Abstract This paper defines qualitative methods and quantitative methods. The author differentiates their uses. The paper assesses their suitability for use in human relations studies.
From the Paper "Research data may be evaluated through the application of either quantitative or qualitative analytical procedures. Quantitative approaches are more easily defined than are qualitative procedures because qualitative research may refer to either the way data are measured or the way such data are evaluated. A quantitative variable is one than can be measured numerically such as annual income. Quantitative data are produced by ordinal interval and ratio scales; while qualitative data are produced by nominal scales. Quantitative data ..."
Abstract This paper shows how the ancient civilizations contributed to the development and advancement of mathematics, a science which could be considered as old as humanity itself. It documents the way mathematics has grown over the centuries thanks to the work and dedication of hard working scientists that have given us the privilege of enjoying the discoveries that they made centuries ago. A description is given of the names and works of mathematicians such as Pythagoras, Democritus, Hippocrates and so many others that promoted the development of mathematics.
From the Paper "The first civilization that used mathematics in an organized way was the Babylonians and the Egyptians. They started to develop this science at the 3rd millennium BC. Their early discoveries were mostly based on arithmetic, measurement and calculation in geometry. The Egyptians used a numerical system similar to that of the Romans. An old Egyptian text, composed about 1800 BC, reveals a decimal numerical system with separate symbols for the successive powers of 10 (1, 10, 100, etc). Addition was done by totaling separately the units- 10s, 100s, and so forth- in the numbers to be added. Multiplication was based on successive doublings, and division was based on the inverse of that process."
Abstract This paper explains that traditional financial thinking relies on assumptions of certainty, complete knowledge and market efficiency and in this context, financial decisions should be relatively straightforward. In the real world though, many times what is observed deviates greatly from what would be expected using traditional financial thinking. This paper therefore uses different game theory models to more accurately explain observed financial decisions dealing with capital structure, corporate acquisitions and initial public offerings (IPOs).
From the Paper "Game theory has made great strides in explaining many of the observed phenomena falling under corporate finance. One example is the capital structure decided upon by a firm's management. Capital structure deals with the firm's decision to raise funds through debt versus equity and what ratio of debt to equity should the firm maintain. Modigliani and Miller in 1958 showed that in perfect capital markets (i.e. no frictions and symmetric information) and no taxes a firm could not change its total value by altering its debt/equity ratio; thus capital structure is irrelevant. However in the real world, capital structure is carefully thought about by every company, and it is in fact not irrelevant because taxes do exist and capital markets are not perfect."
Abstract This paper states that the field of aerodynamics could not exist without calculus. The author discusses the most prevalent and widely used equations. The advent of the computer has greatly improved the use of these equations in the field and allowed the field of aerodynamics to become more precise.
Table of Contents
Introduction
The Myth about Bumblebee Flight
Turbulence
The Bermouli Equation
Continuity Equation
Navier-Stokes Equations
Conclusion
From the Paper "Math is the language of science. The different disciplines of math relate to different areas of science. Science needs math in order to be understood. Algebra allows us to create sentences using numbers to describe an event. Geometry and Trigonometry help us to describe shapes, and Calculus is the tool for describing change. It can be a change in angles as in vector calculus, a change in rate, a change in speed, or almost any other change."
Abstract The paper introduces Benjamin Banneker, an African American born in 1731, who made enormous contributions to the study of mathematics. The paper discusses his spheres of interest in the field, including clock building, astronomy, tide and weather. It discusses, too, his widely publicized almanac that served as a contradiction to the American belief that blacks were inferior, and his contribution to the building of the city of Washington D.C.
From the Paper "In addition to creating America's first clock, his studies in astronomy made a mathematical calculations of the stars and constellations, which he used to correctly predict a solar eclipse that took place on April 14, 1789. Furthermore, Banneker was not quiet about this contradiction. Infact, he was a social critic of slavery. Thus, it was this reason and an attempt to promote change; he sent a copy of his first Almanac to Thomas Jefferson."
Abstract A router is used to manage network traffic and to find the best route for packets to be sent. This paper discusses the algorithms available in order to find the best route to destination for these packets in the network environment. The two main algorithms are "Global routing algorithms" and "Decentralized routing algorithms". The paper evaluates in detail these two methodologies together with their bottlenecks and illustrates examples with diagrams, graphs, tables and code.
From the Paper "In this step, routers should choose the best route for packets to every node. They do it by using an algorithm such as "Dijkstra Shortest Path Algorithm?. In this algorithm, router, based on information that has been collected from other routers, build a graph of network. This graph shows the location of routers in network and their links. Also every link will be labeled with a number that is called weight of link and is also known as cost of link. This number is a function of delay time, average traffic and sometimes simply, it is the number of hops between nodes. For example if there were two links between a node to destination, the router chooses the link with the least weight."
From the Paper "This research reviews the application of mathematics by the ancient Egyptians in the construction of pyramids. This research focuses on two issues. The first issue involves the mathematical principles that, of necessity, were applied in the construction of the pyramids. The second issue concerns the contention by some people that alien civilizations from outer space were the source of mathematical knowledge required for the construction of the pyramids in Egypt, as the Egyptians of that era had not developed the knowledge of mathematics required for such an undertaking.
A pyramid is a polyhedron whose base is a polygon and whose sides are triangles having a common vertex. The pyramids at Giza..."
Abstract This paper discusses Florence Nightingale's work as a statistician upon which the reform of the sanitary conditions in military field hospitals was based. The author points out that Nightingale was the first woman to be a Fellow of the Royal Statistical Society, the first woman to receive the Order of Merit and author of the first nursing textbook.
From the Paper "In 1840, Florence begged her parents to let her study mathematics instead of, ?worsted work and practicing quadrilles.? Her mother did not agree with this idea. Although Mr. Nightingale loved mathematics and had passed this love along to his daughter, he urged her to study subjects more appropriate for a woman. After a long battle with her parents, they finally gave her permission to be tutored in mathematics. This included Sylvester, who developed the theory of invariants with Cayley. She was said to be his most distinguished pupil."
From the Paper "The National Council of Teachers of Mathematics has produced a list of five goals which students in a well-taught classroom should achieve. This paper will outline how these five goals can be attained by students in a fourth-grade classroom using the Saxon text, Math 54: An Incremental Development (Hake & Saxon, 1996). Examples of how to incorporate each goal individually into the class's lessons will follow.
A good mathematics curriculum will help a teacher instill these goals in students. The best method of disseminating these goals to students is within the context of mathematics study and through opportunities for cross-disciplinary teaching; the five goals cannot be effectively taught in isolation from one another or from other subjects.
The five goals can be summarized as follows: .."
From the Paper 'The purpose of this research is to explain the application of statistical procedures to the solution of a realistic problem. In this instance, the problem is related to the domestic economy of the United States.
THE PROBLEM
The level of unemployment is a matter of significant concern to both the general public and political leaders. In order to develop effective policies to address the unemployment issue, it is necessary to understand how the unemployment rate is related to other factors. It is this problem which is addressed in this research.
HYPOTHESES
A total of six hypotheses were formulated for, and tested in ... "
From the Paper "In his book, Innumeracy: Mathematical Illiteracy and Its Consequences, John Allen Paulos uses the term, "innumeracy" in the same way that the term illiteracy is used: to represent an unfamiliarity and ignorance in terms of numbers and mathematics. Besides being well written and entertaining, the book is also informative in explaining common instances of mathematics in everyday life.
Paulos does not confine his discussion only to one aspect of numbers and mathematics. His book is replete with examples of statistics, probability and mathematics. He suggests, for example, that we develop a "safety index" for certain activities or events which would provide the populace as a whole with a quantitative way to evaluate their activities. While such an idea may seem farfetched, it illustrates an idea which occurs .. "
Abstract This paper discusses the way the study of statistics has developed over time and how it is used in a practical manner today. It looks at the history of this topic and how scholars have helped it progress into an independent academic study. Examines some of the famous statistics that are used in everyday life - divorce rate, GDP, high school drop-out rate, poverty rate, literacy rate etc.
From the Paper "Statistics is a branch of mathematics dealing with the collection, organization and analysis of numerical data the application of this information to make informed decisions in a variety of applications. Statistical results may be used to forecast business trends, define the extent of prevailing opinion throughout a given population, changes in availability of resources or assets, and provide quantifiable answers to questions in almost every type of business, social or political area. Professor Edwards of the Andover Theological Seminary defined statistics as ?the ascertaining and bringing together of those facts which are fitted to illustrate the conditions and prospects of society.? "
Abstract This paper explains that Darrell Huff in his text "How to Lie with Statistics" relates that, because there is a fear of numbers in our culture and a great deal of misunderstanding or incomprehension about what number mean, combined with a paradoxical impulse to trust science as objective, people are apt to become confused by the use of numbers, regardless of what the numbers actually say. The author points out that the math is usually computed correctly but is rhetorically twisted and used to suggest an erroneous conclusion, hence Huff's rightful characterization of such misleading evidence as a lie. The paper stresses that perhaps the most relevant information in the book for today's reader pertains to interpreting potentially divisive statistics such as crime rates in cities.
From the Paper "Such an example is not unlike the spurious study cited by Huff that smokers have significantly lower grades in college than nonsmokers. Ergo, said the researcher, smokers wishing to improve their grades should quit smoking! Of course, a statistical study showing that there's a "significant" relation between smoking and low grades doesn't show that smoking is the cause of lower grades -- perhaps educational failure draws people to smoke, suggests Huff, or more seriously, demographic factors such as poorer individual's tendency to smoke as a culturally accepted coping mechanism or to have come from less well-funded and rigorous school districts might also come into play."
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."
Tags: tail, test, test, alternative, null, population
Abstract This essay discusses the life of Sir Issac Newton and the points of his life that brought forth his great advances in the realm of physics and mathematics.
From the Paper "As a child Sir Isaac Newton took little interest in what was being taught to his classmates (Bixby 90). Instead, he found ways to fulfill his desire to learn. He marked where the shadows fell in his yard in order to keep time, thus producing his sundial (Rattansi 12). His interest in rushing water inspired Newton to build a windmill. He created the first horseless carriage. In addition to the pursuit of his numerous boyhood interests, Newton spent time with his landlord as the apothecary and concocted remedies for the illnesses of the locals (Christianson 16)."
