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Papers and Essays 
History Of
The Abacus / From West To East & Beyond : A 15 page paper that provides an
overview of the history and development of the abacus. The report essentially compares the
Chinese, Roman, Greek, Russian and Indian counting methods utilizing similar instruments.
Bibliography lists 6 sources. Abacus.doc
Benefits Of ComputerTaught Math Over Standard Textbook
Practices :
A 10 page study that provides support for the hypothesis that computer taught math
provides significant beneficial outcomes for learners in terms of test scores.
Bibliography lists 10 sources. Mtcomp.wps
Differential Equations : 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. Diffequa.wps
Linear Algebra : 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. Linalgeb.wps
The Derivative In Average & Instantaneous Velocity :
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. Velocity.wps
Graph Theory : 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 principles. Bibliography lists 6 sources. Graph.wps
Number Theory / Chaos Theory : 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 neural nets.
Bibliography lists 8 sources. Chaosthy.wps
Cryptology, Cryptography and Electronic Security : 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 highlevel encryption science
used primarily to ensure privacy in our increasingly electronic age. Electronic messages,
personal data, governmental security issues and secret industrial work are all appropriate
candidates for encrypting, and all routinely are in some form or another when based in
electronic media. Bibliography lists 7 sources. Crypto.wps
Cryptography & The Issue Of Internet Security : 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. Crysc.wps
Algorithm Basics : 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. Algbas.wps
Fear of Mathematics (Math Anxiety) : 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. Mathanxi.wps
Gender and the Capacity for Learning Mathematics :
An indepth, 20 page research paper in which the writer seeks to determine whether which
sex is more apt to have problems grasping math concepts at an early age. Report contains
analysis, methodology, discussion, etc; Numerous studies are cited and it is found that
while girls generally perform better, they are more likely to avoid harder levels of math
than are their male counterparts. Standard bibliography lists 20+ sources and a FREE
annotated ("working") bibliography is included ! Mathgend.wps
The Game Of Blackjack / Card
Counting & Other Strategies : This 5 page paper provides an overview of the
game of Blackjack. A brief history and explanation of the game is included but the focus
is on methods used to increase the odds of winning the game. Card counting, perecentages,
& commonsense ratios are discussed and other strategies are explained in detail.
Bibliography lists 5 sources. Blakjack.wps
The Science of Escher / Symmetry and Metaphor: 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. Escher.doc
Girolamo Cardano / Mathematician : 8 pages in
length. Cardano was a 16 century Italian mathematician best known for his work entitled
"Ars magna" (the "Great Art"), from which many new ideas in algebra
were systematically presented. Among them are Cardano's rule and the linear
transformations that eliminate the second degree terms in a complete cubic equation.
Report is written in part as a sentence outline and contains various pictorial
examples of Cardano's formulas. Bibliography lists 7 sources. Cardano.wps
John Napier / The Creator of Logarithms : A 9 page
research paper on the life, works, and mathematical contributions of John Napier
(15501617)  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 glossary of terms (defined) are included. Bibliography lists 12+ sources. Napier.wps
*A 10 page version of this report is also available with more
personal analysis as Napier2.wps
Napier's Life & Works : 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. Napier3.wps
The Life and Works of Euclid of Alexandria : 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. Euclid.wps
Pythagoras / The Philosopher, The Mathematician : A
15 page account of what is known of the life and scientific and mathematical contributions
of Pythagoras. Particular attention is paid to the religious beliefs of his Pythagorean
Order and how their beliefs has made it difficult to get a true understanding of
Pythagoras’ contributions to science and mathematics. A summary of the contributions
which have been attributed to Pythagoras is included. Emphasis is placed on the
Pythagorean Theorem, the principles which determine the concordant scale, and musical
spheres. Information is also provided regarding current thought regarding Pythagoras’
beliefs concerning vegetarianism, the human and animal soul and reincarnation. A brief
overview of his ethnic origins, his birthplace, his studies, and travels is also included.
Bibliography lists six sources. Pyth.wps
Pythagoras & Morality In Greek Philosophy : 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. Pythagor.wps
Solomon Lefschetz : 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 Russianborn mathematician who, after earning his United States citizenship in
1912, christened a new era in American mathematics by way of his comprehensive methods and
development of algebraic topology. The writer chronicles his life's achievements and
demonstrates how beneficial his accomplishments were to the United States. Bibliography
lists 4 sources. Lefschet.wps
The Importance of Mathematics in Early Greek Culture :
A 12 page comprehensive study of early Greek mathematicians and their cultural
significance. Included in the discussion are Ptolemy, Pythagoras, Aristotle, Plato, and
others. Bibliography lists 9 sources. (also related to Astronomy) Greekmat.wps
Aristotle / Contributions To Mathematics Analyzed :
This 5 page research paper discusses Aristotle's contributions to the field of
mathematics. Specifically discussed are Aristotle's views on mathematics, in terms of the
advancement of science, and his logical approach to mathematical study through syllogisms.
Bibliography lists 7 sources. Arimath.wps
Einstein's Mathematics : 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. Einsmath.wps
Assessment Methods In Current Mathematics Instruction :
A 12 page paper discussing traditional assessments of mathematics proficiency in students
in light of recent changes in overall goals imposed by government and the public.
Bibliography lists 12 sources. Mathtest.doc
Cameras / Focal Points, Aperture & Other Mathematical
Concepts : A 9 page outline of the underlying concepts of photography and their
relation to mathematics. Includes information about different camera types. Emphasizes
methodology for the determination of focal length. Bibliography lists eight sources. Caminfo.wps
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