Abstract This paper explains how Frege's book is an influential and valuable insight into the philosophy of mathematics. It shows how Frege delves deeply into, not only an understanding of numbers, but also looks into much larger questions surrounding meaning and truth. Frege argues against the idea that arithmetic is based on psychology and, instead, notes that logic is the main underpinning of arithmetic.
From the Paper "Friedrich Ludwig Gottlob Frege was born in Germany in 1848. He got his doctoral degree in G?ttingen, and quickly wrote his post-doctoral thesis, and became a university professor. During his long and fruitful academic career, the tireless Frege worked extensively to build up the philosophical foundations of mathematics and science. Among his important contributions is the invention of an artificial language called Begriffsschrift, which was based on logical notation (Frege Biography). Frege wrote extensively, publishing a number of other influential papers during his lengthy career, including Grundgesetze der Arithmetik, Volume I (1893), Logic (1897), Sources of Knowledge of Mathematics and the Mathematical Natural Sciences (1924/5), A Brief Survey of my Logical Doctrines (1906), and Thought (1918) (Frege Biography)."
Abstract This paper explains that prime numbers have upset humanity for the last 2,300 years, ever since Euclid proved that there was infinity. The paper presents Euclid's proof. The author points out that, in the 19th century, the Russian, Tchebychef ,made significant contributions to the study of prime numbers by concluding that if the B(x) from Legendre's equation had a limit, then that limit had to be 1. The paper relates that Bernhardt Riemann, in 1859, continued Euler's work on series of numbers and made fundamental new discoveries within the prime numbers domain.
From the Paper "Let x be a positive real number and let us define ? (x) as the number of primes less or than equal to x. ? (x) is a function and will be studied as such. For small values of x, we can intuit the values for ? (x). Thus, for example, if x is 10, then the primes less then 10 are 2, 3, 5 and 7, so that ? (10) is 4. Similarly, ? (24) = 9. Our concern is for very large values of x."
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.
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."
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)."
Tags: expectations, statistics, overlapping, unit, errors
Abstract This paper examines the results of a factor analysis conducted on Richardson's short version of the ASQ with data obtained from 187 university students. This paper defines factor analysis and describes each step in the factor analysis process, giving a clear explanation for each decision made.
Outline
The ASQ
Factor Analysis Defined
Sample Size
Data Screening & Preliminary Analysis
Descriptives
KMO and Bartlett's Test of Sphericity
Factor Extraction
Factor Rotation
Conclusion
From the Paper "Richardson (1990) developed a short version of the ASQ in an attempt to examine the reliability and replicability of this version, which contained eight subscales of meaning orientation and reproducing orientation. Richardson concluded that this new questionnaire can be used in examining meaning orientation and reproducing orientation in research on student learning, with a factor analysis successfully retrieving these two primary approaches to learning. Richardson did warn however that the validity of the constituent subscales was still rather unclear."
Abstract The current paper comments on a quote by J.M Johnson and H.S Pennypacker that compares inferential statistics to single case designs. It discusses how the statement in question calls to account psychology as a science to abandon a traditional reliance on inferential statistics and group design research and to support its practical focus on the individual with reliance on more individually focused research.
From the Paper "Inferential statistics is a branch of statistics that consists of generalizing from samples to populations, performing hypothesis testing, determining relationships among variables, and making predictions (Tabachnick & Fidell, 2001). This type of research is the most widely used in psychology, with the majority of published studies in this field relying solely on the use of group comparisons. The major argument for the use of inferential statistics is that it increases the external validity of the study and increases the likelihood of the results generalising to other people. These results are gathered by statistical inference where various methods of calculation are used to find a central tendency within a group. The variability of the results between subjects are often explained by measurement error or extraneous variability because well conducted group research introduces the only variability deliberately as an intervention designed to examine and measure its effect(s) on subjects (Hayes, Barlow & Nelson-Gray, 1999)."
Abstract Notwithstanding the adage, "Beauty is in the eye of the beholder," to explain why some humans appear more attractive than others, this paper provides a review of the relevant literature to identify what scientific basis there is for making determinations of beauty and how this can be applied to fashion models today. A discussion of the criticisms being directed against beauty pageants and their directors is followed by a summary of the research in the conclusion.
From the Paper "We have all seen it: the New Miss America proudly walking down the runway, tears streaming down her humble face as she displays her crown and scepter -- showing the whole world exactly what it takes to be considered "beautiful." Some researchers, though, say the swimsuit-and-scholarship competition promotes an "ideal of female undernutrition" by crowning ever-skinnier contestants. A member of the staff at Johns Hopkins School of Public Health said, "Clearly there is a trend toward undernourished winners." In a recent analysis published in the Journal of the American Medical Association, scientists examined the decline in body mass index (BMI) scores among contest winners since first Miss America won the title in 1921. The winner of that contest had a BMI of 20.4. The "BMI reflects a person's weight divided by height to arrive at a number indicative of weight-related health" (Vergano, 2002, n. pag.)."
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)."
Abstract In chapter V of his book, "The Problems of Philosophy," originally published 1912, Bertrand Russell examined how mere humans perceived the world and how this perception occurred. This paper provides a brief biography of Russell. This is followed by a review and discussion of his analysis in "The Problems of Philosophy" to identify how he distinguishes between 'Knowledge by Acquaintance' and 'Knowledge by Description'. The paper also identifies how Russell's theory presents a plausible account of representative realism. A summary of the research is provided in the conclusion.
From the Paper "To help elaborate on this component of his view, Russell says, "We shall say that we have acquaintance with anything of which we are directly aware, without the intermediary of any process of inference or any knowledge of truths." According to Russell, only the objects of immediate experience are known by acquaintance, through our direct awareness of them. Other things are known only by description, through the mediation of our apprehension of true propositions about them. For instance: "I am in a state of hunger now" may be known through acquaintance, but "Eating a pizza will relieve the state of hunger" can be known only by description. In spite of this apparently narrow extent, Bertrand maintains that knowledge by acquaintance provides the foundation for further knowledge by description, discussed further below. "
An assessment of the avenues open to New York schools in terms of training mathematics and science instructors effectively so that there is true communication between the faculty and the students.
Abstract This paper looks at aspects of teacher training and instructional quality in the instruction of mathematics and sciences in New York State schools, concentrating primarily on students in the 7-12 grade range and ways in which teacher training and instructional quality can interact in a planned program. This program is designed to train math and science teachers in more effective uses of pedagogy and the student-centered classroom in New York schools and focuses on the implementation of technology in the classroom as related to these subjects. It begins with a literature review in which instructional methods for mathematics and science teachers are assessed. Current policy is then analyzed, including training programs in other states that have been shown to be effective in teacher training. It advocates a system in which technology in the classroom, combined with more effective teacher-student interaction and subject application, can be introduced into the educational system.
Outline
Introduction
Literature Review
Current Policy
Recommendations
Short-Term and Long-Term Benefits
Conclusion
Bibliography
From the Paper "Teachers can act as advocates of technology by acknowledging their own place in the school's inherent duty to empower students and help them improve their situation in terms of heightened achievements. To help the school fulfill its mission to truly help students and enable them to overcome their disadvantages, a new paradigm of instruction is sought. This new paradigm is based on the integration of computer assisted instruction into schools, and the goal is to improve conditions and monitor achievement through the implementation of teacher-led pilot programs. Computer assisted learning can help children learn to read, learn basic mathematics, and participate purposefully in their own
educational development."
Abstract This paper explores the causes revolving around the exclusion of women from science, math, and technology educational programs and looks towards suggesting remedies.
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."
This paper uses an algebraic model in conjunction with an extended strategy game to prove that the passage of Chinese Anti-Secession bill was empirically and scientifically sound.
Abstract This paper explains the dynamic history of the China-Taiwan relationship especially the controversial Chinese Anti-Secession bill, particularly Article 8, which states that, after exhausting all other avenues, China reserves the right to use military force or embargo to bring the situation with Taiwan to a close, conditional on Taiwan actually declaring independence. The author creates a game with nominal payoffs (a, b,c) creating a situation where China, assumed to be a rational actor, would most prefer, for example, say "c" but could risk getting a payoff of "b". The paper relates that, after computing the minimum threshold using expected utility formulas, arriving at a non-numerical solution, a probability value shows that China was rational in its decision to pass the bill since it saw its chances of being reprimanded by the international community as being much lower than is seen by the international community. Graphy. Formula.
From the Paper "Those supporting Taiwan in this conflict are the US and Japan, and from this US alliance we could see countries like New Zealand and Australia come to Taiwan's aide if the US decides to invoke the conditions of the ANZUS treaty signed in 1951 . Among those supporting China's position are countries like Pakistan , North Korea, and Russia . If the bill was interpreted as a hostile war bill instead of a "fence-mending" bill as China claims it to be, the global community could formally and militarily become involved in the conflict. Setting aside this possible military threat, China must also weigh the economic consequences, with reaction from the global community that could include sanctions."
Abstract This paper explains that any tool, such as a graphing calculator, which can help students gain an improved mastery of the fundamental skills required to complete algebraic problems, must be viewed as educators as a "Good Thing"; but a consistent theme is the need to keep the material relevant in order to maintain student interest. The author points out that, although students should have the experience of entering the program commands themselves, an alternative approach is for the teacher to write the relevant on one calculator and then distribute it to students' calculators by using their linking capabilities. The paper relates that teachers can adapt the material for use with Texas Instruments (TI), Casio, Hewlett-Packard and Sharp graphing calculators.
From the Paper "The use of graphing calculators in a comprehensive algebra curriculum has been advocated by a number of educators. For example, some currently teach their students how to solve and graph linear equations manually, give them a test on it that is worth 50 points where no calculators are allowed during the test, classwork, or homework. Afterwards, they teach students how to solve the same or similar problems using a calculator. Then they give them another test of the same topic as during which problems are to be solved only by using calculators. During chapter tests and exams, students have the freedom to choose whether to use a calculator or not. "
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."
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."
Tags: derivative, calculus, Bernoulli, indeterminate, text
