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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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