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Blaise Pascal, 2006.
An overview of the life and career of seventeenth century mathematical genius, Blaise Pascal.
1,317 words (approx. 5.3 pages), 3 sources, MLA, $ 44.95
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Abstract
This paper examines the life history of Blaise Pascal, born in France in 1662 and who died at the age of 39 from stomach cancer. The paper examines some of the great contributions made by Pacale to the maths field, including the first mathematical device, the creation of "Pascale's Triangle" and his theory of probability and causes.
Paper Outline:
A Genius is Born
Pascal's Education
Acceptance by the Mathematical Community
The Development of the Adding Machine and Other Experiments
Pascal's Triangle
Conclusion
Bibliography
From the Paper
"When he turned fourteen, Pascal began to accompany his father to weekly geometrical discussions with what would later become the French Academy. The geometricians at these meetings included Roberval, Mersenne, Mydorge, Carcavi, Auzout, Mylon, Desargues and other's. The meetings were held at the home of Mersenne. Mersenne was a member of a religious order called the Minims. This is important, because later in his life Pascal would abandon math to study religion for several years."
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How Much Is Two Plus Two?, 2006.
A review of failure at teaching mathematics in America.
3,250 words (approx. 13.0 pages), 8 sources, MLA, $ 93.95
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Abstract
This paper explores why, despite being one of America's national education priorities, mathematics is a 'dreaded subject' for both teachers and students. From student anxiety to lackluster teacher, the paper explores a variety of reasons for the shortcoming. The author goes on to look at proposals for mathematics reform, concluding with his own recommendations.
From the Paper
"If anxiety is one of the causes of students' inability to learn, or their lack of interest in learning, teachers need to be aware of the problems caused when math students, regardless of their age or experience, generally blame themselves for a failure to learn or to respond to the teacher's questions. Sometimes, of course, there is parental pressure to excel and succeed, and parents often have no means of helping their children become more familiar and comfortable with learning mathematics."
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Women and Mathematics, 2005.
This paper uses empirical data to refute the common perception that women are not as skilled at mathematics as their male counterparts.
1,350 words (approx. 5.4 pages), 5 sources, MLA, $ 45.95
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Abstract
This paper explains that gaps do exist between genders in the field of mathematics with females falling into the lower edge of the learning curve; however, the assumption that men are better equipped to solve mathematics equations points to a lack of equitable treatment for females and an unbalanced educational environment in public education. The paper points out that girls and boys with the same math SAT scores do not do equally well in college: Girls actually perform better on average. The paper stresses that, in the middle school, girls generally take more high-ability math courses and make better grades than boys; however, they hold less positive attitudes toward the subject because of their relatively high levels of performance anxiety, little confidence in their personal abilities and a tendency to attribute their success to luck rather than their own efforts and abilities.
From the Paper
"Moreover, the number of women Ph.Ds in mathematics has increased considerably over the years, according to a study conducted by Marie A. Vitulli and Mary E. Flahive. Data collected from the 1991-95 AMS-IMS-MAA Annual Surveys on initial employment of Ph.Ds in mathematics were obtained from questionnaires distributed to math departments with follow-ups to the degree recipients. In this study the researchers focused entirely on new Ph.Ds from Group I-III departments, that is, from departments of mathematics. The high response rate to the questionnaires (95%) from Group I-III departments allowed researchers to regard it as a census. The primary result of the analysis reported that women seem to be getting their share of first jobs, no more and no less."
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Factor Analysis, 2005.
This paper discusses factor analysis, a statistical tool to determine patterns in data.
1,115 words (approx. 4.5 pages), 6 sources, APA, $ 38.95
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Abstract
This paper explains that factor analysis analyzes the patterns of relationship among several variables, with the aim of finding something about the character of the independent variables, which influence them, even though those independent variables, called factors, were not assessed directly. The paper explains that the results gotten by factor analysis are essentially more theoretical and provisional than is true when independent variables are spotted directly. The author stresses that, in order for the factor to be analyzed, the data must be bi-linear; this implies that the row entities and the column entities must be independent of each other.
From the Paper
"Factor analysis can handle over hundred variables at a time; recompense for random and meaningless mistakes, and unravel difficult interrelationships into their major and distinct reliabilities. But, factor analysis has disadvantages. It is mathematically problematic and requires varied and various relevant factors. Its technical terms include strange words like 'eigenvalues, rotate, simple structure, orthogonal, loadings, and communality'. Its product usually takes up a dozen or so pages in a given report, giving little space for a procedural foreword or clarification of terms."
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Professional Development of Teachers, 2005.
This paper discusses professional development for teachers of mathematics.
2,805 words (approx. 11.2 pages), 12 sources, APA, $ 83.95
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Abstract
This paper explains that professional development is an opportunity for existing teachers already in schools to learn new teaching methods thus making them and their programs more effective. The author points out that utilizing outdated or ineffective teaching techniques or an inadequate knowledge of basic technological advances is completely unacceptable in the realm of teaching mathematics because a good knowledge of mathematics is important to all aspects of students' lives. The paper describes two models of professional development programs: (1) CATIE Mentoring Program, which is an extremely successful process for instituting technology into the realm of mathematics teaching and (2) School-within-a-School Model, developed in Canada, which is a project-based learning process strongly supported by the entire school system.
Table of Contents
Introduction
Importance
Good Teachers
Models of Professional Development
Model 1
Model 2
Conclusion
From the Paper
"The program also incorporates parents who pay for students' laptop computers and a local university as a pre-service for the teachers. The program consists of bi-monthly half-day meetings conducted within the participating schools and there they review issues, concerns and topics such as cooperative learning, curriculum integration. The program also has a very effective community model that helps teachers utilize more social and culturally aware notions in the classroom. This helps the teachers teach at a level that is adequate for the various learning levels with in the classrooms."
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Guillaume Francois Antoine de L?Hopital, 2005.
This paper discusses mathematician Guillaume Francois Antoine de L'Hopital, born in Paris, France in 1661.
1,445 words (approx. 5.8 pages), 7 sources, MLA, $ 47.95
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Abstract
This paper explains that L'Hopital, who lived during the conception of modern calculus, was taught by Bernoulli; the result of this tuition was L'Hopital's "Analyse des Infiniments Petits", which became the French reference book in the calculus for a century. The author points out that L'Hopital's name is guaranteed to survive in the memories of thousands of mathematicians because of the L'Hopital rule, which is useful when dealing with indeterminate forms. The paper relates that L'Hopital created the template by which all calculus texts would be modeled and measured against for the next three hundred years. Formulas included.
From the Paper
"A natural progression from his two first works on the topic of calculus would have been a serious examination of the integral calculus. Indeed, this was a project that L'Hopital was capable of and actually began to write before his death. However, one of his contemporaries-Leibniz-made it known to L'Hopital that he also endeavored to publish a work covering the same hole in written calculus of the time. Apparently, out of respect to the mathematician who made much of his fame possible, L'Hopital abandoned the project."
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Florence Nightingale and Mathematics, 2005.
An analysis of the contribution of Florence Nightingale to the field of mathematics.
1,333 words (approx. 5.3 pages), 7 sources, MLA, $ 44.95
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Abstract
This paper examines how although Florence Nightingale is mainly remembered for her compassion and work in the field of nursing. Another of her achievements was in the field of statistics and mathematics. It looks at how she succeeded in augmenting a practical application of statistics to the profession of nursing and how her graphical and statistical representations of deaths in the Crimean conflict promoted the use of sanitary reforms, which were implemented throughout the nursing profession.
From the Paper
"Furthermore, she also made important contributions in the field of epidemiology. This is the study of the demographics of disease processes, including the study of epidemics, which uses statistical procedures. For example, Nightingale "... made a statistical study of sanitation in Indian rural life. She invented a diagram known as the coxcomb or polar area chart to depict changing patient outcomes in the military field hospital she managed". (Campus Program) She had become an expert statistician and in 1858 was elected the first female member of the Statistical Society. She was also made a member of the American Statistical Association. The statistical measurement and innovations used during the Crimean War not only led to a reduction of deaths but also added to her reputation as both a statistician and nurse."
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The Gender Gap and Science, 2005.
An examination of the issues concerning women and science.
2,236 words (approx. 8.9 pages), 3 sources, MLA, $ 69.95
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Abstract
This paper explores the causes revolving around the exclusion of women from science, math, and technology educational programs and looks towards suggesting remedies.
Outline
Introduction
Summary
Evaluation
Mentoring
References
From the Paper
"For quite a number of years researchers have delved deep into the gender equity in science, engineering and technology educational programs. These studies have utilized for interalia raise the consciousness of gender discrimination; convey regarding policy decisions; as also as a drive to tackle instances of gender discrimination. At the moment there is paucity at the national level of computer scientist, engineers and programmers and its effect has fallen badly on USA. The Commission on the Advancement of Women and Minorities in Science, Engineering and Technology Development reports which indicate that in spite of the growth in science, mathematics, and technology jobs, the representation of women in both the jobs is less."
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Statistics, 2005.
A definition of statistics and explanation of the statistical process.
4,594 words (approx. 18.4 pages), 5 sources, MLA, $ 119.95
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Abstract
This paper focuses on statistics by explaining the statistical process and the primary purpose of statistical processes and then outlining the best practices for statistical procedures. The paper also explains the purpose of statistics and how they are used for product research.
Introduction
Statistics and Their Importance to Research Investigation
Correct Statistical Processes
Summary
From the Paper
"Before there can exist any intelligent discussion with respect to the topic of statistics one must understand that a statistical process does not stand alone nor does it function without being a part of a much larger plan, namely, research investigation as a whole. Statistics and their accompanying processes are only one such part of the research plan and, as such, must be viewed in totality of purpose over single identification. Without a formidable research plan a statistical process is without merit and akin to discussing how many angles can be placed on the head of a pin. In general, and from a philosophical perspective, the research plans and statistical analysis, according to Ohlson (1998) "...are not unlike an artist's canvas, as they strive to capture forever the intrinsic and observable subject placed before it" (10)."
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Mathematics in Gambling, 2004.
An examination of the ways in which mathematics is used in gambling and casino games today.
1,000 words (approx. 4.0 pages), 4 sources, MLA, $ 35.95
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Abstract
This paper provides an overview of casinos and casino games and a discussion of vigorish, or the amount of advantage the house has over the gambler. An analysis of how mathematics and statistics can be used to further improve these chances is followed by a summary of the research in the conclusion.
From the Paper
"The casino of the 21st century may also be called a gambling, or gaming, house or club; these are places where people can risk their money against a common gambler, known as "the banker" or "the house". Casinos around the world have an almost a uniform character (Casinos 2004). According to Barker and Britz (2000), casinos are able to calculate their handle for slot operations because the revenue accounting of the win-to-handle ratio is accurately known. Drop and handle are frequently confused terms; however, there is an important distinction between the two. "Handle is the total amount wagered, or bet: A chip may be wagered (bet) many times before the game goes to a decision and the chip is won or lost" (Barker & Britz 6). Video gaming machines are set to report the coins/cash going in and the coins or payouts going out; however, the handle for table games is calculated differently."
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Probability and Normal Distributions in Business Decision-Making, 2005.
A look at the importance of statistical information to businesses and how it allows managers to collect, analyze, and interpret data vital to their company's success.
1,020 words (approx. 4.1 pages), 5 sources, APA, $ 36.95
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Abstract
This paper discusses the importance of statistical information to a company's growth and success. The paper explains how a manager with statistical skills will have a significant business advantage, since business decisions are often based on inferences from data. The paper further explains the many applications of statistical tests and how the the premise for many of these tests relates to two concepts, probability and the normal distribution. Finally, the paper explains both concepts and how these concepts form the basis of most statistical tests.
From the Paper
"A manager must often estimate the characteristics of a population based on information provided by a sample chosen to yield an estimate of population characteristics. Confidence intervals are a mathematical statement of the level of confidence around the estimate. Today's global businesses face dynamic and complex markets. The environments in which these enterprises compete are constantly changing. Successful firms can develop strategies that enable them to be flexible in the changing world. These are firms that manage changes instead of reacting to changes. In order for firms to become proactive in change management, they must be able to quickly analyze different strategies and the impact of different scenarios on the firm's performance. For companies in high technology industries, the dynamic and highly uncertain nature of their businesses makes rapid decision making a key for survival. Thus, it is crucial that businesses develop the capability to analyze business decisions and environments quickly without relying on costly, time-consuming studies and research."
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Determination of Exchange Rates, 2004.
This paper conducts tests to provide a clearer picture of the accuracy of estimation of exchange rate modifications.
2,615 words (approx. 10.5 pages), 30 sources, APA, $ 78.95
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Abstract
This paper analyzes the rational expectation hypothesis relating to the foreign exchange market modifications using various statistical methods and survey data, including three very important exchange rates: German Mark / U.S. Dollar, G.B. Pound / U.S.Dollar, and Japanese Yen / U.S. Dollar. The author points out that overlapping forecasting causes the serial correlation problem, which is corrected by estimating the forecast errors as a moving average process. The paper concludes that the expectations of spot exchange rates at various horizons and the actual rates have unit roots, all exchange rates showed stationary forecast errors for the one-month and three-month ahead estimations and the GB Pound / US Dollar proved stationary for the six-month ahead estimation, which was consistent with the results of the unit root tests.
Table of Contents
Problem Identification
Objectives
Hypothesis
Methodology
Literature Review
Findings and Results
Conclusions and Recommendations
From the Paper
"Testing the rational expectation hypothesis in realtion to the estimation of the Mexican Peso in this time frame is biased beyond doubt. Therefore, applying the standard assumption of normality of the distribution, currently used in statistic tests, will not yeald any valid results. This statistical defect may also be observed in other circumstances, such as the probability (even quite small) of a major modification of the exchange rate in the studied period, a speculative bubble or an important change in fundamentals, especially iF the sample size is not sufficient in order to correct such faults (by applying the central limit theorem)."
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Logical Fallacies, 2005.
A look at how logical fallacies confront people in all aspects of life and the harm they can do do our decision-making process.
774 words (approx. 3.1 pages), 3 sources, APA, $ 27.95
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Abstract
This paper describes how logical fallacies can affect us in academic and scientific research and even in the decisions we make in everyday life. The paper points out that a very valuable skill in making decisions is the ability to identify logical fallacies and to apply tools that help you identify them. Moreover, the paper describes some types of logical fallacies and some of the tools for identifying them, as well.
From the Paper
"There is little question that logical or analytical fallacies can (and have) plagued data analysts in all major fields of knowledge from the beginning of recorded time. Not only can these fallacies of reason cause immense harm due to their capacity to mislead, but they can also ruin an otherwise sound argument or conclusion. For this reason, it is important to utilize varied ?tools? designed to prevent or detect fallacies."
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Hume?s Problem of Induction, 2004.
A discussion of David Hume's problem of induction, which posed the question about what evidence there was to support the instinctive understanding that the future would resemble the past.
3,343 words (approx. 13.4 pages), 6 sources, MLA, $ 95.95
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Abstract
This paper begins with an explanation of deductive and inductive reasoning and then goes on to analyze the questions raised by well-known skeptic and humanist, David Hume, about finding indisputable evidence that the future will resemble the past or that observed instances can predict new instances.
From the Paper
"For some reason, the traditional example of how inductive reasoning works is to ask how it can be known that the sun will rise tomorrow. It is certain that every day as far back as one can remember or research, the sun has risen every day. How does this prove, however, that it will rise tomorrow? Even barring a super nova or an asteroid hit that took Earth off its axis, how could we know that the so-called laws of physics will be still active tomorrow? Mere deduction cannot prove that the sun will rise, though it may be able to explain how it rises. One depends rather on past experience to predict the future. The sun will rise, we believe, because it has always risen in the past."
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Graph Theory and Road Redesign, 2004.
This paper explores the ways in which graph theory can be joined to computer simulation programs to make the planning stages of road redesign more efficient and more accurate.
5,240 words (approx. 21.0 pages), 31 sources, APA, $ 130.95
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Abstract
This paper explains that graphs allow for a simplification of the real world, doing away with extraneous details without sacrificing any information necessary for the task. The author points out that graph theory is the best tool to use to solve the problem of road conversion because it is the most parsimonious. The assumptions made by graph theory more closely than any other model or theory match the real-world conditions. The paper states that, in converting roads, the effect in the real world will be a disruption of what had been the shortest paths between different points, and urban planners will include some consideration of shortest path issues. Tables and figures.
Table of Contents
Introduction
Graph Theory as the Basis for Conversion of Two-Way Roads
Undirected Graphs to Digraphs
Reachability Problem
Shortest Path Problem
Importance of Simulation
Comment on Validity of Data
Conclusion
From the Paper
"The specific shortest path method that is most useful in this particular type of problem is Pallottino?s graph growth algorithm with two queues. It must be emphasized that the determination of the shortest path algorithms is perhaps the most important component of any network analysis. It is also quite often the first step in any network analysis as the determination of the shortest path is often needed as a key datum in making later choices."
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Statistical Education, 2004.
An examination of the importance of learning statistics and how it can help in every aspect of life.
3,102 words (approx. 12.4 pages), 7 sources, MLA, $ 90.95
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Abstract
This paper explains how, in schools, statistical education is primarily taught in mathematics, yet statistical ideas are used in other subjects, including science and economics. It discusses why teachers and researchers need to constantly work towards improving statistical education, leading to a great deal of research in the field. This paper examines existing research to determine how statistical education research can be improved in the future.
From the Paper
"Statistical education has become an important part of curriculums in all levels of education. At both the undergraduate and graduate levels, statistical literacy is now a key objective in many classrooms. As a result, statistics is now being taught across various disciplines and is rapidly becoming a prerequisite course for graduation, regardless of a student's major. The teaching and learning of statistics has recently increased dramatically in many schools. As a result, many U.S. states now emphasize and include statistical thinking in their statewide curriculum guidelines."
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Integrated Studies, 2004.
A discussion of the association between mathematics and science.
1,935 words (approx. 7.7 pages), 7 sources, MLA, $ 61.95
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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."
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Co-integration, 2004.
A research study using co-integration analysis to study the relationship between the stock index cash and futures market in relation to price discovery.
3,752 words (approx. 15.0 pages), 27 sources, MLA, $ 103.95
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Abstract
Co-integration has come to represent an econometric data analysis method that has been utilized to determine the long-run equilibrium relationships among nonstationary economic variables. This paper uses co-integration analysis to determine the relationship between the stock index cash and futures market in relation to price discovery, market stability, and market efficiency. The data for the study was collected from the Athens Derivatives Exchange S.A. (ADEX), with the main data for the study being the returns of the FTSE/ASE-20 futures and spot index. In order to study the relationship between the ADEX stock index cash and futures market in this paper, daily closing price returns of the FTSE/ASE-20 Index are considered for the period from 3 January 2000 to 27 July 2003. The paper includes several graphs and tables.
Paper Outline:
Data
Methodology
OLS Results
Co-integration Results
References
From the Paper
"GARCH modeling represents an important data analyses procedure as it provides a means of further understanding and modeling volatility, taking into account excess kurtosis (i.e., fat tail behavior) and volatility clustering, two important characteristics of financial time series. It provides accurate forecasts of variances and covariances of asset returns through its ability to model time-varying conditional variances. As a consequence, the application of GARCH models has been identified as useful in risk management, portfolio management and asset allocation, option pricing, foreign exchange, and the term structure of interest rates."
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The Meaning of the Word "Implication", 2004.
Looks at John Corcoran's work on the true definition of the word "implications" in all its variations.
2,916 words (approx. 11.7 pages), 12 sources, APA, $ 86.95
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Abstract
This paper summarizes, analyzes, and critiques John Corcoran's work, in which he puts the different definitions of the word "implications" into distinct, well-defined, recognizable contexts. The paper reviews Corcoran's work from the perspectives of history, logic, philosophy, and linguistics.
From the Paper
"In his paper, Corcoran lists several ?implication? phrases in common English usage which presuppose that the premise ?A? is true and that validates the conclusion B. Corcoran also critiques the philosopher/mathematician Frege in that Frege?s thesis on logic is constrained by his instincts. Corcoran avers that Frege included pure logic in his thinking and did not make room for deduction as a major contributor to the concept of implication. ?Frege's strategy was to show that no appeal to intuition is required for the derivation of the theorems of number theory. This in turn required that he show that the latter are derivable using only rules of inference, axioms, and definitions that are purely analytic principles of logic(Ref)??which he did not."
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