Modern Latin America Essay Example | Topics and Well Written Essays - 1250 words

Modern Latin America - Essay Example The colonial age in the Latin world should be considered as the region’s most influential years: the laws, norms, movements and conflicts, were significantly influential in deciding the character of the land today. It is known that the Spanish people were the only prominent power that fought over the Latin world to acquire their control (Keen & Haynes, 2012). This is why they have some much influence even to the Latin world of today. As Spain’s political power was merged in the second half of the 16th century, so was its capacity to control and regulate the colonial economy. Functioning in line with the mercantilistic strictures of that era, Spain endeavored to capitalize on ventures through exporting valuable products, such as silver and later other agricultural commodities and minerals (Keen & Haynes, 2012). They also supplied the new colonial market with already manufactured goods in order to create an encouraging balance of trade for the Latin world. Nevertheless, t he strongly regulated trading dominion, based in Seville, was not always capable of providing the colonies effectively, and; therefore the Latin world later saws its independence (Edwards, 2010). This was after a number of successful fights against the Spanish army. Therefore, what changes marked the transition to independence? This paper will discuss the above question especially noting the issues of the Church, race, political legitimacy, neocolonialism, imperialism, sovereignty and national identity. Some of the three primary factors that this paper considers being the landmark of Latin America’s independence are the Catholic Church (separation of the church from the state), imperialism (a free market, the extension of public education and industrialization) and political legitimacy. Church The Church in Latin America bore the marks of its colonial and Iberian past following independence. Spain Catholics adopted a custom of strong faith, a vital doctrinal of enduring piety and knowledge (Keen & Haynes, 2012). Adherence itself was a means of knowledge because, in the Mass, people learnt the scriptures, the doctrines, as well as the secrets of the Catholic faith. Portugal broadcasted an orthodox Catholicism, as well, but with a lower degree of adherence and a less doctrinal knowledge. Everywhere, religion and faith in Latin America was a religious conviction of the citizens and the Church went to receive the observance and the admiration of the mestizos, Indians and other popular people (Edwards, 2010). Supreme groups were less devoted, and the prominent respect for the Church in the 19th century was the apostasy of the influential people, not the neglect of the masses. The Iberian convention in religion favored a well known, honored and a state-ran Church (Keen & Haynes, 2012). But, following independence, the church opted to separate itself from the states. The influential, wealthy and privileged people of the Church were perceived by the new states as an opponent focus of adherence, a source of revenue and a substitute power. The risk of state control emerged in a new form after independence (Edwards, 2010). The Church, therefore, had to look to its own assets and these, in the early 19th century, were thinning. The church was granted an advantaged position because it was also prevalent in Europe at that time. The entire region was typified by great rates of Catholicism after independence. Catholicism rates reached as high as 90% out of the entire Latin American population. Following independe

Skoda Business Strategy Case Study Example | Topics and Well Written Essays - 2500 words

Skoda Business Strategy - Case Study Example The market picked up and so did profits. For the first time in Skoda history, the company had a wait list of customers in UK. The company registered continuing and ongoing growth in profits for the fifth year in a row. The Auto industry in the world has been going through an excessive change in performance and growth. In the last decade, the rise of China and Asia as manufacturing hubs changed the course of the auto industry in the world. The market in China and India, seem to be picking up and the Chinese market which has only 2% of its population holding four wheelers is already the size of the Japanese market. This makes it an highly probable growth market in the future (Jianxi Luo 2005). With many of the European and American car manufacturers finding their market dwindling and having surplus capacities have been reducing their manpower. They need to look at fresh and growing markets like that of China and Asia. With only a few players controlling the car market of the world, players like Skoda who has been gaining ground in Europe and in Asia need to be watched. The rising market for Skoda and the increasing profitability of the company makes it a company worthy of analysis (Tulder RV & Ruigr ok W Jun1997). Beating some of the seeded players in the European market is no easy task. But Skoda could do that successfully and looks forward to a major break in the profitability of the company in the current year. All this makes the company, the one that needs analysis of their policies and their strategies. This paper aims at analysing the company and its marketing strategy that has led it to the success that it is now facing. 4. Strategies of the Company Skoda was formed in the year 1894 in Czechoslovakia with the aim of making bicycles. Subsequently, they moved into manufacturing motor cycles and later cars, trucks and buses. During the early twentieth century, the company started producing agricultural and other farm equipments for the east European market. By now the cars of the company found their way to the markets in the Western Europe and there was quite some market for them in UK. But the UK market always had a joke about Skoda particularly the appearance of Skoda. Skoda did make inroads into the West European market and in America because of its ruggedness and reliability. Though technologically poor, the engine under its hood was powerful enough to keep running even in the worst conditions. That made the machine one of the most reliable ones in the market at that time. This saw the population of Skoda increasing in UK. After World War II, Skoda tied up with Volkswagen for technical collaboration. VW invested in the company and ensured that the basic design of the Skoda remained in the early days but soon replaced by the Volkswagen Design since the technology adopted by VW as superior. This brought another marketing strategy that had to break through the already crowded market in Western Europe and in USA as much as in the rest of the world (William Kimberley Jun 2001). The perception of Skoda as an ugly duckling was slowly changing but still persisted. 'Oh! It's a Skoda'. But then it was as usual thought to be efficient and reliable. Skoda now had to make use of some bold advertising and marketing strategy

Explain Anselms Ontological Argument Essay Example for Free

Explain Anselms Ontological Argument Essay Anselm wanted to prove the existence of God, so he proposed the ontological argument. The ontological argument is deductive, and uses a priori reasoning. This means that it starts with a statement that is known to be true solely through definition (God is the greatest conceivable being) and develops the implications of this statement in order to reach a reasonable conclusion. The deductive reasoning allows him to simply showing what the definition means. Hence, Anselm states that God exists in the mind, even the mind of those who deny His existence. However he points out that it is greater to exist in reality and in the mind than in the mind alone. Take for example; a pile of notes worth  £1000. If it exists in the mind it is merely a pleasant thought, however, if it exists in reality it can be spent and is greater. Since God is the greatest conceivable being, He must exist in reality and in the mind, because to think otherwise involves contradiction of the theory, which you agree with. Anselm also says that God could possibly be a contingent God, who is dependent on something else for existence. If this was true God would not be worthy of worship and would not be the greatest conceivable being. A necessary God, one whose non existence is impossible, is greater than a contingent God whose non existence is possible. God has no creator, so to have to have someone else to depend on for existence, means they are not God. Therefore, we must accept that god is also necessary, as well as existant in reality, because to think otherwise involves a contradiction. The reason for people being able to deny the existence of God is due to them knowing the definition of the word God, not the existence of God.

Meditation In Zen Buddhism Philosophy Essay

Meditation In Zen Buddhism Philosophy Essay Meditation is the foundation of Zen Buddhism. Zen literally means to meditate. Meditation, in Zen, is the path and the goal. The goal is to meditate. Like all religions, Zen Buddhism has split into sections. Zen has two schools of thought, the gradual and the sudden approach to enlightenment. In the gradual school, there is only one way to practice Zen meditation, which is seated meditation, called zazen. Zazen can be performed in several different ways, but the positions have no spiritual significance. The positions are mainly to create comfort, stability, and ability to breathe through the diaphragm properly. The sudden school believes enlightenment could potentially occur instantly. They use koans, mondos, and turning phrases to help the practitioner gain more insight, and hopefully be enlightened. Koans, mondos, and turning phrases are irrational dialogues or statements that practitioners contemplate upon. The main topics to point out when discussing meditation in Zen Buddhism ar e the goals of their meditation, the gradual school of thought, and the sudden school of thought. In Zen, the path of meditation is the goal. It is similar to riding your bicycle just to ride your bicycle. Through mediation, Zen Buddhists do not attempt to do anything, but to be in the moment. The Vietnamese Zen teacher, Thich Nhat Hanh, says, We practice so that each moment of our life becomes real life. There is no goal in Zen, but to focus on ones being, moment by moment. While practicing meditation, one may also find other benefits, like better health and a more relaxed state of my mind. Unlike many sects of Buddhism, as well as many other religions, Zen Buddhists do not have scriptures to which they should study, but they may do so if they choose. Zen Buddhists focus primarily on one simple act, which is meditation. They believe that achievement of the Buddhahood comes from silence. Zen has two popular sections, gradual and sudden. They both are means to enlightenment, but have two different points of view. In the gradual school of Zen, there is only one technique of meditation, which is called zazen. Zazen literally means sitting meditation. Zazens motto is: To be a Buddha is to sit like a Buddha. That is, while sitting, sit completely. Be aware of the stillness of everything while enjoying not having to do anything but be in the moment. Although there are no doctrines or disciplines in Zen, there are many instructions for meditation postures. In Zen culture, there was less of a difference between body, breath, and mind than in the west. Zen practitioners believe if one aligns their spine correctly, fold their legs properly, sit properly, and keep still; they can achieve stillness of the mind. Much of the stillness of the mind in Zen is believed to be achieved through the correct posture of the body. Many of the Zen postures come from ancient Indian yogic positions developed to increase alignment and awareness. Although they come from yogic postures, they have no divine meaning them; they are only intended to increase comfort, stability, and the ability to breathe well. In Zen, it is believed that awakening must penetrate every cell of the body, so they must engage the body as well as the mind when meditating. Zazen is typically done in one way with several variations. The most effective way of seated meditation is done is with ones legs crossed and spine aligned straight up and curved, giving a pyramid shape to ones posture. It is usually done on the floor, with a soft mat and pillow to sit on to raise the body a little so that ones knees can touch the ground. With ones knees touching the ground, it creates three points of contact with the ground to give the practitioner a sturdy base. The easiest form of zazen is the Burmese position. In the Burmese position, one has their legs crossed, and their feet flat on the floor. In this position it is very easy to keep ones back straight because putting ones feet on the floor forces the practitioner to keep his back curved, which is an essential part of zazen. Two other positions are the half lotus and the full lotus. Both positions are very similar, but the half lotus requires less flexibility, and is easier for most people. To perform the half lotus, one foot placed over the opposite thigh, and the other foot is placed under the opposite leg. The full lotus position is when both legs are put on both thighs. This position is more recommended because it gives the practitioner much more balance. There are also two other zazen positions which are commonly used. The first position is the sieza position. The sieza position is kneeling, with your buttocks on both feet. You can sit on either a pillow, or your bare legs. You can also use a sieza bench to kneel on. The second position is the chair position. The bench keeps ones back straight, and takes the weight off of ones feet. The other position is to simply sit on a chair with ones feet on the floor, arching the back. It is important to keep ones back straight while meditating so that one can breathe with the diaphragm properly. A good sitting posture as well as good hand position allows the body to give uninhibited deep breaths. While doing Zen meditation, one should use the Dhyani mudra hand position. The Dhyani mudra is a way to position ones hands so that they can take deep breaths from their diaphragm. To do so, the practitioner will place both hands on top of one another, with their palms facing up. Their knuckles should be on top of one another as well, with their thumbs touching gently together. Breathing through the diaphragm creates deep, slow breaths, which is quite useful when practicing zazen. Breathing is not only useful while meditating, but it is useful in all aspects of our health. Andrew Weil M.D., an author and physician said, Improper breathing is a common cause of ill health. If I had to limit my advice on healthier living to just one tip, it would be simply to learn how to breathe correctly. Theres no single more powerful or simpler daily practice to further your health and well-being than breath-work. ~ Andrew Weil, M.D. The sudden school of Zen, which believes in sudden enlightenment, has koans as a focal point of meditation. In The Complete Idiots Guide to Buddhism, Gary Gach says that koans are seemingly illogical riddles, like Two hands come together in a clap. What is the sound of one hand? A koan is not a riddle. It doesnt call for a solution (its not a math puzzle with an equation waiting in an answer book); rather, it is a personal breakthrough with a flash of enlightenment. In other words, it is a statement or conversation that cannot be understood by rational thinking; it can only be understood by intuition. Zen Buddhists believe that scriptures will lead scholars to misinterpretations of the original meanings, which is why Zen masters made Koans. Koans go beyond words. They attempt to go beyond the boundaries of intellect and language, and find awakening or enlightenment. Zen master Hakuin, author of the koan, What is the sound of one hand? has said, Whats true meditation? Its to make it all coughing, swallowing, gestures, motion, stillness, words, action, good and evil, success and shame, win and lose, right and wrong into one single koan. Although Zen Buddhists are not against words, they try to limit the amount of description to leave the interpreting to the practitioner who is attempting to gain insight. The primary beginning of using koans in Zen Buddhism originated from Hui Neng, a poor man who gathered and sold firewood for a living. He achieved enlightenment suddenly while he overheard a man reciting the Diamond Sutra, a scripture on emptiness and wisdom which requires great insight to understand. When he overheard the man say, Awaken your mind without fixing it anywhere, he was enlightened on the spot. Koans are meant to be contemplated until they are realized. While one meditates is the optimal time to think about them, but they can also be taken home to contemplate. According to The Complete Idiots Guide to Buddhism, there are about 400 indexed koans and about 1700 in all. There are so many koans because they deal with particular parts of the Way of enlightenment. Many of the koans, such as Hakuins koan, What is the sound of one hand? are designed to take the practitioner past the normal self into Buddha mind. There are also koan related Zen dialogues called mondos. Mondos are question-and-answer banter between people. They are similar to koans because they have the same non-sense questions and statements. An example of a mondo is in the Milindapanha, which reads, King Milinda said to learned monk Nagasena, Im going to ask you a question. Can you answer it? Nagasena replied, Please, ask your question. The King: Ive already asked. Nagasena: Ive already answered. The King: What did you answer? Nagasena: What did you ask? The King: I asked nothing. Nagasena: I answered nothing Also similar to koans and mondos, the sudden school of Zen also used turning phrases to help promote enlightenment and understanding. Examples of a turning phrases are, Not one, not two, Chop wood: carry water, and Form is emptiness; emptiness is form. These are all mottos that are used to help the practitioner gain more insight, and hopefully find sudden enlightenment. Being the foundation of Zen Buddhism, meditation is the main aspect of the religion. Zen essentially is meditation. In Zen, the path is the goal. It is like riding your bicycle simply to ride your bicycle. Zen Buddhism has split into two schools of thought, the gradual and the sudden approach to enlightenment. In the gradual school, there is only one way to practice Zen meditation, which is seated meditation, called zazen. Zazen can be performed in several different ways, but the positions have no significance other than comfort and stability. Breathing is an important part of meditation as well. The sudden school believes enlightenment could potentially occur instantly. They use koans, mondos, and turning phrases to help the practitioner gain more insight, and hopefully be enlightened. Koans, mondos, and turning phrases are irrational dialogues or statements that practitioners contemplate upon. The main topics to point out when discussing meditation in Zen Buddhism are the goals of their meditation, the gradual school of thought, and the sudden school of thought. Gach, Gary. The Complete Idiots Guide to Buddhism. 3rd. New York City, New York: Alpha Books, 2009. 183-200. Print. Saint-Hilaire, J.Barthelemy. The Buddha and His Religion. 1st edition. London: New York E.P. Dutton and Company, 1914. 267-87. Print. Zazen. DharmaRain.org. Dharma Rain Zen Center, 2003. Web. 20 Sep 2010. . Zazen Posture. DharmaRain.org. Dharma Rain Zen Center, 2003. Web. 20 Sep 2010. . Zazen breathing techniques. DharmaRain.org. Dharma Rain Zen Center, 2003. Web. 20 Sep 2010. . Zen Meditation Instructions. mro.org. Mountains and Rivers Order, 2010. Web. 20 Sep 2010. . Phelan, Josho Pat. Zazen Posture. intrex.net. Josho Pat Phelan, 1997. Web. 20 Sep 2010. . About Zen Meditation. Zazen.rutgers.edu. N.P., 04/21/2010. Web. 20 Sep 2010. . Phillips, Fred. A Primer on Zazen. omcl.ogi.edu. Fred Phillips, 1998. Web. 20 Sep 2010. . Breathing and Medicine. oxygengenesis.org. Oxygen Genesis Institute, 2003. Web. 20 Sep 2010. .

Future of Nuclear Energy in America Essay -- The Future Role of Nuclea

Foreword Nuclear Energy has many proponents and much opposition. Many of the groups that oppose nuclear power have legitimate concerns, mainly with the dangers of nuclear material in relation with human health concerns and environmental troubles that are risked by allowing nuclear power plants to increase in number. Yet, many of these opposition groups have made outspoken and radical claims about the â€Å"hidden† motives of why nuclear power is promoted and subsidized by our federal government. For example, The Nuclear Information and Resource Service claim that the federal government has the intention of committing genocide against Native Americans because uranium mining is predominantly done on reservations. Another cry out by nuclear power opponents is the constant reliving of the few nuclear mishaps that occurred decades ago, at Chernobyl or Three Mile Island. No doubt, past accidents have happened worldwide and are important reminders to not play around with nuclear material, b ut technology has improved as well, a fact opponents fail to consider. Many of these organizations feel that other sources should be used to supply America’s energy needs. These types of statements tag many opponents to nuclear energy as misinformed, out of touch with scientific facts, or just closed minded to the whole concept of nuclear power. On the other hand, the proponents of nuclear energy like President Bush see it as cheap, and environmentally friendly. As a result, President Bush passed the Comprehensive Energy Bill in 2005 that would increase production of all types of energy, including nuclear, by giving subsidies and tax breaks to nuclear power producers. Keeping safe America’s capabilities for generating electric power by way of nuclear e... ... Upper Saddle River, NJ: Pearson Prentice Hall FEMA (2006). Are You Ready? Retrieved November 12, 2012 from http://www.fema.gov/areyouready International Nuclear Safety Center (2008). Maps of Nuclear Power Reactors Retrieved November 12, 2012 http://www.insc.anl.gov/pwrmaps/map/united_states.php NIRS (2008). Top 11 Reasons to Oppose Nuclear Power Retrieved November 14, 2012 from http://www.nirs.org/nukerelapse/background/ Parenti, Christian (2008). What Nuclear Renaissance? Retrieved November 10, 2012 from http://www.thenation.com/doc/20080512/parenti Uranium Producers of America (2008). Promoting the Viability of Domestic Uranium Retrieved November 7, 2012 http://www.uraniumproducersamerica.com/supply.html U. S. Department of Energy (2008). Safe handling and disposal of spent nuclear fuel Retrieved November 18, 2012 http://www.ocrwm.doe.gov/

Meniscal Injuries :: essays research papers

The meniscus is one of the most commonly injured structures in the knee. Meniscal injuries can occur in any age group, but causes are somewhat different for each age group. In younger people, the meniscus is fairly tough and rubbery, and tears usually occur as a result of a fairly forceful twisting injury. In the younger age group, meniscal tears are more likely to be caused by athletic activity (Sutton, 1999).   Ã‚  Ã‚  Ã‚  Ã‚  In older people, the meniscus grows weaker with age. The tissue that makes up the meniscus becomes degenerative and much easier to tear. Meniscal injuries in older people occur as a result of a fairly minor injury, even from the up and down motion of squatting. Degenerative tears of the meniscus are commonly seen as a part of the overall condition of osteoarthritis of the knee in the older population. In many cases, there is no one associated injury to the knee that leads to meniscal tears (Sutton, 1999).   Ã‚  Ã‚  Ã‚  Ã‚  In order to understand how the menisci can be injured, you must understand the basic anatomy of the menisci and why they are important. The menisci are two oval (semilunar) fibrocartilages that deepen the articular facets of the tibia and cushion any stresses placed on the knee joint. They enhance the total stability of the knee, assist in the control of normal knee motion, and provide shock absorption against compression forces between the tibia and the femur (Booher, 2000). Articular cartilage covers the ends of the bones that make up the joint. The articular cartilage surface is a tough, very slick material that allows the surfaces to slide against one another without damage to either surface. This ability of the meniscus to spread out the force on the joint surfaces as we walk is important because it protects the articular cartilage from excessive forces occurring in any one area on the joint surface, leading to degeneration over time (Sutton, 1999).   Ã‚  Ã‚  Ã‚  Ã‚  Blood is supplied to each meniscus by the medial genicular artery. Each meniscus can be divided into three circumferential zones: the red-red zone is the outer or peripheral one third and has a good vascular supply; the red-white zone is the middle one third and has a minimal blood supply; and the white-white zone on the inner one third is avascular (Arnheim,1997).   Ã‚  Ã‚  Ã‚  Ã‚  The medial meniscus is larger and more oval or C-shaped in the outline than the lateral meniscus. The medial cartilage is also more firmly fixed to the tibia and the capsule than the lateral meniscus; as a result, it is much more frequently injured than the lateral cartilage.

Women in Mathematics

Women in Mathematics Every human is created with a gift of some sort. Whether it is an athletic ability, a wonderful singing voice, or an ability to relate to other individuals, every one has a special gifting. For many women in history, their ability was deciphering and understanding the intricacies of math. Although various cultures discouraged women mathematicians, these women were able to re-define the standards for women in this field of study. Hypatia of Alexandria was born in Roman Egypt and was the daughter of a teacher of mathematics, Theon of Alexandria.Hypatia studied with her father as well as with many other mathematicians. When she was older, she taught at the Neoplatonist school of philosophy. She wrote on mathematics, philosophy, as well as anatomy. Her studies covered the motion of the planets, conic sections, and number theory, which is â€Å"one of the oldest branches of pure mathematics, and one of the largest. It concerns questions about numbers, typically meani ng whole numbers as well as rational numbers. Although little information about Hypatia survives, it has been discovered that she was a very popular lecturer that drew students from various locations.She is known for her invention of the plane astrolabe, which is an elaborate inclinometer with the ability to locate and predict the locations of the sun, moon, planets, and stars and the graduated brass hydrometer which was used to determine the relative density or specific gravity of liquids. Hypatia's teachings were not accepted by the Christian bishop, Cyril due to her pagan beliefs. His public dislike towards her is said to have been the cause of the attack by a mob that lead to her death.Most of her work was destroyed when the library of Alexandria was burned by the Arab conquerors, however, her studies have been discovered through the work of others who quoted her as well as through letters. I believe Hypatia was one of the first inspirational women mathematicians. Despite the da nger she knew she was facing, she chose to do what she enjoyed. Elena Cornaro Piscopia was born in 1646 in Venice into the family of a public official. Her father provided the means of education to his children.Elena was recognized as a child prodigy when she was seven years old by a parish priest. She then began to study theology, mathematics, Latin, Greek, and music. Clerics, royals, and scientists came to Venice to speak with her due to the widespread attraction of her achievements. As she grew older, Elena was the first woman to apply in theology at a university in Italy. She was also the first woman to earn a doctoral degree. After receiving her master's and doctorate degrees in philosophy, she went on to become a lecturer in mathematics at the University of Padua until her death in 1684.Although she is not famous for discovering any particular math problem, she was very influential in her time and inspired many other women to pursue mathematics. Maria Agnesi was born in Italy in 1718 and was the daughter of Pietro Agnesi, a wealthy nobleman and professor of mathematics. Maria, like Elena, was recognized as a child prodigy and was taught five languages. Her father invited his colleagues over for Maria to present speeches to. By the age of 13 Maria was able to debate in French, Spanish, and Latin.Although Maria did not enjoy giving the speeches, she continued until the age of twenty. That year, Maria made a compilation of the speeches she had given over the years and published them in Latin. The title of the compilations in English is â€Å"Philosophical Propositions. † The topics included celestial mechanics, which refers to the branch of astronomy that deals with the motions of celestial objects and applies to the field of physics, Isaac Newton's Gravitation Theory that states that any two objects in the universe exert gravitational attraction on each other, and elasticity.Maria's father married twice after the death of her mother, causing her to be the eldest of 21 children. She was required to provide education to her siblings. Maria wrote a mathematics textbook over the course of ten years which was titled† Instituzioni Analitiche† which was published in 1748 in two volumes. The first volume contained information on algebra, arithmetic, trigonometry, analytic geometry, and calculus. The second covered infinite series and differential equations. Due to her ability to understand many languages, Maria was able to bring together various ideas from mathematicians of all cultures.The name â€Å"witch of Agnesi† refers to a mathematical problem of finding the equation for a certain bell-shaped curve which was named after her by English mathematician John Colson. When Maria's father passed in 1752, Maria discontinued the education she had been providing to her siblings and devoted her life to helping the less fortunate. I found Maria's story to be very admirable due to the extreme selflessness she possessed. Al though she desired to further her mathematical studies, she spent a large portion of her life educating her younger siblings, and spent the remaining time devoted to the poor.Sophie Germain was born in France in 1776 and was the daughter of Ambroise-Francois Germain, who was a wealthy middle class silk merchant and a French politician. During Sophie's childhood, the French Revolution was occurring, so Sophie was kept isolated from the chaos by staying in her home with her two sisters. She chose to pass the time by reading through the books in her father's extended library. Sophie was particularly fond of the story of Archimedes of Syracuse who was killed while reading geometry. To see a man so captivated by a subject influenced her to pursue math.Sophie taught mathematics to herself in her native language as well as in Latin and Greek so as to be able to gain understanding from a wider range of mathematic books. Her family was not particularly fond of her studying, but she was so en thralled by mathematics that she studied at night until her family accepted what she loved. In eighteenth century France, women were not normally accepted into universities, however, Sophie was able to borrow the notes from mathematic professors and was able to send comments about the work to the professors by hiding behind the pseudonym of a male, â€Å"M. e Blanc. † Sophie Germain studied number theory and Chladni figures, which is a technique that shows the various modes of vibration of a rigid surface. Her study of these figures was the foundation to the mathematics used today when constructing skyscrapers. Her study of number theory lead to partial progress on Fermat's Last Theorem, which states that if x, y, z, and n are integers then xn + yn = zn cannot be solved for any n greater than 2. Sophie was able to show that for prime exponents less than 100, there could be no solutions relatively prime to the exponent of that number.After this work, she was accepted into sess ions at the Institut de France and became the first woman with this privilege. She died in 1831 of breast cancer. I believe Sophie is inspirational due to her extreme intelligence by finding an addition to Fermat's two-century's old theorem. Had she not been diligent in pursuing mathematics although it was inconvenient, she would have never been presented the opportunity to impart such knowledge into history. Sonya Kovalevskaya was drawn to mathematics in a rather peculiar way.As a young child, born in 1850 in Russia, Sonya was mesmerized by the lecture notes of Mikhail Ostrogradsky on differential and integral calculus that made up the wallpaper of her family's estate. Sonya's father did not allow her to study mathematics abroad, and Russia did not allow women to attend the universities, thus Sonya was forced to find an alternative means of furthering her education. She entered into a marriage of convenience with Vladimir Kovalensky, and left Russia with him and her sister. Sonya w ent on to Heidelberg where she was granted permission to study at the university.Two years later, she went on to study mathematics with Karl Weierstrass who assisted her in pursuing a degree in mathematics. Sonya's dissertation on partial differential equations, which refers to an equation that contains unknown multivariable functions and their partial derivatives, resulted in receiving a doctorate without having attended any class at the university and is today called the Cauch-Kovelevskaya Theorem. Sonya was also awarded with the Prix Bordin from the French Academie Royale des Sciences for her research over how Saturn's rings rotated, now referred to as the Kovelevskaya top.She also was appointed to a chair at the Swedish Academy of Sciences- making her the first woman to receive this title. I believe her story is especially inspirational due to her ground-breaking achievements including titles and positions that had never been awarded to women before. All of these women pioneers of mathematics teach a very valuable lesson. The culture during the time of these five particular women did not accept the studies that these mathematicians longed to be educated in.Their extreme ability, or gifting, of solving problems and assembling theorems was not only widely unaccepted, it was also widely unappreciated. Even after the accomplishments of these women, their work is often undermined. In the midst of opposing forces telling them they should not, or even could not go into the field of mathematics, they believed in their ability enough to pursue it whole-heartedly and in return, they have left a legacy and have inspired women to fight what is culturally accepted to follow what is in your heart, and the things for which you have a particular talent in.Citations Lewis, Jone J. â€Å"Women in Mathematics  History. † About. com Women's History. N. p. , n. d. Web. 10 Mar. 2013. Lewis, Jone J. â€Å"Hypatia Of Alexandria. † About. com Women's History. N. p. , n. d. Web. 11 Mar. 2013. â€Å"11: Number Theory. † 11: Number Theory. Ed. Dave Rusin. N. p. , 02 July 2006. Web. 12 Mar. 2013. Swift, Amanda. â€Å"Sophie Germain. † Sophie Germain. N. p. , Apr. 1995. Web. 12 Mar. 2013. â€Å"Partial Differential Equation. † Wikipedia. Wikimedia Foundation, 14 Mar. 2013. Web. 12 Mar. 2013.