From the Paper " Sir Isaac Newton (1642-1727) was one of the greatest scientists in history and, after an initial period of resistance, his discoveries, theories, and methods proved to be a major force in the emergence of modern science. Newton became the best-known scientist in the world and, even though most of the eighteenth-century public understood little of his work, his fame eventually provided the impetus to elevate scientific research to a new level of respectability. Other seventeenth- and eighteenth-century scientists participated in the general move away from the Aristotelian paradigm of science that had dominated the Western world for two millennia. But Newton's inspired work resulted in what has justly been called the Newtonian Revolution in science. Ironically, however, Newton's progress in mathematizing science and opening it up to the full play of scientific method meant..."
From the Paper "The purpose of this research is to examine "The History of Calculus" by Carl B. Boyer. The plan of the research will be to set forth the general ideas in the book, and then to explore details contained in the book that summarize the concepts of calculus that Boyer wants to emphasize.
Boyer's The History of the Calculus is put forward as one of the few histories of how the discipline of calculus evolved, apart from an explanation of how to use it mathematically. It is by positioning the ideas of mathematics and philosophy that influenced calculus that Boyer gradually moves toward an explanation of how calculus can actually be used and applied. The background of Boyer's approach appears to be the idea that a richer understanding of how calculus came to "be" in the world of ideas can lead to an understanding of how it can be employed in ... "
From the Paper "Application of Learning Theories in Early Childhood Mathematics
The major theories of learning which underlie curriculum planning in the schools are generally classified into three groups: behaviorism, cognitive development, and phenomenology or humanistic psychology. Each of these schools of thought arose from distinct philosophies and individuals who developed the theories within the philosophies. It is the purpose of this paper to discuss the major learning theories, the psychologists representing each group, the learning implications for each learning theory, and a representative mathematics curriculum for early childhood applying the various learning theories.
Behaviorism is the oldest learning theory, and it continues to be popular in the United States. Psychologists Thorndike..."
This paper is a review of "The Life of Isaac Newton" by Richard Westfall, a detailed portrait of the English mathematician, physical scientist, and theologian.
1,565 words (approx. 6.3 pages), 2 sources, 2002, $ 51.95
Abstract This paper describes the book, "Life of Isaac Newton" by Richard Westfall, which tells chronologically the life of a solitary scholar, Trinity College professor, government administrator and elder statesman of the English scientific community by showing his accomplishments and human weakness. This paper tells the story of the "apple" and points out that Newton may have gotten the idea when he was young but it took many years for him to develop his theories.
From the Paper "For a number of years, Newton did not publish anything and seemed to immerse himself in the study of chemistry and its "occultist" neighbor, alchemy. Avoiding the more mystical areas of the science, there is no doubt he was searching for both knowledge as well as gold . Newton also was delving into some dangerous theological areas, doubting the existence of the Trinity and attributing it to a corruption of the true earlier Christian religion. Despite holding these beliefs until his death, he successfully kept them a secret, and even managed to be appointed to the Lucasian chair of Trinity College without having to take the usual step of taking on the holy orders. He kept his then-heretical religious beliefs a secret until his deathbed, when he refused to take his final communion "
Abstract This paper begins by providing a brief biographical overview of Isaac Newton, from his birth in England in 1642 to his groundbreaking scientific theories and discoveries. The paper covers Newton's scientific achievements, starting with the fact that he established a unified theory of approach to modern science. It discusses his discoveries relating to the white light, the telescope and to the field of optics in general. The paper also covers Newton's mathematical achievements in the form of calculus and his most famous discovery of all - gravity.
From the Paper "Newton's discoveries in optics were offset by his even more groundbreaking discoveries in pure mathematics and the science of mechanics. One of the most important modern mathematical tools "The Integral Calculus" was the brainchild of Newton. It need not be mentioned that without this mathematical tool the progress that the scientific community achieved in many disciplines would have been significantly delayed. However Newton's discoveries in the field of mechanics outweigh all his other accomplishments. Though Galileo had already discovered the first law of motion his theory was based on the movement of objects without any external influence or attraction between them. Newton's three laws of motion explained the hitherto inexplicable behavior of all physical bodies in motion. Still more astounding was Newton's discovery of gravity. All these four laws put together explained the mechanical motion of all earthly and heavenly bodies. Newton not only proposed these laws but also ratified them by using the integral calculus."
Abstract This paper analyzes cryptography, the encryption or transformation of data into some unreadable form in order to ensure privacy by keeping the information hidden from anyone for whom it is not intended. It provides a brief overview of cryptography, discusses methods of encryption and description and examines cryptographic protection in Microsoft Windows 2000 as an example of cryptography utilization.
From the Paper "Cryptography is the study of mathematical techniques related to aspects of information security such as confidentiality, data integrity, entity authentication, and data origin authentication. It is defined as the science of protecting data. Cryptographic mechanisms help organizations provide a complete suite of security services. The fundamental goal of cryptography is to adequately address systems and information security in the prevention and detection of cheating and malicious activities."
Abstract Discusses differences between a code and a cipher. Requirements of each; how each works. History of encryption. Enigma machine of World War II. Pre-computer encrption. Development of computer program to encrypt data. Function of a "hash" (a number generated from text & smaller than the text itself). Privacy issues. Future of algorithms.
From the Paper "Encryption and Hash Algorithms
Introduction
Stephen Levy (2001), reporting on the latest "unbreakable code" begins his report by quoting Edgar Allan Poe. "It may roundly be asserted that human ingenuity cannot concoct a cipher which human ingenuity cannot resolve" (Levy, 2001, 45). This article was selected to lead off this discussion of encryption because of two elements of confusion.
First, the headline read "An Unbreakable Code"? and the article was about enciphering and deciphering, also called "encryption" and ?decryption.? This is a common, and often-repeated mistake, one which can confuse the very field of study. A "code" is not a "cipher" anymore than a "tennis ball" is a ?cabbage.?
Abstract This paper discusses statistical analysis as a dynamic form of study that evolves over time to meet developing needs and to exploit developing capabilities and technologies. The author points out that statistical analysis is the process through which data becomes knowledge and is a science to assist one in making decisions under conditions of uncertainty. The paper relates that the most appropriate logic bases for the discipline of statistical analysis in the contemporary period are rational, quantitative, positivist and causality.
Table of Contents
Introduction: Reflections on Statistics
Reviewing Statistical Analysis
Defining Statistical Analysis
Alternative Logic Bases for Statistical Analysis
Rational Model versus Naturalistic Model.
Quantitative Model versus Qualitative Model.
Positivist Model versus Normative Model.
Causality Model versus Plausibility Model
Exploratory Model versus Confirmatory Model.
Randomization Model.
Conclusion: Reviewing Statistical Analysis.
Examining the Classical Model of Statistical Analysis
Descriptive Statistical Analysis
Exploratory Statistical Analysis
Inferential Statistical Analysis
Probability Theory and Classical Statistical Analysis
Conclusion: Classical Statistical Analysis
From the Paper "Descriptive statistical analysis describes the performance or activity of one group or class, without attempting to generalize about other groups or classes. Classification, description, and measurement are activities applicable to variables associated with social research. The classification of variables is based on an assumption that social units are comparable within the context of specific definitional criteria. A social researcher attempts to control variation through the classification of variables. The description of variables is an effort to assign some degree of uniqueness to each variable, in order to provide a basis for the establishment of relationships among variables. The measurement of the extent of the uniqueness of variables generates the quantitative indicators of the strength of the relationships between variables. The process of classification, description, and measurement facilitates the development of causal explanations for both regularities and variations in empirical phenomena. Comparisons are made according to the degree of differentiation of structure in data in relation to a common and less differentiated point of origin. Such comparability is dependent upon both the classification of the social unit and the dimension of that social unit that is being measured. The dimension is the variable being measured."
Abstract Resonance is a term belonging to the mathematics of sound, and to different fields of physics and applied physics. In music, resonance involves the cause of sound produced by musical instruments, in effects that affect standing waves of sound due to resonating strings and air columns that create different frequencies.
Abstract This paper is on David Hilbert and mathematics. He became famous for developing his "axiomatic" and "existential" methods. His proposal in 1900 of twenty-three problems for the coming century set the course of much subsequent mathematics. It was in this context that Hilbert came to be seen as the person who set the foundation for many mathematical questions.
Abstract This paper is written on conceptual and procedural knowledge in mathematics. Procedural knowledge-or more appropriately skills-refers to the ability to physically solve a problem through the manipulation of mathematical skills: with pencil and paper, calculator, computer, etc. There is thus, in a theoretical sense, a difference between conceptual and procedural knowledge in mathematics.
Abstract This paper examines the prevailing attitude towards women in mathematics and explains why in our enlightened age, when women are as educated as men, they are still considered by many to be unequal to men in many fields.
Abstract This paper expounds the ?Theory of Everything,? starting with the pioneering theories of Newton's "Laws of Motion" and Einstein's ?General Theory of Relativity,? developing right through to the cutting-edge "string theory" research currently being conducted around the world today. It shows the importance of fields of study as seemingly diverse as calculus, differential geometry, electromagnetism, particle physics and quantum mechanics to the development of a "Theory of Everything". It also demonstrates how those with access to this theory can use the knowledge as power for anything, such as understanding stock markets using the premise that the stock market moving up over time means that these are not random movements and therefore should be explainable.
From the Paper "Stock markets exist over time and space (the geographical markets) that we are able to quantify and understand to a degree. Therefore, as with Einstein, we are fairly comfortable with the stock market in its familiar four dimensions. We have become accustomed to inflation; the rising of prices of goods rise over time and this is obviously a major reason for at least part of the upward rise of share prices. However, what happens when we explore the smaller dimensions ? like the six unknown dimensions string theorists grapple with? Like the string theorists who know that subatomic matter exists but can?t explain or predict its behavior, we often know what influences the stock market but are usually unable to predict it."
Abstract This paper expounds the ?Theory of Everything,? starting with the pioneering theories of Newton's "Laws of Motion" and Einstein's ?General Theory of Relativity,? developing right through to the cutting-edge "string theory" research currently being conducted around the world today. It shows the importance of fields of study as seemingly diverse as calculus, differential geometry, electromagnetism, particle physics and quantum mechanics to the development of a "Theory of Everything".
From the Paper "However, there is a fundamental discord between Einstein's "Theory of General Relativity" and quantum mechanics. Einstein saw the universe in four dimensions (the three dimensions of space plus time). The gravitational force that binds matter to the earth stems from this space-time continuum. Since quantum mechanic's subatomic particles only exist theoretically, they cannot be located in space-time and their motion can only be hypothesized. Thus, we have two theories that work individually but not together. There are also many unanswered questions. Relativity cannot tell us how the big bang created the universe or what black holes consist of. Similarly, quantum theory is not able to make order or sense of the assortment of miniscule matter it describes."
Abstract This paper examines how, for many who lack a strong grounding in math and science, the two are often associated as being the same. The purpose of this paper is to define mathematics and science, showing them as two distinct fields of inquiry and then to show how advances in theoretical mathematics contribute the framework needed for scientists in the study of quantum mechanics, a branch of physics, which in turn, is one of the many branches of science.
Outline
Introduction
Mathematics
Science
Quantum Mechanics
Mathematics and Quantum Mechanics
Science and Quantum Mechanics
From the Paper "Finally, applied mathematics is a term loosely applied to a range of studies which have significant use in the sciences, specifically the empirical sciences, (branches of science open to practical or experiential experimenting). Applied mathematics makes use of numerical methods and computer science, seeking concrete solutions to explicit mathematical problems. In science and technology it has a major use as a way to model and/or simulate natural phenomenon or events. Examples include using mathematical models in computer generated wind tunnel tests to predict the behavior of a given shape of a prototype airplane wing without resorting to expensive actual wind tunnel testing."
