Research Papers on Mathematics

Click on any of the term papers to read a brief synopsis of the research paper. The essay synopsis includes the number of pages and sources cited in the paper.

  • Airline Case Study; Correlation between Age and Maintenance Costs

    This 4 page statistical analysis paper is based on a case study supplied by the student. The paper provides figures for two airlines for the cost of their aircraft maintenance and the average age of their fleets over a number of years. The paper considers why a comparison of the airline cost profiles could be important if the airlines merge and assesses the correlation between age and maintenance costs and looks for similarities of differences between the age and cost pattern of each airline. The bibliography cites 3 sources.

  • Home Runs at Coors Field - A Statistical Review

    This is a 3 page paper that provides an overview of statistical review. The case study of home runs flying further at Coors Field is used to demonstrate the process of analysis. Bibliography lists 1 source.

  • Number 0 and its History

    A 5 page review of the history of the manner in which the number zero came into common mathematical usage. Traces its development to Mesopotamia and through the various other regions of the world. Distinguishes between the mathematical concept and the philosophy of nothingness. Bibliography lists 3 sources.

  • Number e's History and Use

    This 5 page paper introduces the topic with a modern day look at compound interest, then delves into the history of the number e. Both early and modern uses are discussed. Bibliography lists 5 sources.

  • Pythagorean Theorem and its History

    5 pages. An interesting research paper on the background of the Pythagorean Theorem that is used in algebra and geometry. Details the history of the theorem. This is actually a fascinating history and one that is not often discussed in the classroom. The Pythagorean Theorem was founded by a cult that actually worshipped numbers and felt that everything in the Universe was number-related. A very interesting history for a well-known math theory to say the least! Bibliography lists 2 sources.

  • Real Analysis Conceptual History

    This 5 page paper delves into the concept of real analysis and looks at key people integral to the emergence of this mathematical field of study. Several mathematicians are named including Archimedes and Cauchy. Bibliography lists 4 sources.

  • Calculus' History

    This 6 page shows how calculus was derived from the studies in real analysis and lead to the development of calculus. The paper begins with the discoveries of Ancient Greece with thinkers such as Zeno of Elea and Archimedes and looks at many mathematicians such as Valerio, Cavalieri and Fermat finishing with Newton and Leibniz. The bibliography cites 3 sources.

  • Mathematics' History and Critical Milestones

    This 5 page paper discusses three of the more critical milestones in mathematical history. Emphasis is placed on Pythagoras as it pertains to all of the disciplines. Quotes cited from texts. Bibliography lists 4 sources.

  • Calculus History

    Calculus provides methods to deal with varying quantities. O'Connor & Robertson (1996) state that it has been evolving since Zeno in 450 B.C.E, who was supposed to be the first to posit an equation based on the infinite. However, the first infinite equation is believed to have been introduced by Archimedes in 250 B.C.E., bringing with it leaps in logic from theorists like Barrow, Newton and Leibniz. Bibliography lists 4 sources. jvHisClc.rtf

  • Conjecture of Pierre de Fermat Refuted by Mathematician Leonhard Euler

    This is a 3 page paper discussing Euler’s refutation of Fermat’s conjecture. In 1637, French lawyer Pierre de Fermat wrote that he had “discovered a truly marvelous proof which this margin is too narrow to contain” in regards to a mathematical statement which had been unproven for over 1000 years. The basis of Fermat’s (“Last”) theorem or conjecture began with that of the Pythagoras equation [x.sup.2] + [y.sup.2] = [z.sup.2] which he proved “had an infinite set of whole number solutions” which related to the lengths of the sides of a right-angled triangle. Pythagoras did not know “how many solutions existed if the exponent in his equation were a number greater than 2”. Fermat claimed that “for any exponent greater than 2, there were no solutions at all”. During his lifetime however, Fermat often did not supply “proofs” of many of his theorems but many mathematicians since his time have been able to prove his claims to be correct except for that in relation to the Pythagoras equation. Swiss mathematician Leonard Euler (1707-1783) did however work further on many of Fermat’s theorems and “later proved that there are no solutions when the exponent is 3” and “unfortunately, an infinite number of cases remained and the case-by-case method was doomed to fail”. While Fermat’s Last Theorem proved to be difficult to prove, Euler managed to disprove and refute other assertions such as “2^(2^n) = p, where p is a prime number” and found that it is only true for the first four cases provided by Fermat. Bibliography lists 4 sources.

  • Mathematics; Anxiety And Commutative, Associative, And Distributive Laws

    This 3 page paper discusses with two issues. The first part of the paper considers how to help mature students that have a mathematics anxiety may be helped before undertaking a learning course containing maths when they have not tackled the subject for many years. The second part of the paper looks at three laws that are used in algebra; commutative, associative, and distributive and considers which is the most important.

  • Mathematical Contributions of Albert Einstein

    In 5 pages the author discusses Albert Einstein's contributions to the field of science and mathematics while explaining such theories as E=mc2. Bibliography lists 8 sources.

  • Accounting Practice and the Use of Mathematics

    This 3 page paper looks at the use of mathematics in accounting practice. Double entry bookkeeping is used as an example. Bibliography lists 3 sources.

  • Math Anxiety, Understanding the Fear of Mathematics

    9 pages in length. A comprehensive look at the problem of 'math anxiety' and numerous studies that have attempted to help improve our understanding of its treatment. Among other things, the writer discusses how to quantitatively assess Math Anxiety and concludes with recommendations for helping young children who suffer from it. Bibliography lists 20+ sources.

  • Stuik’s “A Concise History of Mathematics”

    This 4 page paper is a review of the book ‘A Concise History of Mathematics’ by Dirk J. Struik. The paper reviews the content and the style of the book which was first published in 1948 and traced the development of mathematical theory form prehistory to the first half of the twentieth century. The bibliography cites 2 source.

  • OVERVIEW OF MATHEMATICS HISTORY

    This 10-page paper provides a brief history of mathematics, as well as some famous mathematicians. Also discusses mathematics applications today. Bibliography lists 5 sources.

  • Math Through the Ages, A Gentle History

    A 4 page book review. William Berlinghoff and Fernando Gouvea offer a fascinating and insightful view of the history of mathematics in their text Math Through the Ages: A Gentle History For Teachers and Others. The authors' intention in this work is to give their readers "a general feel for the lay of the land perhaps to help you become familiar with the significant landmarks" (Berlinghoff and Gouvea 5). In short, this is an overview of math history, a "brief survey" of what is in a gigantic topic (Berlinghoff and Gouvea 5). However, the appeal of this book goes deeper than this, as the authors often offer insight into the topic that helps to explain historical details, helping the reader see how math concepts developed and evolved. No additional sources cited.

  • The History of Mathematics

    This 6 page paper examines three books on the history of math. Some quotes are included. Bibliography lists 3 sources.

  • Child Mathematics' Instruction and Zero

    This 4 page paper examines the use of zero historically and how it presents problems when teaching arithmetic and algebra. Examples of why zero is problematic is presented as well as how it is viewed by experts in the field. Bibliography lists 6 sources.

  • Annotated Bibliography: Origins of Greek Mathematics

    This 3 page paper is an annotated bibliography of 8 sources dealing with the origins of Greek mathematics.

  • Cohen's Equal Exchange Model and Teaching Math

    This 5 page paper considers the role of small group teaching in mathematics according to Cohen’s “Equal Exchange Model”. The witer considers different mathematical topics to differentiate between the topics that should be taught individually, those that can increase value to the student when small groups are used and those where a combination approach may be best. The bibliography cites 4 sources.

  • “The Story of Mathematics”

    A 3 page review of the book by Richard Mankiewicz. This paper outlines the author’s journey through this fascinating discipline from ancient times to the present. No additional sources are listed.

  • 2 Trade Textbooks on Investment and Mathematics Reviewed

    A 3 page overview of Nicholas Dunbar's "Inventing Money: The Story of Long-Term Capital Management and the Legends Behind It" and Roger Lowenstein's "When Genius Failed: The Rise and Fall of Long-Term Capital Management". Each of these books detail specific mathematical applications in the finance trade. The author of this paper explores their coverage of the Black-Scholes Formula and its role in the collapse of the massive hedge fund Long-Term Capital Management. Bibliography lists 3 sources.

  • UK Mathematics and GCSE Level Expansion

    This 9 page paper looks at the difference way in which the A’ level mathematics in the UK education system may be seen as a development and expansion of the GCSE level subject. The writer looks at the syllabus and consider how the transition between the two levels is made, and how it may best be understood by the student. The bibliography cites 8 Sources.

  • Mathematics in Sports

    An 11 page explanation of how mathematics are indeed an important tool in sports. Not only does an understanding of mathematics empower players by enabling them to use their body in the most effective manner to achieve optimum performance, mathematics are also useful in a diversity of other areas that are relevant to sports. Bibliography lists 10 sources.

  • Axiomatic and Intuitive Mathematics

    A paper which considers the difference between intuitive and axiomatic mathematics, and some of the reasons why the former is most commonly found in school curriculums, whereas the latter forms part of university level studies. Bibliography lists 11 sources.

  • A Business Mathematical Principles' Analysis

    This 10-page paper focuses on various business mathematical principles including linear programming, network flow models, queuing analysis, simulation and inventory management. The paper also provides examples of how companies have used these tools to better manage inventory and predict customer demand. Bibliography lists 4 sources.

  • “A History of Mathematics: From Mesopotamia to Modernity”

    A 3 page overview of the book by Richard Hodgkin. This paper emphasizes Hodgkin’s message that mathematics have been a critical element in much of world development. No additional sources are listed.

  • Mathematical Errors in 7th Grade

    This 3 page paper provides an overview of common mistakes made in seventh grade mathematics problems. This paper relates the reasons for these mistakes and their impacts for learning. Bibliography lists 1 source.

  • Mathematics' Systems of Mayan and Roman Civilizations

    A five page paper which looks at some of the differences between the Roman and Mayan mathematical systems, and the relative advantages and disadvantages of both. Bibliography lists 3 sources.

  • Math and Why There Are Some People Who Hate It

    A 3 page paper which examines why people have a tendency to hate math. No sources cited.

  • Math Assessment, Authentic Assessment Programs, and Inconsistencies

    This is a 10 page paper discussing the interpretative and inconsistent nature of math assessment and possible authentic assessment programs. Several issues relate to the inconsistent and interpretative nature of math assessment within the educational curricula today. Firstly, on a national basis, studies reveal the range in attitudes in regards to importance math assessment has in the overall educational curriculum. While math assessment is often mentioned, its importance does not seem as highly weighted as other aspects of assessment of school performance. Secondly, within the school systems themselves, teachers in mathematics vary a great deal in their teaching practices which can affect assessment; perception of their students’ abilities based on social factors and past performance; perception of the importance of national and consistent assessment; and desired learning outcomes. There are many educational assessment tools which are available. However, assessment tools vary in regards to their expense, time, and curriculum considerations which can affect whether or not the tool can be usefully applied. One of the goals of the U.S. educational system is be “the first in the world in mathematics and science achievement” and some educational programs are trying to fulfill this goal by not only developing consistent national education and assessment programs but programs which are comparative on an international scale, such as that found within the International Baccalaureate Program (IB). Bibliography lists 10 sources.

  • Ten of History’s Greatest Mathematicians

    This 7 page paper outlines the accomplishments of Isaac Newton, Leonard Euler, Euclid, Archimedes, Carl Friedrich Gauss, Joseph-Louis Lagrange, Pierre de Fermat, Rene Descartes, Leonard 'Bigollo' Pisano (Fibonacci), and Gottfried Wilhelm von Leibniz. Bibliography lists 10 sources.

  • The Mathematical Contributions of Albert Einstein

    A 5 page paper that reports Einstein's first three papers that led to a new perception of the universe, from evidence for the existence of molecules and atoms to his general theory of relativity that led to a new understanding of the universe, including space, time, motion and gravity. Bibliography lists 4 sources.

  • College Math 'Survival'

    A 3 page informal assessment of the many things that are different about the college environment and the high school environment that might account for decreased performance in mathematics. Noting the different teaching styles, living arrangements, and the many frustrations of life on campus; the author of this paper emphasizes that the only one that can take responsibility for student success is the student themselves. No sources are listed.

  • Budgeting with Math Tools

    This is a 3 page paper that provides an overview of using math for budgeting. Line graphs and budget lines are explored. Bibliography lists 2 sources.

  • Reviewing 2 Mathematics Textbooks

    This 4-page paper provides a review of two mathematics text books: Basic Concepts of Mathematics" by Zakon and "Introduction to Number Theory and Algebra" by Shoup. Bibliography lists 2 sources.

  • Importance of Mathematics and Statistics in Business

    This 5-page paper offers an explanation of the importance of business math and statistics. Other issues covered include calculation of insurance premiums and property taxes, as well as depreciation. Bibliography lists 5 sources.

  • War and Mathematics

    This 8-page paper examines how mathematic applications have been used to help analyze and calcluate wars. Bibliography lists 3 sources.

  • Questions and Prompts Mathematical Thinking

    This 3 page paper looks at the value and use of prompts and questions in the teaching of mathematics in post compulsory education. The paper considers why questions and prompts can be important in developing mathematical thinking and considers the ideas of theorists including Zygfryd Dyrszlag. The bibliography cites 4 sources.

  • The Use of Statistical Analysis

    This 3 page paper provides a response to the following statement and questions: Statistics in psychology are more than numbers because we must ask ourselves, why the individual chose that answer. Hidden factors such as pride, abuse, and self-esteem all affect the answer thereby affecting the scores. On that ground, are statistics in psychology credible? Bibliography lists 2 sources.

  • Theory of 'Indeterminancy of Translation' by Willard V. Quine

    This is a 15 page paper discussing Quine’s theory of indeterminacy of translation. Willard V. Quine was a mathematician and philosopher who lived from 1908-2000. During the last half of the 20th century, Quine developed several theories, one of which was the theory of indeterminacy of translation, which challenged some of the former assumptions used in the fields of psychology, linguists and anthropology. Quine asserted that accurate translations between languages could not be made for a number of reasons. Firstly, linguists could not get basic terms of references, or starting elements, because from a holistic perspective, sentences are the basic form of meaning and all sentences are semantically linked by the native speaker. Secondly, “meaning” could not be considered as an absolute element. In addition to some of these basic changes in the construct of translations, Quine also discussed the idea that not only were correct translations into English not possible but also two translation manuals given the same observational stimuli could also not be interchangeable because of the assumptions and the linguist’s imposition of his own beliefs and patterns onto the native language. Obviously, Quine’s theories were criticized as linguists made the case that several translations were considered successful because smooth negotiation and conversation could take place between native speakers and foreign speakers. However Quine’s dissection of the linguist’s process into one of a mathematical and scientific process is considered one of the most significant within the last fifty years in linguistic philosophy. Bibliography lists 6 sources.

  • Typing Speeds Evaluated Statistically

    A 6 page paper presenting ANOVA analysis of three sets of data addressing environmental conditions in which data entry personnel work. After testing, the company's owner decides she will forego the music but will bring a coffee service into the office. The pro-music contingent is disappointed, but they agree with the decision based on results. Though there is less variation when typists have rock music in the background, per-minute speed is much greater when individuals are working in silence as they do their work while drinking more easily-obtainable coffee. Bibliography lists 3 sources.

  • Golden Mean, Irrational Numbers & Fibonacci Series

    A 3 page research paper that discusses the interrelated nature of the Golden Mean, irrational numbers and Fibonacci series numbers. The writer defines these concepts and then discusses them in regards to music. Bibliography lists 2 sources.

 

Most Relevant Research Papers

Click on any of the term papers to read a brief synopsis of the research paper. The essay synopsis includes the number of pages and sources cited in the paper.

 

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