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Mathematical Concepts, 2006.
Examines the development and application of four mathematical concepts.
2,325 words (approx. 9.3 pages), 14 sources, MLA, $ 71.95
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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."
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Chaos Theory, 2005.
This paper applies chaos theory to business management.
1,070 words (approx. 4.3 pages), 6 sources, MLA, $ 37.95
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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."
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Chaos Theory, 2005.
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".
1,500 words (approx. 6.0 pages), 2 sources, MLA, $ 49.95
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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."
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Stephen William Hawking, 2005.
Examines the life history and writings of this famous physicist and mathematician.
1,945 words (approx. 7.8 pages), 4 sources, MLA, $ 61.95
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Abstract
In the world of science and history there are few great names that can match the name of Stephen William Hawking. Hawking is perhaps one of the best known physicist and mathematicians in history, or at least in modern times. This paper presents a close examination of the life and works of Stephen William Hawking. The writer explores his childhood to help determine how he became what he is today. The writer then examines his adult life, his works and his contributions to the world, as well as some of his more better-known theories and ideas.
From the Paper
"Another difference between Hawking and many other scientists throughout the world is that he understands the world's need for laymen terms. Many scientists are reported to be so scientific and mathematically based that their works and words are boring and over the head of everyone but other scientists. Hawking understands the average person is not going to take time to dissect scientific jargon and he put together a book that explains many of the most mind boggling ideas in history in terms that can be understood by the non scientist."
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Math Anxiety, 2005.
Examines the article "The Causes and Prevention of Math Anxiety" by Marilyn Curtain-Phillips.
791 words (approx. 3.2 pages), 1 source, APA, $ 28.95
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Abstract
Marilyn Curtain-Phillips' article, "The Causes and Prevention of Math Anxiety" attempts to explain the causes of math anxiety among students young and old alike. This paper shows how the
article suggests that while math anxiety is something that is tangible and real, it is also something that can be conquered when it is approached from the right perspective.
From the Paper
"Curtain-Phillips then goes on to suggest that teachers should alter the manner in which they teach math in order to help students feel more successful and realize higher levels of achievement in the classroom and out. The authors cites research conducted by Spikell in 1993 which suggests that students are more able to comprehensively learn actively rather than passively, meaning lessons should be presented in a manner that engages students actively. The article points out that lessons in math should be taught from a visual and special, logical and mathematical, body and kinesthetic, musical as well as verbal and linguistic perspective so that everyone is able to grasp information based on the manner in which they learn best."
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Darrell Huff's "How to Lie with Statistics", 2005.
This paper is a book review of Darrell Huff's classic 1954 text "How to Lie with Statistics".
905 words (approx. 3.6 pages), 1 source, MLA, $ 32.95
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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."
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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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