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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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Godel's Theorem, 2008.
A discussion as the to the proof or lack thereof in support of Godel's theorem of the self-awareness of machines.
1,358 words (approx. 5.4 pages), 3 sources, MLA, $ 45.95
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Abstract
This paper discusses Godel's theorem and its lack of proof, absolute or otherwise, that machines do or may in the future experience self-awareness of one type or another. It discusses the assertions of the theory and the problems with it. The paper then provides a personal response, by the writer, to the issue of the present and future self-consciousness of machines.
Table of Contents:
Discussion
Response
From the Paper
"Free will is a concept that cannot be even remotely defined with any degree of consensus. Talking about free will with religious groups results in completely different concepts of free will than when talking with political groups or academic groups or any number of different types of groups. Conversely, arithmetic calculations are easy to quantify and easy to define within the confines of the overall system. Somehow Smullyan would like his readers to believe that defining free will is as self-apparent as 2 plus 2 or similar arithmetic equation. Some researchers have described Godel's Theorem as being some type of alternate description of a value system: "The system of values could be part of the program the computer followed in making its choices. The computer system would then appear to have those values, and be guided by them (Machina 3). Thus Smullyan's entire argument regarding free will is based on a number of unfounded and unproven assertions that have no basis except in extreme positives or negatives. These equate to a world that is either black or white and all decisions are, ultimately, yes or no questions."
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Stock Charting Techniques, 2007.
This paper discuses stock charting techniques and presents five examples.
1,135 words (approx. 4.5 pages), 7 sources, MLA, $ 39.95
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Abstract
This paper explains that charting, in its most basic forms, is used to put fundamental measurements from an observation into a rational way of thinking ,thus bringing clarity to confusion. The author points out that charting primarily is dependent upon what data is being analyzed and who is doing the analysis. The paper stresses that charting can often become confusing because people make charts that display too much data within a single chart. Five charting techniques are illustrated in this paper: bar chart, candlestick charting, line charts, point and figure charts and three line break charts.
Table of Contents:
Introduction
Charting Rationale
Charting Techniques
Charting Types
The Bar chart
Candlestick Charting
Line Charts
Point & Figure chart
Three Line Break Chart
Conclusion
From the Paper
"This type of charting shown below is very similar to that of the bar chart. Except during the period between the open of trading and the close of trading a solid thick line is drawn in during the time-period in question. The same line appears in the bar chart but is not as defined and is the section between the open and last trade. Often this type of charting is used to analyze the short term forecasts of the stock. In addition to this the basic solid square represents a day which closes with a low and the open square in the chart represents a day where closing is on a high note/price."
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Godel's Theorem, 2008.
An analysis of the advantages of Godel's theorem within mathematics.
1,596 words (approx. 6.4 pages), 5 sources, MLA, $ 52.95
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Abstract
This paper explains Godel's theorem and its application to the machine mind. It describes the advantages of Godel's theorem in mathematics and how it is used in practice by mathematicians who lack understanding of a specific principle. The paper also provides the writer's opinion of the use of the theorem and suggests that it is almost commonsensical in nature.
Table of Contents:
Response to Postings
Discussion
From the Paper
"This could in fact be yet another referral to Cherniak's Riddle but that fact would only be left to the literary critic to decide and because human language is a series of referential signs and symbols that always refer to something else this could never be known absolutely. Here is the key difference in the two languages in question. When a mathematical principle is discovered and proven it is self evident to all and taken as fact. When a literary concept is created it is, conversely, always up for debate and its meaning always at play. Thus, Godel's theorem is both an apologetic and a principle best left explained in the language it was conceived in--mathematics."
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Math Lesson in Literature, 2007.
This paper looks at Eric Carle's book 'The Grouchy Lady Bug' and discusses grade one mathematics lessons involving literature.
1,077 words (approx. 4.3 pages), 3 sources, MLA, $ 37.95
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Abstract
In this article, the writer discusses how Eric Carle's 'The Grouchy Lady Bug' may be used as a first grade math tool. The writer notes that although a number of printed and Internet sources have already expressed how to adapt this book for student exercises in mathematics and literature, this book shows itself amenable to other lessons a teacher devises, directly from the book in relation to what the curriculum must cover. The writer concludes that in its seeming lack of limitation for grade one learners, and others, the book can be strongly recommended to teachers accustomed to using literary and visual sources in the teaching of elementary mathematics.
Outline:
Introduction
Class Activities
Examining the Text
Concluding Remarks
Works Cited
From the Paper
"To generate interest in a book that will be used for a number of lessons, learners can be helped to talk about the ladybug in general. Some Grade One students will say that they have seen one, and others can state words they would use to describe a ladybug to someone who had never seen one. Other students will answer questions as to how large a ladybug is in relation to other things in the room, reinforcing ideas of larger than and smaller than, the teacher framing questions that can be answered in simple responses of "Yes" or "No". Grade One students will giggle when asked if a ladybug is larger than the teacher's chair, or smaller than a speck on the ceiling, if it would fit in the teacher's pocket or handbag, or if a ladybug is larger than a cat? If the teacher had a pet ladybug, would he need to take it for walks?"
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Godel's Theorem, 2007.
A review of Godel's theorem and the limitations of an allegory in trying to understand it.
1,495 words (approx. 6.0 pages), 5 sources, MLA, $ 49.95
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Abstract
This paper discusses Godel's theorem and how it is sometimes used to imply that all machine logic can eventually become self-aware. The paper also discusses the criticisms of the theorem and its limitations. The paper then provides an allegory to explain Godel's theorem and discusses the advantages of this explanation, as well as the limitations in using an allegory to try to understand the theorem.
Table of Contents:
Allegory and Godel: Oil and Water
From the Paper
"Godel recognizes that his theory in fact could not be fully described in human language and concepts and this is a fact that Hofstadter completely misses. When Godel is quoted as saying the epistemological descriptions in a given language cannot be restated in that same language, he directly disallows the use of allegory in retelling his theory. The unfortunate aspect of Hofstadter's allegory is that most readers get lost in trying to decide what the various characters represent, what is meant by the way the dialogue is spoken and, ultimately, what the Omega record player looks like. None of which, of course, has anything to do with Godel's Theorem."
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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, $ 60.95
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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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The Lookback Option, 2007.
This paper discuses lookback options, an "exotic" nonstandard option type as compared to its opposite the usual "vanilla" standard options.
2,960 words (approx. 11.8 pages), 12 sources, MLA, $ 87.95
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Abstract
This paper explains that a lookback option is path dependent, based on the maximum or minimum underlying value reached during the entire life of the option. The author points out that, at the expiration date of these options, the holder may "look back" over the life of the option and exercise it, based on the optimal underlying value achieved during that period thus giving the holder the ability to buy an asset at its lowest price or sell it at its highest price achieved over the life of the option. The paper relates that, through the lookback option, the investor can achieve economic intelligence and value through the benefit of hindsight; however, lookback options carry risk and are more expensive than standard options. The paper includes several formulas.
Table of Contents
Definition of Options
Call and Put Options
Introduction to Lookback Options
Lookback Options in Greater Depth
The Model
Option Pricing
Discrete Lookback Options
Case Study of Lookback Options
From the Paper
"Put options conversely involve the investor aiming for a stock price decrease. The put option, as mentioned in the introduction, allows the holder to sell an asset by a particular date for a certain price. An example demonstrated by Hull (2006) involves a European option involving an investor who buys the option to sell 100 shares with IBM for a strike price of $70. If the current stock price is $65 and the expiration date is in three months, Hull supposes for example that the option to sell one IBM share is $7. The initial investment, therefore, will be $700."
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Manipulatives, 2007.
This paper researches the use of manipulatives in the field of mathematics.
3,446 words (approx. 13.8 pages), 37 sources, MLA, $ 97.95
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Abstract
In this article, the writer researches hands-on manipulatives use in mathematics. This work explores the historical perspective, the effects on education and the supporting theories. In addition, the writer looks at what research has been thus far conducted. Finally, this work researches the special benefits of using algebra tiles. The writer maintains that it is significant to note that algebraic functions are mathematical processes involving abstract or symbolic representation. The writer concludes that it is quite difficult for the beginning algebra student to conceptualize the processes and functions of algebra; however, the use of manipulatives has been shown to assist in this area, making their use in algebra instruction particularly effective in classroom instruction.
Outline:
Objective
Introduction
What are Math Manipulatives?
Why Use Math Manipulatives?
How Should a Teacher Use Math Munipulatives?
Summary
What
Why
How
From the Paper
"Today's mathematics teacher has many resources that are available in assisting the development of appropriate curricula that meets the content standards of the NCTM. Not only are standard tools available but the Internet also offers several web-based learning activities that assist mathematics learning and instruction. Before this development, the teacher often would contact businesses in the community in order to obtain 'real-world' manipulatives for use in the classroom. The work of Shield holds that web-based tools motivate students in learning mathematics content but also the delivery of the information is interesting to the student."
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Hands-On Manipulative in School, 2007.
An exploration of the use of the hands-on manipulatives in the middle school math classroom
3,876 words (approx. 15.5 pages), 25 sources, MLA, $ 106.95
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Abstract
This paper reviews findings in literature stating that hands-on manipulatives are effective in the middle school mathematics classroom. The paper then reports that the findings are of limitations in the use of manipulatives and, specifically, in the misuse of the manipulatives in the classroom. The paper further emphasizes that teachers must be well-educated and trained in the use of manipulatives, whether concrete material or virtual manipulatives for use on the computer and the Web. The paper concludes that it is clear that the use of manipulatives in mathematical instruction and learning in combination with cooperative learning is the best practice for instructional methods in today's mathematics classroom.
Outline:
Objective
Introduction
Historical Perspective
Theories
Research Studies
Virtual Manipulatives
Limitations
Static and Dynamic
Algebra Manipulatives
Summary
From the Paper
"The slide-rule is a manipulative that was used in early education in providing students with a hands-on application in mathematics. Hands-on manipulatives such as blocks, rods, bean sticks and other manipulatives have been historically used in the math classroom as an aid in teaching mathematics. The work of Clements (1999) entitled; 'Concrete Manipulatives, Concrete Ideas" published in the Journal of Contemporary Issues in Early Childhood states that: "The notion of 'concrete' from concrete manipulatives to pedagogical sequences such as 'concrete to abstract' is embedded in educational theories, research and practice, especially in mathematics education."
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George Polya, 2007.
A discussion of the life and career of mathematician George Polya.
1,234 words (approx. 4.9 pages), 3 sources, MLA, $ 42.95
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Abstract
The paper discusses the Hungarian mathematician, George Polya and relates that he is hailed by many as not only one of the greatest mathematicians, but also a great teacher of his time. The paper examines his schooling, his studies in university and the path to his career in mathematics. The paper details all his various accomplishments and promotions.
From the Paper
"Polya's parents, Anna and Jakab, were both Jewish. Jakab's original surname was in fact Pollak, but he changed this for the sake of his professional goals. After his law firm failed, he worked for an international insurance company. However, Jakab's dream was to obtain a research post at a university and pursue his true interests, economics and statistics. It appears therefore that George inherited not only his father's tenacity, but also his interest in numbers. In 1882 Jakab Polya was finally appointed as Privatdozent at the University of Budapest."
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William Gosset, 2007.
A description of th life and achievements of William Sealey Gosset in the realm of statistics.
863 words (approx. 3.5 pages), 2 sources, MLA, $ 30.95
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Abstract
This paper discusses the life and work of William Sealey Gosset, who was one of the leading statisticians of his time, particularly with his work on the concept of standard deviation in small samples. It gives examples of some of his achievements in the realm of statistics. The paper describes Gosset as both brilliant in his professional work as a chemist and statistician and as a loved and respected man.
From the Paper
"After Gosset had worked for many years developing the practical application of his theory, he was involved in a terrible car accident in 1934 which left him incapacitated for many months. During this time, he had the opportunity to continue to work on his statistical work. He recovered enough after a year to move to London where he became the head brewer and scientist of production at a new Guinness brewery. Gosset continued to publish the results of his statistical findings while working in London. He did not hold his position there long as he died in Beaconsfield, England, on October 16, 1937 (O'Connor and Robertson)."
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Reading and Math, 2007.
This paper discusses the role of reading in mathematics.
2,280 words (approx. 9.1 pages), 7 sources, MLA, $ 70.95
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Abstract
The paper explores the connection between math and reading skills and how to improve both skills in students. The paper explains that it may be that the same areas of the brain are used for arithmetic and phonological skills. The paper discusses how the critical problem facing the adoption of new techniques, such as the use of journals in the math classroom, is that teachers do not have the support needed to continue with the new technique.
Outline:
Why is Reading Important to Math?
Strategies for Improvement
Conclusion
From the Paper
"Reading and math were historically thought to be in no way connected. Much time in primary math classes are spent memorizing math facts. With the exception of the occasional word problem, reading skills were virtually ignored as a component of math success. However, the role of inquiry in mathematics is gaining importance as the role of critical thinking becomes tied to the job skills needed as an adult. The new technology paradigm requires the adult to be able to analyze complex situations and to develop solutions to the problems that they encounter."
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