Essays and Research Papers on Mathematics

This 8 page paper examines the way in which Gauss added to number theory, looking specifically congruence and quadratic reciprocity the paper shows how and why this was the start of modern number theory. The law of quadratic reciprocity is also explained with the use of examples. The paper then goes on to look at ...

A 6 page overview of the mathematical discipline of graph theory. As a field of study, graph theory has nothing at all to do with what most people normally associate with the word 'graph,' and is a specialized field. Applications range from analyzing children's games to finding the furthest stretch of graph theory ...

A 3 page overview of the book Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability by Pesic. Bibliography lists 1 source.

A 10 page research paper describing cryptology. Simply put, cryptology is a part of the larger classification of number theory, and provides the mathematical foundation upon which the science of cryptography is built. Cryptography is high-level encryption science used primarily to ensure privacy in our increasingly electronic age. Electronic messages, personal data, ...

A 10 page paper that presents the basics of chaos theory, including mathematical information in a historical context (theorists). The paper covers Lorenz, Ruelle and Takens, Benoit Mandelbrot, Einstein, Shaw and the Santa Cruz collaborative, and modern submissions. The paper concludes with a look at the possibilities of application of chaos theory to ...

A 9 page research paper on the life, works, and mathematical contributions of John Napier (1550-1617) -- the man most commonly associated with the creation of Logarithms. Napier also developed methods for multiplying and dividing small rods known as Napier's Bones, a device that was the forerunner of the slide rule. Some sample equations and ...

A 5 page research paper that looks at the life and contributions of Pierre de Fermat, the founder of modern number theory and probability theory. The writer also looks at Fermat's last theorem, the world's 'most famous unsolved mathematical puzzle.' Bibliography lists 5 sources.

A 9 page research paper on the life, works, and mathematical contributions of John Napier (1550-1617) -- the man most commonly associated with the creation of Logarithms. Napier also developed methods for multiplying and dividing small rods known as Napier's Bones, a device that was the forerunner of the slide rule. Some sample equations and ...

A 10 page paper that provides an overview of the elements of science in the works of Escher, with a focus on symmetry and metaphor based in his mathematical approach. Bibliography lists 8 sources.

This 46 page paper looks at the French nineteenth century mathematician Augustin-Louis Cauchy. The paper begins with an examination of the development of calculus up until the time of Cauchy and then looks at the mathematicians background and how it may have impacted on his work. The majority of the paper looks at his work, ...

A 6 page paper discussing the history and development of the Fibonacci sequence; the development of associated ratios; and their applicability to visual images. Fibonacci published his sequence in 1202, and da Vinci used the concept of "thirds" in much of his work as did some other artists of the period. The paper provides the mathematical basis ...

This 10 page paper gives a brief overview of the Greek mathematician, Euclid. He was the chief architect of the concept and science of geometry. Bibliography lists five sources.

A short, 3 page overview of the life & works of John Napier containing brief descriptions of his major works and other people also associated with the development of logarithms.

5 pages in length. Solomon Lefschetz, touted as one of the most revolutionary mathematicians of all time, played a major role in the progress of American mathematics at the turn of the century and beyond. He was a Russian-born mathematician who, after earning his United States citizenship in 1912, christened a new era in American ...

6 pages. A biographical and historical account of the life of Giovanni Girolamo Saccheri with special emphasis on the contributions he made to the world of mathematics, including his book Logica Demonstrativa. Bibliography lists 4 sources.

A 3 page paper that reports some of the contributions made to mathematics by these two early 13th century mathematicians. Jordanus, for instance, substituted letters for numbers and Fibonacci brought the decimal system to his world. Bibliography lists 4 sources.

This 10 page paper discusses the nature of the difficulties that a student may face in learning about whole numbers, fractions, decimals and their operations and in how these difficulties may be related to the ways in which students learn mathematics. The bibliography cites 11 sources.

A paper which looks at the life and works of the mathematician Leonhard Euler, and his contribution to the different fields of science, technology and mathematics in Europe in the eighteenth century. Bibliography lists 4 sources.

A 10 page research paper exploring the basics of algorithms and data structures in relationship to queues, data types, trees, hashing, heaps, graphing and design. Bibliography lists 11 sources.

A 5 page overview of the importance of Internet users being able to depend on the safety and security of the information they both transmit and receive. Discusses cryptography as a workable solution to the problem of Internet security and contrasts it to the less effective TCP/IP. Bibliography lists 4 sources.

An 18 page research paper on every available aspect of differential equations including Laplace Transforms and much more. A number of graphical illustrations are provided and the bibliography lists more than 8 sources.

A 15 page research paper on various concepts in linear algebra. The writer details multivariables, vectors, determinants, gaussian elimination, and other elements of linear algebra. Bibliography lists 6 sources.

A 5 page paper explaining both average and instantaneous velocities. The writer demonstrates the relationship between the derivative and these primary functions. Bibliography lists 4 sources.

A 9 page paper on theories of morality in Greek philosophy focusing upon the works of Pythagoras. Pythagoreanism is seen only as a theory of the universe but also as a way of salvation. Bibliography lists 5 sources.

5 pages in length. This paper explains the different approaches one might take in preparing a research tool. There are literally hundreds of different methods to collect and analyze the data, but they can all be broken down into two categories. Those procedures that do nothing more than summarize large groups of ...