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Karl Gauss, 2002.
An examination of the many theories developed by Karl Gauss, a famous mathematician, (1777-1855).
1,221 words (approx. 4.9 pages), 3 sources, MLA, $ 41.95
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Abstract
This paper looks at the life and work of Karl Gauss. It examines his theory on Plate Tectonics, the theory of Motion of Heavenly Bodies and several other theories that were developed during his lifetime. The writer first briefly gives a bio of Gauss and then attempts to explain the theories in laymen's terms.
From the Paper
"There are many well known mathematicians from history whose work is well known and position widely recognised. However, there are also many lesser known mathematicians that have also made equally valuable contributions. Karl Friedrich Gauss is one of these, and as such is a worthwhile individual to study. Gauss developed many ideas and theories which are still in use today. He is best known for his theory of plate tectonics and his work entitled ?Theoria Motus Corporum Coelestium? ; Theory of the Motion of Heavenly Bodies in 1809. With Wilhelm E. Weber; a physicist he also developed a theory concerning geomagnetism. Much of his work is still used today, including work in the fields of physics, astronomy, and his statistical theories are even used in software algorithms. In this we see man who has made large contributions to the world of mathematics and related disciplines (Schaaf, 1964)."
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The History and Development of Calculus, 2002.
A study of the origins of mathematics and the growth of calculus.
1,825 words (approx. 7.3 pages), 7 sources, MLA, $ 58.95
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Abstract
This paper presents a detailed examination of the history of calculus. The writer takes the reader on an exploratory path through the origins of mathematics and then on to the history of calculus. The people who are credited with its invention as well as the forms that it took are all included in the discussion.
From the Paper
"The history of mathematics is one in which the topic follows the actual subject. Mathematics are taught by building on foundational blocks. Each block is taught and mastered and when that is completed the next block is introduced. The origin and history of mathematics follows the same path. The history of calculus is perhaps the most interesting of the mathematical techniques. The history and origin of calculus is founded in philosophy as well as science and it is one of the most fascinating of the mathematical theories and practices."
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Georg Cantor: A Genius Out of Time, 2002.
A review of the life and work of the mathematician Georg Cantor.
2,755 words (approx. 11.0 pages), 4 sources, MLA, $ 82.95
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Abstract
This paper is a biographical description of the work of Georg Cantor and his work in the development of set theory. In his time, these hypotheses were considered greatly controversial by other mathematicians. However, now they are an integral part of the study of mathematics.
From the Paper
"Georg attended several private schools in Frankfurt, and in 1859, entered the distinguished Grossherzoglich Hessiche Provinzialrealschule in Darmstadt. He left this institution in 1860 with high recommendations in mathematics. His father discouraged the study of math due to the fact that he wished him to become an engineer, a job that paid considerably more than mathematics. He originally attended Grossherzogliche Hoehere Gewerbeschule (Grand-Ducal Higher Polytechnic, later changed to Technische Hochschule) at Darmstadt following his father?s wishes and studying Engineering. Later, when Georg convinced his father that his heart was truly in math, his father relented and he began the study of Mathematics in 1862 (Johnson, 1997). "
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Fermat?s Last Theorem, 2001.
This paper takes a look at this mathematical theorem and how it has fascinated mathematicians for hundreds of years.
650 words (approx. 2.6 pages), 5 sources, MLA, $ 23.95
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Abstract
This paper briefly gives a background of Pierre de Fermat and states this famous theorem - FLT. It looks at a few working examples of problems related to the theorem and how mathematicians think that they have finally solved them.
From the Paper
"Pierre de Fermat was born near Montauban in 1601. He was born in a family reared by a leather-merchant who was his father and was educated at home. He was essentially a lawyer and was an amateur mathematician. Throughout his life, Fermat published only one mathematical paper, which was written anonymously and appeared as an appendix to a book. He died in 1655. (Ball) Fermat?s Last Theorem (FLT) has been one of the most fascinating theorems in mathematics. This theorem has been one the great, unsolved problems in this field for three hundred and fifty some years. Some experts believe, however, that the problem has been solved."
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Manipulatives in Mathematics Curriculum, 2006.
This paper discusses mathematics education in early education programs.
875 words (approx. 3.5 pages), 5 sources, APA, $ 31.95
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Abstract
In this article, the writer explains that manipulatives are defined as materials that are physically handled by students in order to help them see actual examples of mathematical principles at work. The writer notes that manipulatives are incorporated into curriculum with the aim of helping the student understand mathematics, rather than increasing efficiency in calculation. The writer maintains that manipulatives are very useful especially in early education. The writer notes that there is a wide array of math manipulatives on the Internet. Some may be bought while others can be enjoyed for free on the web. The writer provides examples and pictures and discusses how it would be possible to use them in teaching children.
Outline:
What are Manipulatives?
References
From the Paper
"Manipulatives are incorporated into curriculum with the aim of helping the student understand mathematics, rather than increasing efficiency in calculation. Manipulatives are very useful especially in early education. Moreover, its use is not exclusive to teachers and schools, parents who would choose to help their children with school lessons can also employ them to help their children understand math concepts. Most students dislike math because they think it is very complicated. This prejudice towards this subject result to poor performance of students in math subjects. The development of this negative mind set on the subject may have started when in their childhood. Traditional ways of teaching may have bored them and cause them to dislike the subject, which they will carry to adulthood. That is why it is important that at a young age, kids should learn to enjoy math. And the use of manipulatives can help them enjoy and appreciate it. Manipulatives come in colorful packages that attract children, their interactive design also allows children to play with them as they learn. There is a wide array of math manipulatives in the Internet."
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Archimedes' Stomachion: A Perpetually Recombining Mystery, 2008.
A discussion of the geometric puzzle - Archimedes' Stomachion.
1,674 words (approx. 6.7 pages), 3 sources, APA, $ 54.95
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Abstract
This paper discusses all aspects of the ever complex geometric puzzle - Archimedes' Stomachion. It explains that the Stomachion is a collection of fourteen differently shaped geometrical objects, most self-evidently organizing to form a cube and for this reason, the object or set of objects is often also given the name Loculus of Archimedes, meaning Archimedes' Box. The paper points out that the object is one rife with mystery, from its historical obscurity to its continued rendering of insight and revelation, the Stomachion is an object that is increasingly yielding of questions as much as of answers. The paper also examines the Stomachion's history and its current relevance to mathematics and scientific culture. The paper concludes that there remains any number of aspects of this puzzle that are as yet uncovered and owing both to the condition of the parchment upon which Archimedes' original ideas are expressed and to the unfurling complexity of the puzzle, it remains uncertain what additional implications were either perceived or intended by Archimedes.
From the Paper
"Composing his ideas during the 2nd century BCE, Archimedes is not generally believed to have invented the puzzle in question so much as channeled its implications into a discourse on its mathematical suggestions, which have since proven increasingly extensive. Nothing of Archimedes' investigation here was spoken of for roughly 2000 years, with a parchment communicating through several centuries of mathematical discourse gradually becoming obscured under the oppressive thumb of religious revisionism. What is today known as the Archimedes palimpsest is a document beneath a document, with the former a descendent of Archimedes' preponderance on the subject of the riddle at hand. Its existence was unknown until 1907, when Danish philologist Johan Ludvig Heiberg discovered the forgery untouched by any interested parties for several hundred years in a monastery in Constantinople. (Wikipedia, 1) Using a magnifying glass in accordance with the technology available at the time, he could make out only small fractions of a text divulging the existences of the Stomachion, with only smatterings of information accessible regarding its meaning or purposes."
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The Unit Circle, 2005.
This paper shows how the unit circle contributes to an easier understanding of trigonometry.
1,251 words (approx. 5.0 pages), 3 sources, MLA, $ 42.95
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Abstract
The paper defines the unit circle as a key instrument in learning about trigonometric functions, values and concepts. The paper lists the steps to making a unit circle and provides detailed examples and graphs.
Outline:
What is the Unit Circle?
How Do I Make a Unit Circle?
How To Find Coordinates
How To Find a Reference Angle
Negative Values
In Conclusion
From the Paper
"Well, to first understand the Unit Circle, you must first understand basic graphing, because the Unit Circle is based off the circular graph x2 + y2 = 1. The Unit Circle is a circle whose values are counted counterclockwise starting from the point (1,0). Then the values- in degree and radian measure (don't worry all of this will be further explained later, so don't worry if your lost)- are used to solve trigonometry problems and equations. The values on the Unit Circle are used to find sine, cosine and tangent values as well as to find compliment and supplement angles. Overall, the Unit Circle is one of the most helpful things to know when doing the ever so complicated trigonometry. An easy was to think of the Unit Circle is that the Unit Circle is a box of primary colors, it's your red, blue and yellow. With this Unit Circle/primary color box you are able to make and understand all sorts of other colors and concepts."
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Hypothesis Testing, 2007.
This paper is an introductory description of the five-steps of hypothesis testing.
1,055 words (approx. 4.2 pages), 1 source, APA, $ 37.95
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Abstract
This paper uses the hypothesis statement, "The typical American drinks on average 3 or more 8 oz. caffeine beverages a day" to demonstrate hypothesis testing. The author points out the steps in the five-step hypothesis test: (1) formulate a null and an alternative hypothesis; (2) select a level of significance or risk for the research; (3) identify the test statistic; (4) formulate a decision rule and (5) do the calculations and make a decision. The paper relates that hypothesis testing can be used to test any claim about a parameter.
Table of Contents:
Research Issue
Hypothesis
Five-Step Hypothesis Test
Results
Other Uses of Hypothesis Testing
Excel Spreadsheets
Hypothesis Test: Mean vs. Hypothesized Value
From the Paper
"A one-tail test is a test that indicates a direction. This direction can be indicated by the use of words such as less than or more than, or it can be indicated by the use of the greater or less than mathematical signs. The direction of the tail is determined by which direction the alternate hypothesis points. A two-tail test is needed when the words or signs equal and not equal are used. By looking at the hypotheses, Team B determined that they will be conducting a one-tail test to the right."
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"Wager for Skeptics", 2007.
An exploration of Blaise Pascal's novel argument for the logical belief in God, as presented in "Wager for Skeptics."
1,397 words (approx. 5.6 pages), 2 sources, MLA, $ 46.95
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Abstract
This paper provides a clear explanation of Blaise Pascal's "Wager for Sceptics." It explores, in depth, its merits and its flaws and focuses on the flaws in Pascal's reasoning that resulted in it not achieving his stated goal. This paper demonstrates that, ultimately, the arguments against the "Wager for Skeptics" all stem from the incomprehensible nature of infinity, a notion that lies at the heart of Pascal's work.
From the Paper
"Emanating from his mathematical background, comes Blaise Pascal's Wager - a line of reasoning designed to lure people into the Christian faith. Pascal is acutely aware of human nature, and so bases his campaign around the reader's self-interests, rather than actual theological proofs. The Wager's basic proposition is that if a person believes in the Christian God, there is a chance of them gaining infinite reward. Conversely, if a person does not believe in God, they have no chance of gaining the reward which is on offer. This is a deceptively simple choice: one that immediately appears both enticing and convincing. However, our initial arousal begins to subside just as quickly when we realise that there are major flaws in Pascal's reasoning. Pascal attempts ardently, though unconvincingly, to quash some of the objections that might be proposed. The argument itself, however, if taken as convincing, leads to some unexpected outcomes - ones that do not align with those that Pascal intended. Ultimately, the Wager does not succeed in providing a compelling reason for believing in Pascal's God over any other form of belief."
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Misuse Intrusion Detection, 2007.
This paper discusses data mining for intrusion detection of log files, using hierarchical clustering primarily.
1,276 words (approx. 5.1 pages), 5 sources, MLA, $ 43.95
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Abstract
This paper discusses an intrusion detection algorithm for analyzing university web server log files. It also discusses integrating hierarchical clustering with other algorithms for an intrusion detection system. The paper proposes to use hierarchical clustering as the main back bone of the intrusion detection system and then incorporating other algorithms like statistics and support vector machines (SVM) as needed.
From the Paper
"The initial plan was to use the user signatures method by Seth Freeman or the Traffic Classification technique but the first method seems more suited to an OS than for web server log files and the second seems a lot more complicated and also requires a destination IP, which is not readily available from our log files. I started out by writing a statistics based algorithm but then added hierarchical clustering based on instructor feedback. Eventually I settled on this paper based on hierarchical clustering with other methods as backup although I still like the statistics approach."
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Anomaly Intrusion Detection, 2007.
This paper discusses anomaly intrusion detection using data mining and statistics.
800 words (approx. 3.2 pages), 4 sources, MLA, $ 28.95
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Abstract
This paper is a research project, which uses anomaly intrusion detection to determine if there are any abnormal patterns and, hence, intrusions in the provided log files. The author stresses that a statistics approach seems to be the easiest and most straightforward approach. The paper relates that a common practice in IDS software is to incorporate different techniques to detect intrusion so that other methods such as hierarchical clustering can still be included in the system to search for suspicious/ known data patterns such as viruses. The paper includes charts, graphs and a screen-shot.
From the Paper
"Since we are not building a new system, we will try to implement and base the report on existing work. Viewing sequence algorithms for intrusion detection helps to determine which patterns look like patterns of intrusion. The statistics technique is discussed but will not be programmed at this current time. We will also attempt to show manually how this algorithm will detect the patterns using previous research as it correlates to this specific data using logs provided and some data mining algorithm."
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Statistician Pafnuty Chebyshev, 2007.
This paper discusses the life and work of internationally famous Russian statistician Pafnuty Lvovich Chebyshev, born in 1821, near Moscow.
925 words (approx. 3.7 pages), 9 sources, MLA, $ 32.95
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Abstract
This paper explains that Pafnuty Chebyshev's lifelong work, which left a lasting legacy that influenced the study of mathematics and statistics worldwide, included many subjects such as probability theory, quadratic forms, orthogonal functions, the theory of integrals, the construction of maps and the calculation of geometric volumes. The author points out that, during his pursuit of a doctorate degree, Chebyshev wrote an important prize-winning book "Teoria Sravneny" from which his profound knowledge of probabilities greatly aided the Russian insurance industry.The paper relates that his most notable students were Aleksandr Lyapunov, and Andrew Markov.
From the Paper
"Chebyshev's family moved to Moscow in 1832 mainly for their eldest son's educations. Chebyshev was taught by one of the best teachers in Moscow, P.N. Pogorelski. Pogorelski taught Chebyshev math and physics. Pogorelski was regarded as one of the best elementary math teachers; he had written numerous books about elementary mathematics. Chebyshev was taught by highly known professionals for other subjects as well. With his knowledge of the French language, it helped him speak internationally about math."
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The Golden Ratio, 2006.
This paper explores the popularity of the the Golden Ratio in many areas.
675 words (approx. 2.7 pages), 4 sources, $ 26.95
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Abstract
The paper explains that few mathematical figures have achieved the status that the Golden Ratio has throughout the historical past and well into the modern and post-modern era. The paper discusses how the Golden Ratio (GR) has also been termed the Golden Mean or the Divine Proportion because of its seemingly endless recurrence in nature as well as its perpetual application not only by mathematicians but by artists and architects alike, as well as others (Clawson b. 33). The paper explains that artists and architects seem to enjoy the predictability of the GR as well as its symmetry.
From the Paper
"The GR has been attributed to the Greeks whose quest for knowledge, 0x01 graphic as employed by the Greeks as being representative of the GR in many respects where, "Golden Means. F = AB/BC = CH/BC = IC/HI = 2DE/EF = EG/2DE" (Clawson a. 121). In this respect the GR has also been related to other unique and fascinating mathematical principles."
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The Heb-Sed Festival, 2006.
An examination of the Heb-Sed (or Sed) Festival of ancient Egypt.
2,925 words (approx. 11.7 pages), 6 sources, $ 115.95
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Abstract
This paper discusses how few ancient civilizations have given so much as have the ancient Egyptians. Like their Greek counterparts, the Egyptians' innovations in the areas of mathematics, architectural design, mythology, literature (albeit in the Egyptian case, hieroglyphics) and government were seized upon as exemplars by later empires in both the Western and Middle Eastern worlds. The paper examines a certain aspect of ancient (and still fairly inscrutable) Egyptian society known as the Sed Festival.
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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, $ 53.95
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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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Eratosthenes and Measurement, 2006.
A biographical account of the life of Greek scholar Eratosthenes and his many contributions to the sciences.
1,350 words (approx. 5.4 pages), 3 sources, $ 53.95
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Abstract
This six page paper looks closely at the ancient and historical figure of Eratosthenes, who died around 195 BC. He made many significant contributions to the fields of science, mathematics, astronomy, geography, and many others. His discovery of the diameter of the earth has been proven to be highly accurate today. As thus, his work is of lasting importance.
From the Paper
"Eratosthenes, a Greek scholar from about 276-195 B.C, is remembered chiefly for his scientific measurements of the earth's circumference. His work, albeit somewhat unacknowledged by his contemporaries, resulted in fantastic scientific experiments which are comparably accurate even today. By looking briefly at his biography, and then the results of his experiments, Eratosthenes will be shown to be both a highly important as well as a highly innovative thinker of his age, regardless of how he was considered at the time of his life work. Born in North Africa, Cyrene, Eratosthenes spent much of his educational time in Athens. In Athens he received the education..."
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Godel's Theorem, 2005.
An analysis of the implications of Kurt Godel's theorem on mathematics.
900 words (approx. 3.6 pages), 3 sources, $ 35.95
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Abstract
This paper discusses Godel's theory on mathematical truths as being that they cannot be found in any set of axioms or rules and ultimate truth cannot be achieved. The paper suggests that Kurt Godel's incompleteness theorem encompasses the fact that all formal systems turn out to be incomplete by their very nature and it discusses the implications of this theory.
From the Paper
"Godel stated that there can be no proof of any statement (P). If P is true, there is no proof of it. If P is false, there is a proof that P is true. This is a contradiction. It cannot be decided whether P is true in a symbolic system."
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Statistical methods, 2005.
An analysis of statistical analysis forecasting methods.
675 words (approx. 2.7 pages), 3 sources, $ 26.95
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Abstract
The paper discusses the two statistical analysis forecast methods. The paper explains how they can both be used to trend market areas, one on a broad basis, while the other can be extremely detailed and therefore, more accurate.
From the Paper
"Although there are many approaches to determining accurate forecasting there is one approach, which can be used when little data is available on a local level. This approach is known as the "build up" method and when applied is used to gain basic market information (i.e. market population, product market share and product demand percentage). This data is used to determine market size potential within a given area and is based on the entire market, not segments (Barnett, 1988, p. 28). In addition to this the "build up" method does not take into consideration the initial goals of the company but takes into consideration market conditions only. An example of build up forecasting would show total consumer sales on automobiles across the nation."
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