This paper discusses chaos theory based on James Gleick's "Chaos: Making a New Science" and Ian Stewart's "Does God Play Dice?: The Mathematics of Chaos".
Abstract This paper explains that James Gleick believes that chaos theory is revolution in thinking, a major shift from the ordered universe of Newton and even the less mechanical universe of Einstein. The author points out that chaos theory says that the universe is decided on the basis of chance to a great degree and that the aggregate of those chances cannot be predicted or even discerned to allow a clear cause-and-effect assessment. The paper relates that chaos theory says that a small change in a system, which takes place all the time and cannot be tracked or even relied upon, can produce more and more changes until something much greater and unforeseen occurs.
From the Paper "Ian Stewart is trained as a mathematician, while Gleick writes about science for the New York Times. Stewart is British, and Gleick American. They write about the same subject from different points of view. Stewart begins his book noting that the direction for creation has been first from chaos into order, and that physics has now found that order is something of an illusion masking the continuing chaos of reality. He also cites Newton and the Newtonian era as affirming that nature has laws and man can discover what these laws are. The world described by Newton was a clockwork world which operated like a machine, and Stewart discusses the nature of that world and world-view much more directly than does Gleick."
Abstract This paper explains that organizations are becoming aware of the serious need to cope with and quickly adapt to change; therefore, they increasingly are turning to chaos theory in order to understand and manage change in a dynamic business environment. The author points out that chaos theory, also known as non-linear systems theory, is based on the premise that the world is made up of complex systems that are non-linear, dynamic, unstable and unpredictable, contrasting sharp with Newtonian science, which believed that the universe functioned in an ordered, stable, linear and predictable manner. The paper relates that chaos theory has led to organizations being viewed as organic or living systems that will find orderly solutions if they are allowed to do so; however, organizational management needs to be more sensitized to environmental changes, leading to flexibility, responsiveness, dynamism and a reduced reliance on precise planning.
From the Paper "True, that discerning the underlying structure of the complex systems that bring about change is often difficult because there are a number of myriad factors involved. However, chaos theory is nevertheless useful in understanding and managing what was previously considered to be uncontrollable, chaotic events and behavior. This is achieved by defining chaos as "the range of behaviors that deterministic processes can adopt." One such deterministic process is deemed as the organizational culture and structure itself. Indeed, this is precisely the reason why modern organizations are moving towards decentralized, leaner, flatter structures that allow for employee empowerment, self-organization and emergence."
Abstract This paper explores the development of four concepts: The Golden Ration, fractals, platonic solids and the artifice of Escher. It then examines how these mathematical concepts can be applied to real life.
From the Paper "The concept 'golden section' was first used by Martin Ohm in the 1835 in his book Die Reine Elementar-Mathematik. The first everEnglish use was seen in the article of James Sulley in 1875 which appeared in the 9th edition of the Encyclopedia Britannica. The symbol 'phi' was first used by Mark Barr at the inception of the 20th century in commemoration of the Greek sculptor Phidias, who was an extensive user of golden ratio in his works. Phi has surprising linkage with the continued fractions and the Euclidean algorithm for enumerating the Greatest Common Divisor of two integers and is also known as the Pisot Number."
Abstract The writer of this paper defines a derivative as a contract that specifies the rights and obligations between the issuer of the security and the holder, to receive or deliver future cash flows based on some future event. This paper examines the various uses for derivatives which are standardized much the same as stock futures and traded through a securities exchange or futures exchange. This paper discusses the use of derivative securities as a tool to transfer risk. For example, a business can sell futures contracts on a product to a buyer, even before that particular item hits the shelf. The writer cites the various types of derivative options, such as the swap and the forward contract, which is an agreement between two parties to buy or sell a particular asset. A swap is an agreement in which, generally two, parties agree to exchange future cash flows, arising from financial instruments. This paper details how forward contracts are implemented in the corporate business world, as was the case with Lufthansa, who contracted with Boeing to purchase aircraft in the mid-1980s. This paper delves into the process known as financial engineering, which combines options and other derivatives while at the same time controlling the risk in a given transaction. This paper also discusses how derivatives are used as an option in tax planning.
From the Paper "A common use of options for tax planing involves the deferrment of a gain from one period to another, thereby delaying the payment of taxes. For example, one company may have an investment in another company's stock that has appreciated. Company A would like to lock in the gain on Company B's stock, but does not wish to recognize the gain in the current year. It can accomplish this by using put options. This strategy would involve buying put options at the current stock price, expiring in the next fiscal year. If the stock price declines, the value of the option would increase, locking in the profit. Another strategy would be to sell a call option at the current market price. This would also lock in the gain, as any decrease in the price of the stock would be offset the increased value of the option. These strategies can also be used to reduce the risk of a drop in the stock price without regard to tax issues."
Abstract Calculus is divided into two branches, one being differential and the other being integral. This paper provides an overview of calculus and examines the two branches in more detail. It also looks at the importance of calculus in the world today.
From the Paper "It must be stated that Newton's mathematics that involved 'fluxions' was one of the first forms of the area defined as 'differential calculus'. Although Newton used and preferred to use geometrical methods to algebraic equations, calculus methods had come into importance. However, calculus was not widely accepted at the time, and there were several philosophical objections to the science, but the fact remains that these objections over the years have made no difference to the application of the science."
Abstract This paper explains that Daniel Bernoulli used his analytical skills across a broad range of scientific disciplines including probability, hydrodynamics, the flow of blood and blood pressure and Riccati's differential equations. The author points out that Daniel Bernoulli improved mathematical physics with his recognition of many of Newton's theories and his utilization of the more powerful calculus of Leibniz. The paper relates that Bernoulli's mathematical explanation of the behavior of gas led to Boyle's law.
Table of Contents
Introduction
Bernoulli's Contributions to Mathematics
Effect of Bernoulli's Work on Today's World
From the Paper "Aerodynamics is a subdivision of fluid mechanics that deals with the motion of air and other gaseous fluids, and with the forces acting on bodies in motion relative to such fluids. Some of the examples of aerodynamic actions are: the movement of an aircraft through the air, the wind forces applied on a structure and the working of a windmill. Daniel Bernoulli's principle is the main law dictating the motion of fluids, which links an increase in flow velocity to a decrease in pressure. For instance, for the same quantity of air at the entry to the venturi tube below to flow through the restriction in the middle, the air must accelerate."
Abstract This paper studies how graduate students perceive the study of statistics and the impact that their anxiety about the subject matter has on their overall performance. The paper cites several research studies which indicate that statistics anxiety is quite high. Furthermore, the paper proves that this anxiety significantly erodes the overall quality and level of the students' research projects. The paper then offers suggestions to improve the teaching of statistics, as well as other suggestions to strengthen students' skills at statistical analysis.
From the Paper "Statistics anxiety has been defined simply as anxiety that occurs as a result of encountering statistics in any form and at any level (Onwuegbuzie, DaRos, & Ryan, 1997), and has been found to negatively affect learning (Onwuegbuzie & Seaman, 1995). Many researchers (Lazar, 1990; Lalonde & Gardner, 1993; Onwuegbuzie, 2000b) suggested that learning statistics is as difficult as learning a foreign language. On the other hand, statistics anxiety sometimes is not necessarily due to the lack of training or insufficient skills, but due to the misperception about statistics and negative experiences in a statistical class. For instance, students often think they do not have enough mathematics training so that they cannot do well in statistical classes. With fear of failing the course, they delay enrolling in statistics courses as long as possible, which often leads to failure to complete their degree programs (Onwuegbuzie, 1997). The lack of self-efficacy and higher anxiety in statistics keep many students away from engaging in research work or further to pursue an academic career. Therefore, statistics becomes one of the most anxiety-inducing courses in their programs of study (Blalock, 1987; Caine, Centa, Doroff, Horowitz, & Wisenbaker, 1978; Schacht & Stewart, 1990; Zeidner, 1991)."
Abstract This paper explains that the Black-Scholes method is a very famous method for the valuation of an equity share and other variables related to the value of an equity share in the future months. The author points out that the key characteristics needed for the Black-Scholes formula are the price and price volatility of the underlying stock, coupled with the available rate of return on a risk free stock, under the assumption that trading in the concerned stock, along with the ability for exercise of the option, is continuous and unrestricted. The paper relates that credit derivatives are mechanisms for the credit institutions to separate the credit risk from their loans and treat market risk as a separate category so that their pricing efficiency could be more competitive and the concerned organizations could be more competitive in the market.
From the Paper "One can even buy securities at low prices on a forward basis. Generally, these are used in a manner similar to bonds which have a benchmark of comparable maturity. Thus, a bank may buy from an investor an option on the credit spread of a BBB-rated corporate bond which has a maturity after 5 years. For this, a premium will have to be paid. At the same time, the bank will have the right to sell the bond to the investor at a certain strike price. This strike price is in terms of a difference with treasury notes, and if the actual spread on the date of maturity of the deal, is more than the strike rate specified, then the option will not be used. If the actual difference is higher, then the bond may be purchased."
Abstract This paper describes the goals and objectives of a series of conferences between the Vatican and leading scientists on questions of Infinity. The paper examines the theological issues involved Infinity.
From the Paper "The Vatican has historically grappled with resolving the theological issues that are associated with new scientific discoveries. Recently the Vatican press office announced a new project on science and..."
Tags: Vatica, Roman Catholic CHurch, science, Infinity
Abstract This paper uses a problem from everyday life and sets up an algebraic equation to solve it. It then solves the problem. In this case the problem is a plane flying from San Francisco to Hawaii which experiences an emergency and it is necessary to determine at what point on the flight it is faster to continue to Hawaii than return to San Francisco, given the air speed, the tail wind factor and the distance between San Francisco and Hawaii.
From the Paper " A plane is flying miles from San Francisco to Hawaii. It is flying at a speed of mph and there is a tailwind blowing at mph. Problem How many hours after take off would it be faster to keep on flying to Hawaii than to turn around and fly back to San ..."
Abstract This paper provides a general biography of Rene Descartes, as well as a basic summary of his philosophical tenets. The paper also discusses Descartes' accomplishments in the field of mathematics as well as philosophy.
From the Paper "Often considered the father of modern philosophy, Renee Descartes is one of the most influential ground-breaking thinkers in the history of human thought. Indeed his accomplishments go beyond the field of philosophy as he was an elite mathematician who is credited with inventing analytic geometry. However it is Descartes' work in laying the philosophic foundation for modern scientific thought that is his greatest achievement. Descartes' philosophy was deeply rooted in rationalism because he began his inquiry by questioning the very validity of the knowledge that man believes he possesses."
Tags: descartes, biography, skepticism, philosophy, God, existence, cogito ergo
Abstract This paper looks at the way Alan Lightman's novel, "Einstein' Dreams", handles Einstein's theory of the relativity of time, mainly the "elasticity" of time. The paper discusses this in terms of how it relates to adult cognitive development.
From the Paper "Alan Lightman's book "Einstein's Dreams" is a novel that plays with Einstein's theory of the relativity of time. There is a proverb that says "a watched pot never boils". It requires some level of cognitive development to understand this proverb. It does not mean that the water in the pot will never boil. Depending on the level of heat applied to the pot, the water could boil in as quick a time as three minutes. However, for someone who stands over the pot and ..."
Tags: developmental psychology, Alan Lightman, Einstein's Dreams
Abstract In this article, the writer defines the term of soft computing as a collection of mathematical and reasoning disciplines that when incorporated into decision-making models provide a means for considering the effects of uncertainties on probably future outcomes. The writer reviews the development of soft computing and looks at applications. Further, the writer discusses the future of soft computing.
From the Paper "Soft computing (S.C.) refers to a collection of mathematical and reasoning disciplines that when incorporated into decision-making models provide a means for considering the effects of uncertainties on probably future outcomes. The mathematical and reasoning disciplines typically included in the definition of S.C. are a probabilistic reasoning (P.R.) S.C. models allow analysts to include data characterized by imprecision uncertainty partial truth and approximation in decision analyses ... "
Abstract This paper analyzes how the Telecommunications Act of 1996 sought to end the monopoly that once existed in the telecommunications industry. Since its adoption, the telecommunications industry has been undergoing a period of rapid change and development. The entry of new players into the market encouraged them to seek new ways to attract and keep customers. These changes have led to a rapid influx of new technology and services. Many times what defines a monopoly is not clear in every circumstance and there are many pending lawsuits for violations of Anti-trust laws in the courts today. Economic models are useful in resolving issues of whether a monopoly truly exists, or whether claims are unsubstantiated. Previous models were applicable only in certain situations. These models are unreliable in predicting monopolies outside the parameters for which they were designed. This research evaluates and analyzes economic models that could accurately predict the existence of a monopoly in the Telecommunications sector.
Introduction
Rationale for Study
Scope of Problem
Statement of Hypothesis and Research Questions
Literature Review
Methodology
Sample Population
Data Analysis
Findings
Conclusion
From the Paper "The telecommunications industry is important and considered a vital part of our everyday lives. The telecommunications industry represents only a small portion of the country's Gross Domestic Product, only 1-2% (Stigiltz, 1998). While this amount may seem insignificant, the services that it provides are vital to every other sector in the economy. Telecommunications is the backbone of many other sectors.
The Telecommunications Act of 1996 is one of the most highly debated topics in economics. There are some that say that it has been ineffective and that we now have a monopoly again, as a result of mergers and acquisitions. There are others who say that it has had the intended result, but that the movement towards a competitive marketplace does not happen overnight. Poulson (1997) believes that achieving a fair market in Colorado will not be immediate and will take some time. There are others who believe that it is working in some cases and not working in others. Alaska is moving towards a more competitive marketplace on a local level. Rural communities often have a localized monopoly as there are not enough customers to attract competition (APUC, 1997).
Michael Porter states that "Paradoxically, the enduring competitive advantages in a global economy lie increasingly in local things - knowledge, relationships, and motivation that distant rivals cannot match (Porter, 1998). He is referring to what is known as clusters, which he defines as one place of unusual competitive success in particular fields. Examples of clusters can be found across industries and around the globe. Examples of clusters include Silicon Valley, Hollywood, the California Wine Valley and the Italian Leather Fashion sector.
Clusters can be characterized by the interconnected network of suppliers, service providers and producers who are geographically aligned and who have positive dependencies and cooperation with one another. Alfred Marshall's Principles of Economics points out that location based clusters that conduct specific types of business and economic activities form based on the sharing of "tacit" knowledge among business participants. (Krugman, 1991) The success of a cluster depends not only on what operating strategy firms employ, but also on the surrounding business environment. Clusters differ from the traditional definition of a monopoly in that competition and cooperation are vital to the success of the business. According to Porter, there are three overarching ways that clusters influence competition:
1.Productivity of companies is increased by the dynamics of a cluster.
2.Clusters tend to direct the pace of innovation through competition and cooperation.
3.Clusters actually support the growth of new business - each individual business can benefit from the scale of the cluster."
Abstract This paper takes a look at the game theory, founded by mathematician John von Neumann, and the mathematics, social and behavioral sciences that are involved. This paper also reviews the definition of a game and the fundamental decision theory, a crucial factor pertaining to the game theory.
From the Paper "A game refers to a strategic situation that involves at least two rational and intelligent individuals called players. The fundamental result of decision theory, which forms the foundation of game theory as well, is that each player's goal is to maximize the expected value of his or her own payoff. These payoffs are measured on some utility scale, which is merely a numeric depiction of each outcome that can be gained through the player's actions. Individuals have preferences that give them the opportunity to rank the outcomes with respect to one other. For each pair of outcomes, a player can say whether he or she likes one better than the other or whether he or she is indifferent about the two.
The logical roots for game theory are in Bayesian decision theory. In fact, game theory can be seen as an extension of the decision theory (Myerson, 1991, p.5). In general, a decision theory is an interdisciplinary area of study for practitioners in mathematics, statistics, economics, philosophy, management and psychology. "
