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**mathematicians**"

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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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1649 words (4.7 pages) |
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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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1112 words (3.2 pages) |
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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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Rene Descartes Mathematician - René Descartes: "Father of Modern Mathematics" 1596-1650 René Descartes was born in La Haye, Touraine (France) in March of 1596 and died at Stockholm on February 11, 1650. René, the second of a family of two sons and one daughter, was sent to the Jesuit School at La Flêche at the early age of eight. Since he was of poor health he was permitted to lie in bed till late in the mornings, a custom which he always followed. When Pascal visited in 1647 he told him that the only way to do good work in mathematics and to preserve his health was never to allow anyone to make him get up in the morning before he felt like it On leaving school in 1612 Descartes went to Paris to be introduced to the world of fashion.... [tags: Biography Biographies Bio] | 1298 words (3.7 pages) |
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Carl Friedrich Gauss -
Carl Friedrich Gauss (1777-1855) Introduction: Carl Friedrich Gauss is considered one of the greatest mathematicians of all time. He is a creator in the logical-mathematical domain as he contributed many ideas to the fields of mathematics, astronomy, and physics. Being a math education major, I have come into contact with Gauss’ work quite a few times. He contributed greatly to the different areas of mathematics like linear algebra, calculus, and number theory. Creativity can be seen when a person makes or discovers substantially new ideas that dramatically impact the domain in which the person is working.... [tags: Mathematician Biography Biographical Essays]
:: 3 Works Cited :: 1 Sources Cited |
3547 words (10.1 pages) |
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Liber abaci by Leonardo Fibonacci - Liber abaci by Leonardo Fibonacci (Leonardo Pisano) Leonardo Pisano was the first great mathematician of medieval Christian Europe. He played an important role in reviving ancient mathematics and made great contributions of his own. After his death in 1240, Leonardo Pisano became known as Leonardo Fibonacci. Leonardo Fibonacci was born in Pisa in about 1180, the son of a member of the government of the Republic of Pisa. When he was 12 years old, his father was made administer of Pisa's trading colony in Algeria.... [tags: Mathematician Leonardo Pisano] | 855 words (2.4 pages) |
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Carl Gauss - Carl Gauss Carl Gauss was a man who is known for making a great deal breakthroughs in the wide variety of his work in both mathematics and physics. He is responsible for immeasurable contributions to the fields of number theory, analysis, differential geometry, geodesy, magnetism, astronomy, and optics, as well as many more. The concepts that he himself created have had an immense influence in many areas of the mathematic and scientific world. Carl Gauss was born Johann Carl Friedrich Gauss, on the thirtieth of April, 1777, in Brunswick, Duchy of Brunswick (now Germany).... [tags: Biographies Gauss Mathematician Essays] | 1527 words (4.4 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 (2.3 pages) |
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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 (1.1 pages) |
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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]
:: 3 Works Cited :: 1 Sources Cited |
1359 words (3.9 pages) |
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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]
:: 2 Works Cited :: 1 Sources Cited |
1397 words (4 pages) |
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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]
:: 3 Works Cited :: 4 Sources Cited |
2309 words (6.6 pages) |
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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 (1.2 pages) |
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Fractals: A Mathematical Description of the World Around Us -
Fractals, a Mathematical Description of the World Around us In being characterized with fractional dimensions, Fractals are considered to be a new division of math and art, which is perhaps why the common man recognizes them as nice-looking and appealing pictures that are valuable as background on computer screens and art patterns. But they are more meaningfully understood by way of the recognition that many of nature’s physical systems and a lot of human works of art are not standard geometry forms.... [tags: Mathematics ]
:: 8 Works Cited |
1677 words (4.8 pages) |
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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 (3.3 pages) |
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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 (6.9 pages) |
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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 (5.3 pages) |
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The Four Color Theorem - Since hundred years ago, when people started to make maps to show distinct regions, such as states or countries, the four color theorem has been well known among many mapmakers. Because a mapmaker who can plan very well, will only need four colors to color the map that he makes. The basic rule of coloring a map is that if two regions are next to each other, the mapmaker has to use two different colors to color the adjacent regions. The reason is because when two regions share one boundary can never be the same color.... [tags: Math Research ] | 987 words (2.8 pages) |
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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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903 words (2.6 pages) |
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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 (2.3 pages) |
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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 (2.9 pages) |
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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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1881 words (5.4 pages) |
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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 (1 pages) |
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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 (3.1 pages) |
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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 (1.7 pages) |
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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 (1.6 pages) |
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Solution of the Cubic Equation - Solution of the Cubic Equation The history of any discipline is full of interesting stories and sidelines; however, the development of the formulas to solve cubic equations must be one of the most exciting within the math world. Whereas the method for quadratic equations has existed since the time of the Babylonians, a general solution for all cubic equations eluded mathematicians until the 1500s. Several individuals contributed different parts of the picture (formulas for various types of cubics) until the full solution was reached; these men included Scipione dal Ferro, Nicolo Tartaglia, Girolamo Cardan, and Lodovico Ferrari.... [tags: Math] | 975 words (2.8 pages) |
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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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2222 words (6.3 pages) |
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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 (2.5 pages) |
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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 (1.1 pages) |
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Johann Bernoulli -
On August 6, 1667, a famous Swiss mathematician was born in Basel, Switzerland. He was the tenth child of Nikolaus Bernoulli and Margaretha Schonauer (McElroy 31). They named him Johann Bernoulli, but he was also called Jean and John (Young 52). Bernoulli's family of wealthy merchants from Holland wanted him to follow a career in business. However, he failed as a business person, and followed his brother's pathway in mathematics and sciences (McElroy 31). In 1683, Bernoulli enrolled at the University of Basel (Young 52).... [tags: Biography]
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1341 words (3.8 pages) |
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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 (5.9 pages) |
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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 (4 pages) |
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pascal -
Blaise Pascal Blaise Pascal was a French mathematician, physicist, and religious philosopher. He had many important contributions to the mathematics and physics such as: the construction of mechanical calculators, considerations on probability theory, the study of fluids, concepts of the pressure and vacuum, and the Pascal Triangle. After a divine experience in 1654, he devoted himself to meditating and writing philosophy. His many discoveries in the field of mathematics have made him one of the most important mathematicians in history (Broome).... [tags: essays research papers fc]
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428 words (1.2 pages) |
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Triangulated Polygons -
From the beginning of time there have been many anomalies in humanity. With the advancement of techniques, tools, and knowledge, our understanding of the world aspires to clarify our curiosities. The most beneficial to factors throughout our history would include our knowledge of numbers. Numbers hold great possibilities and bring forth answers to the most complex systems of life. Our mathematics is incorporated into basic aspects of our daily lives, allowing us to unlock our potentials and give keys to uncover the hidden secrets in the universe.... [tags: Mathematics]
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1663 words (4.8 pages) |
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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 (2.6 pages) |
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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 (2 pages) |
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Drawing Conclusions: Ethics and Mathematics - When I was in my 1st year of high school, I decided to join the Debate Team of my school because it was one of the extra-curricular activities that really intrigued me. Being a new member, a lot of the methods the veterans of the team used in their speeches surprised me. Before, I thought that debate mostly involved insulting one’s opponent and making him seem stupid. However, I was proven very wrong as that not only fail to provide any substantial argument that would prove any point, but was also banned and could lead to a loss.... [tags: Logic] | 1302 words (3.7 pages) |
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Game Theory -
Game Theory Picture if you will a group of people making decisions. The decisions that are made do not have to be significant at all. They have to be just significant to the situation at hand. This concept is considered to mathematicians as Game Theory. Game Theory is broken down into tree different types of games. As stated by Thomas S. Ferguson of UCLA “There are three main mathematical models or forms used in the study of games, the extensive form, the strategic form and the coalitional form”.... [tags: Mathematics]
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1379 words (3.9 pages) |
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Mathematical and Musical Harmony -
For most people, mathematics is an unsolvable puzzle characterized by the impression of numbers and calculations taught in school. It is often associated with feelings of rejection and disinterest. To the general population mathematics appears to be to be strictly rational, abstract, cold and soulless. Music, however, is involved with emotion, with feelings, and with life. It exists in all daily routines. Everyone has sung a song, pressed a key on a piano, or blown into a flute, and therefore, in some sense, made music.... [tags: Mathematics]
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1296 words (3.7 pages) |
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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 Essays] | 1420 words (4.1 pages) |
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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 (5.5 pages) |
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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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2682 words (7.7 pages) |
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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 (3.4 pages) |
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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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1743 words (5 pages) |
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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: Free Essays] | 402 words (1.1 pages) |
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Circumference Formula -
... ￼ ( Concentric Circles: Concentric circles are when two or more circles centers coincide. Below is an example of concentric circles. ￼ Concentric circles have different radii but still have the same center so the circumference can still be found by￼. This proves that pi is the same for all size circles. Pi is irrational: Irrational numbers are numbers that cannot be expressed as a fraction. In 1761 Lambert discovered that that pi is irrational by a continued fraction. ￼ He later discovered that x is non-zero and a rational number, which makes the expression irrational.... [tags: Archimedes, Pi, diameter, circle, mathematics]
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975 words (2.8 pages) |
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Amalie Emmy Noether -
By the time Amalie Emmy Noether’s life ended, she had become one of the greatest mathematicians of her time. She was born on March 23rd 1882, in Erlangen, Germany and died on April 14, 1935, at the age of 53, in Bryn Mawr, Pennsylvania. She was the oldest out of the four kids that her mother, Ida Kaufmann, had. Amalie, known as Emmy, to most everybody she knew, was the only female child out of the bunch. Her dad Max Noether was also a famous mathematician. She had an unproblematic time in her early years of school, being smarter than the majority of the kids at an adolescent age gave her an advantage.... [tags: Biography]
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795 words (2.3 pages) |
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Alice in Wonderland and the Mathematics Involved -
... All they have are diagrams, lines, and symbols. The subject of math like the smile of the Cheshire Cat has started to disappear more and more through history. Math is becoming more and more without content just like when the body of the cat disappears and Alice is left to stare at a grin, rendering a simple variable that is left over. The absurdity of symbolic algebra is revealed in the chapter “Advice from a Caterpillar.” Alice has to eat the right amount of each side of the mushroom, the hookah-smoking caterpillar sits on, until she goes back to her original shape and size.... [tags: Lewis Carroll, rational, math, language, limits]
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1188 words (3.4 pages) |
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The Life of Nicolas Copernicus and His Heliocentric Theory - The Life of Nicolas Copernicus and His Heliocentric Theory Nicolas Copernicus died never knowing what a revolution he made in the scientific world. Mathematicians and scientist like Ptolemy, Newton, and Brahe supported his heliocentric theory. He was born in Poland on February 19th, 1473 the baby of four children. His father was Nicholas Copernicus Sr. died in 1483 when Copernicus was at the young age of ten. He and his sibling went to live with his Uncle Lucas Waltzenrode the bishop of Warmia in Germany.... [tags: Science, Biography, Nicolas Copernicus, Heliocentr] | 510 words (1.5 pages) |
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The Last Four Hundred Years - At the turn of the century, it was apparent that we, the human race, could no longer continue at the rate we were going. At several billion people, we were rapidly multiplying at an exponential rate. Scientists declared an international emergency because of drastic depleation of natural resources. It became obvious that in a few decades the continuation of the human way of life would be impossible if we did not find a solution to our problem. We needed more space for our species, and something with which to nourish them and keep them alive.... [tags: Creative Writing Essays] | 780 words (2.2 pages) |
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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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1049 words (3 pages) |
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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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1958 words (5.6 pages) |
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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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2302 words (6.6 pages) |
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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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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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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 (3.1 pages) |
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John Napier - John Napier- John Napier was born in Merchiston Tower in Scotland, 1550. He was known as the “Marvelous Merchiston”, a title received for his genius and imaginative vision in a number of fields. Napier studied briefly at St. Andrews University beginning at the age of 13. On his marriage in 1572, he was provided with an estate by his father, Sir Archibald Napier of Mechiston. He passed the remainder of his life as a land proprietor, devoting his free time to mathematics, invention, and theology.... [tags: essays research papers] | 382 words (1.1 pages) |
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Archimedes - Archimedes Archimedes was born in 287 BC in Syracuse, a Greek seaport colony in Sicily. Archimedes’ father was Phidias. He was an astronomer; this is all we know about his father and we learn this from Archimedes’ work, The Sandreckoner. Archimedes was educated in Alexandria, Egypt. Archimedes’ friend, Heracleides, wrote a biography about him, but this work was lost. Some authors report that he visited Egypt and there invented a tool known as Archimedes' screw. This is a pump, still used today in parts of the world.... [tags: Papers] | 332 words (0.9 pages) |
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Ontology of Mathematics -
An ontological theorist generally begins his discussion with a preconceived notion of what kind of thing an object will turn out to be. Instead, we will here begin with a Thomassonian approach to the ontology of mathematics. First, let us consider what happens when we rst come to determine a mathematical proposition (which I will use synonymously with 'mathematical entitty'). A mathematician does not feel as though he creates mathematical theories. Pythagoras can hardly be thought to have created the claim that a2 + b2 = c2.... [tags: Mathematics]
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1511 words (4.3 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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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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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 (5.6 pages) |
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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 (1.4 pages) |
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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 (3.5 pages) |
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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 (4 pages) |
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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 (1.6 pages) |
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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 (2.8 pages) |
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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 (3.5 pages) |
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Personal Statement - My best (and favorite) subject in school is Math. Ever since I was very little I have loved math, and worked very hard at it. When I do not fully understand topics I do extra problems to make sure that they become clear to me. I spend a lot of time working on math to make sure I understand the topics throughly. I have been in math clubs since 4th grade, and in 7th grade I represented my school at the MathCounts® competition where I won a two silver pins. I won the Virginia State Math Award in 7th grade, and this year I got an 800 in math on my SSAT.... [tags: Personal Experience] | 759 words (2.2 pages) |
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The Evolution of Differential Calculus -
Differential calculus is a subfield of Calculus that focuses on derivates, which are used to describe rates of change that are not constants. The term ‘differential’ comes from the process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, “We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).” Not only are derivatives used to determine how to maximize or minimize functions, but they are also used in determining how two related variables are changing over time in relation to each other.... [tags: Math]
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The Mathematical Genius of Sir Isaac Newton -
Sir Isaac Newton once said, “We build too many walls and not enough bridges.” Aside from his countless contributions to the worlds of math and science, this may be his most important quote because it is what he based his life on—building bridges of knowledge. Throughout his life he was devoted to expanding his and others knowledge past previously known realms. Often regarded of the father of calculus, Newton contributed many notable ideas and functions to the world through his creation of calculus and the various divisions of calculus.... [tags: Biography ]
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1448 words (4.1 pages) |
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The Word of Sir Isaac Newton -
Over the centuries, math has evolved in an astounding way. Since the beginning of time, there have been many mathematicians that has influenced and contributed to the math we know today. None compares to the work of Sir Isaac Newton. He was influential as a person, as well as in his work. Sir Isaac Newton was born on December 25, 1642 in Wools Thorpe, Lincolnshire. Shortly after his father’s death, Newton was born premature and was not expected to survive. After his father’s death, his mother got remarried to an ignorant man.... [tags: Biography ]
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1389 words (4 pages) |
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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 (1.8 pages) |
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Humanism the Gateway to Individualism - The greatest and most influential intellectual movement of Renaissance Italy was humanism. The humanists believed that the Greek and Latin classics contained all the lessons one needed to lead a moral and effective life and were the best models for a person to live by. They developed a new kind of classical scholarship, with which they corrected and tried to understand the works of the Greeks and Romans, which was important to them. Both the republic elites of Florence and Venice, and the ruling families of Milan, Ferrara, and Urbino hired humanists to teach their children classical morality and to write elegant, classical letters, histories, and propaganda.... [tags: renaissance, italian renaissance, humanist] | 515 words (1.5 pages) |
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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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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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1799 words (5.1 pages) |
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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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1566 words (4.5 pages) |
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