furthermore, research had indicated that lower tracks tend to be disproportionately composed of lower-income and ethnic minority students, thus compounding the disadvantage many students already face." (NWREL, 2001) The data also has indicated that "in some cases students of color with the necessary scores for high-track placements are less likely to be placed in those classes than their European American peers." (NWREL, 2001)"
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Summer Mathematics Program, 2008.
A literature review in preparation for the development of a summer mathematics program.
4,625 words (approx. 18.5 pages), 16 sources, APA, $ 119.95
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Abstract
This paper explains the importance of a summer mathematic program is because of new requirements in Michigan, which will immediately endanger the graduation track of students who struggle early in their ninth grade Algebra course. The author presents the rational for a summer support algebra program and reviews the literature upon which to develop the project. The paper summarizes this literature by stating the need for new innovative methods of teaching specifically relevant to the instruction of Algebra. In addition, the author states that the traditional algebra instruction methods have left a generation of students who not only see no practical need for algebra but also view it as a frivolous waste of academic time and resources.
Table of Contents:
Introduction
Problem Statement
Importance and Rationale of the Project
Background of the Project
Statement of Purpose
Research Objectives
Limitations of the Project
Literature Review
Mathematics Curricula
Computer-Assisted Instruction (CAI) Programs
Instructional Process Programs
Summary
From the Paper
"Another program used in addressing student achievement in Algebra is 'The Algebra Online Program' as reported by the Louisiana Department of Education - Center for Educational Technology. This program involved a team of planners all of whom are certified in teaching mathematics who met to discuss, design, format, supplementary textbook selection and implementation of the course. This is a distance-learning curriculum."
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Mario Livio's "The Golden Ratio", 2008.
A review of Mario Livio's book "The Golden Ratio: The Story of Phi, the World's Most Astonishing Number', which chronicles the history of this number.
1,260 words (approx. 5.0 pages), 1 source, APA, $ 42.95
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Abstract
This paper explains that Mario Livio's book "The Golden Ratio: The Story of Phi, the World's Most Astonishing Number", chronicles the history of, not of a person, thing, or concept, but a number. The paper then relates that this number phi, or notion of proportionality or the 'Golden Ratio', however, has been invested with so much cultural, emotional, and religious importance that it has taken on a character of its own. Next, the paper points out that the reason that phi is astonishing is because, for centuries, our fascination with proportion and beauty has made its properties an object of wonder. The paper concludes that, although Livio ultimately deflates the mystery of phi, his book is a helpful explanation not just of the number but also of why balance and symmetry dominates so many modern discussions of art and architecture.
From the Paper
"But ultimately, astrophysicist Mario Livio says that creating this mysterious proportion is no different than a person cutting a piece of string into pieces. While the 'Golden Ratio' appears in many natural phenomena, some supposed appearances are really not true 'Golden Ratios' (such as the Pyramids and Parthenon) and all appearance of perfection is based in human notions of proportionality. It is evidence of humans looking at nature, not that nature or God through nature looking back at us. We see perfection and proportionality because we are looking for it in nature."
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H.E. Huntley's "The Divine Proportion", 2008.
A review of H.E. Huntley's book, "The Divine Proportion", which argues that mathematics can be beautiful.
1,175 words (approx. 4.7 pages), 1 source, APA, $ 40.95
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Abstract
This paper explains that H.E. Huntley, in his book "The Divine Proportion" claims that beauty exists as a principle, which is external and transcendent to any individual human being's ability to create either equations or art. The paper also discusses Huntley's arguement that the 'Golden Ratio', also known as phi, is the supreme proof that God is a mathematician and that the mathematician and creator God appreciates nature. The paper concludes that Huntley's book is clearly not aimed at mathematicians, given that he is trying to defend his profession and the beauty of math; however, most people lacking fairly solid math skills would find this book a very difficult read, except for its first and last chapters.
From the Paper
"Huntley's last chapters shift somewhat from the defense of the 'Golden Ratio' as proof of the existence of universal ideals of beauty and proportionality, and moves on into a more general defense of mathematics as a discipline that is in pursuit of beauty no less than sculpture or art. But why does mathematics need to defend itself as beautiful, to hold its place beside art, poetry, and philosophy? The divisions between the disciplines that did not exist for the ancient Greeks say more about the development of our culture into a split between the sciences and the arts than a failure to recognize the capabilities of mathematics' contribution to the world in general."
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Technology in the Classroom, 2008.
An Instructional Technology Plan for the use of technology in teaching maths.
1,338 words (approx. 5.4 pages), 1 source, APA, $ 44.95
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Abstract
The paper looks at an article "Enhancing Curriculum and Instruction Through Technology" by S. Rigeman and N. McIntire that outlines some ways in which computer technology can help students in middle and high school classrooms bolster their math skills and give classroom instructors a tool with which to be more responsive to the varied needs of their pupils. The paper discusses some of the limitations inherent in using the Rigeman and McIntire math program and presents an alternative Instructional Technology Plan. The paper supports interactive computer technology which allows students to move at their own pace and in an individualized context.
From the Paper
"To begin with, Sally Rigeman and Nancy McIntire (2005) state that Iowa's Area Education Agencies (AEA) district superintendents met recently to discuss how technology could be applied to the augmentation of classroom instruction. 17 of Iowa's 21 AEA districts chose to participate in the implementation of a "technology-rich, research-based, National Science Foundation (NSF)-designated 'exemplary' mathematics program - Cognitive Tutor Algebra I" (Rigeman & McIntire, 2005, p.31). The other four districts stayed with their existing math programs (all of which were NSF-approved) and acted as controls (Rigeman & McIntire, 2005). The Cognitive Tutor Algebra I curriculum used 6 research -based strategies in shaping student learning: "real-world situations; mastery learning; cooperative learning; direct instruction; group and individual presentations; and student use of technology" (Rigeman & McIntire, 2005, p.31). Within the Cognitive Tutor Algebra I classrooms of the participating districts, teachers actually guided classroom instruction about 60 percent of the time while students used the other 40 percent of the time to progress sequentially through sections of the Computer Tutor program at their own pace; the program, apparently, is also geared to accommodate the individual needs of students, as well."
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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, $ 27.95
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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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Linear Transformation, 2008.
An analysis of linear transformation and its applications.
1,060 words (approx. 4.2 pages), 3 sources, APA, $ 37.95
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Abstract
The paper is an in depth explanatory narrative on the subject of linear transformation. After an analytical definition of the term, the paper gives examples of the many applications of linear transformation and explains that linear transformation is a method of altering geometric figures into another form. The paper also explains the basic requirements for this and quotes examples. The paper also provides descriptive explanations of linear transformation (also referred to as the algebra of matrices )and interprets how the process occurs. The paper further relates an extensive explanation on conic sections and how they are determined. Throughout the paper the various terms are fully explained together with examples and methods of application.
From the Paper
"For then transformation (of the plane), let S be the set of points in the plane. A transformation of the plane is then a one-to-one mapping from S to S. The most important transformations of the plane are the linear transformations, meaning those that can be represented by linear equations. For a linear transformation T, there are constants a, b, c, d, h and k such that T maps the point P with coordinates (x, y) to the point P' with coordinates (x', y') where h = k = 0. The origin O is a fixed point, since T maps O to itself, at which point the transformation can be written x' = Ax. Such transformations include rotations about O, reflections in lines through O, and dilatations from O. Translations are examples of linear transformations in which O is not a fixed point."
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Origins and Significance of Hyperbolic Geometry, 2008.
An analysis of the origins and importance of hyperbolic (non-Euclidean) geometry.
1,279 words (approx. 5.1 pages), 6 sources, MLA, $ 43.95
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Abstract
This paper examines the origins and significance of hyperbolic geometry. Specifically,it briefly discusses the men who conceived of it, as well as how hyperbolic geometry differs from Euclidean geometry. Finally, and most importantly, the paper looks at the significance of hyperbolic geometry when it comes to exploring the universe around us.
From the Paper
"Delving deeper, the contemporary significance of non-Euclidean geometry grows more and more unavoidable - even to those disinclined to give it its "due". For one thing, it is well-known that hyperbolic geometry has shed some light on the immersion and curvature of spaces. More importantly, Einstein's theory of relativity is, at least in part, indebted to non-Euclidean geometry - though it is admittedly not clear from the available literature the precise extent to which hyperbolic geometry made his revolutionary findings vis-a-vis relativity possible. In any event, this writer - drawing upon course work completed in previous introductory classes that dealt with geometry and its relationship to modern cosmology - would be remiss if he did not also point out the fact that the "empty" regions in outer space where no matter exists can really only be described adequately using a hyperbolic model. In effect, understanding the Hubble Constant involves understanding and appreciating non-Euclidean, hyperbolic geometry."
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Symmetry in Islamic Art, 2008.
This paper explains how geometric concepts can be taught based on the symmetry found in Islamic art.
2,537 words (approx. 10.1 pages), 13 sources, MLA, $ 76.95
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Abstract
The paper looks at the extensive use of geometric and symmetrical patterns in Islamic art. The paper provides a definition of geometry and looks at translations, rotations and reflections in Islamic art. The paper then examines the mathematics of symmetry and how symmetry, as manifested in Islamic art, can be utilized to teach geometry in the contemporary classroom.
Outline:
Introduction
Symmetry in Islamic art, Part I
Symmetry in Islamic Art, Part II
Symmetry in Islamic Art, Part III
From the Paper
"Many civilizations have long used artistic designs for a variety of purposes. For instance, some civilizations have used artistic designs for emblematic purposes, while some have used artistic designs for ornamental and/or architectural purposes; still others, perhaps unsurprisingly, have used artistic designs for spiritual symbolism. Another thing that is not at all a surprise is that artistic designs almost invariably utilize mathematical concepts. Specifically, within the Islamic art tradition, there has long been the extensive use of geometric and symmetrical patterns - so much so that it may be put forward that one of the defining features of Islamic art is its ability to incorporate mathematical concepts and ideas in ways that are rich, vibrant and aesthetically pleasing."
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The Mathematical Contributions of Galileo, 2008.
A review of some of the important contributions of Galileo Galilei to the field of mathematics and science.
1,015 words (approx. 4.1 pages), 3 sources, MLA, $ 35.95
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Abstract
This paper discusses the significant contributions of Galileo Galilei to the field of mathematics. It provides a brief history of his life and then focuses on some examples of the contributions that he made to mathematics. The paper also discusses his misinterpreted-battle between science and religion and how it overshadows many of the other contributions that Galileo made during his lifetime as a scientist and mathematician.
From the Paper
"We often hear of a Copernican revolution in science, but Galileo was the instigator of a much more fundamental revolution that influenced both science and mathematics. The worldview that Galileo created to replace the Aristotelian worldview that dominated at the time contended that the world was made up only of matter whose properties and motions could be described in terms of mathematics (Machamer). In other words, Galileo advanced the now-obvious notion that mathematics was nothing short of the language of the universe. Using mathematics, Galileo was able to describe and understand the mechanics of the universe, effectively gaining a deeper understanding of the way that the world is put together. This is Galileo's most significant contribution to mathematics. He removed the idle, superstitious philosophy from the study of the natural world and pushed mathematics to the forefront of natural inquiries, demonstrating again and again that it could be used to understand the way the world works."
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Napier's Logarithms, 2008.
This paper discusses the historical development of Napier's logarithms and their lack of a base with current logarithms, which employ a base 10.
2,090 words (approx. 8.4 pages), 5 sources, MLA, $ 65.95
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Abstract
This paper explains that John Napier, in 1614, took an algebraic approach by defining logarithms as a ratio of two distances within a geometric pattern, base 1/e, which substituted for his lack of a base as in the currently used common logarithmic base 10. The author points out that the real benefit of these logarithms was that they simplified mathematical calculations by providing a shortcut for exponential factors just as exponents are a shortcut for multiplication. The paper relates that, since Napier's original logarithms lacked a common base, they were more consistently accurate but not as easy to manipulate as the common logarithms employed today. The author states that the common logarithms are much easier to calculate but only sufficiently accurate as compared to Napier's original logarithms. The paper includes graphs.
Table of Contents:
Introduction
Historical Background
Napier's Logarithms
Base 10 Logarithms
Conclusion
From the Paper
"While initially Napier's logarithms did not employ a base in the traditional sense he eventually adjusted his logarithms to account for a consistent base in much the same way they are currently employed today. Napier worked with another mathematician, a man by the name of Henry Briggs, to change his logarithmic forms to the form now currently common which is the L/e equation. Thus, Naperian logarithms now are described as points that are moving along a straight trajectory and indicated by units prescribed in length."
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Stepran's Infinity Puzzle, 2008.
This paper discuses Stepran's infinity puzzle as an excellent method to explore the character of infinity relative to tangible outcomes.
1,625 words (approx. 6.5 pages), 3 sources, MLA, $ 52.95
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Abstract
This paper explains that the solution to Stepran's infinity puzzle
is not so difficult and has nothing to do with infinity, although the calculus of this equation may in fact be infinite. The author underscores that the puzzle is not a puzzle at all and is not indicative of infinity but rather is purely an exercise in the limitations of physics. The paper agrees with Rucker's concept of infinity as simply a natural element of the universe or of being one of the basic functional elements of mathematical device. The author concludes that the useful concept of infinity is that it does naturally occupy points in both physical and mathematical space ,which truly cements it within the context of a tangible mathematical and physics principle rather than some far-off rationale construct created and identifiable only by mathematical theorists.
Table of Contents:
The Puzzle
The Solution
Response Page to Postings
Discussion
From the Paper
"Stepran's states that a person is tasked with turning a light switch off and on starting with on at 2 minutes and then in increments by half of the time remaining flipping the switch to the opposite position. On the surface the outcome appears as if it will be a simple persuasion of the ineluctable quality of time; that, time is unavoidable and all things must come to an end. Yet, as one begins the calculations it becomes apparent that the half increments are, apparently, infinite starting with two in terms of seconds: 120, 60, 30, 15, 7.5, 3.75, 1.875, .93, .46, .23, .117, .058, .029, ad infinitum, at least to the extent that a common calculator is capable of dividing."
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Industrial Relations and Game Theory, 2007.
This paper applies game theory (GT) to industrial relations, especially in the area of collective bargaining.
1,770 words (approx. 7.1 pages), 12 sources, APA, $ 57.95
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Abstract
This paper explains that industrial relations within the context of the British economy and the character of its workforce have long been dominated by the power and presence of its unions. The author points out that, because of the stakes involved in the collective bargaining negotiations, game theory (GT) and coalition theory, which is a subset of GT, is relied upon to achieve fractional improvements in contract negotiations. The paper relates that game theory (GT) is most often associated with a zero-sum scenario; however, it also encompasses positive-sum and negative-sum scenarios where a party may gain or win without the necessity of an equivalent loser. The author relates that, because of the necessity to form alliances in order to reach consensus among diverse stakeholders, industrial relations often employ a type of GT known as coalition theory,which examines the nature, reasons and underlying dynamics of these coalitions that form in all the various settings. The paper includes graphs.
Table of Contents
Introduction
Game Theory
Industrial Relations and Game Theory
Conclusion
From the Paper
"Of particular value has been research integrating sender-receiver frameworks that analyze how knowledge is transferred, both symmetrically and asymmetrically, with GT whereby advantages gained through asymmetrical knowledge transfer creates zero-sum advantages for one player or the other in an industrial relations setting such as the collective bargaining platform. This concept is explained in terms of being a signal that one side uses to inform the other of a possible solution, such as concessions that can be made on benefits."
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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, $ 50.95
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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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