"Mathematics / Statistics" Essays

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Human Factors Affecting Safe Operation Data Analysis Chapter

Data Analysis Chapter  |  15 pages (4,150 words)
Bibliography Sources: 2


¶ … Human Factors Affecting Safe

Operation Of The UAV

Study of Selected Human Factors affecting safe operation of the UAV

This chapter presents the findings of the thesis. The survey questionnaires are collected from the 35 respondents. The data are collected to test the following hypotheses:

Ho: "Majority of UAV pilots do not agree that graduating from Undergraduate Pilot… [read more]

NBA Stats Term Paper

Term Paper  |  2 pages (614 words)
Bibliography Sources: 0


1 (for points). Mean height is 78.7 and mean points is 16.843, so calculating the covariance of this data pair would look like this:

(72 -- 78.7)(13.1-16.843) = 25.0781

In order to develop the value for each pair, two new columns were created in the Excel sheet to calculate the difference of the data point and the mean with the following formulas:

=a2-78.7 (for height, pasted into the other 99 rows which automatically adjust the cell value for each row, as =a3-78.7, a4-78.7, etc.), and =b2-16.843 (for points, also pasted).

A third column with the following formula created the product of each row in these two columns:

=c2*d2 (pasted for all rows).

The average function was used to determine the mean of this last row, which is the covariance: 2.1679. Standard deviations are 3.60274867 (for height) and 3.74805687 (for points), meaning Pearson's coefficient is calculated as:

2.1679/(3.60274867 * 3.74805687) = 0.160545859.

Linear regression attempts to find the line of best fit for a data sample. The basic equation of any line for variables x and y is given as y = a + bx. For a linear regression slope (b) is calculated as:

((n*?xy)-(?x)(?y)) / ((n*?x2)-(?x) 2)

Adding another column to the spreadsheet enabled the quick calculation of height * points (xy) for each data pair, and a column for x2 was also added; the SUM function was used to calculate ?xy (132771.2), ?x (7870), ?y (1684.3), and ?x2 (620654). With n (population size) 100, the slope (b) of the equation becomes:

((100*132771.2)-(7870)(1684.3))/((100*620654)-(78702) = 0.168708171.

The intercept (a) is calculated as:

(?y-b (?x))/n which with the substituted values becomes

(1684.3-(0.168708171*7870))/100 = 3.56566694.

The full linear regression equation for this data set, then, is given as:

points = 3.56566694 + (0.168708171*height)

Chi-square analysis cannot be applied…… [read more]

Mathematical Knowledge for Teaching Article Review

Article Review  |  4 pages (1,055 words)
Bibliography Sources: 0


Mathematical Knowledge in Education

Differentiating Types of Mathematical Knowledge and Relevance to Education

Ball, D.L., Lubienski, S., and Mewborn, D. (2001). "Research on teaching mathematics:

The unsolved problem of teachers' mathematical knowledge." (In Handbook of Research on Teaching. New York: Macmillan).

Generally, mathematics proficiency among teachers corresponds to higher achievement in their students. While that conclusion has been supported by a substantial volume of empirical research, much less empirical research has been devoted to trying to understand how and why teacher achievement in mathematics benefits student outcomes, or what it is about mathematics, specifically, that generates this apparent relationship. Most importantly, there is a need to understand whether and to what extent teacher mathematics achievement in different aspects of mathematics matters with regard to the positive effect on learners.

According to the authors of this article, there is a fundamental difference between teaching mathematics and teaching through mathematics. In many ways, that distinction helps explain why, in general, mathematics proficiency among teachers tends to correspond to better learning outcomes. More particularly, understanding that distinction may help explain why the positive benefit of mathematics knowledge among teachers is much more evident in connection with their academic study of mathematical method than in connection with their academic study of advanced mathematics. Furthermore, it could explain why advanced mathematical achievement among teachers also corresponds to higher incidence of negative affects on some learners whereas that is not true in the case of teachers whose high achievement in mathematics relates more to their non-pedagogical content knowledge than to their pedagogical content knowledge.

In principle, the value of teaching mathematics is much broader than the value of the substantive material, particularly in contemporary society that provides instant and accessible electronic calculation to solve the types of mathematical problems that could typically arise in everyday adult life. Study after study suggests that teachers who are more knowledgeable about mathematics tend to promote learning better than teachers who are less proficient in mathematics.

However, there is evidence that suggest that this relationship is much more complex than simply a direct transfer of pedagogical mathematical knowledge. For example, one unexpected finding is that the benefit of greater mathematics proficiency exists in the first grade. Presumably, all teachers are equally proficient at first-grade addition and subtraction; moreover, the academic study of mathematics in greater depth (i.e. post-calculus) should not have any impact on the level of teacher understanding of first-grade mathematics concepts. Similarly, there is no intuitive reason that either the mathematical proficiency of teachers or their highest level of mathematical study should translate to better teaching of elementary mathematical concepts. In that background, the correspondence between teachers having studied mathematical method and the highest identifiable benefits to learning seem to explain the basis of the phenomenon.

Specifically, mathematics (especially at the elementary level), can be taught rigidly and by rote rule or by conceptual understanding. Apparently, teachers with more extensive experience in studying mathematical method are better equipped to deliver mathematics lessons in a manner conducive to inspiring… [read more]

Butts, R.E. ). Galileo. In W.H. Newton-Smith Annotated Bibliography

Annotated Bibliography  |  3 pages (864 words)
Bibliography Sources: 0


Butts, R.E. (2001). Galileo. In W.H. Newton-Smith (Author), a companion to the philosophy of science (pp. 149-152). Malden, MA: Blackwell Pub.

This excerpt from a reference work is a biographical sketch of Galileo, 17th

century Italian scientist. It outlines five crucial achievements that he made, a few of which include his divergence from Aristotelian theories of science, his advocacy of the real-world applications of mathematics, and his use of experimentation. The author outlines the origins of Galileo's scientific research, particularly in cosmology and his work with the telescope. His work also centered around making geometry less abstract. He pointed out how geometric laws worked in concert with both the natural and mechanical worlds. The most compelling point the author makes, which has application even today to teachers and researchers, is about Galileo's rejection of the dominant philosophies of the era. Though he created controversy, opposition drove his science to advance, leading ultimately to success.

Frodeman, R., & Parker, J. (2009). Intellectual merit and broader impact: The National

Science Foundation's broader impacts criterion and the question of peer review.

Social Epistemology, 23(3-4), 337-345.

The article examines how scientific discovery dictates social values, and how the philosophy of science has evolved. Science has historically been funded with an eye to how it will benefit society. The specific focus of the piece is on the NSF

peer review process and the change of criteria used to allocate funding that occurred in 1997. This change created two criteria: intellectual merit and broader impacts. The broader impacts criteria include education/outreach and an effort to broaden diversity. But the question remains: How is benefit to society determined and measured? The article also raises the question of whether these two criteria categories should be merged, and if intellectual merit is actually a subset of broader impact. This is brought up to point of the potential pitfalls of peer review and to call for a closer examination of its procedures. This is relevant to math education in that research into education practice should be viewed with a mind toward its application in the lives of students and its greater impact on society.

Lesser, L.M. (2000). Reunion of broken parts: Experiencing diversity in algebra.

Mathematics Teacher, 93(1), 62-67.

The author employs a central metaphor of the meaning of algebra, that being the reunion of broken parts. He compares this to the way students interact with algebra, given that they can feel disconnected from it and it is the job of teachers to provide real world applications that will make connections for the students. He takes aim particularly at the need to…… [read more]

Derivatives and Definite Integrals Word Term Paper

Term Paper  |  2 pages (688 words)
Bibliography Sources: 2


This is done with a "time derivative" which defines the rate of change over time. The instantaneous velocity of an object is calculated by the coordinate derivative relative to time. To know how quickly the velocity of a given object will change in the course of time, another value called acceleration is defined. Thus, acceleration is the time-derivative of an object's velocity.

How are derivatives used to solve maximum and minimum problems? The maxima and the minima, also known as the extremum, are the values of the largest and smallest limits that a function may take in a given point. They are expressed as a set of greatest and least values. Derivatives are used to determine these points. The derivative of a function is interpreted geometrically as the slope of the curve of the mathematical function y (t), whereas the function of t is plotted. The derivative is noted as positive when a function increases toward a maximum; the maximum being horizontal at zero. It is considered negative just beyond the maximum. The second derivative notates the rate of change. It is called negative since the process of the slope, as described, is always getting smaller. The second derivative is always negative and corresponds to a maximum.

How is the definite integral used to solve area problems? A definite integral is an integral with upper and lower limits. It is used to calculate the area of certain regions in the plane. In the calculation of the area of a region, the region finds a limit above by the graph of a function f (x), below by the x -axis, and on two sides by vertical lines that correspond to the equations x = a and x = b.


Nave, R. Derivatives and integrals. Hyper Physics, Retrieved from http://hyperphysics.phy-astr.gsu.edu

Kouba, D.A. The Calculus Page, U.C. Davis Department of Mathematics. http://www.math.ucdavis.edu, Retrieved January 25, 2011

Weisstein, E. Wolfram Mathworld. http://mathworld.wolfram.com, Retrieved January 25, 2011… [read more]

Measurement Scales That Are Used in Collecting Essay

Essay  |  2 pages (716 words)
Bibliography Sources: 0


¶ … measurement scales that are used in collecting and organizing research data. The scales discussed in this text are: nominal; ordinal' interval' and ratio. The differences between the measurement scales determine how data can be manipulated and studied and which kinds of conclusions can be reached using the data.

Nominal scales are the simplest of the measuring devices. These scales only measure the classification of items. Either the data does or does not fit the scheme. An example of this is gender. When you ask for a respondent's gender on a survey form, this is a nominal question. There are only two answers, and the only arithmetic you can use on the data is to count how many of each kind are in each classification.

Ordinal scales include the classification involved in nominal scales, but they can also measure preferential order. In addition to classifying popcorn, for example, as air-popped or oil-popped, the respondent can also rank the different flavors of popcorn in order of best to worst. The limitation of using ordinal scales is that there is no uniform interval between the rankings. The difference between "highest" and "high" isn't necessarily the same in the respondent's mind between "lowest" and "low."

Interval scales take care of the problem with ordinal scales, as they allow for classification, order and an equality of difference between rankings. The difference between 1 and 2 is the same as the difference between 4 and 5, for example. The data is relatively symmetrical and researchers can do operations like plotting a standard deviation and finding the mean. Intervals can be used to find averages, which is not possible with ordinal rankings.

Ratio scales are the most complicated and can be the most useful. They include all the qualities of nominal, ordinal, and interval scales, plus the provision for an absolute zero. Measurements like distance, volume, length, money, population counts, etc. are all measured on a scale that begins at zero. Ratios are most useful with data that can be definitively measured and they are more useful in the hard sciences than behavioral sciences.

Choosing a measurement scale inherently involves looking at white…… [read more]

Early Reading or Fluency and Word Identification Essay

Essay  |  2 pages (661 words)
Bibliography Sources: 2


Jeffery Case Study

Background for Jeffery

Jeffery has problem understanding algebraic concepts such as polynomials and factoring. Jeffery doesn't require any special aids and his learning capabilities are normal for his age.

Ability to solve polynomials and factorization with the help of Mnemonic device such as FOIL

develop the ability to understand order in which polynomials are solved

Become familiar with complex algebraic terms with the help of vocabulary teaching.

Supporting information for set goals

John Steele (2003) explains that children having difficulty with mathematical concepts can be helped with the use of mnemonic devices because "Mnemonics are useful for memorizing rules, steps, and procedures." (p. 624)

Vocabulary teaching is also critical for developing good understanding of algebraic concepts. This has been proven by Richard Drake's research of 1940 and was later supported by studied carried out by others. Myszczak found that vocabulary learning is significant because it teaches students the ability to focus on the question and what is being asked as "students often search the problem for numbers rather than attempting to comprehend what is truly being asked in the problem" (p. 28)

Schoenberger and Liming (2001) focused on the teaching of a specific list of words that could help students learn mathematical concepts. They believed that "Students should be able to use and understand vocabulary in order to think about and discuss mathematical situations" (p. 27).

Apart from teaching vocabulary, it was also found that simply communicating with students while teaching mathematical concepts could help facilitate better understanding of the concepts. In other words, students could communicate the problem and seek the solution by talking to their teachers. "Language is a major medium of teaching and learning mathematics; we serve students well when we support them in learning mathematical language with meaning and fluency" (Rubenstein, 2007, p. 206).


First Jeffery needs to understand that any two sets in parenthesis without any sign in the middle means multiplication. Once he understands that he needs to understand the…… [read more]

Dot Maps of Three Datasets Term Paper

Term Paper  |  3 pages (910 words)
Bibliography Sources: 0


In the same figure, pine tree data points are randomly distributed in grids. The distribution density changes by changing the size of quadrat area (see Figure 5). For example, 8th and 13th quadrats of redwood data exhibit the highest density of data points whereas 1st, 6th and 14th quadrats do not contain any data point.

In order to test the CRS hypothesis, the appropriate quadrat counts were visually investigated (see Figure 2, 3, and 6. Eventually, the grid size is chosen as 10x10. The mean value, variance, standard deviation and VMR for each dataset were calculated by using MATLAB scripts (i.e., mean, var, std). The results are shown in table 3.

Table 3. Mean, variance, standard deviation and VMR values calculated for 10x10 quadrats.




















The mean values of Redwood and pine datasets are similar; however, it was already analyzed that these two datasets show different distribution characteristics. Variance (square of standard deviation) is another value used to describe the distribution of datasets. Since the variance provides the information about the relative distance between mean and data point, one could say that the cell data is the most uniform data within analyzed datasets. The last value calculated in table 3 is the variance mean ratio (VMR). This ratio of the variance value to the mean value is used to identify whether the dataset is dispersed or clustered compared to CSR hypothesis. Finally, VMR value would quantify the distribution model of any dataset. The VMR value for Poisson distribution is defined as 1.The negative binomial distribution requires a VMR value larger than 1 while binomial distribution has a VMR value smaller than 1. In this regard, the cell and the pine datasets are under-dispersed. In other words, the data points are distributed uniformly in the spatial domain. Therefore, these two datasets obey the definition of binomial distribution. The redwood data is over-dispersed meaning the data points are clustered together. Thus, the underlying distribution model for redwood is negative binomial distribution.

Taken all together, one can define the distribution models of the datasets; however, the relationship between individual data points cannot be discussed only by quadrat count method.

Figure 6. 25x25 Grid.

To validate a null hypothesis the z-scores of three datasets is calculated using CrimeStat-III. The criteria for z scores (95% confident) are as follows.

(1) Region of significance (rejection of the hypothesis) if the set of z scores is outside of the range -1.96 to 1.96

(2) Region of non-significance (acceptance of the hypothesis )if the set…… [read more]

Digital Audio Book Report

Book Report  |  2 pages (679 words)
Bibliography Sources: 1


Digital Audio

Over the last several years, digital audio has been continually innovating the way that people listen to and write various forms of music. This is because, how sound waves travel can be challenging, as the different instruments will reflect: the pitch, tone, bass and timber in varying degrees. When trying to record these sounds this can be challenging, with the various waves reflecting certain amounts of frequency. The problem begins with trying to reflect these various tones in real life, as different analogue and acoustic devices are only focused on the continuous flow of the music. When this is replayed, the various sounds will often be distorted, because they cannot reflect the actual extremes of these reverberations in real life. In the last few years, digital audio has become an increasingly popular solution in addressing these different challenges. With this form of recording focused on the specific mathematical values that the music will represent. As various mathematical formulas using decimals will be used to more accurately reflect, the different sounds that are being recorded. This is important, because it shows how digital recordings are working to accurately reflect the various sounds that are recorded. To fully understand how this new technology is able to accurately, capture the overall collection of different sounds requires: comparing these forms of technology with one another. Once this takes place, it will provide the greatest insights, as to the how digital audio technology is improving the way everyone listens to and records music. (Pohlmann, n.d. )

Digital Recording vs. Analogue and Acoustic Recording

The big difference between digital recording and analogue / acoustic recording is the way the various sounds are represented in a binary number. These are the different mathematical calculations that are used to convert the various sounds being recorded, into actual resonance on the recording device. What makes digital audio more accurate is the way that the binary code is represented. Where, it is more concerned about the actual decimals of the numbers vs. The underlying wave. In mathematics,…… [read more]

Spiritual Principle: So Teach Us to Number Term Paper

Term Paper  |  2 pages (571 words)
Bibliography Sources: 3


Spiritual Principle:

So teach us to number our days, that we may apply our hearts unto wisdom. (KJV Psalm 90:12)

The school year consists of two semesters. Within each semester are three units. During unit one of the first semester which is four weeks, students will learn about functions. During the second unit of the first semester which is five weeks long, students will learn about algebra investigations. During the third unit of the first semester which is seven weeks long, students will learn the geometry gallery. The second semester of the school year also consists of three units. During the fourth unit which is six weeks in duration, the chance of winning will be covered. The fifth unit of the second semester is also six weeks long and students will learn algebra in context. The objective of the sixth and last unit is for students to learn coordinate geometry. The last unit is four weeks long.

Suggested Activities and Experiences:

1. To learn functions, students will spend lab time exploring the National Library of Virtual Manipulatives (http://nlvm.usu.edu/en/nav/grade_g_4.html). By clicking on the functions button, students can play the game that allows them to drag an input number into a machine which then gives the output. Based on the pattern of inputs and outputs, students can figure out what the remaining inputs and outputs will be based on the pattern established by playing the game. This game will allow the students to learn the basic concepts of function in order to move on to other more challenging concepts.

2. To learn algebra investigations, students will download the Mathematics I Frameworks: Student Edition document (https://www.georgiastandards.org/.../9-12%20Math%20I%20Student%20Edition%20Unit%202%20Algebra%20In...). On page seven (7) of this document is an exercise called the…… [read more]

Geometry of Design Elam, Kimberly. ) Book Review

Book Review  |  4 pages (1,184 words)
Bibliography Sources: 1


Geometry of Design

Elam, Kimberly. (2001). The Geometry of Design. New York: Princeton Architectural Press.

The Geometry of Design is not a book about nature, physics, or even of design. Instead, it is a relatively short and simple overview of the role of geometry within nature -- whether it is the analysis after the fact from a human perspective or the way nature works that we find pleasant, the book explains the prevalence of the Golden Mean and other geometrical thermos within nature's design.

Proportion in Man and Nature - Proportion is all around us, it is in everything designed within the sphere of nature; a leaf, a shell, a flower. And these proportions are instinctively pleasurable for us, which is likely the reason why much of design and architecture is based on the very same principles of ratio, proportion, and structure. The basis for this design structure is the Golden Ratio, or 1:1.618. Since the Renaissance, this is the proportion that has been used by artists and architects to proportion their works for mass appeal. Fascinating, however, is just how many objects in nature follow this exact proportion.

Talking Points-

Nature is typically proportionate in design, showing smaller objects to be part of a greater whole.

Even animals show this same proportion, a fish for example, when split into individual rectangles, retains the 1:1.618 ratio.

Similarly, the human body in classical drawing (Leonardo, the Greeks, etc.) form similar ratios.

Preferred facial proportions also follow the ratio; faces that do not are often considered less pleasing.

Chapter 2 -- Architectural Proportions - Through a series of dynamic rectangles, humans have developed their entire building system off this ratio. The harmony of space, e.g. windows, doors, arches, etc., especially in public buildings (governmental locations, arenas, religious buildings), all serves both to inspire and make one comfortable.

Talking Points

Ancient architects were very concerned with the way a building was shaped, laid-out, and built. It had to conform to strict proportions in order to be appropriate from a symboligist viewpoint to its function.

Each architectural discovery and innovation resulted in a reestablishment of the principles of appropriate design (e.g. circular stained glass windows in cathedrals, etc.)

This tradition remained in effect for several centuries; progressing through styles like the Baroque, Gothic, Romantic, etc.

In 1931, a French architect, Le Corbusier, expanded this into a more complex merging of mathematics and geometry -- regulating lines. He believed "with regulating lines, you make God a recipe."

In a way, this invigorated the reemphasis on proportion and meaning to form a more 20-21st century way of applying the Golden ratio to modern construction and design.

Chapter 3- Golden Section- the Golden section of any rectangle is a ratio of the Divine Proportion. The Divine Proportion is derived from the division of a line segment into two segments such that the ratio of the whole segment is the same, as 1: 1.61803. This ratio can be found in any portion or sub-portion of a triangle, rectangle,… [read more]

Group Will Behave, We Make a Hypothesis Term Paper

Term Paper  |  2 pages (580 words)
Bibliography Sources: 3


¶ … group will behave, we make a hypothesis, a testable proposition (or set of propositions) that are believed to be true which seeks to explain the occurrence of some specified group of phenomena, (Random House, 2010). For example, let's say that the widget making department is producing fewer widgets per hour this year than last year despite the fact that the number of employees has remained constant. You hypothesize that their decreased productivity is because of low morale but how do you know if your hypothesis is correct?

Hypothesis testing is a statistical way of testing the validity of a hypothesis. In business and the social sciences, hypothesis testing allows us to generalize about a population based on sample information by using methods that allow the research to separate the effects of systemic variation of a variable from mere chance effects (Sarich, 2010). This is particularly important in business because we often cannot isolate or control for phenomena in a laboratory -- type setting the way a physicist or biologist can (Sarich, 2010).

A 1999 study on the automobile insurance industry appearing in the Journal of Economics and Business illustrates the real world applicability of hypothesis testing. The study entitled Modeling Market Shares of the Leading Personal Automobile Insurance Companies, looks to identify the advantages that give one firm more market share over another. The author uses several hypothesis tests to analyze the market share of the leading personal auto liability insurers from 1980 to 1994, discovering in the process that automation and advertising are significant sources of competitive advantage, and that price-cutting, reductions in commission rates and concentration in the private passenger line of insurance are not - useful information in helping an insurer to decide where to…… [read more]

History and Present Day Applications of Logarithms Essay

Essay  |  3 pages (877 words)
Bibliography Sources: 4



History and Modern Applications of Logarithms

The first time a publication contained a mention of logarithms, their method of derivation, and a table of logarithms was in 1614 with the publication of Mirifici Logarithmorum Canonis Descriptio by the Scottish nobleman John Napier (ST 2005). Napeir's book did not describe or list logarithms as they are known today, but rather the logarithms contained in this work were meant to replace the trigonometric multiplication functions needed in astronomy and other branches of science with a simplified addition from other established figures (Capmbell-Kelly 2003). Henry Briggs, a professor of geometry at Oxford, was very inspired by Napier's work, developing his own ideas based on those in the Descriptio and meeting with Napier to discuss developments and recalibrations of the logarithms contained in Napier's original and pioneering work on the subject (Campbell-Kelly 2003).

Briggs would go on to publish his own table of logarithms for common numbers (as opposed to the logarithms for sines contained in Napier's column); Briggs' tables showed the logarithms for every whole number below 1000 carried out to eight decimal places, providing a very useful tool to the navigators, astronomers, and mathematicians working in this day centuries before the advent of computer and calculators (ST 2005). This was published in 1617, the year of Napier's death, and by 1624 Briggs had expanded his tables to include all integers from 1 to 20,000 and from 90,000 to 100,000, carried out to fourteen decimal points (ST 2005). These tables led to a massive increase in use of logarithms in certain fields where their usefulness was already established, and this subsequently led to expansions in the applications for logarithms generally (Campbell-Kelly 2003).

There are many different modern applications for logarithms that have nothing to do with the distances of navigation and astronomy -- or any physical measurements at all -- proving that logarithms are indeed an incredibly useful mathematic tool on a scale that Napier himself did not really envision. Anything that involves exponential growth can most easily and accurately be calculated using logarithms; studies of population growth, nuclear reactions, and any other scientific inquiries depend on the use of logarithms to develop real and usable data and projections (Tom 2002). Logarithmic scales also exist in electrical engineering, as a means for testing for signal decay, and there are many bodily functions and reactions that are logarithmic in nature, leading to many other biological and medical uses and needs for an understanding and utilization of logarithms (Tom 2002).

Another common use for logarithms is in the world of banking, specifically in the calculation of interest and periods of repayment on…… [read more]

Digital Audio Broadcasting System Case Study

Case Study  |  5 pages (1,283 words)
Bibliography Sources: 5


Analogue and Digital Converter

This is an electronic device that helps in the conversion of continuous signals to discrete or isolated digital numbers. When an analogue voltage or current is fed into the device as an input, it converts it into a digital number relative to the voltage or current magnitude. There are a number of terminologies related to ADC, which include resolution, accuracy, response type, sampling rate, aliasing, dither, oversampling, relative speed and precision, and the sliding scale principle, however, just a few of them will be considered in this study.

The resolution of an ADC refers to an indication of the isolated values that in can generate over the range of analogue values. Since the electronic storage of these values is in binary form the resolution is normally expressed in bits and the available discrete values being a power of two. For instance, an ADC whose resolution is 6 bits has the capability of encoding an analog input to one in 64 varied levels, given that 26=64. It is also possible to define resolution electrically and give the expression in volts. The voltage resolution of an ADC is found by dividing the overall voltage measurement range by the number of isolated intervals. The formula is written as:


Q= resolution in volts/step i.e. (volts/output codes-1)

EFSR= full scale voltage range which is given by VRefHi -- VRefLow

M= ADC's resolution in bits

N= number of intervals= 2M -- 1 (Knoll 1989)

Consider an example given by Knoll (1989) where the Full scale measurement range is 0 to 7 volts, the ADC resolution will be 3 bits which means 8 quantization level sie. 23. When this is given in terms of ADC voltage resolution it equals 7V/7 steps which give 1V/step.

The ADC is not exempted from errors that are encountered by other instruments and has errors that have a number of sources which brings about the question of accuracy. These errors are categorized as quantization error, non-linearity error and aperture error. Quantization error is caused by the finite resolution of the ADC and cannot be avoided in any ADC while non-linearity error occurs due to the physical imperfections of the ADC which leads to a deviation between the output and the input from a linear function. The third error is caused by a clock jitter and is usually exposed when digitizing a signal that is time variant. The non-linearity error can be toned down by calibration or eve averted by testing. In most ADCs the range of input values that map to every output value are linearly related to that output value and are referred to as linear ADCs.

The speed and precision of an ADC varies depending on the type of the ADC with the Wilkinson ADCs being considered the best since they exhibit the best differential non-linearity. ADCs are usually represented using a symbol; the conventional electrical symbol used is as below (schematic).

Demodulator (Band pass filter)

A band pass filter is a device that helps… [read more]

Educational Standards Thesis

Thesis  |  2 pages (431 words)
Style: APA  |  Bibliography Sources: 1


Communicating No Child Left Behind Daily Standards

Grade-Appropriate Restatement of New York State 2nd Grade Math Standards

Original Statement of 2.PS.1:

"Explore, examine, and make observations about a social problem or mathematical situation"


of 2.PS.1:

We're going to look at the kinds of problems people have and the kinds of problems that mathematics can help us solve.

Original Statement of 2.PS.2:

"Interpret information correctly, identify the problem, and generate possible solutions"

Restatement of 2.PS.2:

We're going to learn how to understand what kinds of problems we have to solve and how we can use mathematics to do that.

Original Statement of 2.PS.4:

"Formulate problems and solutions from everyday situations (e.g., counting the number of children in the class, using the calendar to teach counting)"

Restatement of 2.PS.4:

Some of the problems we're going to look at are the kinds of things that people need to figure out all the time, like how to count how many students are in a big room without counting on our fingers and toes.

4. Original Statement of 2.RP.3:

"Investigate the use of knowledgeable guessing as a mathematical tool"

4. Restatement of 2.RP.3:

We're going to learn what an "educated guess" is, how that is different from regular guessing, and how to use educated guesses in mathematics.

5. Original…… [read more]

Operational Definitions Essay

Essay  |  8 pages (2,354 words)
Bibliography Sources: 5


¶ … Operational Definitions of Each of These

It states clearly the expected relationship between the variables

It states the nature of the relationship

It states the direction of the relationship

It implies that the predicted relationship can be tested empirically

It is grounded in theory.

The article What is a null hypothesis? explains what distinguishes a null hypothesis from… [read more]

Teaching Calculus to Young Children Thesis

Thesis  |  2 pages (638 words)
Style: APA  |  Bibliography Sources: 2


Mamikon's Approach To Teaching Calculus

Mamikon's A. Mnatsakanian, often along with his colleague Tom M. Apostol, has published many papers detailing new instructional methods for explaining otherwise complex concepts in the realm of calculus, as well as new ways of understanding these concepts. His emphasis is on a visual understanding of calculus, which is more easily observed and intuited by students -- and at a younger age, it seems increasingly evident -- than traditional textual and purely mathematic explanations and understandings. For years, a website has been available with several puzzles and games that help to visually express many of the mathematical measurements and principles of calculus. Several brief examples of Mamikon's teaching style make it clear how the principles of calculus build on lower mathematic understanding, and are in fact easily understood themselves.

Measuring the area of a curved space is essential for many applications of calculus, yet can be one of the more difficult among the basic principles and practices of the average calculus student. Mamikon's illustration of the curving bicycle, and subsequent related illustrations, show quickly and easily how the area described by such a curve is the same as the area -- or partial area -- of a circle (CalTech). The preceding sentence is proof of how difficult such concepts can be to clearly and efficiently explain, but accompanied by Mamikon's illustrations the principle is instantly observed and far more easily remembered and recognized.

A more thorough and elegant explanation of the same concept is provided on Mamikon;s paper (with Apostol) entitled "Subtangents -- An Aid to Visual Calculus." Again, Mamikon starts with a visual explanation of the principle, but goes on to detail this principles work in calculus (Apostol & Mamikon 2002). Thus, his method of teaching calculus visually creates at least a rudimentary understanding of a principle or practice before any theorem or even a simple equation is introduced. This is the opposite…… [read more]

Errors Type I/Type II Errors Statistical Analysis Thesis

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¶ … Errors

Type I/Type II Errors

Statistical analysis can lead to many different errors of many different types, both in the gathering of data and the manipulation of it to produce results in a practical and relevant manner. Often, errors arise as a result of the complex mathematical manipulations that must occur in order to make useful sense of data. These mathematical errors can compound and lead to wildly incorrect interpretations of data, producing results that cannot be trusted or validly used. Other errors can occur in the interpretive phase of data analysis; these can often be far more egregious, and at the same time they are often more difficult to catch. Errors made in that actual mathematic manipulation of data often delivers results that -- for obvious reasons -- simply do not make sense. Interpretive errors, however, are more difficult to catch almost by definition. The data itself may be entirely sound, and therefore the results are more likely to be trusted, but an error in interpretation can still cause the data to be incorrectly applied.

There are two rather basic and fairly straightforward errors, known as Type I and Type II errors, that are commonly made in data analysis. Both refer to a basic mistake regarding the status quo from which the analysis is meant to measure change. This status quo is called the null hypothesis, the idea/belief that there was no change in the phenomenon measured during the test. When there is no change in the situation or phenomenon, the null hypothesis is said to be true (that is, nothing happened). If a change in the situation/phenomenon has in fact occurred, then the null hypothesis (the idea that nothing has happened) is quite clearly false. A Type I error occurs when there is a false positive -- when the data analysis suggests a change has occurred, when in fact there has been no change. Thus, in a Type I error the null hypothesis is true…… [read more]

Fractal, in Its Completed and Perhaps Complex Essay

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Fractal, in its completed and perhaps complex form, resembles a fracture or a series of complicated and uncoordinated breaks. Indeed, the word can trace its origins to the Latin fractus, which means fractured or broken. A fractal, as is mathematically understood, is the end product (or a product that is in the process of completion in a recursive manner) of… [read more]

Pi Is Interwoven With the History Essay

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¶ … pi is interwoven with the history of humanity. Remarkably, "By 2000 BC, men had grasped the significance of the constant that is today denoted by pi, and…had found a rough approximation of its value," (Beckmann 9). Math historians assume that the study of pi began as an analysis of magnitude: that circles remained circles no matter how big or small. Beckmann suggests that early humans contemplated "the peculiarly regular shape of the circle," which was visible everywhere in nature in "its infinite symmetry," (9). Pi remains a mystery in spite of thousands of years of scholarship and investigation. The number is both irrational (it cannot be represented as a ratio of two integers) and transcendental (it is never the solution of a polynomial equation that involves rational numbers). Pi is remarkable in its scope. Professor Yasumasa Kanada of the University of Tokyo writes computer programs that are designed to calculate pi, and has continually broken his own world records. Kanada has computed pi to well over one trillion decimal places and remains "intent on achieving new world records" (Arndt, Haenel, Lischka, and Lischka 1). Because of Kanada's work, pi is now the mathematical constant "which has been calculated to the greatest number of decimal places," (Arndt et al. 1). In addition to performing the calculations for pure pleasure, Kanada and other mathematicians study pi in search of patterns. Understanding pi would be a significant epiphany, a major evolution in human history.

So far pi has yet to reveal itself fully and the number remains a major mathematical mystery. Pi can be understood easily on its most basic level: that of Euclidian geometry. The fundamental realization that the wider a circle is "across," the longer it is "around" is what led to the discovery of pi in the first place (Beckmann 11). That discovery seems to have occurred in multiple cultures, as pi was studied among the ancient Mesopotamians, Egyptians, and Chinese. The ancient Greeks delved deeply into the study of pi, especially pi's relationship to geometry. Pi was revealed as a constant ratio not just of circumference to diameter but also of radius to area. The existence of both constants was well-known, but the fact that both constants were in fact one and the same number represented a major breakthrough. Arndt et al. note that the ancient Greeks first drew the connection between both ratios as they related to the circle. In 414 BCE, Aristophanes presented the problem known as "squaring the circle," which has become the quintessential problem of pi.

Pi has numerous applications, and not just in the world of geometry. Number theorists hope to discover meaning in the endless stream of digits represented by pi, and pi could in fact be meaningful to the study of theoretical physics. Arndt et al. point out that calculating pi sometimes depends on time as well as space. Pi is also meaningful for probability theories, such as the Wallis product (Arndt et al. 9). Moreover, pi may be related… [read more]

Greek Numeration Systems Thesis

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Greek numeration system is one of the oldest in the world and still in use in many parts of Greece, especially for the ordinal numbers. The Greek numeration system was based both on its internal invention, as well as the constant interaction with some of the neighboring people, most notably the Phoenicians, the Egyptians and the Babylonians, all who had developed their own numeration systems and who thus influenced the Greek one.

There are two types of Greek numerations systems, depending on the moment they came into existence. The first type, predominantly referred to as Herodianic was used as early as 500 BC. As most of the old numeration systems, this was primarily an additive one, with the letters being allocated to the numbers based primarily on the first letter of the way the number was said. For example, penta was five, so the letter pi was designated to be the one representing the number five. In a similar manner, the letter symbol for 10 was the letter delta, which was because the number was referred to as deka and thus started with that respective letter.

This system was pretty much replaced with the Ionic system later on. The Ionic system was primarily based on the Greek alphabet, because it implied that for each unit 1 through 9, a letter of the alphabet would be allocated, a mechanism which was also applied for the tens (10 through to 90) and the hundreds (100 through to 900). However, the Greek alphabet only had 24 letters, which meant that three new ones were added for this purpose alone. These letters were digamma (an almost double gamma), qoppa and sampi. These letters were allocated for 9, 90 and 900 respectively.

At the same time, after each number thus written, a small sign would be added in the form of…… [read more]

Oxford Murders Matinez, Guillermo. Book Report

Book Report  |  1 pages (318 words)
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Oxford Murders

Matinez, Guillermo. The Oxford Murders. MacAdam/Cage, 2005.

The Oxford Murders is the story of an unnamed Argentinean mathematician studying at Oxford. One day, while accompanied by his landlady's friend, the don and professor of mathematics Arthur Seldom, the two find Mrs. Eagleton murdered on her sofa. The only clue, other than the fact that the old woman worked on the Enigma Code during World War II, is a circle left by the killer in a mysterious note sent to Seldom, along with the lines, "the first in a series." Soon it becomes clear there is apparently 'serial' killing occurring, on a very literal level. Seldom receives a note, accompanied by a symbol, every time a murder takes place. Seldom fears that the killer is effectively parodying his mathematical work on theories of patterns or series in mathematics. One of Seldom's areas of expertise is Wittgenstein's theories about series and the possibilities for deviation in numerical series.

The…… [read more]

How Does My Calculus Class Help or Relate to a Business Management Major? Essay

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The world of business is comprised of many unique disciplines. The manager can expect to synthesize all of them as part of their work. Therefore, a strong multidisciplinary background is essential in the pursuit of a major in Business Management. The subjects learned in this major will require a wide range of basic knowledge including economics, sociology, psychology and statistics. Calculus also plays a role, providing both a functional and a theoretical backdrop.

It is often considered that the basic functions of calculus are not used in the acquisition of a business education. However, understanding the fundamentals of calculus allows the student to derive formulae in financial courses. Students of Business Management should have a strong knowledge of corporate finance, and this requires some basic calculus. The models used to price derivatives are based on calculus. A stock option, for example, comprises an underlying asset with an intrinsic value and a fluid time value. This concept can be extended to any asset. Business Management is, at its core, managing assets. But to manage those assets requires the ability to understand how the value of those assets is derived.

Differential calculus forms a key component of the business world. Many important concepts in business management relate directly back to calculus. For example the yield curves on bonds, or the demand curve of a product relative to macroeconomic variables. There are many instances where a manager must interpret complex, interrelated and fluid variables in order to predict the future.

Integral calculus is useful when examining concepts involving fluidity. The business world is constantly changing. The numbers used to interpret the world in order to make managerial decisions are also constantly changing. The relationship between those numbers is also subject to constant flux. It is impossible to understand the business environment without understanding these relationships. A sound knowledge of calculus fundamentals allows for that.

The concept of limits also proves useful to the Business Management student. Management is a subject based on finding ways to achieve objectives. In many cases those objectives are quantifiable, thus to derive the best way to achieve those objectives requires calculus. The concepts, however, can also be applied to non-quantifiable objectives once the student understands the basic principles. The manager can then understand how to bring a variable such the organizational culture closer to a limit such as having a strong emphasis on integrity. Even without numbers, the principles of analyzing the relationships between variables remain the same.

A…… [read more]

Eudoxus of Cnidus Essay

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Eudoxus of Cnidus

Boyer, in his "A History of Mathematics" gives a quote from Eudoxus that is quite self-descriptive of this genius, "Willingly would I burn to death like Phaeton, were this the price for reaching the sun and learning its shape, its size and its substance."

It is descriptive of the man from Cnidus because it shows us the mind of this genius, the curiosity he displayed during his lifetime and why he contributed so much, in particular, to the fields of mathematics and astronomy.

Unfortunately, all of his works are lost to history. We have snippets, pieces, basic facts about Eudoxus' life and work, and some words from others through the ages who have dug up what could be found and put it together in biographies and descriptions of his work.


We know that Eudoxus was born in Cnidus, Asia Minor (now Turkey). Actually, historical documents claim a birth sometime between 408 B.C. To 390 B.C. And his death at the age of 50 to 53 years old. Best guess is 408-355 B.C.

He is known for his revolutionary work as a mathematician, astronomer, and philosopher. However, at some point in his life he was also a theologian, meteorologist, doctor, and "http: geographer. He studied mathematics in Italy under the tutelage of Archytas, the Greek mathematician and philosopher. Many historians claim that Eudoxus worked with Plato in Athens, but others dispute whether there is enough data to support that and are unclear about this relationship between the two great intellectuals. (O'Connor & Robertson, 1999) Archytas and Plato were close friends, so it is possible that Eudoxus met Plato, and, perhaps, this too, could explain part of the confusion whether or not Plato and Eudoxus actually worked with each other.

It is somewhat clear from historical records that Eudoxus had little respect for Plato's analytic ability, but since Plato was not the mathematician that Eudoxus was, that is to be expected. It does not appear as if either had much influence on the other's work. (O'Connor & Robertson, 1999)

Diogenes Laertius, the Roman biographer of Greek philosophers, claims that Eudoxus did, indeed, study in Athens under Plato. However, some of Laertius' usually solid work has come under question by other scholars, and, since Laertius' lived in the third century A.D., we can't be certain he was correct, since, again, all of Eudoxus' work is lost. (Soylent Communications, 2008)

He traveled to Sicily where he studied medicine with Philiston. After that, we surmise, with the help of financial aid from friends, he went to Egypt to learn astronomy with the priests at Heliopolis, and made astronomical observations from an observatory located between Heliopolis and Cercesura. From there Eudoxus travelled to Cyzicus, in northwestern Asia Minor on the south shore of the Sea of Marmara. There he established his own school which proved to be quite popular. As a matter of historical record, it appears that Plato became somewhat jealous of Eudoxus' success with his school. Not much more is… [read more]

Math Webliography Coolmath4kids.com Term Paper

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Math Webliography

CoolMath4Kids.com (http://www.coolmath4kids.com/)

By Karen," this site is self-described as an "amusement park of math and more." colorful icons against a black background constitute child-friendly visuals, and menu items like "Number Monster" and "The Geometry of Crop Circles" are also guaranteed to please curious young and adult minds alike.

KidsNumbers.com (http://www.kidsnumbers.com/)

Not as visually appealing as it could be, Kidsnumbers is still a valuable resource tool for teachers and parents. Several "Let's Practice" sections encourage children to play and interact.

Mathcats.com (http://www.mathcats.com/) chalkboard cat icon welcomes children and their parents to the Web site, which several separate sections include "Math Cats Explore the World." However, the activities contained on the site are geared toward children older than the cute drawings would suggest. Mathcats is not for youngsters but is lacking in the sophistication that might draw a more mature audience.

TeachRKidsMath (http://www.teachrkids.com/)

Seemingly geared toward teachers instead of students, TeachRKidsMath is not as child-friendly as it could be. The exercises are, however, good resources for math teachers needing some activities for their students.

Wolfram MathWorld (http://mathworld.wolfram.com/)

Wolfram might indeed live up to its self-proclaimed subtitle, "web's most extensive mathematics resource." Containing a wealth of information on every mathematics topic of interest to advanced students from…… [read more]

PHI Golden Ratio Term Paper

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History Of Phi, Mathematical Connections, And Fibonacci Numbers: Nature's Golden Ratio

Throughout history, humans have been seeking to define beauty in quantifiable and meaningful ways. For many observers, the connection between beauty and the rhythmic patterns evinced in the Fibonacci series is clear. While the Fibonacci series is named for an early 13th century Italian mathematician, the so-called Golden Ratio… [read more]

Memory Ronald T. Kellogg's Working Memory Components Term Paper

Term Paper  |  5 pages (1,248 words)
Bibliography Sources: 1



Ronald T. Kellogg's "Working Memory Components in Written Sentence Generation": A Review and Further Research Inspired by the Study

In his article, "Working Memory Components in Written Sentence Generation," Ronald T. Kellogg used quantitative research in order to how working memory is impeded during distraction. Kellogg begins his article with a literature review detailing the types of research that psychologists have completed regarding memory in the past. He cites Baddely's 1986 work, which created the Baddeley model, a "phonological loop for storing and rehearsing verbal representations, a visuospatial sketchpad for visual object representation and their locations, and a central executive for attentional and supervisory functions" (341). In addition to this model, Kellogg also more modern research by Jonides and Smith that suggests the "visual, spatial, and possibly semantic stores are dissociable from the verbal store" (341). By considering both this old and new research concerning working memory, Kellogg designed his own research in order to increase psychologists' understanding of working memory.


Kellogg designed his study in order to increase others' understanding of working memory. Specifically, Kellogg was interested in understanding if "planning conceptual representations" and "linguistically encoding these into words and sentences" depends on working memory (341). According to Kellogg, putting together a sentence, or sentence generation, requires "planning conceptual content," or deciding what one wants to say in writing, and "linguistically encoding it into a grammatical string of words," or placing those ideas and concepts into a well-formed, grammatically correct sentence (341). If one or either depended on working memory, a second purpose of the study was to review the strength of this dependence.


College students in a General Psychology class were chosen as the subjects to be tested. The students were assembled, given keyboards, and then given a visual prompt of two words, nouns. Subjects were then to write a "meaningful sentence" using the two nouns (344). At the same time, students were told to complete a "memory task," such as remembering certain digits. First, students' typing speed was assessed via trials. Next, students were given directions, followed by the two visual prompts, and then time to type their sentences and submit them to a computer. Finally, students were asked to complete the memory task they had been assigned correctly and were given feedback concerning whether or not they had made the correct response. Some students were asked to write sentences using nouns that were related, while others were asked to write sentences using nouns that were unrelated. In one group, students were asked to produce complex sentences; while in the other students were told to write simple sentences (344).

IV. Findings

In accordance with the methods above, the researchers derived results concerning, initiation time, sentence length and typing time, grammatical and spelling errors, and concurrent task performance. Only those students who were asked to remember six digits produced shorter sentences, while the memory tasks did not affect the length of any other students' sentences. Similarly, spelling and grammar were not affected by the memory… [read more]

Mathematician Biography and Works: The Mathematician Blaise Term Paper

Term Paper  |  4 pages (1,353 words)
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¶ … Mathematician

Biography and Works: The Mathematician Blaise Pascal

The Life of Pascal

Blaise Pascal, along with Rene Descartes, is the rare case of a mathematician equally famous for his religious devotion and contributions to theology as he is for his work with numbers. In fact, Pascal would likely prefer to be remembered as a philosopher of religion rather than a mathematician, theorist, and scientist, as he is today. One biographer of famous mathematician tartly observed that Pascal's "mathematical reputation rests more on what he might have done than on what he actually effected, as during a considerable part of his life he deemed it his duty to devote his whole time to religious exercises" (Ball 1908). However, other biographers have seen Pascal's religion and mathematical gifts as complementary.

For example, "Pascal's Wager" is based upon the proposition that a person should believe in God because as a bet, the idea makes sense. There is so much to be gained potentially by believing in God if one is 'correct.' Likewise, there is so much to lose if one is an unbeliever, and one is 'incorrect.' Conversely, there is little to be lost by a person whose belief is in error. A proof of Pascal's Wager might look like this: 1) the probability of God's existence is 50/50. (2) Wagering for God brings infinite reward if God exists (Hajek 2005). If God does not, there is no net loss. Wagering against God brings no gain, and a great loss.

Despite the modernity, even humor, inherent in such moral calculations, Pascal was largely a man of his time, and a devout Christian. Blaise Pascal was born during the 17th century at Clermont on June 19, 1623, and died in Paris on August 19, 1662. Although the Frenchman's early education was confined to modern languages, when his father noted that the boy had unusual mathematical aptitude in geometry (Pascal intuited as a child why the sum of the angles of a triangle is equal to two right angles), his father gave his son a copy of Euclid's Elements. It would not be an understatement to call the young Pascal a prodigy. At the age of fourteen Pascal was admitted to the weekly meetings of French geometricians, at sixteen he wrote an essay on conic sections and at the age of eighteen, he constructed the first arithmetical machine, a kind of prototypical adding machine or calculator (Ball 1908).

However, Pascal suddenly abandoned mathematics in 1647, "after being advised to seek diversions from study and attempted for a time to live in Paris in a deliberately frivolous manner," because of his health ("Blaise Pascal," Island of Freedom, 2008). Pascal's interest in probability theory "has been attributed to his interest in calculating the odds involved in the various gambling games he played during this period" ("Blaise Pascal," Island of Freedom, 2008). However, Pascal's account in his Pensees is different. He says wished to "contemplate the greatness and the misery of man" in a purely religious… [read more]

Math Curriculum Development Term Paper

Term Paper  |  13 pages (4,174 words)
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Math Curriculum

Science and its modes of studies are very much reliant on the mathematical techniques which have been heavily evaluated over the past few years. Numerous studies like the ones conducted by Mike Cass et al. (2003) and Lynn T. Goldsmith and June Mark (1999) have analyzed both the teaching techniques used for mathematics as well as the overall… [read more]

Pythagoras, the Pythagorean Theorem and Its Relationship Term Paper

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¶ … Pythagoras, the Pythagorean theorem and its relationship to the area of a circle.

Biography of Pythagoras:

Pythagoras was a Greek sage of the 6th century B.C.. He was born on the Greek island of Samos, off the coast of Asia Minor. Pythagoras was introduced to mathematics by Thales of Miletus and his pupil Anaximander, according Iamblichus, the Syrian historian. He traveled to Egypt, around 535 B.C., to continue his studies, but was captured by Cambyses II of Persia, in 535 B.C., and was taken to Babylon ("Pythagorean," 2007).

Eventually, Pythagoras emigrated to the Greek colonial city-state of Croton, in Southern Italy (Mourelatos, 2007; "Pythagoras," 2007).

Pythagoras was a "teacher and leader of extraordinary charisma. Pythagoras founded in Croton a society or brotherhood of religious-ethical orientation. The society fostered strong bonds of friendship and a sense of elitism among its initiates through ritual, esoteric symbolism and a code of rigorous self-control, including lists of taboos" (Mourelatos, 2007). This was known as Pythagoreanism. Pythagoreanism became politically influential in Pythagoras' home town of Croton, and eventually spread to other cities in the region ("Pythagoras," 2007).

Pythagoras' teachings were basically ethical, mystical, and religious. He believed in the transmigration of souls from one body to another, known as metempsychosis, either human or animal.

It's unclear whether Pythagoras believed that this led to the immortality of the soul; however, it did lay the foundations for some of the practices of the Pythagorean society he founded. These included vegetarianism and the rituals of purification, in an effort to promote the chances of superior reincarnation (Mourelatos, 2007).

A legend grew around Pythagoras, according to Mourelatos (2007), involving superhuman abilities and feats. However, he believes that this legend was based on the historical reality that Pythagoras was a Greek shaman. Some modern scholars theorize that the religious movement of Orphism, as well as Indian and Persian religious beliefs, influenced Pythagoras.

Although Pythagoras' contemporaries honored him as a polymath, modern scholars question this. Today, many "discount the tradition that he was the founder of Greek mathematics, or even that he proved the geometric theorem named for him" (Mourelatos, 2007).

Pythagoras died in Metapontum, near modern-day Metaponto, in approximately 500 B.C. ("Pythagorean," 2007).

History of the Pythagorean Theorem:

The Pythagorean theorem holds that "the square of the hypotenuse of a right triangle is equal to the sum of the squares of its other two sides" (Meserve, 2007). During Pythagoras' lifetime, the square of a number was represented by the area of a square with the side of a length of that number. With this representation, the Pythagorean theorem can then be stated as "the area of the square…… [read more]

Finding the Diameter Term Paper

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Diameter Problem

In this experiment, measuring of the diameter of the sun relative to the average radius of the earth's orbit requires some basic geometric knowledge, particularly in the properties of angles. Understanding these properties will provide us the mathematical relationship between the data provided in the problem and the data to be taken throughout the experiment. We must consider, however, that the mathematical aspect is just half of the story. Reckless experimentation often results to errors which are intolerable.

The choosing of favorable conditions under which an experiment is to be done, the careful set up of the materials to be used, and the precise measurements of data all contribute to finding the best result to the experiment. These three factors, however, are subjects to a certain degree of errors no matter how careful the person conducting the experiment may be. Human error is always present; and materials have limitations that affect the result of the experiment. Precision of the materials used and of the measurements taken are determining factors of how precise the result is.

As I conducted this experiment, however, I carefully set up the materials needed. I used a flat mirror covered by a white paper with a hole in the middle. I measured the hole to be approximately seven (7) millimeters. Finding a suitable place for the experiment was relatively easy; the hard part was putting the mirror in the right angle such that the image of the sun on the beige-colored wall was not oblong or ellipse, but rather very close to a circle; and what's even harder was setting the distance of the mirror to the reflected image at almost exactly six (6) meters. I finished setting up at 3:07 in the afternoon. Afterwards, starting at 3:10, I took the required measurements with ten-minute intervals.

Treating then the problem mathematically and scientifically, I had to identify what is required in the problem, what data are given, what variables are needed to be derived, and what formulas are involved in the solution. This step-by-step procedure is the key to getting the desired result. Hence, the required in the problem is D: the diameter of the sun; the given datum is L: the average radius of the earth's orbit which is equal to 150,000,000 kilometers; the derived measurements are: the distance "l" from the mirror to the reflected image on the wall, and the diameter "d" of the image itself; and the formula to be used is simple ratio and proportion, which is: D:L = d:l or D/L = d/l. From this formula, we can derive the formula for D. where we can supply our data. Hence, we get D = (d/l)

L. The…… [read more]

8th Grade Math Introduction to Fractals Lesson Term Paper

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8th Grade Math

Introduction to Fractals

Lesson Title:

Why Study Fractals and What Are They?

Learning Objectives/EALRs:


Investigate situations and search for patterns


Extend mathematical patterns & ideas to other disciplines

Describe examples of contributions to the development of mathematics


Recognize use of mathematics outside the classroom



Quotes by Mandelbrot - "Fractals represent a new geometry that mirrors the universe."

Quote from Fractals, the Patterns of Chaos, p. 70:."..whether the fractal is..."

Definition of a fractal


Summary of lives of Sierpinski,

Mandelbrot & Koch [

Page 1 & Page 2]

Internet sites loaded on computers ahead of time:

Fractal of the Day: http://sprot.physics.wisc.edu/fractals.htm

African Fractals:


Photo posters:

Sierpinski, Mandelbrot, Koch, Mandelbrot Set, Sierpinski Gasket, Snowflake

Butcher paper for chart

Set up:

Schedule computer lab

Overhead projector

Collect overheads & visuals

Display visuals on white board for reference and interest

Draw chart on butcher paper for recording student ideas


We're exploring and collecting ideas and perceptions about fractals because:

They're something fairly new in math.

We, as 8th graders, can understand lots about them.

Fractals often look like objects in nature.

Point out the photos displayed of Sierpinski, Mandelbrot, and Koch and the fractals they are associated with.

Distribute the mathematician background handout and briefly talk about Koch, Sierpinski, and Mandelbrot. Ask students to look for mention of these names as they browse the fractal internet sites marked on their computers.

Search the following internet sites. Go to Fractal of the Day:


Number a piece of paper 0-15. View the fractals for today and…… [read more]

Hart, B. And Risely, T ) Term Paper

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Hart, B. And Risely, T (2003). The early catastrophe: The 30 million word gap by age 3. American Educator, Spring

Fairly commenting on an investigator's research endeavor is a task that must be taken seriously. Although it is quite easy to have an opinion of another's research, it is something quite different to be able to evaluate the research activity in terms of topic specificity and soundness, intent or purpose, data analysis, and informational importance. The focus of this paper was on whether or not the research investigators of the above cited research publication were prudent in stating a research question and a testable hypothesis along with informing the reader of the chosen research design, statistical data analysis and reporting the results, limitations, limitations and implications for future practice - all of which must lead to a best fit research decision.

The authors of this particular research report not only failed to state a research question and testable null hypothesis but selected a sample (N=42 families) on a non-random basis. In fact the sample selection was reported as being "pre-selected." As such any results garnered from a statistical data analysis can only be inferred back to the selected population and not to a wider universe of language growth deficient children. In fact, the authors set out to examine language deficiency of lower income children yet, included in their analysis a disproportionate number of upper income (13), middle income (10), lower income families (13), and welfare (6). Not only was there disparity among family selection the authors failed to report how many children were included in each of the four socio-economic status categories, thus producing error contamination of the results.

In addition to the errors associated with failure to state a research question and testable null hypothesis the authors of the article failed to alert the readers that a cross-sectional research investigation is point in time…… [read more]

Archimedes Many Experts Consider Term Paper

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Many experts consider Archimedes to have been the greatest mathematician of his era. The contributions that he made to the field of math, including geometry are considered phenomenal. In addition he is often credited with understanding and anticipating the advent of calculus 2,000 years before it happened. When he was not busy cracking the code to mathematical equations he spent his time inventing machines that included the pulley. Today, many commonly used mathematical concepts are directly related to the mind and development of Archimedes (Archimedes of Syracuse (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Archimedes.html).


He began his life in 287 BC in a city called Syracuse by the sea in Sicily, Italy. His birth date was determined when he died and those who knew him claimed that he was 75 years old at the time (Biography (http://en.wikipedia.org/wiki/Archimedes#Biography).

He was born to a father who spent his life as an astronomer.

He spent his life building the foundation for many of today's mathematical calculations, formulas and concepts as well as providing the world with valuable inventions like the pulley. He died in 212 BC in the middle of the Second Punic War.

According to the popular account, Archimedes was busy contemplating a mathematical drawing in the sand. He was interrupted by a Roman soldier and replied impatiently: "Do not disturb my circles." The soldier was enraged by this, and killed Archimedes with his sword (Biography (http://en.wikipedia.org/wiki/Archimedes#Biography)."

Discoveries and Achievements

Many experts refer to Archimedes as the first math physicist. He contributed the foundation for the later works of Newton and Galileo. One of the things he is most well-known for discovering is the principal behind buoyancy. Legend has it that a crown was prepared for a king and Archimedes was asked to verify its gold qualities and to determine whether gold had been placed in it as well.

He was asked to make these determinations without destroying the crown so he figured out that the density of the crown would determine how fast it would sink in liquid.

Another achievement of his was the Archimedes screw. This invention is a machine that has a revolving screw shaped end that was often used to transfer water from low lying bodies to irrigation canals.

Archimedes cannot be credited with inventing the level however, he was the one who developed the principles that explained how a lever works.

His Law of the Lever states: Magnitudes…… [read more]

Proof David Auburn's "Proof" -- Catherine Term Paper

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David Auburn's "Proof" -- Catherine vs. Claire

How can two sisters from the same family be so different?

Both fulfill different functions and roles in the family dynamic. Catherine is the caretaker, and the mathematical problem-solver. Claire is the problem-solver, in a practical sense.

Temperamentally, Claire takes risks in finance, Catherine hides from the world, locked in her father's reality, and does not embrace risk, only intellectual risks on the Both represent two different aspects of mathematics. Catherine represents mathematics' theoretical side, while Claire's career in finance and concern with money demonstrate the worldly value of numbers

Catherine's characteristics

Compassionate, as manifested by her role in the caretaker of her mathematician father until recently freed by his death

Confined socially, limited professionally, and kept in a childlike state personally by her father's mental illness

Depressive, reluctant to move forward even after a change, pessimistic

Allied with her father, even after he dies -- experiences his presence in a ghostly fashion

Still young in terms of her sexual experience, even though she is in her 20s

Over the course of the play, says she has discovered revolutionary mathematical theory amongst her dead father's papers -- Claire expresses surprise

Protective of father's memory as a great man

Protective also of father emotionally, did not, when he was living, allow him to be fully cognizant of the extend of his illness, while Claire believes she sees her father's illness (and her sister's) clearly However, in doing so, may also have been protecting herself from moving out into the world, which her older sister Claire was able to do much more successfully

Loves father without reservation -- finds her identity in caring for her father, unlike Claire who finds her identity by breaking away from the family and becoming engaged in professional, normal life

Moody, withdrawn, emotionally unstable

Might be author of the supposedly new proof --…… [read more]

Euclid -- 323-285 Term Paper

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The cause that such a proof was in great demand for such a long time was due to the fact that Euclid's other postulates seem to be easy, self evident, and naturally clear, the fifth postulate basically described the intersection of lines at potentially infinite distances -- the notion of infinity being at the time, was mathematically, problematic. (Euclid: www.mathdaily.com)

Therefore, the fifth postulate seemed as a sort of blotch in the otherwise apparently perfect logical edifice which is Euclid's Elements. Whereas Elements was referred and used into the 20th century as the original geometry textbook and has been regarded a fine example of the formally precise axiomatic method, Euclid's study fails to meet the modern standards and several logically necessary axioms are not there. The first correct axiomatic treatment of geometry was given by Hilbert during the year 1899. Nearly nothing is available regarding Euclid, apart from what is presented in Elements and some of his other surviving books and whatever scanty biographical information the world has comes mostly from explanations by Proclus and Pappus of Alexandria. (Euclid: www.mathdaily.com)


Dietz, Elizabeth. "Euclid 323-285 B.C. Biography" Retrieved from http://www.albertson.edu/math/History/edietz/Classical/biography.htm

Accessed on 8 August, 2005

Dietz, Elizabeth. "Euclid 323-285 B.C: Discoveries" Retrieved from http://www.albertson.edu/math/History/edietz/Classical/discoveries.htm

Accessed on 8 August, 2005

"Euclid's Elements" Wikipedia, the free encyclopedia. Retrieved from http://en.wikipedia.org/wiki/Euclid%27s_Elements

Accessed on 8 August, 2005

"Euclidean Geometry" Wikipedia, the free encyclopedia. Retrieved from http://en.wikipedia.org/wiki/Euclidean_geometry

Accessed on 8 August, 2005

"Euclid" Retrieved from http://www.mathdaily.com/lessons/Euclid

Accessed on 8 August, 2005

"Euclid" Wikipedia, the free encyclopedia. Retrieved from http://en.wikipedia.org/wiki/Euclid

Accessed on 8 August, 2005… [read more]

Hypatia of Alexandria Term Paper

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Historian Coffin continues, "She wanted to help her students understand the mathematics she was teaching, so she wrote books that gave explanations that were easier to understand than the original books" (Coffin, 1998, p. 95). She taught many well-known young men of the time, both Christians and pagans, and most found her an excellent teacher, scientist, and philosopher. She had many friends and supporters in Alexandria, but she also had many detractors.

It is important to note that at the time, it was not especially prestigious or even socially wise to be a mathematician. At the time, astrology and mathematics were closely linked, there were many astrologists and numerologists who were considered mathematicians too, and so, the profession came to be seen in a bad light. Hypatia, "The bad currency drove out the good. Reputable astronomers and geometers like Theon and Hypatia got confused in the popular and in the ecclesiastical mind with these fly-by-nights. All were lumped together as 'mathematicians'" (Deakin, 1997). This was a dangerous position at the time, because Christianity was becoming the dominant religion in Egypt and beyond, and many Christians distrusted science and education. Coffin states, "The Romans did not appreciate Greek mathematics and in fact thought it was subversive. The Romans had not been greatly involved in the development of mathematics; hence their mathematicians did not compare favorably to the Greeks" (Coffin, 1998, p. 96). Thus, as Christianity spread throughout the area, Hypatia found herself in a dangerous situation. Many pagans left the city to save themselves, but Hypatia did not.

In addition to her notoriety as a female scholar and philosopher, Hypatia made no secret of the fact she was a pagan who did not believe in Christianity, and this further alienated her from the Christian majority. She made a strong political and religious enemy when she angered Cyril, the Roman Catholic bishop and leader of Alexandria. Cyril was adamantly against pagans and Jews, and issued many sanctions against them during his forty-year reign. Cyril considered Hypatia an enemy, and where there are not actual texts tying him to her death, most historians regard Cyril as the force behind the mob that eventually attacked and killed Hypatia. Some say Cyril made it known there would be a reward for those who killed the woman.

Eventually, Cyril and his supporters did manage to murder Hypatia, and her death was especially grisly. As she rode through the city in a carriage, her enemies overtook her. Another historian states, "She was seized from her carriage and dragged into the Caesareum, the former temple of the imperial cult, which was now the cathedral. There she was stripped and stoned to death with broken roof tiles. Her body was then hacked to pieces and burned" (Russell, 2000, p. 9). Later, legend has it that her remains were scattered all throughout the city as a warning to other pagans and scientists. The year was 415, and Hypatia was anywhere between 40 and 60 years old.

Unfortunately, none of the… [read more]

Mathematician Nassar, Sylvia. A Beautiful Mind Term Paper

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¶ … Mathematician

Nassar, Sylvia. A Beautiful Mind. New York: Touchstone Books, 1998.

The story of the 1994 Nobel-Prize winning mathematician and economist John Nash has proved to be an inspiration to all individuals who have heard and read about the great Princeton genius, and not simply because of Nash's ground breaking insights about the mathematics of game theory. Nash is equally famous for his return from his prison of mental illness. He is now once again dwelling in the lucid world of his previous, brilliant mind, in a state of sanity. Author Sylvia Nassar's biography A Beautiful Mind tells the story of how Nash was born in the Ozarks, one of the poorest regions of America. As a young man, he was arrogant yet intellectually talented. After becoming a graduate student at Princeton, he even challenged Albert Einstein face-to face about the older man's theory of relativity. Einstein dismissed the young Nash's concerns from a mathematical point-of-view, but was impressed by Nash's bravado.

Nash became famous as a young man because of his unique insights into game theory, a theory that attempted to rationally predict how human beings made decisions with imperfect information, as people must in certain kinds of games, worldwide diplomacy, and economics. Ironically, although Nash's mathematical theories are used to predict human behavior with numbers and equations, even before he began to lose his reason, Nash had a great deal of difficulty relating to other people, even his fellow mathematicians. One of the reasons Nash loved mathematics was that he did not need to deal with other people's emotions in a world of numbers. According to Nassar's book, even before he developed the symptoms of schizophrenia, his contemporaries, "found him immensely strange," and "aloof." (Nassar, p. 13) Even so, by the 1950s, Nash had carved a brilliant career "at the apex of the mathematics profession, traveled, lectured, taught," and met "the most famous mathematicians of…… [read more]

Why Algebra Term Paper

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How Algebra can be used in real Life

Algebra can easily be used in real life, in many of the calculations which we make every day. The most common example I can think of is using algebra in some way to calculate a rate of change. Let's say for example the hypothetical person who has passed his algebra classes with flying colors and has won a job working for the college has been asked to calculate the rate of change in the number of students who will be attending the school and need to take classes in the next ten years. In this matter, one has to take the formula, which just uses x's and y's and change them into something which has meaning, in this case, the people that will be attending the school. Since we know that in this case, the independent variable we are discussing is the number of students coming to school, we can also make the subject a little bit more complex. We know that the variable can increase, increase exponentially, decrease, remain constant, or any of a number of different things.

So in this case let us make the number of students the function x. By just looking at x we cannot tell what it is going to do, it is too unpredictable. We can only give meaning to x by placing it in context to our study. By this we…… [read more]

Calculus? Calculus Is a Vast Topic Term Paper

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¶ … Calculus? Calculus is a vast topic and it also forms the basic foundation of any calculations that are based on math. Calculus is divided into two branches, one being differential, and the other being integral. Differential calculus deals with the study of the rates of changes that may happen in functions. For example, it teaches how to find the derivative of a particular function when the function is to determine the angle of the slope of a graph, which deals with that function, at a particular point. Integral calculus generally helps the beginner to deals with certain primitive functions, like for example, indefinite integrals, and also for finding, for example, the area under a curve, known as a definite integral. (Quick math, Automatic Math Solution)

In other words, calculus can be defined as a branch of mathematics that pertains to the rates of change. Although its basic roots can be traced back to Ancient Greece and to Ancient China, its actual origins are indicated in the time of Newton and Leibnitz in the seventeenth century. In the modern world, calculus has proved its usefulness time and again, and it is used extensively in many different areas of science. The there ideas of 'limit', 'derivative', and 'integral' are interwoven into the principles of calculus, wherein while derivative indicates the instantaneous rate of change, in comparison to something else, the integral generally indicates the area under its graph, or a sort of total 'over time'. For example, when the derivative of 'height' in respect to its position, is 'slope', then the derivative of 'position' with respect to 'time', is velocity', and when 'velocity' is taken with respect to 'time', then the derivative would be 'acceleration', and so on. As far as integrals are concerned, the area under the graph is taken into consideration, and this means that when the integral of 'slope', in respect to a constant, is 'height', then the integral of 'velocity', up to a constant, 'position', and thereafter, the integral of 'acceleration', with respect to 'time', is 'velocity'. It is quite evident therefore, that derivatives and integrals are inter-related and are also at times, complete opposites. (Preparing for University Calculus: At Atlantic Canadian Universities)

Why is 'calculus' important in today's world? Science today studies many processes that involve change, and since calculus deals with changes, it is very important. (Preparing for University Calculus: At Atlantic Canadian Universities) One particular High School teacher gave her students concrete examples of how calculus can be applied in real life to solve real problems. The links between the physics concepts of position and velocity and acceleration and the totally calculus concepts of function, derivative and anti-derivative were found. (Dosemagen; Schwalbach, 54) Another teacher toot found that when physics is applied to calculus, the problems would be solved easily. When compared to the way in which these students found it difficult to use mathematics for their calculations, and how they preferred to use physics as a better option, it can be seen… [read more]

Development and Application of These Concepts in Real Life Term Paper

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¶ … Real Life

Golden Ratio:

The golden ratio is acknowledged as the divine proportion golden mean, or golden section is represented as a number mostly confronted while considering the ratios of distances in simple geometric diagrams like pentagram, decagon and dodecagon. It is indicated by the symbol 'phi'. The concept 'golden section' was first used by Martin Ohm in… [read more]

Pre-Post Test Knowledge of Ultrasound Content Term Paper

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Pre-Post Test Knowledge of Ultrasound Content Knowledge for Sonographers

When an investigative research study ins set up on the basis of a pre and post testing situation the investigator is afforded the opportunity not only to determine differences in mean test scores for the before and after criterion but also establish whether or not there exists a relationship between the pre and post test situation. The latter statistical process is known as a correlation study. In addition the investigator is also able, on an individual participant basis, able to determine wherein each individual places with respect to the average scores on a pre-test basis and on a post-test basis in respect to the group average. This calculation is known as a Z Score.

Descriptive Statistics Results

Pre-Test Ability to Detect Abnormalities







B. Post-Test Ability to Detect Abnormalities







C. Mean and Median Graphic Presentation of Differences

Between Pre-test and Post-Test Results

Conclusion: On the basis of the raw data (i.e., non-statistical significant difference) there appears to be a slight increase in ultrasound content knowledge as result of individuals participating in the academic course. Whether or not the reported difference is statistically significant is not known from a review of the raw data. In addition, the conclusion can be drawn that the variability of ultrasound knowledge is more variable before the course vs. after the course.

D. Statistical Analysis of Raw Data visa via "t" Test Calculation:

value and statistical significance:

The two-tailed P. value equals 0.0033

By…… [read more]

Java Application (Parking Simulator) Interface Description Form Term Paper

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Java Application (parking Simulator)

Interface description


When user launches the application the form1 appears. From form1 we can go to parking form by clicking on "Park." Actions of "Park" button will be viewed later. By the use of panel menu we can do the following:

File-exit - exits the application

Change statistics->Coins available- calls from2 that shows coins available in parking machine

Clicking on button "OK" returns user to Change statistics->Add funds calls form3 that allows to add funds to the machine


Clicking "OK" button adds funds inputted into the machine and return the user to the form1. In order to change the available funds user can view menu Change statistics->Coins available;

Change statistics->General statistics

About-> contains information about the program's


By clicking on park button on form1 user gets to the form4 which shows parking actions. Here the driver has to choose number of hours and pay for them. He can view the indicator of current time and ending time of parking for which he is supposed to pay. Also the form shows the amount that has to be paid and the amount the driver had already paid. If user makes a mistake in inputting data either for parking time or for amount paid he can cancel payment and will be returned to the form1. In the upper section of the window there are coins of different value for parking payment. By clicking on these coins user will pay corresponding amount of money for parking. When payment is complete buttons become unavailable- user can not add any more money. After the payment is complete and user had paid more than it is supposed, he will get a change menu message form5.


On the change menu he can choose the way he want to get change in different variants. He can also watch the change available. After he chooses the variant of payment the program checks for available funds and if the funds are unavailable program gives an error message-Form6


Then the application returns user to form1.

The data about parking payments can be viewed from report file or in the menu: Change statistics->General statistics Form7


Information about payments is saved into dynamically creating file Report.txt for future…… [read more]

Job Satisfaction Survey Research Studies Term Paper

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Job Satisfaction Survey

Research studies, whether they are clinical trial based, experimental, case study designed, or descriptive, must exhibit and command interest, enthusiasm, and passionate commitment. The research investigator must catch the essential quality of the excitement of discovery that comes from research well done if expected results are to be gained. To this end the researcher is bound by a very stringent protocol for the development of all research endeavors. Not only must the investigator clearly define the research problem but must also plainly state a research question, followed by a testable research null hypothesis. Contained within the format of the research purpose, question, and hypothesis are various inherent constraints that will alert the reader as to the investigator's knowledge of, and adherence to, those tenets that make for sound, credible, and purposeful research (Ohlson, 1998). Included in the aforementioned three research requirements are statements of, and a rational for the use of, specifically chosen variables (independent and dependent), measurement or data assessment tools, statistical data analysis techniques, and potential error sources. Wherein most research fails to deliver scientific information for the advancement of content knowledge is in the area of study error. The remainder of this report will examine one source of possible error, namely that associated with sampling. Once sampling theory has been examined the garnered information will be applied to a specific study using a job satisfaction survey.

Sampling. The most succinct and effective way to view research sampling is to look at the process as being a part of a whole that represents a larger connection (Ohlson, 1998). Briefly defined sampling is the taking any portion of a population or universe, as representative of that population or universe. Sampling alone can skew testing results, infuse…… [read more]

Permutations and Combinations Term Paper

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(Dr. Math, 2004)

Beyond speculating about advertising, however, the use of permutations and combinations can be useful, for instance, when a business desires to allocate its advertising for several products along several potential sources, all from the same media such as television or magazines, but wishes to make sure that the combinations of the different publications did not overlap in terms of the combinations. To calculate, the various letters could be used to represent the publications, and the products also allocated various letters, to ensure that there was no overlap of particular products and sources.

Restaurant owners could use permutations and combinations to determine various pairings of toppings, to determine if this was economically feasible to achieve -- for instance, what is the maximum amount of combinations a pizza can have, given a fixed array of toppings, and also, what is the maximum amount of toppings that any singular pie can possess? Thus, the owner could calculate the maximum amount of funds the pizza could possibly allocate to the owner of the pizza business.

Permutations in combination could also be used to pair off different members of staff, when needed, on the floor of a store or a restaurant. For instance, it could be assumed that the establishment would likely have a certain number of tables filled on one particular night, and thus would require a certain number of members of the wait staff, busboys, and cooks, per table, to ensure that the table was adequately attended to over the course of the evening. From an inventory perspective as well, certain products must always be paired together in combination in terms of need, such as coffee cups and stirrers. Thus, permutations in combinations are not simply interesting and speculative statistical tools, but are used in the daily world of business mathematics.

Works Cited

Dr. Math. "Permutations." (2004) Math FAQ. Retrieved on October 7, 2004 at http://mathforum.org/dr.math/faq/faq.comb.perm.html

Dr. Math. "Fast Food Combinations." (2004) Math FAQ. Retrieved on October 7, 2004 at http://mathforum.org/dr.math/faq/faq.mcdonalds.html… [read more]

Scientific Investigation Includes Both Independent Term Paper

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This particular type of ANOVA shows differences that are a result of "effect" and not differences between mean scores. Again, a wrong choice was made.

Assuming the "t" test were the appropriate tool the authors failed again in not pre-selecting their level of statistical acceptance. Whether or not this was a clever move on the part of the authors or not is not know. What is being implied here is that when there is no stated testable null hypothesis there is no reason to pre-set an alpha or probability level for accepting or rejecting the null hypothesis. In cases like this researchers are free to explain any result they choose to and not bound by controls pre-set in the beginning of the study. This, as most research pundits would express is sloppy research.

Results and Implications Because of all the errors in research design, measurement instrument selection, and statistical tool selection interpreting the results of this study cannot take place. The errors are so great that offering an interpretation of the results would only add error to error. At not time can there be faith placed in research findings that are fraught with error. To warrant the results of this study as being useful to the advancement and understanding or learning disabled student simply cannot take place. The bar of excellence must be raised significantly for this study to garner support, as the external error for this study is magnanimous. What is suggested is as follows:

Restate the research question in proper investigative form.

Specifically state all testable null hypotheses.

Pre-set a probability level for the acceptance or rejection of any and all null hypotheses

Select statistical tools that can effectively analysis data gathered in support of the specific research question.

Fully expound upon the measurement tools used to collect the test data to be analyzed.

Specifically state the limitations and delimitations of the study

Support the need for such a study through a review of literature

Explicitly define the terms used in the study including both independent and dependent variables.

Explain all testing procedures in detail.

List all possible intervening variables and internal and external error.

Make use of…… [read more]

Nursing Research Report the Structure Term Paper

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Other considerations that a researcher must account for within the design section of the study are directly related to the manner by which a sample has been selected, the fashion by which the assessment instrument is administered, possible limitations and delimitations surrounding the investigation, and the applied control procedures. Should these factors not be taken into account there exists a… [read more]

Power of Statistical Analysis Term Paper

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The mean, median and mode are all equal in this type of measurement, and the scores at either end of the distribution, those which are extremely high, or extremely low, occur less often. For example, a curve representing the results of an intelligence test would have the highest number of people in the middle, or measuring within the 'average' intelligence… [read more]

Frege's Much-Discussed Book, the Foundations Book Review

Book Review  |  4 pages (1,207 words)
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Importantly, Frege argued that analytic judgments govern the laws of arithmetic, and thus these laws exist a priori. This analysis was likely one of the most important contributions of The Foundations of Arithmetic.

As defined in The Foundations of Arithmetic, Frege's main analysis that the laws of arithmetic are a priori has important consequences. Frege notes that the definition of the laws of arithmetic as a priori results in the following: "Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction."

Frege has a great number of influential and important admires. For example, the well-known philosopher Michael Dummet notes that Frege's work on the criterion of identity is "brilliant and philosophically fruitful." Further, Dummet gives Frege high praise for uniqueness, noting that The Foundations of Arithmetic is truly the first work of analytical philosophy (Frege Biography).

In spite of the great praise heaped upon the book, Frege's analysis is sometimes somewhat flawed. For example, Frege's analysis is often somewhat weak in terms of psychological references. He easily notes the difference between concept and object, and yet he does not clearly define sense and references. Barbosa notes that after The Foundations of Mathematics was written, Frege rejected his contextual preference, which argued that words refer to something based on context.

Frege has also been accused of distorting the ideas of other philosophers to his own benefit. Notes Barbosa, "Sometimes (Frege) distorts a little bit what others say about logic, so he argues against those thinkers more effectively." This is indeed a serious criticism, and implies that Frege was, at least in this case, not scrupulously rigorous or honest in his philosophical arguments.

Frege was always willing to correct inconsistencies in his works, and the issue of contextual preference was no exception. Barbosa notes that after Frege "wrote the book, he would reject this principle, because of his doctrine of sense and reference: the sense of the words determine the sense of the sentence; and the reference of the words determine the reference of the sentence."

In conclusion, Gottlob Frege's The Foundations of Arithmetic has made a lasting and influential contribution to the philosophy of mathematics. This book is essential reading for anyone interested in the philosophy of mathematics, and is also invaluable for anyone interested in the broader field of analytical psychology. The Foundations of Arithmetic provides a convincing argument that logic is the basis of arithmetic, rather than psychology, and also makes the important argument that analytic judgments govern the laws of arithmetic, and thus these laws exist a priori. It was in these discussions that Frege likely made his greatest contributions to the philosophy of mathematics. Despite his great critical success and long-lasting influence, Frege's works were not without their weaknesses. Importantly, many psychological terms within The Foundations of Arithmetic are not thoroughly defined, and critics have argued… [read more]

Multiplicative Number Theory Term Paper

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All integers are divisors of 0. All integers 'a' are divisible by and If a has any other divisors, then it is called a composite. Otherwise, it is called a prime, unless which are called units. Of the positive integers not greater than 20, the composite numbers are

The prime numbers less than 20 are

Primality testing and factorization

The… [read more]

Algebra Lesson Plans and Curriculum Term Paper

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(p. 38).

A large category of algebra misconceptions has been documented in Algebra: Some Common Misconceptions under the category of "The Meaning of Letters." These relate to students' difficulty with the meaning of letter variables. They may completely ignore letters and consider them irrelevant. For example, add 3 to x + 4 and the answer is 7. Or they may… [read more]

Structure the Research Term Paper

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Individual researchers must monitor a vast number of research results and activities that have a bearing on their own particular specialties.

By definition, measurement must be objective, quantitative and statistically valid. Simply put, it's about numbers, objective hard data. A scientifically calculated sample of people from a population is asked a set of questions on a survey to determine the frequency and percentage of their responses. For example: 240 people, 79%, of a sample population, said they are more confident of their personal future today than they were a year ago. Because the sample size is statistically valid, the 79% finding can be projected to the entire population from which the sample was selected. Simply put, this is quantitative research. Qualitative research, is much more subjective than quantitative research and uses very different methods of collecting information, mainly individual, in-depth interviews and focus groups. The nature of this type of research is exploratory and open-ended. Small numbers of people are interviewed in-depth and/or a relatively small number of focus groups are conducted. Participants are asked to respond to general questions, and the interviewer or group moderator probes and explores their responses to identify and define peoples' perceptions, opinions and feelings about the topic or idea being discussed and to determine the degree of agreement that exists in the group. The quality of the findings from qualitative research is directly dependent upon the skill, experience and sensitivity of the interviewer or group moderator.

The term "Epidemiology" comes from three separate words: "epi" - which means "upon," "demos" - which means people/population, and "ology" - which means the science. Hence it means the study of things that occur upon the population. Epidemiology is the study of how diseases and other health outcomes are distributed in the population and the factors that influence or determine this distribution.

Today, research is increasingly diverse in its objectives, scope and modes of organization. Research involves individual endeavors, small and large teams, major regional or national research networks, and international consortia. The need to concentrate intellectual and financial resources has spurred the creation of new research centers and institutes that transcend the traditional academic organization based on disciplines. Budgetary pressures and the benefits of collaboration encourage the pooling of expertise…… [read more]

Lives of Archimedes and Carl Term Paper

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The Latin translation influenced the work of the foremost mathematicians and physicists of the time, including Johannes Kepler and Galileo. A 1615 Latin translation of his complete works, was enormously influential in the work of Rene Descartes and Pierre de Fermat. The mathematical advances in Europe from 1550 to 1650 was build largely on the work of the ancient mathematicians, especially Archimedes ("Archimedes").

In contrast, Gauss's work had immediate impact on both theoretical and applied mathematics. This was partly because Gauss himself was interested in the applications of his work. Gauss also lived during the dawn of the Industrial Age, a time of unprecedented scientific advancement.

Gauss's interest in gravitation and magnetism led to a published paper in 1840 on real analysis. This paper became the starting point for the modern theory of potential. In the beginning of the 20th century, mathematicians re-developed potential theory, on the basis of Gauss's initial conclusions. In 1830, Gauss's mathematical investigations of fluids at rest contributed to the development of the Law of Conservation of Energy. His collaborative work with William Weber on electromagnetism paved the way for the invention of the telegraph. In addition to electromagnetism, Gauss's works in algebra and numbers theory continues to have significant impact on current mathematical research, including geometry and modern telecommunications ("Gauss").


In conclusion, the work of Archimedes and Gauss continues to make significant contributions to all fields of mathematics. Many mathematical disciplines would not even be possible without their work.

Both men faced significant obstacles to their mathematical research. Archimedes lived in a time of very limited mathematical knowledge. Even commonplace mathematical concepts today - the ideas of the infinitesimal, pi, and infinity - were unheard of during his time. The cumbersome Greek and Roman numeral systems were unwieldy for his computational needs so he had to devise his own.

Gauss, on the other hand, was born into poverty and did not have his family's support. He lived in or close to poverty for much of his life.

However, both men eventually overcame these obstacles to produce their research. Centuries after their deaths, the work of these two great minds continues to revolutionize the science of mathematics.

Works Cited

Archimedes," in Guide to the History of Calculus. Retrieved 30 November 2002 from http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib/custom3/bios/archimedes.htm

Bell, E.T. Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincare. New York and London: Simon and Schuster, 1965.

Boyer, Carl B. A History of Mathematics, 2nd ed. New York: John Wiley and Sons, 1991.

Gauss," in Guide to the History of Calculus. Retrieved 30 November 2002 from http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/chapter1/medialib/custom3/bios/gauss.htm

Muir, Jane. Of Men and Numbers: The Story of the Great Mathematicians. New York: Dover Publications, 1996.

Riley, Mark T. "Archimedes"…… [read more]

Isaac Newton Was the Greatest Term Paper

Term Paper  |  2 pages (707 words)
Bibliography Sources: 1+


Newton's three laws of motion explained the hitherto inexplicable behavior of all physical bodies in motion. Still more astounding was Newton's discovery of gravity. All these four laws put together explained the mechanical motion of all earthly and heavenly bodies. Newton not only proposed these laws but also ratified them by using the integral calculus.

Newton published his laws of motion and gravity in his famed work 'Mathematical Principles of Natural Philosophy' (Principia) in 1687. [Microsoft Encarta] Newton's revolutionary discoveries were applied to a wide array of subjects. The field of Astronomy in particular got a tremendous impetus from his laws of motion. Using these laws Newton was able to precisely identify and predict the position of planets and other heavenly bodies. This was a significant milestone in the field of astronomy and for this reason Newton is rightly regarded by many as the greatest of all astronomers.

As for Newton's accomplishments we can do better by quoting some of the other great scientists. The great French scientist Laplace said, " The Principia is preeminent above any other production of human genius." Lagrange, another famous mathematician opined that Newton was the greatest genius who ever lived. Ernst Mach on his part said "All that has been accomplished in mathematics since his day has been a deductive, formal, and mathematical development of mechanics on the basis of Newton's laws." [Michael.H. Hart]. In conclusion we can say that in the history of science Newton's name is indelibly imprinted and perhaps his laws and discoveries are the most referenced by the scientific world. It is clear that Newton is not only one of the greatest scientists but also one of the most influential scientific personalities.


Michael.H. Hart, "The 100, A Ranking of the Most influential Persons in History"

Isaac Newton', 1999, Meeraa publications.

Microsoft Encarta, "Isaac Newton," Accessed on 2nd, December 2002, http://www.newton.cam.ac.uk/newtlife.html

D.R.Wilkins, "Sir Isaac Newton (1642-1727)," Accessed on 2nd, 2002

http://www.maths.tcd.ie/pub/HistMath/People/Newton/RouseBall/RB_Newton.html… [read more]

Euclid's Fifth Postulate Philosophical Term Paper

Term Paper  |  5 pages (1,735 words)
Bibliography Sources: 1+


Whether the fifth postulate is true or false also affects the kind of geometry that is being used. For example, if the postulate is true, than Euclidian geometry works. If the postulate is false, then it creates a non-Euclidian type of geometry where similar triangles must always be congruent and the Pythagorean Theorem is no longer valid (Bennett, 2000).

Whether Euclid's fifth postulate is true, false, or both, it will continue to be debated by scholars and mathematicians for many years to come. Whether it will ever be 'solved' or proved remains to be seen. Either way, it is a fascinating and problematic piece of information that will carry on Euclid's legacy for centuries. If someday it is proven to be either true or false, and the decision is agreed upon, then it could change the way mathematics are done and the way geometry is looked at during the present time and also well into the future. Euclid would have likely enjoyed the attention his simple thoughts are receiving.

Works Cited

Bennett, Andrew G. The Axiomatic Method. 2000. Math 572 Home. 2 December 2002. http://www.math.ksu.edu/math572/notes/824.html.

Bogomolny, Alexander. The fifth postulate: attempts to prove. 2002. Cut the Knot. 2 December 2002. http://www.cut-the-knot.com/triangle/pythpar/Attempts.shtml.

Parallel lines and planes. 2002. Connecting Geometry. 2 December 2002. http://www.k12.hi.us/~csanders/ch_07Parallels.html.… [read more]

Fractal Geometry Term Paper

Term Paper  |  4 pages (1,018 words)
Bibliography Sources: 1+


His mind was a visual one, a geometric mind, yet he was not taught this way.

Mandelbrot claims he could not do algebra well yet managed to receive the highest grades by translating the questions mentally into pictures. When he finished school, he came to the United States, where IBM gave him the freedom to pursue his mathematical interests, as he deemed worthy.

Mandelbrot's research led to a huge breakthrough summarized by a simple mathematical formula: z -> z^2 + c. This formula is now called the Mandelbrot set. It is important to understand that this formula, and the Law of Wisdom which it represents, could not have been discovered without computers. Many say that this mathematical breakthrough, which occurred in the research laboratories of I.B.M., is the greatest in twentieth century mathematics.

The Mandelbrot set is a dynamic calculation based on the iteration of complex numbers with zero at the beginning. The order behind the chaotic production of numbers created by the formula can only be seen by the computer calculation and graphic portrayal of these numbers on computers. Otherwise the formula appears to generate a totally random and meaningless set of numbers. It is only when millions of calculations are mechanically performed and plotted on a computer screen that the hidden geometric order of the Mandelbrot set is seen. The order is of a beautiful yet different kind, containing self-similar recursiveness over an infinite scale.

Euclidian geometry was unable to describe the shape of a cloud, coastline, a hill or a tree. As Mandelbrot says in his book the Fractal Geometry of Nature:

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line."

Mandelbrot broke the long-term chain of thinking that held that most of nature's systems were too complex and strange to be described in mathematical terms. Fractal geometry opened a new world of mathematics that is capable of describing mathematically the most strange and complicated forms of the real world. In Mandelbrot words: "Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently."

The Mandelbrot set has done much more than just produce beautiful pictures. When pictures are thoroughly examined, innumerable empirical observations are found that can be restated in the form of mathematical conjectures. Many of these have already led to brilliant theorems and proofs. Fractal geometry has inspired a new approach to mathematics, using a computer screen.

The discovery simply started a new way of thinking, which will undoubtedly change the way many things in the world work. Fractal geometry is opening doors to significant new insights into complex phenomena, including cells, hearts, brains, coastlines, mountains, earthquakes, economies, political systems, art, music, climate & life.


Mandelbrot, Benoit B. The Fractal Geometry of Nature W.H. Freeman and Company, 1977.

Crilly, R.A. Fractals and Chaos. Springer-Verlag, 1991.

Dictionary of Scientists, Oxford University Press, Market House Books Ltd., 1999… [read more]

Georg Cantor: A Genius Out Term Paper

Term Paper  |  9 pages (2,882 words)
Bibliography Sources: 1+


Cantor's most criticized concept presented in this paper is that the power of the continuum is independent from its number of dimensions. It was commonly believed that points in two dimensional space cannot be traced back to one dimensional space, and Cantor had thought that he could get higher transfinite powers by going from the one-dimensional to the multi-dimensional. Here… [read more]

Euclid of Alexandria: 325 Term Paper

Term Paper  |  2 pages (527 words)
Bibliography Sources: 1+


"; a clear insight into his apparent wisdom. The second story concerns a student who, after his first lesson, asked what he would gain in life from learning such things as he was in the school; Euclid called his slave and said: "Give him a coin since he must make gain by what he learns."

Arabian and Syrian writers have said Euclid's father was Naucrates, and his grandfather, Zenarchus. They also said he was a Greek who was born in Tyre and lived in Damascus. Unfortunately, most of this information has little evidence of validity. Added perplexity began around 14th century when the Byzantine writer Theodorus Metochita (d. 1332) wrote "Euclid of Megara, the Socratic philosopher, contemporary of Plato." This Euclid, Euclid of Megara, lived around 400 B.C.E. And was actually a pupil of Socrates who founded a philosophical school, which Plato did not like. Nothing is known of Euclid's death.

Other works of Euclid include: The Data, for use in the solution of problems by geometrical analysis, On Divisions (of figures), The Optics, and The Phenomena, a treatise on the geometry of the sphere for use in astronomy. His lost Elements of Music may have provided the basis for the extant Sectio Canonis on the Pythagorean theory of music.


Gillispie, Charles C. ed. The Dictionary of Scientific

Biography, 16 vols. 2 supps. New York: Charles Scribner's

Sons, 1970-1990. S.v. "Euclid: Life and Works" by Ivor


Heath, Thomas L. The Thirteen Books of Euclid's Elements, 2

vols. Cambridge: Cambridge University Press, 1926.

Frankland, William Barrett. The first book of Euclid's Elements…… [read more]

Stigmatization and Therapy Counseling of Gay Men Research Paper

Research Paper  |  11 pages (4,032 words)
Bibliography Sources: 1+


Unnatural sexual orientation is not an independent, standalone issue for those professing inclination towards same sex individuals for their sexual needs. Such individuals invariably face difficulties, humiliation, and consternation in many other areas of their lives, thereby being isolated, stigmatized, and finding it difficult to lead normative, meaningful life. In recent times, there are concerted efforts to address their concerns… [read more]

Gay and Lesbian Themes in Film A2 Coursework

A2 Coursework  |  2 pages (424 words)
Bibliography Sources: 0


Gopinath, Gayatri. "Queering Bollywood."

What does Gopinath mean by "queer diasporic viewing practices?"

What types of problems does a queer diasporic viewing practice present, in terms of biased readings into Indian-produced cinema? In other words, is Gopinath superimposing Western values onto Indian normative sexuality?

What evidence does Gopinath present of gender bending in Indian cinema?

How are gender bending, gender performativity, and homoeroticism portrayed in Indian cinema in general?

What evidence is there that Indian cinema contains deliberately subversive messages about sexuality?

Warner, Michael. "Normal and Normaller."

Does the institution of marriage contradict queer identity as being inherently oppositional to the dominant heteronormative culture?

Warner notes that gay marriage has until recently been less important than issues such as AIDS prevention, anti-gay violence, and "the saturation of everyday life with heterosexual privilege." Do you believe that the fight for marriage equality detracts from these causes?

3. How does marriage equality reconstruct marriage as a social institution, removing its patriarchal associations?

4. Do you agree with Warner that "as long as people marry, the state will regulate the sexual lives of those who do not," such as by de-legimizing consensual sex that does not fall within the established normative framework of marriage?

5. Marriage equality confers status as well as a veneer of…… [read more]

Theory of Numbers and Operations A2 Outline Answer

A2 Outline Answer  |  3 pages (1,036 words)
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Theory/Knowledge of Numbers/Operations

The student in Question A1 will earn an A if the teacher rounds the student's percentage to a whole number. 299 divided by 334 equals .89520958, which would come to 89.5%. Rounding up 89.5 to a whole number makes this 90%, which is the requirement for an A grade.

The student in Question A2 will presumably not receive an A if 89.5 is truncated down to 89%.

Truncating an income tax rate of 27.8% would mean disregarding what follows the decimal point. A taxpayer would prefer a rate of 27% to a rate of 27.8% because this means the taxpayer gets to retain almost 1% (in reality 4/5 of a percentage point) of income that would otherwise be paid to the government in taxes.

The government requires the taxpayer to round up a 27.8% tax rate rather than truncate it for precisely this reason. This would be rounded up to 28% and would also save trouble if, for example, the taxpayer's income already was reckoned down to the last cent -- this could leave a tax bill that is reckoned in tenths or hundredths of a single cent, which is an amount that cannot be paid in real currency. A hypothetical taxpayer with a 27.8% tax rate who earned one dollar last year could not be expected to pay the government .278 cents, because there is no coinage to designate four-fifths of one penny.

C1. Let us suppose we are calculating a 27.8% income tax for a hypothetical income of 50,000 dollars. This is simple for mental math. The 27.8% tax for 100,000 can be calculated mentally -- it is 27,800 dollars, a little more than a quarter. Now we only need to divide this number mentally by 2, in order to get the calculation for 50,000 (which is one-half of 100,000), and it comes out to $13,900 as the 27.8% tax on a $50,000 income.

C2. Imagine that we had to divide 102.5 apple pies among four people. The easiest way to do this is by truncating: we truncate the number to 100 apples, and calculate that each of four people would take 25, then we concentrate actual division on the remaining 2.5 apples. Truncating could also be used to calculate a 15% tip for a bad waitress -- if the bill comes out to 102.5 dollars, we can truncate this to 100 and leave slightly less than 15% in recognition of lousy service. Rounding up can be convenient in estimating sales tax: if we know that a new laptop costs 899 dollars, and that Pennsylvania has a 6% sales tax, then we know to bring around 910 dollars to the computer store to cover the sales tax of the purchase. Rounding up can also be useful in making sure you have enough food for guests. If we are planning to have 17 persons at the Superbowl party and we estimate that each person can probably eat about 5.5 buffalo wings, then it makes sense to… [read more]

Solutions to a Math Problem Reaction Paper

Reaction Paper  |  4 pages (1,249 words)
Bibliography Sources: 1


Problem Solving Report

The task that was proposed to the students was as follows: Conrad's Taxi Service charges $1.50 for the first mile and $.90 for each additional mile. How far could Mr. Kulp go for $20 if he gives the driver a $2 tip? (taken from Holtz and Malen). The students were 7th grade students, and a group of 5 students was formed. According to the instructions, the students worked separately to solve the problem, then jointly. It is interesting to note (and this will be further expanded when describing the choice and interaction between the students) that some of the students were able to solve the problem individually on their own and that, for them, the interaction phase implied convincing the other students of the viability of their solutions.

The standard used here was CCSS.MATH.CONTENT.7.EE.B.4, which states the "use of variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities" (Common Core). Particularly CCSS.MATH.CONTENT.7.EE.B.4.A was useful in this case, namely the solving word problems by conceiving equations of the form px + q = r and p (x + q) = r, where p, q, and r are specific rational numbers.

The group was formed relying on the principle of differentiation. To the degree to which this was possible, the aim was for a mixed group boys/girls. At the same time, there was a preference for an uniform representation knowledge-wise: the student were selected to have average math scores and no obvious aptitude or extraordinary performance in this field. In order to further study the interaction of particular individuals with the rest of the group, an ESL student was included in the group.

In terms of the learning trait, two of the students included in the group were known for their extracurricular activities in art-related areas, including drama, art and music. The reason they were selected was so as to compare their solution to the problem to the others'. One would want to understand whether particular hobbies or higher creativity provide different approaches and solutions to a math problem.

There were five students, three boys and two girls. They were also taking the same math class and this is how they were selected for the test. They were also among the best math students, so their proficiency was an additional argument in their selection. There was a meeting with their math teacher (and without the students) so as to understand more of their individual characteristics and personalities. With that in mind, this is how I have come to know so much about them.

This was important to understand whether someone who worked out the problem on his own would also be willing to share it with the others in the group or whether he preferred to wait for a group solution to be successfully worked out. It would also be interesting to understand whether some of the group participants would try to impose their… [read more]

Theory-Building, Applied Research Journal

Journal  |  2 pages (577 words)
Bibliography Sources: 1


The researcher assumes the alternative hypothesis is true. Rejecting the null hypothesis suggests that the alternative hypothesis may be true.

Qualitative research begins with the specific and moves toward the general. The data collecting process in qualitative research is field-based and personal. Patterns emerge from the data during the process of analysis. Throughout the data collecting process, researchers typically record their thoughts and impressions about the emerging data patterns. Qualitative researchers gather data about their research from many different sources, using a process called triangulation to ensure that data can be verified. When enough data has been collected, the researcher will interpret the data.

A research study includes an abstract, a very brief introduction, and a literature research of relevant theoretical articles that serves as the larger introduction to the research. The methodology section includes the statement of purpose, researchable questions, the research design, the instrumentation, the participants, the data collection methods and the procedures for analysis. The discussion section includes the results of the data collection and the discussion. This section also usually includes the benefits and limitations of the study, as well as recommendations for future study.

The research study reports or summaries are written as how-to reports, experimental reports, or empirical research or experimental replication. The philosophical grounding of the research includes scientific realism, social constructivism, advocacy-liberatory, and pragmatism. Research procedures require and institutional review board, and article summary sheets, usually produced in pdf format. The summary reports of the research may be emailed to and from a lit of subscribers via listserv.


Lodico, M., Spaulding, D., & Voegtle, K. (2010). Methods in educational research: From theory to practice (2nd ed.) San Francisco, CA: John Wiley &…… [read more]

Dispel Article Review

Article Review  |  2 pages (919 words)
Bibliography Sources: 1


1045). If these considerations are not met then the proposed question may not be appropriate for research study.

Other considerations include statistical consideration such as the statistical power needed to find a significant result, the costs associated with the proposed project, and alternative ways to answer the question. Research questions are often quantitative in nature and many questions did not lend themselves to quantitative measurements (Beya & Nicoll, 1998, p. 1045-1046).


There is no formal discussion section, but affect the entire paper is a discussion of the practicality of research in specific instances and when students should consider using research and type of questions/qualifications the need to be met in order to use research to answer particular questions. Beya and Nicoll (1998) state that for some issues, such as the notion that hospital -- laundered surgical attire is the most appropriate higher for reducing infection in the hospital, are not answer my research but instead by sound scientific principles. There are no research studies that the authors know of to support this notion; however, it is a universal practice in hospitals. There are many important questions that can be answered by research and many that cannot.

Personal Reaction

I found the paper interesting and generally agree with the assumptions and conclusions of the authors. However, the authors lose a lot of credibility in the very beginning of the paper when they discuss the notion of proof. There correct in assuming that a single research study really proves anything; however, there notion that research studies seek to "disprove" the null hypothesis is blatantly wrong (Beya & Nicoll, 1998, p 1044). In fact, formal statistical reasoning attempts to reject the null hypothesis in favor of the alternative hypothesis. Neither can be proven or disproven and in quantitative research studies the null hypothesis, which states that the measurement of two or more variables is equal (no difference), is rarely true to begin with if the variables are measured on a continuous interval or ratio level scale. It is the degree to which the difference is significant that the researcher attempts to ascertain.

Nonetheless, the authors provide a sufficient checklist of questions/qualifications that novice researchers can use to decide whether a particular question of interest or idea is one that is amenable to a formal empirical research study. Moreover, the authors' discussion of how to ascertain practicality and feasibility for particular research study is particularly important to enthusiastic, novice, researchers who think that any question should be empirically validated.


Beyea, S.C., & Nicoll, L.H. (1998). Dispelling the myth that…… [read more]

Bottling Company the Mean Case Study

Case Study  |  2 pages (541 words)
Bibliography Sources: 0


I'm not entirely sure what the third possibility would be. Either the measurement is off or the amount of liquid is off -- I'm curious what the third option might be here. It seems that there could not be too many other options available.

To avoid the problem in the future requires dealing with whichever is the major problem here. It is reasonable to assume that with two possible problems, the solution lies with identifying which of the possible problems is the issue and just dealing with that. So the problem can be addressed as follows. If the issue is that the measures are off, then the measuring devices need to be recalibrated. If the issue is that the filling device is off, then the filling device needs to be recalibrated. Clearly, some third party equipment that has been independently calibrated will be needed, in order to define the parameters by which we are measuring. But at the end of the day, the critical factor is that once all of the devices have been recalibrated, the problem should be solved and no more will there be issues with underfilling of bottles.

The important thing here is that we are quite confident that the bottles are not filling as much as they need to be. To get onside with the government, we need to work with a 95% confidence interval and the results on these bottle fills are nowhere near that. It is evident that the bottle fills are well below expectations. As a…… [read more]

Tag Members of a Population Term Paper

Term Paper  |  2 pages (733 words)
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The assignment is to solve for y and identity the type of equation that results when solving for y. The number sentence given is: y-1/x+3 = -3/4. Using cross multiplication gets rid of the denominators and yields the following equation: 4(y-1) = -3(x+3). The goal is then to isolate y on the left side of the equation, which gives one an equation solving for y. Without additional information, the equation cannot be solved for either the numerical value of x or y because doing so requires multiple equations or providing what x or y is. This information suggests immediately that the equation represents not a single set of coordinates, but a line. As a result, one is already thinking that the end-result of the process will be an equation for a line. The slope, intercept form of an equation for a line is popularly represented as y=mx + b where m represents the slope of the line and b represents the y intercept of the line. (The y intercept is the point on the line where it intercepts the y axis; in other words, the y intercept is the point on the line where x=0). Knowing this basic form of an equation helps guide the shaping of the equation as one solves for y.

The first step is to multiply each side of the equation. 4(y-1) becomes 4y-4. -3(x+3) becomes -3x -9. The equation them comes 4y-4 = -3x -9. The next thing to do is to add 4 to both sides as the next step in isolating y. The resulting equation is 4y= -3x -9 + 4 or 4y=-3x-5. One then divides both sides by 4 to continue isolating y. The resulting equation is y=(-3x-5)/4. The four is distributed throughout the equation, yielding the following equation y=-3/4x -5/4. That equation is an equation for a line with the slope -3/4 and a y intercept of -5/4. The y intercept provides the solver with a set of numbers that can be applied to the equation (0,-5/4). Plugging these numbers back into the equation allows one to eliminate the possibility of an extraneous response. y-1/x+3 = -3/4. Does (-5/4- 1) / 3 = -3/4? -5/4-4/4=…… [read more]

Pythagorean Theorem Ahmed Has Half Research Paper

Research Paper  |  1 pages (379 words)
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The coefficient is negative, there will be positive and negative factors. Two factors of -20 should add up to -8. 10 and 2 are factors of 20 that would also add up to 8 if the greater factor is negative and lower factor, positive. The result are two binomials to be solved using zero factor.

(x -- 10) (x + 2) = 0

After solving the binomials, the result is a compound equation expressed as follows (also the possible solutions for the problem):

x = 10 or x = -2

Considering the values of x solved through Pythagoras theorem, x=10 is more plausible given the buried treasure problem (negative distance is not applicable in the problem presented).

Computing for the binomials at x=10:

The treasure lies 10 paces…… [read more]

Math Inequalities Ozark Furniture Essay

Essay  |  2 pages (628 words)
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However, the company does not have to produce to its maximum. If the company received an order for 125 modern rockers and 50 classic rockers, the point (125,30) would lie inside of the shaded area. The resulting equation would be 15(30) + 12(125) = 1950, which is less than or equal to the 3,000 board feet. However, it is critical to realize that the line serves to maximize the number of rockers that can be created in conjunction with another type of rocker. The point (125,200) falls outside of the shaded area created by the inequality. 15(200) + 12(125) = 4500. As 4,500 is not less than or equal to 3,000, it is clear that Ozark cannot manufacture this particular combination of rockers with its existing lumber supply.

When the chain furniture store faxes an order for 175 modern rocking chairs and 125 classic rocking chairs to Ozark, a quick glance at the graph demonstrates that Ozark cannot fulfill the order. The point (175,125) does not fall on the line or inside the shaded area created by the equation, but, instead, falls to the right of the line, indicating that the limits set by the amount of available board would be exceeded by the order. To verify this, one can test the equation for the total number of board feet used and see if the total number of board feet used would exceed the 3,000 board feet limit. Taking away the limitation, that equation becomes: 15C + 12M= total number of board feet. Substituting in numbers yields the equation: 15(125) + 12(175) = 3,975 board feet. Obviously, 3,975 board feet is not less than or equal to 3,000 board feet. The company would need 3,975 feet to fulfill that order. They presently have 3,000 feet. To find out how many additional…… [read more]

Exercise Choosing the Selection Method Essay

Essay  |  2 pages (561 words)
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Application of assessment










Work Experience





Math skills





Verification knowledge





Interpersonal skills





Work motivation





a. The applicant who scored the best are Maria and Jenna

b. The fact that one candidate would score poorly in one area, indeed at times a reject and score very well in another area presented a challenge of whether to discard or still consider for next level of interview.

c. Yes, I would change the threshold used in assessing the areas, especially work experience, maths and verification knowledge.









Work Experience



Math skills




Verification knowledge




Interpersonal skills




Work motivation





a. Maria scored the highest

b. Yes she is the best since she scores well in the very important fields like work experience and interpersonal skills which are important for a bank teller.

c. Lori and Steve scored the lowest.

Analysis of the answers

1. The most important here is the work experience since as a teller, the turnover of clients and accuracy is of essence and an experienced person here can do better than a new person.

2. Recorded

3. The least important a scores in Math and work motivation

4. Done









Work Experience



Math skills





Verification knowledge




Interpersonal skills




Work motivation



15…… [read more]

Hypnosis in Investigation Essay

Essay  |  2 pages (859 words)
Bibliography Sources: 2


The hypnotist should present situations as true as possible and maintain the accuracy of information derived from the subject.

The other problem with hypnosis is that the subject often tend to exhibit increases in suggestibility to leading questions and misleading post-event information. For instance, there is likelihood of the subject incorporating into their accounts details suggested to them by the hypnotist. Unfortunately, even with much skill and attention, the hypnotist cannot avoid making suggestions to the subject. Such suggestions are not necessary verbal, but can be communicated through attitude, character, and expectations of the hypnotist. Other forms of communication may include tonal variation in voice, and body language (Lynn and Sherman, 2000). However, the hypnotists should try as much as possible to avoid giving deliberate suggestions to subject, this way the subject will give independent account of events thereby improving the accuracy of information. This is very important because the hypnotist has power over the hypnotized individual and can easily manipulate the subject, the intentions must always be right.

One other problem associated with hypnosis is that the confidence of the subject usually increases regardless of accuracy (Anderton, 1986). For instance, the subject could be very confident that the information he/she is giving is accurate even when it is incorrect. This confidence will lead to continuous giving of false information without realization. This confidence if usually created by the fact that the subject is controlled by the hypnotist and whenever the hypnotist agrees with the information given then the subject will feel the information is correct even when it is not. This confidence can however be used positively by ensuring that the subject is led into giving correct information.

Taking into consideration the problems associated with hypnosis, it should not be used at all since such information cannot be reliable. The law should therefore require the exclusion of testimony obtained from previously hypnotized witnesses, this is because the witness, as a matter of fact, has been rendered incompetent to testify. Hypnosis should be restricted to clinical use where there is a desired change in a patient which is more positive.


American Psychological Association, Division of Psychological Hypnosis. (1994). Definition and description of hypnosis. Contemporary Hypnosis, 11, 143.

Anderton, C.H. (1986). The forensic use of hypnosis. In F.A. De Piano & H.C. Salzberg (Eds.),

Clinical applications of hypnosis (pp. 197-223). Norwood, NJ: Ablex.

Lynn, S.J. & Sherman, S.J. (2000). The clinical importance of sociocognitive models of hypnosis: Response set theory and Milton Erickson's strategic interventions. American Journal of…… [read more]

Predictors of the Transition Data Analysis Chapter

Data Analysis Chapter  |  3 pages (971 words)
Bibliography Sources: 3


That allowed three categories to be analyzed, but I determined that there were also three other reasons why multinomial logistic regression was used. These other reasons were incorporating such a complex sampling design, examining multicollinearity between all the covariates, and managing any missing data with multiple imputation. By taking all those steps, better conclusions could be drawn by the authors.

Level of Significance

The concept of "level of significance" is important because it provides a likelihood that the sample chosen for the study will not be an accurate representation of the current population (Denzin & Lincoln, 2011). If a level of significance is very low for a study, that would indicate that the authors are highly confident that the results can be replicated (Gorard, 2013). For example, if the level of significance is 0.05, there is a 95% chance that the study can be replicated, and if the level of significance is 0.01, there is a 99% chance that the study can be replicated (Franklin, 2012). Testing this level begins with the null hypothesis, as that is where many quantitative studies begin (Franklin, 2012). The 0.01 and 0.05 significance levels are the two most commonly seen levels in the majority of educational research (Denzin & Lincoln, 2011).

Significance Level for the Current Study

I believe the level of significance reported in this study falls within the 0.01 range. I think that because it provides a large sample of people and a clear, direct way to conduct the study, which allows the study to be easily replicated by others. The authors of the study indicated that another group of data from the same age group would produce essentially the same results, because of the way the study was conducted and the analysis of the information itself (Park, Weaver, & Romer, 2009). Because the study is clear and follows quantitative methods, and because it creates a strong null hypothesis to test, I believe it is easily able to be replicated by many other researchers in the future.

I feel that the examination of longitudinal data is an important strength of the study, as are the maximization of the information available and how easy it is to generalize the results to adolescents throughout the United States. However, I also think that other factors that were not included in the model could affect smoking behavior. With that in mind, it is important to remember that the significance level for the study is a measure of what the authors of that study believe to be accurate, and that it can vary.


Denzin, N.K., & Lincoln, Y.S. (2011). The SAGE Handbook of qualitative research ( 4th ed.). CA: Sage Publications.

Franklin, M.I. (2012). Understanding research: Coping with the quantitative-qualitative divide. London/New York: Routledge

Gorard, S. (2013)…… [read more]

Simultaneously Term Paper

Term Paper  |  4 pages (1,229 words)
Bibliography Sources: 1+


This theory is committed to research and discovery through direct contact with the social world (Shah & Corley, 2006). It rejects priori theorizing. The fact that it rejects priori theorizing does not therefore mean that researches should enter the field lacking an understanding of the literature or the theoretical question to be addressed. Researchers have to generate theories out of their data collection experiences. Theory building involves identifying theoretical question of interest, choosing an appropriate research context, sampling within the context so that data collection facilitates the emerging theory (Shah & Corley, 2006). Choice of procedures for gathering and documenting data is the preserve of the researcher. Questions asked should explore new areas, uncover processes, lay bare poorly understood phenomena, understand ill structured linkages, and examine variables that cannot be studied by experimentation (Shah & Corley, 2006).

Theoretical sampling should endeavor to direct data gathering efforts towards collecting information that best supports the development of a theoretical framework. Samples chosen should support emergent theory or even refine and extend the emergent theory (Shah & Corley, 2006). Refining and extending emergent theory calls for settling on a data collection context that shows that the theory applies across a variety of contexts. For researchers to assign and create meaning from observations recorded in data constant comparison method has to be put in place. This helps in comparing incidents applicable to each category, integrating categories and their properties, focusing the theory, and writing the theory (Shah & Corley, 2006). These processes are integral in explaining patterns in the data. Constant comparisons made throughout the process of data collection influences data collection efforts and theory development.

Goel, Johnson, Junglas, & Ives (2011) propose and test a model to predict users' intention to return to virtual world to remedy organizations failure to lure customers and employees into their education, entertainment, and commerce initiatives. Goel et al. (2011) rely on the interactionist theory of place attachment to explain the links among the organizations construct model. Their hypothesis is grounded on the fact that the more meaningful the interactions that occur, the more meaningful a place will become. This is the basis of their focus on users' intention to return to the virtual world. Their method was tested through quasi-experiment conducted within Second Life. Experiments were done in the physical lab. Activities related to testing their research model were done in a simulated or virtual lab in Second Life. Social awareness was measured using instruments focused on perceived message understanding. Items were selected based on their definition of the social awareness concept. Measures of intention to return to Virtual World consisted of items that related to what users were able to do in the Virtual World and their intention to return to it for such purposes by choice. Evidence from the research shows that the data used in this research were drawn from experimental work that was conducted in the physical laboratory. It is worth noting that Goel et al. relied on the interactionist theory of place… [read more]

National and State Subject Matter Essay

Essay  |  2 pages (720 words)
Style: MLA  |  Bibliography Sources: 2


One such California-specific standard is: "verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve real-world and mathematical problems" (Common Core Standards, California Department of Education: 74).

Regarding Algebra I, the standards for the subject in California are defined as pertaining to three critical areas: "deepen and extend understanding of linear and exponential relationships; contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions; extend the laws of exponents to square and cube roots; and apply linear models to data that exhibit a linear trend" (Common Core Standards, California Department of Education:60). In contrast, the federal Common Core standards begin with a more theoretical discussion of algebraic equations, what they contain, and algebraic distinction between equations and inequalities.

The standards of both California and the federal Common Core contain a great deal of overlap, similar to their congruence with geometry standards. For example, both require that students: "explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method" (Common Core Standards, Official Website CCSS.Math.Content.HSA-REI.A.1; California Department of Education 65). As with the geometry section, California includes several state-specific guidelines regarding the capabilities of students such as the ability to "solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context," which more specifically guides the type of approaches teachers must present in the classroom, usually with a greater emphasis on contextual applications of abstract theories (Common Core Standards, California Department of Education 65).

Works Cited

Common Core Standards. California Department of Education. ca.gov. [21 Oct 2013] http://www.cde.ca.gov/be/st/ss/documents/ccssmathstandardaug2013.pdf

Common Core Standards. Official Website. [21 Oct 2013]

http://www.corestandards.org/Math/Content/HSG/introduction… [read more]

Design of an Automotive Control System to Follow a Drive Cycle A2 Coursework

A2 Coursework  |  14 pages (3,980 words)
Style: Harvard  |  Bibliography Sources: 5


¶ … Automotive Control System to Follow a Drive Cycle.

Automotive control is a driving force within the automotive innovation. To lower fuel consumption, improved safety and lower exhaustive consumption as well as enhancing convenience and comfort function, there is a need to apply automotive control. Automotive control system is fundamental principles used for successful design of automobile automatic control… [read more]

Normal Distribution Term Paper

Term Paper  |  2 pages (804 words)
Bibliography Sources: 0


We assume that Approach B (?1) will be more efficient than Approach A (?2). Thus, Ha: 1 - ?2 > 0. Approach B. is more efficient than Approach A. And Ho: 1 - ?2 < or = 0. There is no difference between Approach A and Approach B.

Research Question - t test for dependent samples

We use a matched sample design (dependent samples) for this question. We select a simple random sample of workers. Each worker first uses one Approach A and then the other Approach B. The order of the two approaches is randomly assigned to the workers, such that some workers perform Approach A first and some workers perform Approach B. first. In this manner, each worker provides a pair of data values, one for each approach. We will use a procedure based on the t distribution with n1 + n2 -- 3 degree of freedom. We assume that both populations have normal probability distribution and that the variances of the populations are equal. In the matched sample design, the variation between the workers is eliminated as a source of sampling error. Is there a mean difference between the work completion rates of the two approaches is the means of the difference between the values for the population of workers. Thus, the null hypothesis is that there is no difference between the means of the difference for the values of the two groups. However, we reject the null hypothesis since the completion times do differ between the two approaches.

Standard score -- "Also known as a z-score. A standard score gives us the position of a data value comparison to the mean. We also knew, by looking at the z score, whether this was a great score or not. Remember that a z score tells you, in standard deviation units, how far away the score is from the mean. Positive scores are above the mean while negative scores are below the mean. A z-score of 2.12 on a national exam is great. We have scored 2.12 standard deviations ABOVE the mean!! How rare is that? If we looked at our graph of a normal distribution below, we can see that going out just two standard deviations from the mean on each side covers at least 95% of the distribution. Our score puts us past that, into the less than 5% area in the tails of the distribution…… [read more]

Long-Term Memory Demonstration Analysis Term Paper

Term Paper  |  2 pages (675 words)
Bibliography Sources: 1


For me, I remembered the words relatively easily; yet, I began to have issues discerning whether or not the math problem was correct or not. My STM simply could not handle both stimuli, and so relied on the one I was more familiar with, which was the verbal visualization and practice.

The third demonstration tested the STM and our own ability to organize and categorize the stimuli we are being exposed to. The ability to rehearse categories can help take information out of the STM and into the long-term memory (LTM) because of shared common traits that help us compartmentalize and place information into various categories we are already familiar with in our LTM. Yet, our short-term store (STS) is often not capable enough of practicing the type of organization involved with LTM practices, and so when exposed to demonstrations such as Organization: Categories, it can be difficult to recall the information, even though we would have been able to conceive those categories from our LTM. Thus, it seems from this demonstration that organization tends to occur more in the LTM compared to the STM.

Finally, there was the Verbal Rehearsal demonstration. This was a test where the test taker had to say out loud a series of words. Some repeated several times, while other were seen only once. This tested the STS, but also what elements could possibly leak into the long-term store (LTS). It seemed that the words that were repeated the most were the easiest to recall. Thus, the more practice one have with these words, the more able they were to be recalled to the memory when-based to write the list. However, the words that were not repeated, or never repeated were almost lost in this exercise. This essentially does show that repetition and practice helps make the STM stronger for certain concepts.


MacKay, David J. (2011). The Cognitive Neuroscience of Memory. Inference Group. Web. Retrieved October 22, 2012 from http://www.inference.phy.cam.ac.uk/jmb86/memory.pdf… [read more]

Cartesian Graph Essay

Essay  |  3 pages (846 words)
Bibliography Sources: 3


If x is the number of plates of food eaten, and y is the price, the table of coordinates might be as follows:

Plates (x)

Price (y)











The equation for that would be represented by y=5 and the graph of the equation would be the same as in the sample graph for y=5 provided above.

Interestingly, in real life, what one would say about the line would probably only be true for a fixed set of x values. For example, it is impossible to eat a negative number of plates of food. Likewise, even all-you can eat buffets generally limit their diners to one meal-period, so that there is a finite number of plates the diner could consume. However, those conditions would actually change the form of the equation, transform it from a simple linear equation, and would not be represented by the conditions described.

What are the differences among expressions, equations, and functions? Provide examples of each.

An expression is "a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add, subtract, multiply and divide") (Highline Advanced Math Program, 2008, Algebraic expression).

Examples of expressions are:

y -- x


An equation is "a math sentence that says that 2 things are equal. An equation always has an equal (=) sign. The thing or things that are on the left side of the equal sign are equal to the things on the right side of the equal sign" (Highline Advanced Math Program, 2008, Equation).

Examples of equations are:

x + 2 = y y -- x = 5

5y = 25

A function "relates each element of a set with exactly one element of another set (possibly the same set)" (Math is Fun, 2012). Functions are generally expressed as f (x).

Examples of functions are:

f (x) = x + 2

f (y)= 5y


Harmsworth, A.P. (2012). Plotting x-y graphs. Retrieved October 16, 2012 from GCSE.com website: http://www.gcse.com/maths/graphs3.htm

Highline Advanced Math Program. (2008). Algebraic expression. Retrieved October 16, 2012

from: http://home.avvanta.com/~math/def2.cgi?t=expression

Highline Advanced Math Program. (2008). Equation. Retrieved October 16, 2012

from: http://home.avvanta.com/~math/def2.cgi?t=equation

Math is Fun. (2012). What is a function? Retrieved October 16, 2012 from http://www.mathsisfun.com/sets/function.html

Rehill, G.S. (2012). Horizontal and vertical lines. Retrieved October 16, 2012…… [read more]

Slow the Illusion of Validity Term Paper

Term Paper  |  2 pages (867 words)
Bibliography Sources: 3


Nurses and firefighters are an example of experts whose intuition can be trustworthy -- political pundits and stockbrokers only display confidence, and thus the illusion of skill.

Chapter 23: The Outside View

There are two different approaches to forecasting, the "inside view" and the "outside view." Individual members of a committee may think the committee's task can be accomplished in 1 or 2 years, but an external study of such committees can note that it usually takes 8 to 10 years, even though the individual members are still predicting 1 or 2 years. In many cases, we can have an accurate view of "baseline" predictions for something (i.e., the most likely result statistically), but fail to apply that information to making our own prediction because we are "inside" the situation. The "planning fallacy" describes when someone making plans estimates or predicts too optimistically. This can be avoided with "reference class forecasting" where the prediction is measured in advance against a comparable baseline. This optimism bias of the "inside view" explains why people do things when the odds are against them -- ranging from starting wars, to filing a lawsuit, to starting a small business. But taking the outside view goes against our instincts.

Chapter 24: The Engine of Capitalism

This chapter continues the examination of the "optimism bias" discussed in the previous chapter. Optimism is frequently the reason why people or institutions take on significant risks. A small business in the U.S.A. has a 35% chance of lasting 5 years, yet entrepreneurs will repeatedly attempt to start small businesses because of the optimism bias. So in some sense optimism is the engine of capitalism, since it permits entrepreneurs to start businesses despite the fact that 2 out of 3 businesses will fail within 5 years. The optimism bias gives people the illusion of control -- especially regarding outside factors (such as competition or general economic conditions). Competitor neglect is the bias where people making decisions do not evaluate the possible actions of the competition, because they are focused on their own action and their own coherent narrative. The WYSIATI principle discussed earlier causes people to be overconfident: they do not have an accurate measure of uncertainty. As a way of overcoming the optimism bias, Kahneman suggests a policy called the "premortem" -- before an organization takes a major decision, ask all individuals to imagine that, 1 year from now, the decision was taken and was a horrible failure. Then ask them to imagine the reasons they'd give for explaining the failure in 1 year. This allows individuals to use…… [read more]

Z Score Fill in the Answers Term Paper

Term Paper  |  6 pages (1,646 words)
Bibliography Sources: 10


Z Score

Fill in the answers for each table and answer the concluding FOUR questions below. Please round up your z scores to the hundredths spot, two decimals to the right and p values to the thousandths spot three decimals to the right as needed. If the p value is less than .001, please report p < .001. Please note… [read more]

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