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The Important Role of Mathematicians in Society - The Important Role of Mathematicians in Society Thesis Statement This report will focus on the professional field of mathematicians. It will highlight some of the history, responsibilities, opportunities, and requirements of this occupation. Outline I. Introduction A. A condensed history of mathematics B. Famous mathematicians and their accomplishments II. Body A. Opportunities for mathematicians B. Education and training C. Requirements D. Earnings III. Conclusion A. Good mathematicians are problem solvers Mathematicians: Making numerous contributions A mathematician is described as someone who uses logic or theory to solve problems....   [tags: essays research papers fc]
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Women Mathematicians: Why So Few? - Women Mathematicians: Why So Few. The great field of mathematics stretches back in history some 8 millennia to the age of primitive man, who learned to count to ten on his fingers. This led to the development of the decimal scale, the numeric scale of base ten (Hooper 4). Mathematics has grown greatly since those primitive times, in the present day there are literally thousands of laws, theorems, and equations which govern the use of ten simple symbols representing the ten base numbers. The field of mathematics is ever changing, and therefor, there is a great demand for mathematicians to keep improving our skills in utilizing the numeric system....   [tags: Argumentative Persuasive Papers]
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Semantic Realism: Why Mathematicians Mean What They Say - Semantic Realism: Why Mathematicians Mean What They Say ABSTRACT: I argue that if we distinguish between ontological realism and semantic realism, then we no longer have to choose between platonism and formalism. If we take category theory as the language of mathematics, then a linguistic analysis of the content and structure of what we say in and about mathematical theories allows us to justify the inclusion of mathematical concepts and theories as legitimate objects of philosophical study. Insofar as this analysis relies on a distinction between ontological and semantic realism, it relies also on an implicit distinction between mathematics as a descriptive science and mathematics as a descriptive discourse....   [tags: Mathematics Mathematical Math Essays]
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Differential Scientists - Differential Scientists If at a social gathering a man or woman with a nicely tucked in shirt and shoes that do not quite match their outfit regales listeners with the musical version of the quadratic formula (set to the tune of “Jingle Bells”), chances are that that person is either a mathematician or a physicist. But how does one know whether the clever soul selflessly sharing their dry wit studies numbers or physical science. Does it even matter. Are not the words “physicist” and “mathematician” simply two different ways to label a socially inept intellectual who does nothing but research scientific material that no one else on the planet could ever hope to understand....   [tags: Mathematicians Science Essays] 1283 words
(3.7 pages)
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Biography of Gottfried Wilhelm Leibnitz - Biography of Gottfried Wilhelm Leibnitz Gottfried Wilhelm Leibnitz was born on the July 1, 1646 in Leipzig, Germany and died on November 14, 1716 in Hanover, Germany. He was the son of Friedrich Leibnitz, a professor of moral philosophy at Leipzig. Friedrich Leibnitz was evidently a competent though not original scholar, who devoted his time to his offices and to his family as a pious, Christian father. His mother was Catharina Schmuck, the daughter of a lawyer and Friedrich’s third wife. Friedrich died when Leibnitz was only six years old and he was brought up by his mother....   [tags: Gottfried Wilhelm Leibnitz Mathematicians Essays] 3620 words
(10.3 pages)
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history of algebra - Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or developed) in the Arab countries along side geometry. Many mathematicians worked and developed the system of math to be known as the algebra of today. European countries did not obtain information on algebra until relatively later years of the 12th century. After algebra was discovered in Europe, mathematicians put the information to use in very remarkable ways. Also, algebraic and geometric ways of thinking were considered to be two separate parts of math and were not unified until the mid 17th century....   [tags: essays research papers] 1187 words
(3.4 pages)
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John Charles Fields - John Charles Fields John Charles Fields is perhaps one of the most famous Canadian Mathematicians of all time. He was born on May 14, 1863 in Hamilton Ontario, and died August 9, 1932 in Toronto, Ontario (Young, 1998). He graduated from the University of Toronto at the age of 21 with a B.A in Mathematics and went on to get his Ph.D. at John Hopkins University in 1887. Fields was very interested to study at John Hopkins University because apparently it was the only university in North America which really stressed research at the time (Fields Institute, n.d.)....   [tags: essays research papers] 804 words
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Male Superiority In Math: Fact or Fiction? - Male Superiority In Math: Fact or Fiction. One true mystery of mathematics is the small number of female mathematicians. When most people think of mathematicians, they automatically assume that they are male. This leads to the idea that boys are mathematically superior to girls, which has long been a popular belief. Recent studies, however, may prove this to be wrong. The fact is that there are numerous female mathematicians who have made very important contributions to the mathematical world throughout history....   [tags: Argumentative Persuasive Papers]
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1359 words
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Human Gender and Mathematics - Human Gender and Mathematics Is there a difference in the mathematical ability between men and women. Historians have no precise method of quantifying or comparing their individual accomplishments (Olsen). Not only in mathematics, but also in many other career areas in the past, women were looked upon as inferior to their male counterparts. Women were not encouraged to pursue a career in mathematics. Historically, women were seen working around the home, cleaning the house, taking care of the children, and cooking the food....   [tags: Argumentative Persuasive papers]
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1397 words
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Topology - Topology Topology is the study of those properties of geometric figures that are unchanged when the shape of the figure is twisted, stretched, shrunk, or otherwise distorted without breaking. It is sometimes referred to as "rubber sheet geometry" (West 577). Topology is a basic and essential part of any post school mathematics curriculum. Johann Benedict Listing introduced this subject, while Euler is regarded as the founder of topology. Mathematicians such as August Ferdinand Möbius, Felix Christian Klein, Camille Marie Ennemond Jordan and others have contributed to this field of mathematics....   [tags: Mathematics Geometry Essays]
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The Nature of Mathematics - The Nature of Mathematics Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its basic interest. The essence of mathematics lies in its beauty and its intellectual challenge. This essay is divided into three sections, which are patterns and relationships, mathematics, science and technology and mathematical inquiry. Firstly, Mathematics is the science of patterns and relationships. As a theoretical order, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have counterparts in the real world....   [tags: Papers] 1019 words
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The Mathematical Abilities of Women - The Mathematical Abilities of Women Tests have proved that women have the same mathematical abilities than men do. Since there is no difference in ability, you would think that the field is equally occupied by both genders. Many people have thought about a seemingly simply asked question and have failed to come up with a practical answer why it is so. The question, "How come you know more male mathematicians than female?" is one that I, previously uninformed on this subject plan to supply data that may help to lead to one clearly defined answer....   [tags: Math Mathmatics Women]
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1138 words
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Women and Mathematics - Women and Mathematics Call me a bigot if you want but men are better mathematicians than women. Year after year, men score higher on the SAT’s, more men receive prestigious educations from the best technical schools in the nation, and men obtain more degrees, secure more jobs and get promoted more often. “The ETS report on students taking the SAT examinations indicates that males have traditionally scored 40-50 points higher on the mathematics section” (Women) “In 1996, California Institute of Technology’s enrollment was 75% male, Massachusetts Institute of Technology’s enrollment was 62% male, Renssalear Polytechnic Institute’s enrollment was 77% male, Rochester Institute of Technology’s enrollment was is 68% male, and Worchester Institute of Technology’s enrollment was 79% male” (Baron’s)....   [tags: Argumentative Persuasive Essays]
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Fractals: A New-Age Mathematics to Explain Our World - Fractals: A New-Age Mathematics to Explain Our World Fractal art is a new-age art that tantalizes the eyes and mind with patterns, shapes, colors, and abstract imagery. Artists have once again found a way to harness the abstractedness of mathematics and integrate it into their work. So where does this new art form of fractal design stem from. The reality is that fractals themselves are relatively young in the mathematical world. Of course since the beginning of art and history and mathematics, self-similar objects have existed and been intriguing to the human mind....   [tags: Fractals Mathematics Math Papers]
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1852 words
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The History of Math - The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems. The basic of mathematics was inherited by the Greeks and independent by the Greeks beg the major Greek progress in mathematics was from 300 BC to 200 AD....   [tags: essays research papers] 810 words
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Mathematical Realism And Its D - Reuben Hersh, a mathematician and mathematics philosopher, believes humans created math. He reasons that math is all in the heads of humans, and is a “social phenomenon”. According to Hersh math is not “physical, not mental, but social”. Math to Hersh is a creation of humans that would not be found in other regions of the universe. According to Hersh if there were other life forms out there in the universe they would not have the same math that we have. Hersh agrees that there could very well be aliens out there in the universe who use mathematics, but he feels that their math would much different than ours....   [tags: essays research papers] 394 words
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The Mathematics of Map Coloring - The Mathematics of Map Coloring The four-color conjecture has been one of several unsolved mathematical problems. From 1852 to this day, practically every mathematician has studied the problem long and hard, but to no avail. The conjecture looks as though it has been solved by Wolfgang Haken and Kenneth Appel, both of the University of Illinois. They have used computer technology to prove the conjecture. The calculation itself goes on for about 1200 hours. The staggering length of the computation of the proof is what creates some controversy in the mathematical world....   [tags: Colors Science Essays]
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Women's Contributions to Mathematics - Women's Contributions to Mathematics Women in the world of mathematics is a subject that people rarely hear about. The only time people do is if it’s a female math teacher. But what many do not know is that women have made extremely important contributions to the world of mathematics. Women have been documented to be involved in mathematics, since as early as the fifth century A.D. Women such as Hypatia, Maria Gaetana Agnesi, Sophie Germain, Emmy Noether, Ruth Moufang and Sun-Yung Alice Chang....   [tags: Papers] 2428 words
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The History of Imaginary Numbers - The History of Imaginary Numbers The origin of imaginary numbers dates back to the ancient Greeks. Although, at one time they believed that all numbers were rational numbers. Through the years mathematicians would not accept the fact that equations could have solutions that were less than zero. Those type of numbers are what we refer to today as negative numbers. Unfortunately, because of the lack of knowledge of negative numbers, many equations over the centuries seemed to be unsolvable. So, from the new found knowledge of negative numbers mathematicians discovered imaginary numbers....   [tags: Papers] 1077 words
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Fractals: A Mathematical Description of the World Around Us - ... To create the Set we pick a point C on the complex plane. The complex number corresponding with the point can be found by the equation C= a +b i, where a is the horizontal real x-axis b is the imaginary y-axis.. After calculating this expression we use the equation using zero as the value of  and get C for the result. Next we assign the result to and repeat the calculation. The result is the complex number . Then we have to assign the value to and repeat the process again and again....   [tags: Mathematics ]
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The Classical World - The Classical World The Classical World made many contributions to the development of science, literature, and ethics. These contributions have influenced the modern world today. Many mathematicians, astronomers, and scientists contributed to the development of many of the luxuries we enjoy today. Homer, author of The Iliad and The Odyssey, made contributions to the field of literature through his writing. In the field of ethics, many philosophers from the Classical World contributed to the standards, values, and principles of our society today....   [tags: essays research papers] 551 words
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I Am a Ponarvian - I Am a Ponarvian Some of you have already scoured the dictionary in vain for a definition of the word "Ponarvian." One of my greatest ambitions is to get this word safely into Websters where it belongs. Until that happy time, the following definition will have to do: PONARV (PO narv) n. [acronym] A project of no apparent redeeming value. Hence, Ponarvian: one who pursues such projects. It is my contention that not some, but MOST of the greatest human triumphs in art, science, and technology have their root in the humble ponarv....   [tags: Personal Narrative 123 essays] 1420 words
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Fermat’s Last Theorem - Fermat’s Last Theorem The year is 1637. Pierre de Fermat sits in his library, huddled over a copy of Arithmetica written by the Greek mathematician Diaphantus in the third century A. D. Turning the page, Fermat comes across the Pythagorean equation: x 2 + y 2 = z 2. He leans back in his chair to think and wonders if this property is limited to the power of two only. He bends over the book again, scanning ahead through the pages to look for any clues. Suddenly, he begins writing intensely in the margin: “It is impossible for a cube to be written as a sum of two cubes, or for a fourth power to be written as the sum of two fourth powers or, in general, for any number which is a power greater than the second to be written as a sum of two like powers....   [tags: Pierre Fermat Math Mathematics Papers]
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Euclid - EUCLID: The Man Who Created a Math Class Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also....   [tags: essays research papers] 873 words
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Georg Cantor - Georg Cantor I. Georg Cantor Georg Cantor founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He also advanced the study of trigonometric series and was the first to prove the nondenumerability of the real numbers. Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg, Russia, on March 3, 1845. His family stayed in Russia for eleven years until the father's sickly health forced them to move to the more acceptable environment of Frankfurt, Germany, the place where Georg would spend the rest of his life....   [tags: essays research papers] 2070 words
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Euclid and Mathematics - Euclid and Mathematics Euclid is one of the most influential and best read mathematician of all time. His prize work, Elements, was the textbook of elementary geometry and logic up to the early twentieth century. For his work in the field, he is known as the father of geometry and is considered one of the great Greek mathematicians. Very little is known about the life of Euclid. Both the dates and places of his birth and death are unknown. It is believed that he was educated at Plato's academy in Athens and stayed there until he was invited by Ptolemy I to teach at his newly founded university in Alexandria....   [tags: Papers] 611 words
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Abstract Geometry - Abstract Geometry The ancient Egyptians and Babylonians discovered abstract Geometry. They developed these ideas that were used to build pyramids and help with reestablishing land boundaries. While, the Babylonians used abstract geometry for measuring, construction buildings, and surveying. Abstract geometry uses postulates, rules, definitions and propositions before and up to the time of the Euclid. Abstract geometry is deductive reasoning and axiomatic organization. Deductive reasoning deals with statements that have already been accepted....   [tags: Papers] 402 words
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The Concept of Infinity - The Concept of Infinity The concept of infinity has been evaluated many times throughout history. Only recently, in the nineteenth century, has major progress evolved in the field. The chapter "Beyond Infinity" answers the questions, "what is mathematics and why should I study it?" by reviewing several mathematician's theories of infinity. First, the author mentioned Galileo who theorized that a line which measured 3 inches long contained the same amount of points as a line twice it's length....   [tags: Papers] 360 words
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Leonardo Fibbonaci's Famous Formulas - Some people hate math and some love it. Other people devote their time to finding math patterns because they do not have a life. Leonardo Pisano Fibonacci, or Leonardo of Pisa, was one of those people. He was the "greatest European mathematician of the middle ages". Fibonacci was born 1175 AD in Pisa, Italy. His father was named Guilielmo, a member of the Bonacci Family and his mother Alessandra died when he was only nine years old. Fibonacci grew up with a North African Education because his father worked a trading post in that location....   [tags: essays research papers] 402 words
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Greece's Role in Shaping the Western Civilization - Greece's Role in Shaping the Western Civilization The ancient Greeks contributed much to Western civilizations. They made contributions with architecture and government. Ancient Greece's philosophers and mathematicians have made contributions to western civilizations. The art and drama of Greece also affected western civilizations. The Ancient Greece culture has made many contributions to western civilizations. Ancient Greece contributed architecture and government to western civilizations. The Parthenon was built to dedicate the goddess, Athena....   [tags: History, Social Studies] 433 words
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Simon Cook and the Digital World - Simon Cook and the Digital World Industrialization and the Digital A contemporary, Simon Cook, argues that the origins of the digital world can be traced to the times of Late-Victorian thought. Though he provides a compelling history of the visual, the digital world on a whole does not derive from the Late-Victorian pictorial diagrams from such logicians as Venn, Carroll, or Marshall as Cook contends. My argument throughout the rest of this paper will use the work of three economists— Adam Smith, Charles Babbage, and Alfred Marshall— to show that the origins of Cook’s visual interface in Late-Victorian times do not coincide with the foundation of the digital; rather, the establishment of modern digital processes can be seen thirty years earlier when the mechanization of physical and mental tasks emerged during the Industrial Revolution....   [tags: Simon Cook Argumentative Persuasive Essays] 1912 words
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A Notion of Zero in the Philosophy of Aristotle - A Notion of Zero in the Philosophy of Aristotle ABSTRACT: This article shows that Aristotle created the first notion of a zero in the history of human thought. Since this notion stood in evident contradiction to the basic principles of his metaphysics and logic, he rejected it. The origin and development of mathematical symbols was closely connected with the development of mathematics itself and development of philosophy. It resulted from the fact that philosophy provided the motivation for investigations and creation of adequate and good mathematical symbols....   [tags: Philosophical Math Essays] 2038 words
(5.8 pages)
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Euclid’s Elements and the Axiomatic Method - Euclid’s Elements and the Axiomatic Method “There is no royal road to geometry.” – Euclid Euclid’s Elements are predominantly the most fundamental concepts of mathematics, but his perspective on geometry was the model for over two millennia. He is believed by many to be the leading mathematics teacher of all time. However, little is known about his life outside of mathematics, or even when he was born or when he died. According to a passage written by Proclus, Euclid probably lived after Ptolemy and the pupils of Plato, but came before Archimedes and Eratosthenes....   [tags: Mathematics Geometry Essays]
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The Role of the Proof in Math - The Role of the Proof in Math The notion of proof has long played a key role in the study of mathematics. It is in my opinion the role of proof that separates mathematics from the sciences and other fields of study. It is the existence of proofs that give mathematicians the confidence that their work is credible and thus allows them to continue to build upon prior work without the need to second guess what has previously been accomplished. Based upon this observation, it becomes natural to ask the questions pertaining to the use of proof in learning and understanding mathematics....   [tags: Mathematics Mathematical Papers]
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Archimedes - Archimedes S. Romano Archimedes was a native of Syracuse, Sicily. Some authors have said that he visited Egypt and invented a device there now known as Archimedes' screw. This screw is a pump, still used in many parts of the world. When Archimedes was a young man, he studied with the descendants of Euclid in Alexandria. He was familiar with the mathematics used there, and he knew personally the mathematicians working there and he sent his results to Alexandria with personal messages....   [tags: essays research papers] 908 words
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Biography of Augustus DeMorgan - Augustus DeMorgan was an English mathematician, logician, and bibliographer. He was born in June 1806 at Madura, Madras presidency, India and educated at Trinity College, Cambridge in 1823. Augustus DeMorgan had passed away on March 18, 1871, in London. Augustus was recognized as far superior in mathematical ability to any other person there, but his refusal to commit to studying resulted in his finishing only in fourth place in his class. In 1828 he became professor of mathematics at the newly established University College in London....   [tags: essays research papers] 700 words
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Chaos Theory - Chaos Theory      Since its inception, science relied on predictability and order. The true beauty of science was its uncanny ability to find patterns and regularity in seemingly random systems. For centuries the human mind as easily grasped and mastered the concepts of linearity. Physics illustrated the magnificent order to which the natural world obeyed. If there is a God he is indeed mathematical. Until the 19th century Physics explained the processes of the natural world successfully, for the most part....   [tags: Science Chaos Essays] 1962 words
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Gods Gift To Calculators: The Taylor Series - Gods Gift to Calculators: The Taylor Series It is incredible how far calculators have come since my parents were in college, which was when the square root key came out. Calculators since then have evolved into machines that can take natural logarithms, sines, cosines, arcsines, and so on. The funny thing is that calculators have not gotten any "smarter" since then. In fact, calculators are still basically limited to the four basic operations: addition, subtraction, multiplication, and division....   [tags: essays research papers] 496 words
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Prime Numbers - Prime Numbers Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers. A perfect number is one whose proper divisors sum to the number itself. e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors 1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28....   [tags: Papers] 1205 words
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Analyzing The Universe and The Teacup - Analyzing The Universe and The Teacup The Universe and the Teacup is a pretty interesting book with one purpose: To make math seem relevant and cool to people who have decided that they don't like math. K. C. Cole pushes this idea by explaining how math applies to every imaginable thing in the universe, and how mathematicians are, in a sense, scientists. She also uses quotes to promote the coolness of math: "Understanding is a lot like sex," states the first line of the book. This rather blunt analogy, as well as the passage that explains how bubbles meet at 120-degree angles, supports Cole's theory that math can be applied to any subject....   [tags: Papers] 1219 words
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Differences in Geometry - Differences in Geometry Geometry is the branch of mathematics that deals with the properties of space. Geometry is classified between two separate branches, Euclidean and Non-Euclidean Geometry. Being based off different postulates, theorems, and proofs, Euclidean Geometry deals mostly with two-dimensional figures, while Demonstrative, Analytic, Descriptive, Conic, Spherical, Hyperbolic, are Non-Euclidean, dealing with figures containing more than two-dimensions. The main difference between Euclidean, and Non-Euclidean Geometry is the assumption of how many lines are parallel to another....   [tags: Papers] 1389 words
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The Life and Work of Archimedes - The Life and Work of Archimedes Archimedes was a very intelligent and a great man. He is thought of as one of the three greatest mathematicians of all time, along with Newton and Gauss. In his time he was referred to by such great aliases as “The wise one”, “The Master”, and “The Great Geometer”. And his work has yet to have been forgotten. He was indubitably was one of the last of the great Greek mathematical minds that this world has ever seen. I will attempt to show you what the mere presence of Archimedes in our history has meant to mathematics and even the colony of Syracuse itself....   [tags: Papers] 550 words
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The Organisation and Work of the People at Bletchley Park - The Organisation and Work of the People at Bletchley Park The organisation and work of the people at Bletchley Park was very important this was because in the First World War code-breaking had become more important for the first time because messaging had gone more technical and opposite armies were able to get their hand on messages from the enemy quicker and easier. The British Government wanted to be able to decode all enemy communications so they decided to build a base that would house all of Britain’s secret weapons....   [tags: Papers] 978 words
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How topoisomerases unknot knots that are formed in DNA - How topoisomerases unknot knots that are formed in DNA Introduction: The study of properties of geometric objects under deformations is called topology; the subfield of topology that I will be discussing in this essay is called knot theory (Adams 6). Mathematical knots have two primary differences: one, they are infinitely thin, and two, they are always closed. Something very similar to the size and shape of mathematical knots is DNA. Not surprisingly, knots occur in DNA frequently on a normal basis....   [tags: math mathematics]
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Nancy Kopell - In recent years there have been many strides in equality among the sexes and this new trend has lead to some well deserved recognition and opportunities for some of our more prominent female mathematicians. Mathematics has traditionally been a male dominated field of study and it has taken the work of several brilliant and strong willed women over the past several decades to demonstrate that women deserve a place in this area of study as well as the men. These women have been tireless in their efforts and they have provided like-minded females with role models that they can connect with and try to emulate....   [tags: Biography] 1394 words
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Solution of the Cubic Equation - ... His scars were covered in adulthood with a beard, but the stammering that resulted persisted throughout his life. Tartaglia learned mathematics on his own for many years until a patron made possible some study at Padua. This education gave Tartaglia a high sense of pride that others often resented. For a while, he was merely a mathematics teacher but gained fame by participating in local contests. As was common in this age, Fior challenged Tartaglia to a public mathematics contest in 1535. Each would propose questions to the other in the hopes of solving more than his opponent within a given time period (here, 40 to 50 days)....   [tags: Math] 975 words
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Drawing Conclusions: Ethics and Mathematics - ... Of course, they would also have rational counter-claims of their own, but one of the biggest factors that attracts people to a stance is their emotion, which includes their ability to empathize with people affected by a certain issue, typical feelings such as disgust, and their faiths, beliefs and religion. For example, in the issue regarding gay marriage, some Christians groups are assert that marriage must only be between a man and a woman, citing Bible verses that supposedly say so. This claim is not only emotionally-motivated, but it is also a fallacious argument....   [tags: Logic] 1302 words
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My Personal Philosophy of Education - Philosophy of Education I believe all students have the potential to think critically and mathematically. However, each student manifests this ability at a different level and pace. Thus, it is the role of the teacher to facilitate learning by providing each student with the opportunity to grasp mathematical concepts. Too often teachers assume that only those who have demonstrated a high level of achievement in the classroom will be able to experience higher-order problem solving situations. Often, problems that require critical thinking are simplified to mere procedures and rules....   [tags: Education Teachers Reflective Writing Essays] 641 words
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How Humanism Contributed to Rennaisance Ideals - How Humanism Contributed to Rennaisance Ideals Through the groundwork laid by the Hundred Years War, the Black Death, and the Protestant Reformation, Italian Renaissance humanism nearly single-handedly allowed for the modern concept of individuality. The rebirth of classical literature, and especially the attempts among the philosophical elite to translate this literature, helped bring this "enlightening" knowledge to the gradually more literate masses. Also, the frenzy for education of these masses allowed the concept of individuality to spread to all social classes....   [tags: European Europe History] 399 words
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History Of Monte Carlo Method - It could be argued that current physics research could be divided into three areas - theoretical, experimental and computational. Numerical approach, in which systems are mimicked as accurately as possible using a computer or in which computer models are set up to provide well - behaved experimental systems are increasingly providing a bridge between theory and experiment, for instance; the Monte Carlo method (MC) and the molecular-dynamics method (MD). In Monte Carlo method the exact dynamical behavior of a system is replaced by a stochastic process, whereas the MD methods are based on a simpler principle and consists of solving a system of Newton's equations for an N-body system....   [tags: essays research papers] 365 words
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Marin Mersenne and Theory of Numbers - Theory of Numbers Mersenne Marin Mersenne was a French number theorist who lived from 1588 to 1648. Mersenne attended the College of Mans, the Jesuit College, and then Sorbonne to study theology. In 1611, he joined the religious order of the Minims. Once in the order, Mersenne continued his studies at Nigeon and Meaux. He became a priest at the Place Royale. The area in Paris, where Mersenne taught, became a meeting ground for Fermat, Pascal, and others who later became the core of the French Academy....   [tags: Biography, History, Mathematics] 325 words
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Adam Smith Biography - Adam Smith was born on July 5, 1723 in Kirkcaldy, Scotland. At the age of fourteen, Smith entered the University of Glasgow, where he studied moral philosophy under Francis Hutcheson. Here Smith developed his strong passion for liberty, reason, and free speech. In 1740 he was awarded the Snell Exhibition and entered Balliol College, Oxford. In 1746 Smith left Oxford. In 1748 Smith began delivering public lectures in Edinburgh under the patronage of the Lord Kames. In 1751 Smith Was appointed the Chair of Logic at University of Glasgow, the next year he was appointed the Chair of Moral Philosophy, which was the position of his old teacher Francis Hutcheson....   [tags: essays research papers] 369 words
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Art And Mathematics:Escher And Tessellations - Art And Mathematics:Escher And Tessellations On first thought, mathematics and art seem to be totally opposite fields of study with absolutely no connections. However, after careful consideration, the great degree of relation between these two subjects is amazing. Mathematics is the central ingredient in many artworks. Through the exploration of many artists and their works, common mathematical themes can be discovered. For instance, the art of tessellations, or tilings, relies on geometry....   [tags: Math Artistic Papers]
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Career Opportunities For Recipients Of Degrees In Mathematics - The Many Career Opportunities For Recipients Of Degrees In Mathematics I have chosen to do Possibility 7. It states that once a person decides to study mathematics they are limited to the possible fields of work that is available to them. According to this statement the only possible jobs are teaching jobs at the school, college, and university levels. It also talks about how this can be dull to some and how a person can't become a millionaire this way. I am in total opposition of this statement....   [tags: Argumentative Persuasive Papers]
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Mathematics Education in America: A Troubled System in Need of Change - Mathematics Education in America: A Troubled System in Need of Change On a trip to Fidler concrete in Goshen, Indiana, a man ordered forty feet of rebar for home use. When he went to pick up the rebar, the adult employee in charge asked the man what size pieces he would like. The man asked for six-foot sections. The employee furrowed his brow and said, “Now, if it were five foot sections, that would be ten of them for forty feet, right?” The man replied, “No, ten of the five footers would be fifty feet.” The employee pondered that and said, “So in the six-footers…Ah, I’ll just give you twelve....   [tags: Education Math Learning Essays]
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Fractals: The Organization of Chaos - Fractals: The Organization of Chaos Please ignore the references to pictures or figures. I no longer have them, so I could not include them on this page. Thanks. Fractals are a relatively new concept in geometry. Most concepts for Euclidean geomtery, the division of geometry which deals with lines, circles, triangles, and other standard shapes, stem from the Late Greek and Early Rioman times. Considering the age of mathematics, the study of fractals is new becasue it dates to the beginning of this century....   [tags: Mathematics Geometry Essays]
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Logic: An Empirical Study of A Priori Truths - Logic: An Empirical Study of A Priori Truths ABSTRACT: I distinguish a priori knowledge from a priori truths or statements. A priori knowledge either is evident or is derived from evident premisses by means of correct reasoning. An a priori statement is one that reflects features of the conceptual framework within which it is placed. The statement either describes semantic relations between concepts of the framework or it characterizes the application of the framework to experience and the world....   [tags: Logical Philosophy Philosophical Essays] 3263 words
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The Issue of Experiment in Mathematics - The Issue of Experiment in Mathematics ABSTRACT: The issue of the status of mathematical knowledge a priori or a posteriori has been repeatedly considered by the philosophy of mathematics. At present, the development of computer technology and their enhancement of the everyday work of mathematicians have set a new light on the problem. It seems that a computer performs two main functions in mathematics: it carries out numerical calculations and it presents new areas of research. Thanks to cooperation with the computer, a mathematician can gather different data and facts concerning the issue of interest....   [tags: Math Philosophy Philosophical Papers]
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Understanding Mathematics - Understanding Mathematics This paper is an attempt to explain the structure of the process of understanding mathematical objects such as notions, definitions, theorems, or mathematical theories. Understanding is an indirect process of cognition which consists in grasping the sense of what is to be understood, showing itself in the ability to apply what is understood in other circumstances and situations. Thus understanding should be treated functionally: as acquiring sense. We can distinguish three basic planes on which the process of understanding mathematics takes place....   [tags: Math History Learning Papers]
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Leonardo Fibonacci - Leonardo Fibonacci Leonardo Fibonacci was one of the great mathematicians of his time. His lifestyle allowed him to travel and study math in various countries, and he ended up combining his cultural knowledge to discover the most effective ways of doing mathematics. He is most famous for his contributions to the European number system and for his sequence of numbers known as the Fibonacci numbers. Starting with 0 and 1 as the first two numbers, each number in the sequence is the sum of the two preceding numbers....   [tags: Mathematics Papers]
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Set Theory in the Flesh - Set Theory in the Flesh The idea of infinity has been around for thousands of years. It it impossible to even conceive of this number or anything that pertains to the infinite. There is always one more. A billion is a fairly large number, 1 with 9 zeros after it. If one counted by seconds without breaks, it would take over 32 years to reach it. A Google, is a number written as 1 with one hundred zeros after it. One couldn't even count the number of lifetimes it would take to count to this number....   [tags: Numbers Mathematics Essays]
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Graph Theory: The Four Coloring Theorem - Graph Theory: The Four Coloring Theorem "Every planar map is four colorable," seems like a pretty basic and easily provable statement. However, this simple concept took over one hundred years and involved more than a dozen mathematicians to finally prove it. Throughout the century that many men pondered this idea, many other problems, solutions, and mathematical concepts were created. I find the Four Coloring Theorem to be very interesting because of it's apparent simplicity paired with it's long, laborious struggle to be proved....   [tags: Graph Geography Essays]
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Usefulness of Mathematics Education - Usefulness of Mathematics Education There has been much discussion over the years about the usefulness of mathematical studies. Everyone seems to have a different viewpoint on the issue. Some believe that mathematics has little use in the working world and so is not a subject that should be taught at higher levels in secondary school. Others argue that mathematics does serve a profound purpose, albeit one that is subtle and not obvious in the vocational world. G. H. Hardy and Underwood Dudley, two great mathematicians of the twentieth century, have differing views, and our current Secretary of Education Richard Riley has his thoughts as well....   [tags: Math Mathematical Jobs Essays]
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The Solution - The Solution The business man behind a desk, the scientist in the lab, the artist approaching his canvas, the mathematician examining the symbols he placed on the blackboard--the thoughts going through each of their heads are very different in many ways, yet amazingly similar. For example, the business man must come up with an idea to cut costs and increase revenue for his company. He must find a creative twist to an old idea, a new combination of numbers that allows the company to increase profit and drop costs....   [tags: Philosophy Philosophical Papers] 1496 words
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Proof - Proof Proof. What is it and why does this simple term cause such a stir among mathematics educators and mathematics students. If you were to ask a young child to prove a mathematical fact, they would be happy to show you many examples of how it works. This does not constitute a proof but it is a step in the right direction. If you were to ask a high school student or first year college student to do a proof, you will most likely be met with groans and feelings of disgust. Students at this age have probably encountered proof in a geometry class where they were expected to follow a strict format without much freedom to express proofs on their own....   [tags: Math Education Papers]
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Carl Friedrich Gauss - Carl Friedrich Gauss Carl Friedrich Gauss was born in Brunswick, Germany in 1777. His father was a laborer and had very unappreciative ideas of education. Gauss’ mother on the other hand was quite the contrary. She encouraged young Carl’s in his studies possibly because she had never been educated herself. (Eves 476) Gauss is regarded as the greatest mathematician of the nineteenth century and, along with Archimedes and Isaac Newton, one of the three greatest mathematicians of all time....   [tags: Essays Papers]
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Albert Einstein - “The search for truth is more precious than its possession'; Albert Einstein, also known as “The Father of The Nuclear Age,'; perhaps one of the most brilliant minds ever to exist was a very quiet man. “Einstein’s Theory of Relativity revolutionized scientific brought with new conceptions of time, space, mass, motion, and gravitation'; (Unknown, World Book Inc.) Albert Einstein contributed more than any other scientist to the modern vision of physical reality....   [tags: essays research papers] 1650 words
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Asdf - Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay. This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car....   [tags: essays research papers] 1302 words
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Blaise Pascal - The French mathematician, theologian, physicist and man-of-letters, Blaise Pascal is a mathematician who has a reputation that rests more on what he might have done rather than what he might have actually done. Pascal has devoted a considerable amount of his life towards the devotion of religious exercise. Blaise Pascal was born in Clermont-Ferrand, Auvergne. Which is now known as Clermont-Ferrand, on June 19, 1623. And he died in Paris on Aug. 19, 1662. Pascal was the son of the president of the Court of Exchequer....   [tags: essays research papers fc]
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Choas Theory In Biology - Chaos In Biological Systems In today’s world of high-tech methods to study just about anything that exists, we are still imperfect. Scientists continue to look for ways to understand, explain, and even predict the actions and reactions of the universe. In the last two centuries, scientists have been looking in every possible place to understand the universe; from science, to math, even religion. They have turned to mathematicians and their strange theories of determinism and predictability. This search to understand the universe has spawned several new areas of science; there are now scientists devoted solely to the research of mere theories, such as chaos theorists....   [tags: essays research papers] 2032 words
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Infinity - The mathematical notion of infinity can be conceptualized in many different ways. First, as counting by hundreds for the rest of our lives, an endless quantity. It can also be thought of as digging a whole in hell for eternity, negative infinity. The concept I will explore, however, is infinitely smaller quantities, through radioactive decay Infinity is by definition an indefinitely large quantity. It is hard to grasp the magnitude of such an idea. When we examine infinity further by setting up one-to-one correspondence’s between sets we see a few peculiarities....   [tags: essays research papers] 933 words
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Mathematical Impacts - Mathematical Impacts The art of mathematics is an intrinsic part of the many physical sciences which humanity strives to learn; it began as a way to explain the celestial guides, which became the science of astronomy and astrophysics. This essay will explain the use of math in astronomy, chemistry, physics, and their relation. The study of astronomy is the oldest of the physical sciences it began as an inspiration. For the purpose of this essay, the study will begin with the ancient’s knowledge of this science....   [tags: essays research papers] 1819 words
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Nothing Is Certain - Theory of Knowledge Writing Assignment “Nothing can be known with certainty'; Is this statement true. Are you certain. In this essay I plan to show that nothing can be known with certainty, I will examine the truth and certainty of life and of humans, and prove that nothing can be known for certain. Sir Isaac Newton came up with many theories of time and space. Euclid said that there can be a concept of a straight line but Newton said nothing could ever travel in a straight line, see illustration below....   [tags: essays research papers fc]
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Newtons Method - Finding roots of a function is often a task which faces mathematicians. For simple functions, such as linear ones, the task is simple. When functions become more complex, such as with cubic and quadratic functions, mathematicians call upon more convoluted methods of finding roots. For many functions, there exist formulas which allow us to find roots. The most common such formula is, perhaps, the quadratic formula. When functions reach a degree of five and higher, a convenient, root-finding formula ceases to exist....   [tags: essays research papers fc]
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Standardizing The Mind - Standardizing the Mind Is it safe to assume that all people are capable of learning the same things. Should the educational system be allowed to say what is useful information and what is not for human learning and development. These questions deserve attention since the answers can determine so much about someone's future. One standard set for students is the SAT test. Most Colleges use this single test score along with GPA to determine whether or not a potential student will be allowed enrollment to their school....   [tags: essays research papers] 1282 words
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Archimedes of Syracuse - Archimedes of Syracuse (278 B.C.E. - 212 B.C.E.) "The importance of the role played by Archimedes in the history of science can scarcely be exaggerated. He was emulated and admired in his own day and at successive periods in later times" (Clagett, 1). During the time period before Archimedes, Aristotle had already effectively drawn a line between philosophy and mathematics. After his date philosophy is carried on without mathematical inspiration. There is an outbreak, known as the Golden Age of Greek mathematics, that just happens to occur in Alexandria during the period 300 to 200 B.C.E.....   [tags: Essays Papers]
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Scientific Empiricism - Scientific Empiricism In 1513, Nicholas Copernicus, composed a brief theory that stated that the sun is at rest and the earth is in rotation around the sun. In 1543, just days before his death, Copernicus published this theory in On the Revolutions of the Heavenly Spheres. This theory was meant to dissolve the long lived belief in Ptolemyís theory which stated, "The earth was at the center because it was the heaviest of objects(Kagan331)." This was a common belief at that time, which supported the religious beliefs that the earth was the center of the universe and God in the heavens were surrounding the earth....   [tags: Essays Papers]
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Recurring Decimals - Recurring Decimals Infinite yet rational, recurring decimals are a different breed of numbers. Mathematicians, in turn, have been fascinated by these special numbers for over two thousand years. The Hindu-Arabic base 10 system we use today was inspired by the Chinese method of decimals which was actually around 10000 years old. Decimals may have been around for a very long time, but what about recurring decimals. In fact the ancient Greeks were one of the first to deal with recurring decimals....   [tags: Mathematics Math Infinite Numbers] 1400 words
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Rene Descartes - Rene Descartes was a famous French mathematician, scientist and philosopher. He was arguably the first major philosopher in the modern era to make a serious effort to defeat skepticism. His views about knowledge and certainty, as well as his views about the relationship between mind and body have been very influential over the last three centuries. Descartes was born at La Haye (now called Descartes), and educated at the Jesuit College of La Flèche between 1606 and 1614. Descartes later claimed that his education gave him little of substance and that only mathematics had given him certain knowledge....   [tags: Biographies Bio Biography] 1096 words
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Islmaic Achievements and Muslim Contributions and Their Spread - The Muslim Empire grew to encompass a wide range of territory. Their empire included India, Greece, and Rome in addition to many other places. The Muslims were much more advanced than other nations because of their tolerance of other cultures. This enabled them to adopt many of the developments and innovations of the people whose land they conquered. They were able to attain intelligence at the highest level of the time from a specific area they conquered whose main focus of study was that field....   [tags: Islam] 1229 words
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