Mathematics Essays (Examples)

Filter results by:


View Full Essay

Mathematic v Conceptual Modeling Limitations

Words: 342 Length: 1 Pages Document Type: Essay Paper #: 11907322

" This reflects the gap that exists between the complexities of the real world and the abilities of abstract models. Models are by definition simplified ways of understanding complex phenomenon; they are necessarily incomplete in their estimations and valuations of real world figures and occurrences. This is why "all models are wrong." "Some models are useful," however, because they are able to approximate to a high degree the outcomes of real world events despite the incomplete nature of the information processed by the model. To make a model useful, bias must be removed. This is not an issue with the certainty of mathematical models, but conceptual models are necessarily subjective, built on the modeler's understanding of an issue. educing bias is key to the model's performance.


Aspinall, D. (2007). "Designing interaction." University of Edinburgh. Accessed 30 July 2009.

Kay, J. (2006). "Amaranth and the limits of mathematical modeling."…… [Read More]


Aspinall, D. (2007). "Designing interaction." University of Edinburgh. Accessed 30 July 2009. 

Kay, J. (2006). "Amaranth and the limits of mathematical modeling." Financial times, 10 October. Accessed 30 July 2009.
View Full Essay

strategies to improve mathematic performance for children

Words: 1361 Length: 4 Pages Document Type: Essay Paper #: 56539671

Improve Mathematic Performance for Children With Learning Difficulties and Their Effectiveness

Students with learning disabilities face several problems. More often than not, these students advanced approximately one academic year for every two academic years they attended school. Strategies employed by teachers can have a major impact on enhancing this particular performance in all levels of schooling. The lack of comprehensive strategies and interventions students with mathematics disabilities end up considerably lagging behind compared to their peers. Statistics indicated that approximately 25% to 35% of students experience difficulty with math knowledge and application skills. Moreover, 5 to 8% of all students in school have such considerable deficits that influence their capability to solve computation problems (Sayeski and Paulsen, 2010). In accordance to Hott et al. (2014), strategy training has been beneficial to students with learning disability when learning math conceptions and practices. As presented in the article one of the strategies…… [Read More]


de Boer, H., Donker-Bergstra, A. S., & Konstons, D. D. N. M. (2012). Effective strategies for self-regulated learning: A meta-analysis. Gronings Instituut voor Onderzoek van Onderwijs, Rijksuniversiteit Groningen, Groningen.

Hott, B. L., Isbell, L., & Oettinger, T. (2014). Strategies and Interventions to Support Students with Mathematics Disabilities. Council for Learning Disabilities.

Maag, J. W., Reid, R., & DiGangi, S. A. (1993). DIFFERENTIAL EFFECTS OF SELF-MONITORING ATTENTION, ACCURACY, AND PRODUCTIVITY. Journal of Applied Behavior Analysis, 26(3), 329-344.

Mercer, C. D., Mercer, A. R., & Pullen, P. C. (2011). Teaching students with learning problems (8th ed.). Upper Saddle River, NJ: Pearson Education.
View Full Essay

Three Mathematic Textbooks Review

Words: 1840 Length: 6 Pages Document Type: Essay Paper #: 99003285

Precalculus With Limits by on Larson

This book as well as the other two books are for college freshman level or college introductory level mathematics courses. The strengths of the book are mainly focused on its layout. For example, the book has a great way to demonstrate a varied and large amount of information easily and simply. This means that people reading the text just have to look for certain visual cues like colors or pictures that will point the information they seek. For example, the diagrams have a different background color than the text. All of this removes time spent looking for things. The use of bold also further differentiates the text, highlighting key words, phrases and things to memorize.

The weaknesses are in lack of context surrounding the topics and footnotes. Another book reviewed has footnotes and yet another provides adequate background for each topic. This book sacrifices…… [Read More]


Larson, R., Hostetler, R., & Edwards, B. (2011). Calculus I, with precalculus (3rd ed.). Boston: Houghton Mifflin.

Larson, R., Hostetler, R., Edwards, B., & Heyd, D. (2013). Precalculus with limits (3rd ed.). Boston: Houghton Mifflin.

Mirsky, L. (2012). Introduction to Linear Algebra. Dover Publications.
View Full Essay

George Cantor

Words: 673 Length: 2 Pages Document Type: Essay Paper #: 15623545


George Cantor

The purpose of the paper is to develop a concept of the connection between mathematics and society from a historical perspective. Specifically, it will discuss the subject, what George Cantor accomplished for mathematics and what that did for society. George Cantor's set theory changed the way mathematicians of the time looked at their science, and he revolutionized the way the world looks at numbers.

George Cantor was a brilliant mathematician and philosopher who developed the modern mathematical idea of infinity, along with the idea of an infinite set of real numbers, called transfinite sets, or the "set theory." In addition, Cantor found that real numbers were not countable, while algebraic numbers were countable (Breen). Cantor's views were quite controversial when he first developed them in the late 1800s, and some mathematicians today question some of his hypothesis ("Transfinite Number"), however, his work is recognized as some of…… [Read More]


Author not Available. "Georg Cantor." 2004. 13 April 2004. 

Breen, Craig. "Georg Cantor Page." Personal Web Page. 2004. 13 April 2004.

Everdell, William R. The First Moderns: Profiles in the Origins of Twentieth-Century Thought. Chicago: University of Chicago Press, 1997.

O'Connor, J.J. And Robertson, E.F. "Georg Cantor." University of St. Andrews. 1998. 13 April 2004.
View Full Essay

Workshop Teacher

Words: 620 Length: 2 Pages Document Type: Essay Paper #: 26655832

Mathematics Summer Institute Statement of Goals

Attending the 2002 Summer Institute for Elementary School Teachers represents and exciting opportunity for me to further explore my interest in teaching mathematics, as well as an opportunity for me to apply and share my knowledge and experience with like-minded educators.

I am a strongly committed to and enthusiastic about mathematics education at the elementary school level. I believe that ensuring that children are engaged and interested in mathematics in early elementary school is essential to building strong numeracy in our youth. When young children develop an interest in math and strong skills as youngsters, they are more likely to continue studying mathematics as they grow older. In addition to these academic benefits, understanding and being able to apply math principles and concepts helps children grow into effective critical thinkers with a broader skill set.

I hope to achieve several personal learning goals by…… [Read More]

View Full Essay

Techniques Correlation

Words: 484 Length: 2 Pages Document Type: Essay Paper #: 26083929


Analysis Techniques: Correlation

A positive correlation between annual income and amount spent on car would be expected. This means that there is a relationship between the two and that, in general, higher annual income would show an increase in the amount spent on car, while lower annual income would show a decrease in the amount spent on car.

However, it would not be expected that this would be a strong relationship because other factors would influence the amount spent on car. For example, some individuals with an income in the middle range may consider an expensive car a key priority, while others would have other priorities. In addition, annual income level is not a true measure of wealth because it does not take into account a person's expenses. For example, a young single person without a family and without a mortgage would have more disposable income than a married…… [Read More]

View Full Essay

Capturing Astronomical Geometry the Greek Way

Words: 580 Length: 2 Pages Document Type: Essay Paper #: 90109615

Mathematics -- to the Moon & Back

Once upon a time, Alexander, a young man from Athens fell in love with a local girl, Adrianna, whose beauty was far greater than any other young woman he had ever seen. Alexander was so smitten with Adrianna that he promised her the moon. Being an astute girl, Adrianna told Alexander that she wasn't at all sure that he could deliver the moon, but he could begin to convince her that he was intelligent and clever by measuring the distance from the earth to the moon. Alexander had long heard the stories about his Greek ancestors who were experts in mathematics and astronomy, so he sought out some wise elders to learn more.

Alexander spent some time with two elders, one of whom told him he knew how to measure the size of the earth (which, Alexander mused, was bound to impress, Adrianna),…… [Read More]

View Full Essay

Globalization and the Structures of

Words: 1054 Length: 3 Pages Document Type: Essay Paper #: 28982792

Use the appropriate representations to model problems in the physical and social sciences (Ibid.)

Numeration Systems and Number Theory -- Number theory is a basis for all areas of mathematics. Number theory and sense are precludes to computation, to estimate, and to have an understanding of the ways numbers are represented and interrelated. Fluency of also understanding the way positive and negative numbers can be visually represented on a line, or how numerical values interrelate, are essential prior to moving toward higher level concepts (Kane, 2002).

Algebraic Thinking and Problem Solving -- ather than viewing the subject of algebra as certain sets of problems, the appropriate way to introduce it into elementary levels is as the relationship among quantities, the use of symbols, the modeling of phenomena, and the study of change. Students should be able to understand patterns, relations, and functions and how numbers may be represented in different…… [Read More]


Askey, R. (1999). "Knowing and Teaching Elementary Mathematics." American

Educator. Fall 1999, Cited in:

Blanton, M. (2008). Algebra and the Elementary Classroom. Heinemann.
View Full Essay

Personal Statement University Waterloo I'm Applying

Words: 929 Length: 3 Pages Document Type: Essay Paper #: 73007798

personal statement University Waterloo . I'm applying Mathematics (Co-op Regular ) . Please write essay stating reasons choosing program waterloo 1. Education Goals 2. Interest chosen programs

My life experiences have come to define who I am today and the choices that I am currently making reflect my background. From a very young age I realized that I enjoy studying and applying formal sciences and this practically influenced me to achieve better results in these fields, as I enjoy doing what I like and this felt natural. Whenever someone questioned me about my degree or about how I saw my future I always responded by saying a joke involving mathematics hoping that the respective individual would immediately understand that this particular domain is very important for me.

Many people in the contemporary society tend to ignore the importance of mathematics because of its "cooler" counterparts. With technology experiencing significant advancement…… [Read More]

View Full Essay

Aristotle and His Contribution to

Words: 685 Length: 2 Pages Document Type: Essay Paper #: 13309586

Aristotle used mathematics in many of his other studies, as well. Another writer notes, "Aristotle used mathematics to try to 'see' the invisible patterns of sound that we recognize as music. Aristotle also used mathematics to try to describe the invisible structure of a dramatic performance" (Devlin 75-76). Aristotle used mathematics as a tool to enhance his other studies, and saw the value of creating and understanding theories of mathematics in everyday life and philosophy.

During his life, Aristotle also worked with theories developed by Eudoxus and others, and helped develop the theories of physics and some geometric theories, as well. Two authors quote Aristotle on mathematics. He writes, "These are in a way the converse of geometry. While geometry investigates physical lines but not qua physical, optics investigates mathematical lines, but qua physical, not qua mathematical" (O'Conner and obinson). He also commented on infinity, and did not believe that…… [Read More]


Devlin, Keith E. The Math Gene: How Mathematical Thinking Evolved and Why Numbers Are like Gossip. 1st ed. New York: Basic Books, 2000.

Lane, David. "Plato and Aristotle." The University of Virginia's College at Wise. 2007. 18 June 2007.

O'Connor, John J. And Edmund F. Robertson. "Aristotle on Physics and Mathematics." Saint Andrews University. 2006. 18 June 2007. 

Robinson, Timothy a. Aristotle in Outline. Indianapolis: Hackett, 1995.
View Full Essay

Division by Zero

Words: 1382 Length: 4 Pages Document Type: Essay Paper #: 7447267

Division by Zero

Mathematics is unique in that it is an objective subject. hen answering a question, something is either empirically true or it is completely false; there is little if any subjectivity about it in most situations. One of the most interesting aspects about math is that there are certain laws which are irrefutable and must be accepted in order for the correct answer to be discovered. A particularly intriguing and potentially frustrating aspect of math has to do with the division of zero. According to the laws of math, division by zero is impossible. hen someone solves a problem and finds themselves with a fraction where zero is in the denominator, the answer is always undefined because in mathematics, there is no such number. Mathematically, it is not possible to divide a numerator by zero and have either a real or imaginary number for an answer.

There are…… [Read More]

Works Cited:

Czajko, J. (2004). On Cantorian spacetime over number systems with division by zero. Chaos,

Solitons and Fractals. (21:2). 261-71.

Fosnot & Dolk (2001). Young Mathematics at Work: Constructing Multiplication and Division.

Heinemann: Portsmouth, NH.
View Full Essay

Greek Letter Pi Equations and

Words: 749 Length: 2 Pages Document Type: Essay Paper #: 56141920

Thus, in 1 Kings 7:23, the word "line" is written Kuf Vov Heh, but the Heh does not need to be there, and is not pronounced. With the extra letter, the word has a value of 111, but without it, the value is 106. (Kuf=100, Vov=6, Heh=5). The ratio of pi to 3 is very close to the ratio of 111 to 106. In other words, pi/3 = 111/106 approximately; solving for pi, is pi = 3.1415094... (Tsaban, 78). This figure is much more accurate than any other value that had been calculated up to that point, and would hold the record for the greatest number of correct digits for several hundred years afterwards. Unfortunately, very few people know this fact.

Archimedes of Greece was the first person to make serious use of the pi calculation. In 287 to 212 BC, he focused on the polygons' perimeters as opposed to…… [Read More]


Archimedes. "Measurement of a Circle" in Pi: A Source Book. Heidelberg: Springer

Verlag, 1997.

Baumgart, J.K.J.K.)." The history of algebra: An overview." In Historical topics for the mathematics classroom. 31st National Council of Teachers of Mathematics Yearbook. Washington, DC: NCTM, 1969

Blatner, David. The Joy of Pi. Walker Publishing Company, Inc. New York, 1997.
View Full Essay

Low Math Scores of American Elementary Students

Words: 2870 Length: 8 Pages Document Type: Essay Paper #: 59310843

Low math scores of American elementary students has been a major issue in education for some time. The Third International Mathematics and Science Study (TIMMS) conducted in 1995 showed the extent of the problem. The TIMMS study compared students in 42 countries, allowing American students to be compared with international students. The study rated the math ability of American students as adequate in fourth grade and poor in twelfth grade compared to other countries. This study was not the first time that concerns had been raised about American students achieving poorly in science and math. It was however, the largest and most comprehensive look at the real extent of the problem. The study made people realize the significance of the issue and resulted in the awareness of the public, the government and education and mathematics researchers. The major question that needs answering is why the low math scores occur, and…… [Read More]

Works Cited

Ma, L. Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, 1999.

Mokros, J., Russell, S.J., and Economopoulos, K. Beyond Arithmetic: Changing Mathematics in the Elementary Classroom. Palo Alto, CA: Dale Seymour Publications, 1995.
View Full Essay

NCTM Process Standards Problem-Solving in

Words: 649 Length: 2 Pages Document Type: Essay Paper #: 27216512

This engaged the whole class, regardless of their previous comfort level with mathematics. Graphing was also helpful for students to visualize what things really 'meant' in terms of the numbers they were studying.


Solving word problems as a class in a hands-on fashion forced all students to communicate with one another about mathematics. This increased student comfort levels and generated a collective interest in the mathematical solving process.

Students were given stories that illustrated mathematical concepts to read and asked to tell their own 'stories' to show they could understand mathematical concepts in a qualitative fashion. They were often asked to interpret graphs using verbal descriptions.

One of the most popular activities was the use of online research. Students were asked to research concepts on the web, such as examples of fractions, proportional rectangles, or the use of certain calculation techniques, and report back on their independent research the…… [Read More]

View Full Essay

Standards Five Process Standards Describe

Words: 1149 Length: 3 Pages Document Type: Essay Paper #: 45737537

If the captain knows the position of the lighthouses from a map, can the captain determine the position of the ship?"

Analysis of the five processes in the context of problem solving

Problem solving

Using problem solving to solve a mathematical problem, the student does not know which method they will use when they start tackling the problem to reach the solution. The student will arrive at the correct solution by employing a couple of other ideas instead of just using mathematical calculations.

easoning and proof

Thinking on their feet students will learn how to be analytical of every situation they are encountered with. They will not only apply this analytical thinking in mathematics but will also apply it to other situations that they encounter. For the problem given in the, the first thing a student will need to analyses is how many legs chickens have and how many legs…… [Read More]


Mathematics, N.C. o. T. o. (2000). Principles and standards for school mathematics. 1906 Association Drive, Reston, VA 20191-1502: National Council of Teachers of Mathematics.
View Full Essay

Organizational Health Educational Institutions Generally Approach Organizational

Words: 2709 Length: 8 Pages Document Type: Essay Paper #: 11719523

Organizational Health

Educational institutions generally approach organizational improvement by addressing the performance standards to which students, educators, and administrators are held. The standards movement has been a dominant theme in educational policy arenas and in the public eye. With roots in the 1950s Cold War mentality, the thrust of educational improvement has been prodded by perceptions of international industrial and scientific competition. If the rigor of educational standards in the nation -- according to the logic of this argument -- falls below that of other countries, our economy will falter and the balance of trade will be compromised, perhaps beyond the point of recovery.

Fears for the future of the country and our citizens run deep; these fears propel a course of action that is not particularly based on rational thinking and lacks a base of evidence. The course of action adopted by educational policy makers and educational leaders in…… [Read More]


Barth, P. (1997, November 26). Want to keep American jobs and avert class division? Try high school trig. Education Week, 30,33.

Bosch, G. (2000). The Dual System of Vocational Training in Germany. In Tremblay, D.-G. And Doray, P. (2000). Vers de nouveaux modes de formation professionnelle? Le role des acteurs et des collaborations. Quebec: Presses de l'Universite du Quebec.

____. (1998). Business Coalition for Education Reform. The Formula for Success: A Business Leader's Guide to Supporting Math and Science Achievement. Washington, DC: U.S. Department of Education.

Hacker, A. (2012, July 20). Is algebra necessary? The New York Times [national ed.], SR1, SR6.
View Full Essay

Mathematician Maria Gaetana Agnesi

Words: 587 Length: 2 Pages Document Type: Essay Paper #: 34412770

Mathematician - Maria Gaetana Agnesi


Maria Gaetana Agnesi

Since the olden days, mathematics has been an area of study that has contributed much to diverse discoveries, inventions, and innovations of science and technology. Without mathematics, we will not experience the remarkable events of science, as well as the convenience that high technology brings to us. The academic mastery of mathematics is dominated by men, even up to these days. There are very few mathematician women who made a name in the field of mathematics. More especially in the past, social prejudices became a hindrance for women to master mathematics. At present, only three women captured success in the field of mathematics. They are Sonia Kovalevsky of Russia, Emmy Noether of Germany and U.S., and Maria Gaetana Agnesi of Italy (from Maria Agnesi and Her "Witch"). The following discussions in this paper is about Maria Gaetana Agnesi and her mathematics.…… [Read More]


Crowley, Paul. Maria Gaetana Agnesi.

New Advent. 08 Dec 2003. 

Unlu, Elif. Maria Gaetana Agnesi.

1995. Agnes Scott College. 08 Dec 2003.
View Full Essay

George Polya the Hungarian Mathematician

Words: 1317 Length: 4 Pages Document Type: Essay Paper #: 96083587

He however refused. Because of this, Polya could only return to his home country many years after the end of the war. Having taken wiss citizenship, Polya then married a wiss girl, tella Vera Weber, the daughter of a physics professor. He returned to Hungary only in 1967.

George Polya's professional life was as interesting as his personal pursuits. Before accepting an offer for an appointment in Frankfurt, Polya took time to travel to Paris in 1914, where he once again came into contact with a wide range of mathematicians.

Hurwitz influenced him greatly, and also held the chair of mathematics at the Eidgenssische Technische Hochschule Zurich. This mathematician arranged an appointment as Privatdozent for Polya at this institution, which the latter then accepted in favor of the Frankfurt appointment.

In addition to his teaching duties, Polya further pursued his passion for mathematics via his research efforts. He collaborated with…… [Read More]


Motter, a. "George Polya, 1887-1985. 

O'Connor, J.J. And Robertson, E.F. "George Polya." 2002. 

Polya Math Center. "George Polya, a Short Biography." University of Idaho, 2005.
View Full Essay

Guess and Check Is a Strategy That

Words: 615 Length: 2 Pages Document Type: Essay Paper #: 94667810

Guess and check is a strategy that can be used with middle school math students to help them develop skills in mathematical thinking and problem-solving. As Guerrero (2010) points out, the guess and check lets students focus on the quantitative relationships between numbers rather than their mathematical value. Many students find word problems difficult because they have trouble seeing these relationships. Using the guess and check method, students choose a reasonable number to "plug in" to an equation to see if it makes mathematical sense and satisfies the conditions posed by the problem.

With increased emphasis on algebra in the K-8 curriculum, teachers are encouraged to foster discussions about mathematical relationships as part of their lessons and to help their students focus on "sense making rather than merely applying rote computational strategies" (Guerrero). When students are able to develop this deeper understanding of mathematics, Guerrero asserts, teachers can "potentially influence…… [Read More]


Guerrero, S.M. (2010). The value of guess and check. Mathematics Teaching in the Middle

School 15(7), pp. 392-398.
View Full Essay

Geometry Proof Geometry as a

Words: 1680 Length: 5 Pages Document Type: Essay Paper #: 9888180

The student then places it on the playing field. The system allows a chosen playing card to be dragged by means of a mouse to the playing field and, if properly placed, to "stick" in place on the playing field. (Improperly placed cards "snap" back to their original file position.) After each card has been correctly placed, a line between properly placed cards is generated connecting proper statements and reasons to each other and the GIVEN or CONCLUSION displays the completed proof (Herbst, 2002).

In working with geometric proofs, it is important for the student and teacher alike to approach this new and intimidating subject with an open mind. Even though students may have never experienced any type of logic or reasoning prior to the introduction of proofs, if presented correctly, this new way of approaching math can be both fun and enlightening. Teachers should keep this in mind when…… [Read More]


Discovering Geometry: A Guide for Parents. 2008, Key Curriculum Press. Retrieved October 19, 2009 at

Herbst, Patricio G. Establishing a Custom of Proving in American School Geometry: Evolution of the Two-Column Proof in the Early Twentieth Century, Educational Studies in Mathematics, Vol. 49, No. 3 (2002), pp. 283-312,
View Full Essay

Nova Episode the Proof

Words: 1088 Length: 3 Pages Document Type: Essay Paper #: 50106405

Proof, a NOVA episode aired on PS [...] review the video, with a focus on what the video tells us about how people learn to do mathematics. Compare and contrast this with your own experiences with mathematics, particularly your approach toward learning about new mathematical problems and trying to solve them. "The Proof" is more than just a video about solving a complex mathematical problem. It is a story of determination, setting goals, and finding out that solutions come from many different places and ideas. You have to be open to new ideas when you try to solve anything, whether it is a complex mathematical problem, or a personal problem. The proof is really about keeping an open mind, and looking at all the angles of a problem.

The Proof

The Proof" is an interesting look at one man's obsession with proving (or disproving) a theory (Fermat's Last Theorem), written…… [Read More]


The Proof." Dir. Simon Singh. Perf. By Andrew Wiles, Stacey Keach. NOVA. 28 Oct. 1997.
View Full Essay

Chaos Theory Has Filtered Down

Words: 1570 Length: 6 Pages Document Type: Essay Paper #: 68288574

Gleick's explanation is more conversational and has a popular appeal, as noted, while Stewart's explanation, while not impenetrable by any means, is more mathematical in nature, more technical, and more extensive in many ways. He is not telling the story of chaos as much as he is showing how it was derived and how it is applied in different scientific fields of investigation. He even follows poets in considering the nature of such chaotic systems as water flowing in a brook, something that has long fascinated poets and physicists alike and something that is not easy to analyze or predict. Different tools have been developed for measuring different physical properties, such as oscillators and various sound equipment. Stewart looks at these for what they show about both order and chaos at the same time. Stewart also raises the Hyperion issue and how it illuminates chaos theory and is in turn…… [Read More]

Works Cited

Gleick, James. Chaos: Making a New Science. New York: Penguin, 1988.

Stewart, Ian. Does God Play Dice?: The Mathematics of Chaos. New York: Basil Blackwell, 1987.
View Full Essay

Geometry Manipulative Elementary Geometry Manipulative

Words: 586 Length: 2 Pages Document Type: Essay Paper #: 16427374

This will not only introduce elementary students to geometry, but also begin the complicated thinking associated with algebraic concepts. Using the formula to plug in the known degrees and then find the x is the beginning of much more abstract algebraic thinking.


Circles rule our lives and have rules of their own! Each circle measures to 350 degrees, and with this knowledge we can begin to find unknown angles!

If a circle measures 360, that means that a half circle measures half -- 180 degrees. In a half circle, there are many different angle combinations. But, we know that they all equal out to 180 degrees.

Knowing this, we can find the great unknown!

Well, we know that the total of the two angles equals 180 degrees. Therefore, angle 1 = angle 2 = 180 degrees.

Let's just plug the numbers into the equation.

63 + x = 180.…… [Read More]


National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.



View Full Essay

Person Hired a Firm to

Words: 403 Length: 1 Pages Document Type: Essay Paper #: 66385489

The formula is found in Mathematics in Our World on page 273.

Sn = the sum of n terms of the sequence (currently unknown)

a1 = the first term of the sequence an = the nth term of the sequence a1= 100

an= 300

Sn= n (a1+an)

Sn= 9(100 + 300)

Sn = 9(400)

Sn = 4.5(400) = 1800

It will cost $1,800 to build a 90-foot tower.

Question 37: A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account?

Each year, 5% is added to the balance (B) in the savings account. This problem represents a Geometric sequence because each year is multiplied by the same number. In this case it is 1.05. It is 1 plus an additional 5% each year.

B + B (.05)

B…… [Read More]


Bluman, a.G. (2005). Mathematics in our world (Ashford University Custom Edition). United States: McGraw-Hill.
View Full Essay

Students at the End of

Words: 944 Length: 3 Pages Document Type: Essay Paper #: 14093439

They must also solve polynomial, exponential and logarithmic equations both analytically and graphically.

tandard 4: tudents must be able to understand and use matrices to perform basic operations. This includes addition, subtraction, multiplication and inversion of matrices. They must also be able to identify the appropriate methods and technology to accomplish this. In addition, students must demonstrate the ability to find the inverses of two-by-two matrices without only with the use of pencil and paper, without additional technology.

tandards for Grade Level 11

tandard 1: At the end of this grade level, students must be able to explore rational functions in terms of investigating and explaining the characteristics of rational functions. Elements such as domain, range, zeros, points of discontinuation, and intervals of increase and decrease must be included in this ability. They must also find the inverses of rational functions with discussions of domain and range, symmetry, and function…… [Read More]


Cox, K. (2006). Georgia Performance Standards: Mathematics 2. Georgia Dept of Education. Retrieved from

Cox, K. (2006). Georgia Performance Standards: Mathematics 3. Georgia Dept of Education. Retrieved from

Cox, K. (2006). Georgia Performance Standards: Mathematics 4. Georgia Dept of Education. Retrieved from

Dillon, S. (2010, Mar 10). Panel Proposes Single Standard for All Schools. The New York Times. Retrieved from
View Full Essay

Carl Friedrich Gauss This Is

Words: 598 Length: 2 Pages Document Type: Essay Paper #: 84120603

He made three main contributions to the theory of numbers: congruence theory, studies on the separation of the circle into equal parts, and theory of quadratic forms.

Algebra and Analysis

Up to Gauss's time, no one had been able to prove that every algebraic equation has at least one root. Gauss offered three proofs. And he modified the definition of a prime number.

Astronomical Calculations

We discussed briefly his assistance to astronomers in relocating Ceres. His success in this effort spurred him to develop the mathematical methods he used further. In 1809 his Theoria motus corporum coelestium used the method of least squares to determine the orbits of celestial bodies from observational data. In arguing his method, Gauss invented the Gaussian law of error, or, as we know it today, the normal distribution.

Non-Euclidean Geometry

Mathematicians, for centuries, had been attempting to prove Euclid's postulate concerning parallels (the sum of…… [Read More]


Bell, E. (1986). Men of mathematics. New York: Simon Schuster.

Dunnington, G., Gray, J., & Dohse, F. (2004). Carl Frederich Gauss: titan of science.

Washington D.C.: MAA.

Encyclopedia of World Biography. (2005). Karl Friedrich Gauss biography. Retrieved September 29, 2009, from (Encyclopedia of World Biography):