Mathematics in Digital Photography
The advances in both digital photography and computing have allowed more detailed and complex images to be shown on more realistic media than was ever previously possible. Through the use of more specialized equipment and digital imaging techniques the resulting photos of even the most novice user today can rival those of professionals from years before. This level of photographic precision could never have been achieved were it not for the tremendous advantages made in computing that allow both the hardware and software involved in digital photography to function at extremely high levels. Both hardware and software made today are capable of performing the necessary calculations in a fraction of a second, making focusing and editing pictures easier than ever before. The incorporation of mathematics directly into the digital photography process has been the primary impetus for the explosion of high-quality digital images available almost anywhere we…...

mla

References

Higham, N. (2007). The mathematics of digital photography. Retrieved from:

 http://www.maths.manchester.ac.uk/~higham/talks/digphot.pdf .

Hoggar, S.G. (2006). Mathematics of digital images. Cambridge, UK: Cambridge

Image Compression: How Math Led to the JPEG2000 Standard. (2011). Society for Industrial

alacheff (1987) described four levels of justification, which are those as follows: (1) Native empiricism;

2) Crucial experiment;

3) Generic example; and 4) Thought experiment. (Taflin, nd)

Naive empiricism is stated to be "an assertion based on a small number of cases." (Taflin, nd) Crucial experiment is stated to be "an assertion based on a particular case, but the case was used as an example of a class of objects." (Taflin, nd) the generic example is stated to be "...an assertion based on a particular case, but the case was used as an example of a class of objects." (Taflin, nd) Thought experiment is "an assertion detached from particular examples and begins to move toward conceptual proofs." (Taflin, nd)

The work entitled: "Adding it Up: Helping Children Learn Mathematics" states that proficiency in instruction of mathematics is "related to effectiveness: consistently helping students learn worthwhile mathematical content. It also entails versability: being able to…...

mla

Bibliography

Jones, Tammy (2000) Instructional Approaches to Teaching Problem Solving in Mathematics: Integrating Theories of Learning and Technology. Online available at http://www.mindymac.com/educ6100projects/TjonesProblem6100.htm

Adding it Up: Helping Children Learn Mathematics (Free Executive Summary)

 http://www.nap.edu/catalog/9822.html 

Barr, Leslie (2003) it's Elementary: Introducing Algebraic Thinking Before High School. SEDL Newsletter - Mathematics & Science. Volume XV Number 1, December 2003.

Islamic art not only demonstrates the symbolic significance of geometric forms and their psychological, social, religious, and aesthetic functions. In addition to these purposes, Islamic art also demonstrates symmetry. Symmetry's appeal is well-known: babies tend to favor faces with symmetrical features over those with lop-sided noses or askew eyes. Although absolute symmetry is by no means a prerequisite for beauty, symmetry is usually perceived with pleasure. The Spirograph forms, explicated by Karin Deck, are sublimely symmetrical.

Spirograph hypotrochoids and epitrocoids illustrate the value of symmetry in aesthetics and they also demonstrate the prevalence of mathematics in visual art. While Spirograph patterns may not normally be considered fine art, they are nevertheless pleasing to the eye as well as the mind. Their symmetry no doubt contributes to their aesthetic appeal but Spirograph trochoids, like Islamic friezes, draw order out of chaos and reveal the prevalence of patterns throughout the universe. Moreover, Spirograph…...

mla

References

Abas, S.J. And AS Salman: Symmetries of Islamic Geometrical Patterns. Symmetry in Ethnomathematics 12(1-2). Retrieved July 29, 2006 at  http://www.ethnomath.org/resources/abas2001.pdf 

Deck, K. Spirograph Math. Humanistic Mathematics Journal March 1999, Vol.19, p13-17. Retrieved July 29, 2006 at  http://web.stcloudstate.edu/szkeith/index11.html 

Patterns, Order, and Chaos."

Mathematics Concepts in Profession
Mathematics Concepts in the Teaching Profession

Mathematical concepts in professions

My Profession and Applicable Math Concepts

Mathematics is a branch of knowledge dealing with scientific notions of logical qualitative and quantitative arrangements. It extensively covers different aspects as well as having several subdivisions. It is a tool specially designed to handle and implement relative concepts, regardless of the kind of situational problem presented. Alongside the concepts, mathematics uses invented formulas to help in solving the computations systematically. These concepts keep up a correspondence to the quantitative association to the computations they carry out.

Many career opportunities in life apply knowledge of mathematics and the subsequent concepts of the subject. All fields are dependable of conceptual facts and formulas taught in the math course. From critical analysis of career opportunities globally, and through applicable knowledge, I have settled my professional interests in becoming a mathematics instructor. Through this choice, I believe I…...

mla

References

Ben-Zvi, D and Garfield, J. (2008). Introducing the Emerging Disciplines of Statistics Education. School Science & Mathematics. Vol 108, Issue 8. Pg 355-361.

Liu, C., Chang, J and Yang, A. (2011). Information Computing and Applications: Second International Conference, ICICA 2011, Qinhuangdao, China, October 28-31, 2011. Proceedings, Part 1. New York: Springer.

Mathematics
a) Spreadsheet Data Analysis

b) State hypotheses:

Ho: Type of soft drink and resident are independent. (null hypothesis)

Ha: Type of soft drink and resident are not independent. (alternate hypothesis)

c) Conduct chi-square test of independence at 0.05 significance level: = 0.05

d) Calculate degrees of freedom: Number of rows = 2, Number of columns = 2

Degrees of freedom (df) = (Number of rows - 1) x (Number of columns - 1) = (2-1)(2-1) = 1

e) Calculate the expected frequencies from actual data:

f) Calculate the chi-square statistic using both actual and expected frequency tables:

In excel, the cursor was placed in cell M17 and the formula of chi test typed as:

=CHITEST (actual frequency range, expected frequency range)

=CHITEST (L4:M5, L13:M14), as shown in the formula bar above

The result gives, the calculated chi-square probability, p = 1.2203 x 10-10

g) Look up the Chi-Square value, ?2 from chi-square distribution tables for df = 1 and ? = 0.05

2…...

SIAM's mission is to build cooperation between mathematics and the worlds of science and technology through its publications, research, and community. Over the last 50 years SIAM's goals have remained constant:
• They want to advance the application of mathematics and computational science to engineering, industry, science, and society.

• To was to promote research that will lead to effective new mathematical and computational methods and techniques for science, engineering, industry, and society.

• They want to provide media for the exchange of information and ideas among mathematicians, engineers, and scientists.

The applied mathematics and computational sciences have become essential tools in the development of advancements in science and technology. Ground-breaking mathematical and computational techniques have become prevalent in areas such as the biological sciences, information technology, climatology, combustion and emission control, and finance and investment. It is through its publications, conferences, and community, that Society of Industrial Applied Mathematics continues to foster…...

mla

References

"About the AMS." (2009). Retrieved April 22, 2009, from American Mathematical Society Web

site:  http://www.ams.org/ams/about.html 

"About Siam." (2009). Retrieved April 22, 2009, from Society for Industrial and Applied

Mathematics Web site: http://www.siam.org/about/pdf/brochure09.pdf

Mathematics Teaching
Learners Studying Basic Mathematics To Enable Helping Their Children With Their Education

The work of Jackson and Ginsburg (2008) reports on a series of algebra classes involving a group of African-American mother and elementary-aged children, who are low income and who "had limited and negative formal experiences with algebra." (p. 10) The women in the study who arrived to the algebra classes are reported to have had "well-informed view of what algebra was -- a disconnected body of knowledge that they did not understand -- and corresponding views of who could 'do' algebra." (Jackson and Ginsburg, 2008, p. 11) The study resulted in the women's views of who could 'do' algebra being changed "through genuine, intellectual inquiry into the mathematics of algebra." (Jackson and Ginsburg, 2008, p. 11) It is reported that questioning "is recognized as a critical instructional tool in the teaching of mathematics for understanding." (Jackson and Ginsburg,…...

mla

REFERENCES

Allexsaht-Snider, M. And Marshall, M. (2008) Linking Community, Families and School: Opportunities for the Mathematics Education of Children from Excluded Communities. ALM International Journal Volume 3(2a), pp 8-9. Retrieved from:  http://www.academia.edu/6750909/Adults_Learning_Mathematics_An_International_Journal 

Askew M., Brown M., Rhodes V., Johnson D. And William D. (1997) Effective Teachers of Numeracy, Final Report London Kings College

Askew M., Brown., V., Johnson D. And William D. (1997) Effective teachers of numeracy, Final Report London Kings College.

Bandura, A. (nd) Social Learning Theory. University of Pennsylvania. Retrieved from: faculty.mwsu.edu/psychology/paul.guthrie/powerpoint/bandura2.ppt

Mathematics and Art
Mathematics

The application that I researched and found of mathematics and art is Data Visualization, which is closely related to Infographics. On a very simple level, data visualizations are artistic, aesthetic representations of data. The ways in which the data visualization can be "drawn" or created involves different kinds of mathematics, including vectors, fractals, algorithms, and statistics. Data visualization is a fairly new field, indigenous to the 21st century. There have been other ways to represent data graphically, but not with the detail, precision, and beauty offered by data visualization.

Presentation and aesthetics are very important in the consideration of data visualization. I found this application of mathematics and art particularly compelling because its existence seems to fly in the face of the long held stereotype that there are strict boundaries between science and art. Data visualization seems to be the artistic version or expression of science (and mathematics) and…...

mla

References:

Meersschaert, K. (2012). Does Math + Art = Teachable Data Visualization? Columbia University, Web, Available from:   2013 June 14.http://edlab.tc.columbia.edu/index.php?q=node/8057 .

Mathematics Textbooks
Technology used in Mathematics Textbooks

Mathematics probably frustrates more students than any other subject in their course load. It seems that a logical, left brain is something that must be inborn and many students are not gifted with that natural ability. This means that there need to be some simple methods by which every student can be made to understand mathematical concepts. While many different teaching methods have been attempted with varying levels of success, none have been completely successful. However, with the advent of technology, this task is made simpler for the math teacher. Technology allows the student to work the problem successfully while helping the individual understand the application of the problems. Technology can be used via a text itself, or a teacher can utilize a text which offers parallel instruction via a companion web site. The following report will discuss how technology is used by the text…...

mla

References

Math Archives (2010). Mathematics contests and competitions. Retrieved December 18, 2010 from  http://archives.math.utk.edu/contests/ 

Rock, N.M. (2006). Seventh grade math is easy! So easy. Los Angeles: Team Rock Publishing.

Teachers and students alike must have the ability and the opportunity to move freely about, especially in high traffic areas, so congestion does not build to a level that causes distraction or frustration, whether from students or from teachers.
When teachers group desks in functional ways, according to activity, for example desks for high-activity or high traffic desks grouped separately from desks for test-taking, students are more likely to demonstrate superior behavior because their teachers (Brophy, 1983) can easily meet their instructional requirements (Marsh, 2004). The classroom arranged in a manner that reduces congestion produces an environment with more discipline, safety and respect, which is important especially among students at the 8th grade level and above, when students are more likely to demonstrate behaviors akin to their personality and interests. A mathematics classroom organized around function creates an environment that stimulates students to participate in learning, and concentrate on subject…...

mla

References

Brophy, J.E. (1983, Mar). Classroom organization and management. The Elementary

School Journal, 83(4): 264-285.

Marsh, C.J. (2004). Key concepts for understanding curriculum. New York: Routledge

Umich. (n.d.) ED 422: Teaching Science in the Secondary School. Retrieved July 11, 2007:

27% payoff. "He would begin with the $100 and get back $93.27 (theoretically) the first time he ran his money through the machine. If he continued to play until his $100 bankroll was gone, he would have put his money through the machine 71 times for a total of 1,967 plays on the machine" (7). The gambler's total wager (handle) would then be $1,475; however, the win (gambling revenue) for the casino would be $100, the amount of the player's original bankroll (Barker & Britz 2000). According to the International Gaming and agering Business (IGB, 1998, 5), a player could statistically generate a handle of $10,000 at a table game with a casino advantage of 1% before losing a bankroll of $100 (in Barker & Britz 7). This casino advantage is known as the "vigorish," which is discussed further below.
Vigorish. John inn is credited with inventing the book, the quarter…...

mla

Works Cited

Barker, Thomas and Marjie Britz. Jokers Wild: Legalized Gambling in the Twenty-First Century. Westport, CT: Praeger, 2000.

Casinos. (2004). Encyclopedia Britannica.com [premium service].

Coyle, Cynthia a. And Chamont Wang. (1993). Wanna Bet?: On Gambling Strategies That May or May Not Work in a Casino. The American Statistician, 47(2):108.

The Vigorish. (2002). Craps Gambling Casinos. Available: http://www.craps-gambling-casinos.com/the-Vigorish.htm.

Students will present their findings to the class.
2. In groups, students will graph population growth and predict future trends using exponential functions (Ormond 2010). A data set is available at: http://serc.carleton.edu/files/quantskills/events/NAGT02/quantskillsworldpop.pdf. Students will discuss the political and environmental implications of their findings.

3. Students will perform an exercise using exponential functions graphing increases in atmospheric CO2 concentrations (Ormond 2010). A data set is available at: http://serc.carleton.edu/files/quantskills/events/NAGT02/co2moe2edit.pdf

Students will discuss the political and environmental implications of their findings.

Standard 3:

4. Students will be divided into groups, given problems of quadratic inequalities and 'race' to see what group can come up with the correct solutions the fastest.

5. Students will be asked to periodically write and graph homework problems on the board to 'teach' graphing to the rest of the class.

6. Students will be given examples of graphs or tables of values of functions and asked to identify what type of function they are, based…...

mla

Resources

Exponential function. (2010). Purple Math Forums. Retrieved July 26, 2010 at  http://www.purplemath.com/modules/expofcns2.htm 

Mathematics benchmarks. (2010). UT Dana Center. Retrieved July 26, 2010 at  http://www.utdanacenter.org/k12mathbenchmarks/secondary/algebra.php 

McClain, Liz & Steve Rieves (2010). Teaching techniques to tackle some sticky topics in Algebra 2. Retrieved July 26, 2010 at nctm.mrrives.com/NCTM%20Piecewise%20PP.ppt

Ormond, Kathy (et al. 2010). Atmospheric CO2 concentration. Retrieved July 28, 2010.

The foundations of high stakes testing indicate that their intention is to formulate change that is traceable and transparent. Accountability is essential to outcomes but instruction must be aligned to the needs of students and educators and most importantly must be inclusive of the perceptions and perceived needs of real life classroom teachers. Tracing the effectiveness of high stakes reforms and reforms that would be considered the fall out of such is essential to the development of alignment between curriculum and test results. (Bolt 2003) These changes cannot under any circumstances be judged solely on the perceptions of administers, as has been shown by this work administrators give a great deal more positive assessment of reform, prior to the acceptance of such reform as positive by real world classroom teachers. This is especially true with regard to those students who are clearly already at a disadvantage in the system, a…...

mla

Parent involvement in instruction and classroom success must also be reiterated continually, during and after change implementation. Parents, just like teachers and students must be sold on the ideal of reform-based standards so they can ultimately assist students in achieving greater exam outcomes as well as real classroom outcomes. Continued assessment of parent involvement and improvement of such is essential to reform success.

Last but certainly not least student perception of assessment reform and instructional reform is also essential to success of assessment reform applications. Students must understand the stakes of assessments both for themselves and for their schools and districts and must give the assessments the proper credence in correlation with real instructional growth in the classroom. A whole perceptual study regarding students, at every level of proficiency, would constitute a completely different and informative assessment of how students perceive reform changes and how effective they believe them to have been for themselves or fellow students post high stakes testing reform.

Draft August 24, 2008

In an open-ended study of 42 teachers decided to leave with the peer assistance being a contributing factor while in another research carried out with 99 teachers, only 4 said that the peer assistance was one of the decisive factors (Billingsley et al., 1993 & 1995). Some of the factors for the variation in these studies could be the way the teachers were asked these questions (like, open-ended polls vs. questionnaires), purpose to leave or the leaving conduct was calculated, as well as the huge trial dimension distinction of the two studies.

Therefore, in light of the mentioned study conclusions, the educational institutions should treat peer assistance as a determining factor to augment preservation of the teachers as well as the school system.

Support through Induction and Mentoring

Special attention needs to be given to the upcoming teachers in this particular field, to give them confidence and a sense of contribution to the…...

mla

References

Billingsley, B.S. (1993). Teacher retention and attrition in special and general education: A critical review of the literature. The Journal of Special Education, 27, 137-174.

Billingsley, B., Carlson, E., & Klein, S. (in press). The working conditions and induction support of early career special educators. Exceptional Children.

Billingsley, B.S., & Cross, L.H. (1992). Predictors of commitment, job satisfaction, and intent to stay in teaching: A comparison of general and special educators. The Journal of Special Education, 25, 453-471.

Billingsley, B., Pyecha, J., Smith-Davis, J., Murray, K., & Hendricks, M.B. (1995). Improving the retention of special education teachers: Final report (Prepared for Office of Special Education Programs, Office of Special Education and Rehabilitative Services, U.S. Department of Education, under Cooperative Agreement H023Q10001). (ERIC Document Reproduction Service No. ED379860)

The nature of the instrument, with true and false answers and patterns that are readily identifiable, has prompted the development of books to supply interpretations of the results. The interpretations are given in the form of descriptive statements that tend to be true of clients whose scores yield certain profiles. When used by a skilled and experienced psychologist, the MMPI is a powerful instrument. The psychologist administering and interpreting the MMPI must pay attention to all relevant factors, including age, sex, education, social class, religious background, place of residence, and other historical data (Karp and Karp, 2009). The criterion groups for this test were selected from patients at the University of Minnesota hospitals (Minnesota Multiphasic Personality Inventory, n.d.).

The MMPI has ten clinical scales and three validity scales in addition to many supplementary scales. It has been found to be difficult to consistently bias the MMPI because of the complexity and…...

mla

References

Karp, Cheryl L. And Karp, Leonard. (2009). MMPI: Questions to Ask. Retrieved June 29, 2009,

from Web site:  http://www.falseallegations.com/mmpi-bw.htm 

Minnesota Multiphasic Personality Inventory. (n.d.). Retrieved June 29, 2009, from Web site:

http://www.cps.nova.edu/~cpphelp/MMPI.html

Growth matters because models of growth show how something increases in a particular setting.  Anything with the capability of increasing can exhibit growth.  Linear growth is growth that is constant.  It grows the same amount for each unit of time.  Exponential growth refers to growth that increases exponentially over a set period of time. 

Exponential growth rapidly overtakes linear growth in terms of how quickly something increases.  It can result in huge increases in the original number of items over a very short period of time.  For example, people in animal rescue advocate spaying or neutering pets because....

Literacy is important in all subjects because it plays a crucial role in fostering effective communication and comprehension. It enables students to understand and interpret information, allowing them to engage with various subjects effectively. Here's the answer with proper spacing and format:

1. Improved Communication: Literacy skills provide students with the ability to read, write, speak, and listen effectively. These skills enhance communication, enabling students to articulate their thoughts, ideas, and opinions clearly in any subject.

2. Comprehension and Critical Thinking: Literacy equips students with the ability to understand and interpret various texts, whether they are related to mathematics, science, humanities, or....

1. Explain the concept of the Forms in Plato's philosophy and discuss its significance in his understanding of reality.

2. Compare and contrast Plato's views on education with contemporary educational practices.

3. Analyze Plato's theory of justice as articulated in his Republic and consider its implications for contemporary society.

4. Discuss the role of women in Plato's ideal society as outlined in The Republic and evaluate his views on gender equality.

5. Explore the concept of "philosopher-kings" in Plato's political philosophy and assess their suitability as rulers.

6. Examine Plato's belief in the immortality of the soul and consider its implications for his ethical and....

Unit Lesson Essay Topic Ideas

History

The Causes and Consequences of the American Civil War: Analyze the complex factors that led to the outbreak of the American Civil War and explore its far-reaching social, political, and economic consequences.
The Impact of the Industrial Revolution on European Society: Examine the technological, economic, and social changes brought about by the Industrial Revolution, considering its effects on workers, urbanization, and the balance of power.
The Rise and Fall of the Roman Empire: Investigate the reasons for the rise and eventual decline of the Roman Empire, analyzing its political, social, military, and economic strengths and....