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European History/Scientific Revolution and Enlightenment

The Age of Science of the 1600s and the Enlightenment of the 1700s, also dubbed the Age of Enlightenment, introduced countless new concepts to European society. These ideas continue to permeate modern society. Many modern institutions have much of their foundations in the ideals of these times.

An Era of Enlightened Rulers
A new form of government began to replace absolutism across the continent. Whilst monarchs were reluctant to give up their powers, many also recognized that their states could potentially benefit from the spread of Enlightenment ideas. The most prominent of these rulers were Frederick II the Great Hohenzollern of Prussia, Joseph II Hapsburg of Austria, and Catherine II the Great Romanov of Russia.

In order to understand the actions of the European monarchs of this period, it is important to understand their key beliefs. Enlightened despots rejected the concept of absolutism and the divine right to rule. They justified their position based on their usefulness to the state. These rulers based their decisions upon their reason, and they stressed religious toleration and the importance of education. They enacted codified, uniform laws, repressed local authority, nobles, and the church, and often acted impulsively and instilled change at an incredibly fast rate.

Catherine the Great 1762-1796
Catherine the Great came to power because Peter III failed to bear a male heir to the throne and was killed.

Her enlightened reforms include:

 * Restrictions on torture
 * Religious toleration
 * Education for girls
 * 1767 Legislative Commission, which reported to her on the state of the Russian people
 * Trained and educated her grandson Alexander I so that he could progress in society because of his merit rather than his blood line

She was friends with Diderot, Rousseau, Voltaire. However, Catherine also took a number of decidedly unenlightened actions. In 1773 she violently suppressed Pugachev's Rebellion, a massive peasant rebellion against the degradation of the serfs. She conceded more power to the nobles and eliminated state service. Also, serfdom became equivalent to slavery under her.

Foreign Policy
Catherine combated the Ottoman Empire. In 1774, Russia gained a warm water port on the Black Sea.

Frederick II the Great 1740-1786
Frederick II Hohenzollern of Prussia declared himself "The First Servant of the State," believing that it was his duty to serve the state and do well for his nation. He extended education to all classes, and established a professional bureaucracy and civil servants. He created a uniform judicial system and abolished torture. During his tenure, Prussia innovated agriculture by using potatoes and turnips to replenish the soil. Also, Frederick established religious freedom in Prussia.

Joseph II Habsburg 1765-1790
Joseph II Habsburg (also spelled as Hapsburg) of Austria could be considered perhaps the greatest enlightened ruler, and he was purely enlightened, working solely for the good of his country. He was anti-feudalism, anti-church, and anti-nobility. He famously stated, "The state should provide the greatest good for the greatest number." He created equal punishment and taxation regardless of class, complete freedom of the press, toleration of all religions, and civil rights for Jews. Under Joseph II a uniform law code was established, and in 1781 he abolished serfdom and in 1789 ordered the General School Ordinance, which required compulsory education for Austrian children. However, Joseph failed because he angered people by making changes far too swiftly, and even the serfs weren't satisfied with their abrupt freedom.

England
As a result of the Glorious Revolution of 1688, England already had a Parliament and thus the concept of enlightened ruler did not take hold in England.

France
After Louis XIV the "Sun King," Louis XV took control from 1715 until 1774. Like his predecessor, he was an absolute monarch who enacted mercantilism. As a result of the influence and control of absolutism in France, France also did not encounter an enlightened ruler. In order to consummate an alliance between his nation and Austria, Maria Theresa of Austria married her daughter, Marie Antoinette, to Louis XV's heir, Louis XVI. Louis XV recognized that the fragile institutions of absolutism were crumbling in France, and he famously stated, "Après moi, le déluge", or "After me, the flood."

War of Austrian Succession
The war of Austrian Succession of 1740 to 1748 pitted Austria, England, and the Dutch against Prussia, France, and Spain. Upon Maria Theresa's acquisition of the Austrian throne, Frederick the Great of Prussia attacked Silesia, and war broke out. In 1748 peace came at the Treaty of Aix la Chapelle. The treaty preserved the balance of power and the status quo ante bellum. Austria survived but lost Silesia, which began "German Dualism" or the fight between Prussia and Austria over who would dominate and eventually unite Germany.

The Seven Years War
The peace in 1748 was recognized as temporary by all, and in 1756 Austria and France allied in what was known as the Diplomatic Revolution. The reversal of the traditional France versus Austria situation occurred as a result of both nation's fear of a rising, militant Prussia. To consummate the marriage, Louis XVI married Marie Antionette. The Seven Years War engaged Austria, France, Russia, Spain, Sweden, and Saxony against Prussia and England. The purpose of the war was to annihilate Prussia, and took place at a number of fronts: in Europe, in America (where American citizens know it as the French and Indian War) and in India. At the Peace of Paris in 1763, the war concluded, and Prussia retained all of its territory, including Silesia. France ceded Canada to Britain and the North American interior to Spain, and removed its armies from India. It did, however, get to keep its West Indies colonies.

At this point, Great Britain became the supreme naval power and it began its domination of India.

The Partitioning of Poland
Poland was first partitioned on February 19, 1772, between Russia, Austria, and Prussia, in an agreement between them to gain more land and power in Europe. Poland was able to be partitioned because it was weak and had no ability to stop the larger and more powerful nations. The balance of power was not taken into consideration by France or England because the partitioning did not upset the great powers of Europe. The second partition involved Russia and Prussia taking additional land from Poland. After the second partition, which occurred on January 21, 1792, the majority of their remaining land was lost to Prussia and Russia. The third partition of Poland took place in October of 1795, giving Russia, Prussia, and Austria the remainder of the Polish land. Russia ended up with 120,000 square kilometres, Austria 47,000 square kilometres, and Prussia 55,000 square kilometres. This took Poland off of the map.

Science and Technology
The Enlightenment was notable for its scientific revolution, which changed the manner in which the people of Europe approached both science and technology. This was the direct result of philosophic enquiry into the ways in which science should be approached. The most important figures in this change of thinking were Descartes and Bacon.

The philosopher René Descartes presented the notion of deductive reasoning - that is, to start with a premise and to then discard evidence that doesn't support the premise. However, Sir Francis Bacon introduced a new method of thought. He suggested that instead of using deductive reasoning, people should use inductive reasoning - in other words, they should gather evidence and then reach a conclusion based on the evidence. This line of thought also became known as the Scientific Method.

Changes in Astronomy
The Scientific Revolution began with discoveries in astronomy, most importantly dealing with the concept of a solar system. These discoveries generated controversy, and some were forced by church authorities to recant their theories.

Pre-Revolution: Aristotle and Ptolemy
The geocentric (earth-centred) view of the universe had been taught since the days of Aristotle. Ptomely's "Almagest" (c.2nd century CE) was the standard text used to teach students astronomy and remained so for hundreds of years. Ptolemy's theories are a mixture of science and religion and to modern readers may come across as unusual though it must always be borne in mind that Ptolemy was building upon the works of earlier astronomers. Surprisingly a Greek philosopher called Aristarchus (310 BC - ca.230 BC) suggested that the earth moved around the sun and though this was common knowledge amongst all who studied astronomy it would be over a thousand years before he was proved right. The early christian church (c.4th century CE) adopted the Ptolemaic system since it was in accord with biblical teaching. A universe without the earth at its center would negate divine purpose and Ptolemy's idea of the spheres in harmony strengthened the creationist argument. The Enlightenment, which is also referred to as the Age of Reason, was a period when European philosophers emphasized the use of reason as the best method for learning the truth.

Nicolaus Copernicus (1473-1543)
During the Renaissance, study of astronomy at universities began. Regiomontanus and Nicolas of Cusa developed new advances in mathematics and methods of calculation.

Copernicus, although a devout Christian, doubted whether the views held by Aristotle and Ptolemy were completely correct. Using mathematics and visual observations with only the naked eye, he developed the Heliocentric, or Copernican, Theory of the Universe, stating that the Earth revolves around the sun.

Tycho Brahe (1546-1601)
Tycho Brahe created a mass of scientific data on astronomy during his lifetime; although he made no major contributions to science, he laid the groundwork for Kepler's discoveries.

Johannes Kepler (1571-1630)
Kepler was a student of Brahe. He used Brahe's body of data to write Kepler's Three Laws of Planetary Motion, most significantly noting that planets' orbits are elliptical instead of circular.

Galileo Galilei (1564-1642)
Galileo is generally given credit for invention of the telescope; although the device itself is not of Galileo's design, he was the first to use it for astronomy. With this tool, he proved the Copernican Theory of the Universe.

Galileo spread news of his work through letters to friends and colleagues. Although the Church forced him to recant his ideas and spend the rest of his life under house arrest, his works had already been published and could not be disregarded.

Isaac Newton (1642-1727)
Newton is often considered the greatest scientific mind in history. His Principia Mathematica (1687) includes Newton's Law of Gravity, an incredibly ground-breaking study. Newton's work destroyed the old notion of an Earth-centred universe.

Newton also had a great influence outside of science. For example, he was to become the hero of Thomas Jefferson.

Andreas Vesalius (1514-1564)
Vesalius studied human cadavers, a practice forbidden by church doctrine. His writing The Structure of the Human Body in 1543 renewed and modernized the study of the human body.

William Harvey (1578-1657)
William Harvey wrote On the Movement of the Heart and Blood in 1628, on the circulatory system. He was a doctor and an anatomist.

Society and Culture
As a result of new learning from the Scientific Revolution, the world was less of a mystical place, as natural phenomena became increasingly explainable by science. According to Enlightened philosophers:
 * The universe is a fully tangible place governed by natural rather than supernatural forces.
 * Rigorous application of the scientific method can answer fundamental questions in all areas of inquiry.
 * The human race can be educated to achieve nearly infinite improvement.

Perhaps most importantly, though, Enlightened philosophers stressed that people are all equal because all of us possess reason.

Precursors
There were a number of precursors to the Enlightenment. One of the most important was the Age of Science of the 1600s, which presented inductive thinking, and using evidence to reach a conclusion. The ideas of Locke and Hobbes and the notion of the social contract challenged traditional thinking and also contributed to the Enlightenment. Scepticism, which questioned traditional authority and ideas, contributed as well. Finally, the idea of moral relativism arose - assailing people for judging people who are different from themselves.

The Legacy of the Enlightenment
The Enlightenment began in France, as a result of its well-developed town and city life, as well as its large middle class that wanted to learn the ideas. The Enlightenment promoted the use of one's reason, rather than accepting tradition. It rejected the traditional attitudes of the Catholic Church. Many "philosophers," or people who thought about subjects in an enquiring, inductive manner, became prominent. Salons were hosted by upper-middle class women who wanted to discuss topics of the day, such as politics.

The Enlightenment stressed that we are products of experience and environment, and that we should have the utmost confidence in the unlimited capacity of the human mind. It stressed the unlimited progress of humans, and the ideas of atheism and deism became especially prominent. Adam Smith's concept of free market capitalism sent European economics in a new direction. Enlightened despots such as Catherine the Great and Joseph II replaced absolute monarchs and used their states as agents of progress. Education and literacy expanded vastly, and people recognized the importance of intellectual freedoms of speech, thought, and press.

Changing Views of Childhood and Education
Prior to the Enlightenment, the dominant idea of childhood was that children were just smaller versions of adults, but this began to change as Enlightenment ideals emphasized the importance of childhood and the growing middle class allowed more time and resources to be invested in a child’s growth. Enlightenment thinkers advocated for the idea of childhood as a developmental stage. One example of this is in John Locke’s  tabula rasa, which argued that knowledge and behavior comes from experience. Another voice on the topic was Jean-Jacques Rousseau who argued that childhood should be a pure and protected time before adulthood in which children should be free to learn, hands-on, about the world around them, in his novel Emile.

Together,  Scientific Revolution thought and Enlightenment ideas bred an increased emphasis on education. John Amos Comenius, a seventeenth century Czech educator often considered the father of modern education, influenced many Enlightenment thinkers with his model of a comprehensive and universal education system. In the late 18th century, Prussia became the first nation to create a mandatory universal education system. This system had compulsory education for children ages six to thirteen, and included studies of folktales and history, all taught in a common language, which increased nationalist ideals. During the French Revolution, Nicolas de Condorcet created a system of public schools for young men, and in 1802, Napoleon created a comprehensive school system which is the model for the country’s current system.

Conflict with the Church
Although the ideas of the Enlightenment clashed with Church dogma, it was mostly not a movement against the Church. Most Enlightened philosophers considered themselves to be followers of deism, believing that God created an utterly flawless universe and left it alone, some describing God as the "divine clockmaker."

Thomas Hobbes (1588-1679)

 * dies before the enlightenment
 * English Revolution shapes his political outlook
 * Leviathan (1651) - life is "nasty, brutish, and short" - people are naturally bad and need a strong government to control them.
 * may be considered to be the father of the enlightenment: because of all the opposition he inspired.

John Locke (1632-1704)
Born in 1632 amidst one of the most tumultuous eras of mass rebellion and political unrest, British philosopher John Locke is often called the father of liberalism. Locke  introduced Western society to progressive reform through his works. Locke’s beliefs in natural law, which argued for equality amongst all men, egalitarian theories of land ownership, and separation of church and state, heavily influenced not only the French Revolution but also political movements centuries after his time. Locke began his career in Oxford as a scholar and tutor and did not enter the philosophical sphere until he was appointed to the Stuart Court by Anthony Ashley Cooper, the Earl of Shaftesbury. Alarmed by the monarchy’s promotion of slavery and nobility, Locke published The Two Treatises of Government, which argued against inherited status and the rights of the monarchy. Another one of Locke’s prominent works, An Essay Concerning Human Understanding, explores the boundaries and limitations of the human mind. By questioning beliefs  accepted as common knowledge, John Locke gave prominence to empiricism and liberalism in a society formerly structured on religious values.
 * specifically refuted Hobbes
 * humanity is only governed by laws of nature, man has right to life, liberty, and property
 * there is a natural social contract that binds the people and their government together; the people have a responsibility to their government, and their government likewise has a responsibility to its people
 * Two Treatises on Civil Government justified supremacy of Parliament
 * Essay Concerning Human Understanding (1690) - Tabula rasa - human progress is in the hands of society

Voltaire (1694-1776)

 * stressed religious tolerance

Baron de Montesquieu (1689-1755)

 * Spirit of the Laws - checks and balances on government, no one group having sole power

David Hume (1711-1776)
The Enlightenment sparked a period of theorizing about how to approach the world with rationality and knowledge. David Hume (1711-1776), known for his philosophical theory of Skepticism, was one of the main figures in the Scottish Enlightenment. Skepticism was the idea that all knowledge should be approached with doubt. Skepticism was more radical than both the theories of Deism and atheism; it undermined both religious authority and Enlightenment ideas. Hume was skeptical of not only rationality and knowledge but also of miracles and God’s existence. In his An Enquiry Concerning Human Understanding (1758), he used logic to argue against religious miracles, undermining traditional religious texts. Hume’s goal was not to deny belief but to deny the certainty of belief. Traditional Christianity was based on proof of the divinity of Christ and miracles from the gospels, but Hume claimed that miracles were violations of the laws of nature. Evidence of a miracle, Hume reasoned, would always be outweighed by the evidence of nature. Human reason, he argued, was not enough to prove the existence of God. He claimed, “Our evidence for the truth of the Christian religion is less than our evidence for the truth of our senses.” Hume’s work and ideas have become important for the process of skepticism in scientific inquiry and research.

Jean-Jacques Rousseau (1712-1778)

 * social contract
 * "general will" - government acts for the majority

Olympe de Gouges (1748 - 1793)

Olympe de Gouges was an early feminist thinker and French revolutionary who is often overlooked in Enlightenment history. Born Marie Gouze in southwest France to peasant parents but claimed noble ancestry, she moved to Paris in 1770 and began frequenting salons like the that of Sophia de Condorcet. Throughout her time in Paris, she wrote over sixty political essays, plays, and pamphlets covering what would come to be known as “human rights.” Her writing career culminated with the publication of The Declaration of the Rights of Woman and of Female Citizen. She wrote this essay in direct response to Marquis de La Fayette’s The Declaration of the Rights of Man and of the Citizen, which discussed the freedoms that should be afforded to all men; but, this document left out women and their importance in society. In the preamble, de Gouges writes, “the sex that is superior in beauty as in courage, needed in maternal sufferings, recognizes and declares, in the presence and under the auspices of the Supreme Being, the following rights of woman and the citizens,” which establishes the importance of women and argues that in some aspects women are not only equal to men but are superior. She goes on to list the rights that women should have but are being denied, including the right to bare arms, the right to vote, and right to an education. Ultimately, it was not de Gouges’ writings on women’s rights that led to her death. She was beheaded on November 3, 1793 after refusing to denounce her statement against the execution of King Louis XVI. Her legacy on women’s rights influenced the suffragettes, the feminist movement of the 1970s, and modern-day women’s rights.

Zera Yacob (1599 - 1692)
While European philosophes like John Locke and Voltaire are credited for spreading Enlightenment ideas, an Ethiopian philosopher named Zera Yacob espoused these principles decades earlier.

Yacob was born in 1599 outside the Ethiopian capital city of Axum. As a boy, he excelled in school and later became a professor. However, when a Portuguese Jesuit converted King Susenyos to Catholicism, Susenyos established Catholicism as the national religion and suppressed freedom of thought and speech.

When Yacob advocated that no religion is superior to any other, he was forced to flee the area under the threat of prosecution. Living alone in a cave for two years, he delved into philosophy. Once he was able to return to society in 1667, he wrote Hatäta, which was a compilation of his ideas. In this groundbreaking text, he criticized Ethiopian people for following tradition instead of thinking independently, denounced slavery and declared that all people are equal, and approached religion with a more agnostic, open-minded mentality than was common in the 17th century.

Finally, he considered women’s perspectives in his philosophy. For example, he criticized the Law of Moses that declared the menstrual cycle impure because it impeded the life and love of a woman. He later married a poor servant woman not for her looks but for her intelligence, and he truly considered her a peer. In contrast, philosophe John Locke declared all men were equal but also invested in the slave trade. In this way, Yacob spread and lived his enlightenment principles decades before many philosophes, but he often gets overlooked as an Enlightenment figure.

Rococo Art

The Rococo Art movement of the 1700s emphasized elaborate, decorative, frivolous, and aristocratic art. Often depicted were playful intrigue, love, and courtship. The use of wispy brush strokes and pastels was common in Rococo Art. Rococo Art is especially associated with the reign of Louis XV Bourbon in France. The French artist Boucher painted for Madame Pompadour, the mistress of Louis XV. The most famous paintings of Boucher include Diana Leaving her Bath and Pastorale, a painting of a wealthy couple under a tree.

Historia de Europa/La Ilustración Lịch sử châu Âu/Cách mạng Khoa học và Thời kỳ Khai sáng


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European History/Revolution in France

The First French Revolution of 1789 was a pivotal moment in French and European history. It marks the rise of the Third Estate, consisting of the merchant, artisan, and working poor. They revolted after centuries of paying high tax to the French monarchy. The revolution centered around anger over centuries of overtaxation and underrepresentation influenced by democratic ideals of the Enlightenment. Following the Seven Years’ War, this anger peaked due to a tax raise, massive droughts, and the rule of King Louis XVI as well as the lavish spender Queen Marie Antoinette. The people of France in 1789 were further influenced by an angered media’s reporting of the Queen’s lavish spending of public money and her many love affairs. The 5th of October, 1789 marked the start of the Revolution, when around 7,000 market women—and men dressed as women—marched on the Palace of Versailles, demanding the Queen's head and the King's immediate return to Paris. They started the march to protest the high cost of bread caused by famine and overtaxation. This march was a key event in the revolution. The women were successful in bringing the Royal family back to Paris and thus closer to the control of the leaders of the revolution. This was the first link in a chain of events that would lead to a new democratic government in France. That government would prove to be unstable, leading to a “Reign of Terror” which led to an increasingly unstable France that would ultimately lead to the reign of the dictator Napoleon. Though the revolution failed, its ideals lived on, influencing Western political, economic, and social thought for centuries to come.

Reasons for the French Revolution
The French Revolution was the result of the rejection of ideals of premodern Europe. Countless ideas from the Enlightenment contributed to the French Revolution, including John Locke's Social Contract, which states that government is given power by the consent of the governed, so when the government fails in its duties, the people have the obligation to overthrow said government. It was also influenced by Rousseau's ideas of the general will. These ideas became common as the French government failed to respond to growing internal issues in France. The Enlightenment also critiqued religion, especially Catholicism. Philosophers such as Voltaire and Rousseau directly attacked the church and the divine right theory that Louis XVI of France used to justify his position. These ideas spread quickly in Salons and Coffeehouses, where philosophers shared ideas, and in encyclopedias, invented by Rousseau, which disseminated revolutionary ideals to many citizens.

Additionally, a harsh winter had resulted in no harvest and the lack of food, especially bread, causing massive food shortages across France. The Crown also waged constant wars and expensive revolutions, such as the global 7 Years War and American Revolution, which were both unpopular and expensive for the French People. The lavish spending habits of the government and king, led to debt and a disconnect from the struggles of the French People. Moreover, this spending, combined with some existing systemic financial issues led to the financial crisis in France. One of the most prominent of these issues was the fact that the nobles were tax-exempt, and the nobles resisted any attempt by Louis to tax them. French tax collectors also were corrupt, which led to tremendous wastes of money. As a result, Louis called the Estates General, for assistance and advice to resolve the financial crisis

The Estates General was the French equivalent of the English Parliament. It was unlike Parliament however, as it had been shut down by the king and stripped of almost all its powers, except for taxation. The Estates General consisted of three estates: the first estate was made up of clergymen, the second estate was made up of nobles, and the third estate was made up of commoners, who represented at least 95% of the populace. Each Estate was afforded 1 vote, leading to the first two estates outvoting the Third to protect their interests from taxation. The third estate, angry over their disproportionate representation and their inability to act according to their needs, rebelled, and declared itself the National Assembly. In response King Louis barred the Third Estate from the Estates General leading to the delegates of the third estate taking the Oath of the Tennis Court, at an indoor tennis court nearby. They swore allegiance to the French nation and drew up a list of grievances (cahiers de doléances) against the king. They aimed to democratically represent the will of the people and give the people a constitution to prevent the abuses seen during the reign of Louis the 14th.

Storming of the Bastille

On July 14, 1789, egged on by the signers of the Tennis Court Oath, a revolting Paris mob stormed the Bastille. While only seven prisoners were housed behind its walls, none of whom could be considered political in any way, this event was essential because it symbolized that the people were rising of the people against the tyranny of absolutism. The fall of the Bastille was also the first time, but certainly not the last, during the Revolution that popular mobs would rise up and take action outside of the legislature. These later risings, known in French as journees, would prove to be both extremely influential on public opinion and a cause for major hand-wringing on the part of the legislature, who did not want to risk a massive popular revolution as opposed to the controlled "bourgeois" revolution.

Women’s March on Versailles
The Women’s March on Versailles, which occurred in October 1789, saw nearly 7,000 working-class women stride fourteen miles from Paris, France to the Palace of Versailles in the pouring rain. They chanted “Bread! Bread!” as they stormed the palace gates, and eventually pushed past the 20,000 royal guards protecting the palace. They killed two guards and forced King Louis XVI to agree to the following terms: distribute all of the bread that the palace hoarded, accept the Declaration of the Rights of Man and of the Citizen, and accompany the women back to Paris to see how citizens lived. From this moment forward, King Louis XVI's reign came to an end, and he became a prisoner of the revolution.

New Governments
The revolutionaries in France established a new government in order to accomplish what they desired.

National Assembly 1789-1791
The members of the National Assembly came from the members of the third estate in the Estates General. These members tended to be from the upper middle class, or bourgeois. The factions that began to form were the moderate Girondins, who pushed for a constitutional monarchy. The other faction was often referred to as "Jacobins" since they frequently met in Jacobin clubs to discuss revolutionary ideals.

The lower class third estate, or the rest of the citizenry, led the fighting arm of the revolution and the National Assembly at this time. They did not, however, take part in the government. The urban middle class led the storming on the Bastille and the march on Versailles. .

Efforts to Remake Society
The National Assembly took a number of actions to remake society. They established social equality, and signed the Declaration of Rights of Man and Citizen, which was a social contract. It provided for freedom of religion, taxation of equality, legal equality, and freedom of press and expression. Due to the lack of women’s representation in this document, Olympe de Gouges wrote the Declaration of the Rights of Women which argued for women’s rights in the new society. The National Assembly mostly ignored this document and wrote a constitution that established a constitutional monarchy with a parliament which excluded women. The parliament was to be run by the bourgeois, who were considered "active" citizens, while the rest of the citizens were considered "passive" citizens and would not be allowed to take part in government. People in government were to progress based upon merit. Finally, the National Assembly established the Civil Constitution of the Clergy (1790), which clergymen would eventually be required to swear an oath to in 1791. In addition to nationalizing church property, the Civil Constitution also abolished religious vows and turned all Church clerics (including monks and nuns) into civil servants who received their pay and assignments not from Rome, but from Paris. While this was initially well received by many Frenchmen who applauded the "bringing home" of the church, the subsequent punitive measures taken against clergy who did not swear the oath (also known as the refractory clergy) would be a cause of great resentment in the Western provinces, and was one of the causes behind the Vendee rising in 1793.

Legislative Assembly 1791-1792
The provisions of the National Assembly established what was supposed to be a permanent constitutional monarchy, the Legislative Assembly, with Louis XVI as the monarch. However, the Legislative Assembly failed very quickly for a number of reasons. The lower third estate felt abandoned by the bourgeois politically. In addition, the Legislative Assembly failed to fix the food and unemployment problems. As a result, the working men of France, or the sans-culottes, rose against the Legislative Assembly.

War with Austria and Prussia
Emigres, or nobility that had fled France during the Revolution, in Austria wanted the Austrian government to crush the Revolution. Other nations feared revolution in their own countries. Austria signed the Declaration of Pillnitz (1791), which stated that if the other powers attack France, so would Austria. The French interpreted this as a virtual declaration of war.

The Brunswick Manifesto (1792) by Prussia stated that the Prussians would punish the citizens of Paris if they did anything to harm Louis XVI or Marie Antionette. Prussia and Austria allied for the balance of power, in order to weaken France. The draining of war on the newly formed government also contributed to its downfall.

Convention 1792-1795

The convention was an emergency republic with universal male suffrage. The leading body of the convention was the Committee of Public Safety, who worked to suppress dissent and protect the revolution. The committee was composed of twelve members, of whom the dominant individual was Maximilien de Robespierre. The leadership of the Convention split into two factions: the Montagnards (or "Mountain"), who was more radical and included Robespierre, and the Girondin, which was more middle class.

The convention had a number of issues to address. First, and perhaps most importantly, they were actively engaged in war with Prussia and Austria. They instituted the first draft, called the levee en masse, and a nationalist feeling rose among troops. In 1794, the French army invaded Austria and was successful.

In addition, the Convention needed to remake society. Members instituted "dechristianization," which was essentially the purging of Christians in France.

The convention also needed to address the food problem, and established the "General Maximum" that controlled bread prices and wages.

Finally, the Convention needed to stop the counter-revolution and write a new constitution. During a period known as "The Terror," Robespierre and the Committee of Public Safety utilized the newly invented guillotine to execute tens of thousands of counter-revolutionaries. The Convention successfully wrote a new constitution, establishing a government known as the Directory as a permanent republic.

On 27 July ("9 Thermidor" in the Revolutionary Calendar) 1794, Robespierre himself was arrested, and was executed the next day. The resulting "Thermidorian Reaction" was a response to France's swing to the left, during which the government briefly went to the right, and finally back to the center. The Jacobins and other Montagnards were replaced with the more moderate Girondins (Bourgeois), and many Montagnard members were executed.

Directory 1795-1799
The Directory was the first constitutional republic, which had an executive body of five directors, as well as a bicameral legislative body consisting of the Council of Ancients and the Council of 500. In 1797, the first free elections were held, and the people of France astonished members of the Directory by electing a majority of royalists to the legislature. Unwilling to risk the reversal of everything achieved since 1789, left-wing members of the legislature, combined with support from the military, purged the Directory of rightist members in the coup of 18 Fructidor, which established a dictatorship controlled by left-wing Directors. However, people grew fearful of a possible return of the Terror, thus, when Napoleon Bonaparte and Abbe Sieyes launched the coup of 18 Brumaire to end the Directory and instead establish the consulate, there was little opposition.

The Haitian Revolution 1791-1804
Following the French Revolution (1789-1799), a new revolution was staged by enslaved plantation workers in the French colony known as Saint-Domingue. Inspired by the quest for liberty, equality, and fraternity in France and fed up with the violent treatment of their people, the enslaved population in St. Domingue sought a new life for themselves. Saint-Domingue was one of the world’s most prosperous colonies; however, it relied on plantations exploiting slave labor to fuel its economy. Through the use of chattel slavery, the colony grew and exported cane sugar at a rapid rate, providing extensive wealth for plantation owners. The colony made money through the cultivation of sugar, however, African slaves, who accounted for 89% of the population in St. Domingue, were worked to death in horrific living conditions, often being tortured as a way of punishment.

In 1791, a violent slave rebellion spread through the colony led by Toussaint L’Ouverture (1743-1803). L’Ouverture, a black man born a slave who would eventually be freed, shared similar rage towards slave owners, which propelled him to take command of the revolt. L’Ouverture trained his troops using guerilla warfare, a military tactic used by small populations against larger regular armies. The enslaved population took control and burned plantations as an act of defiance, then divided the plantations into small plots of land for African families. In 1794, The French National Convention declared slaves free, and L’Ouverture was appointed governor of St. Domingue by the previous French governor. For the following decade, the French army, headed by Napolean Bonaparte, would attempt to re-establish slavery in the colony but were unsuccessful. Eventually, in 1804, St. Domingue achieved independence from France and became known as Haiti. The Haitian Revolution started due to the political, social, and economic outbreaks in France, and it is a central outcome to the story of  the French Revolution. The French Revolution inspired many revolutions, rebellions, and revolts across the globe. In fact, historian Laurent Dubois writes, “Haiti, not the US or France, was where the assertion of human rights reached its defining climax in the Age of Revolution

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: European History/Revolution in France


text: User:Exabyte~enwikibooks

title: User:Exabyte~enwikibooks


text:
User:Margebtk

ENCUENTRE EL POLINOMIO DE GRADO 2 CUYA GRÁFICA PASA A TRAVÉS DE LOS PUNTOS DADOS:

2. (1,14), (2,22), (3,32)

 * $$\ a_0+a_1+a_2 = 14$$
 * $$\ a_0+2a_1+4a_2 = 22$$
 * $$\ a_0+3a_1+9a_2 = 32$$

$$\begin{pmatrix} 1 & 1 & 1 & 14 \\ 1 & 2 & 4 & 22 \\ 1 & 3 & 9 & 32\end{pmatrix}$$ $$\approx$$ $$f_2-f_1 \quad y\quad f_3-f_1$$

$$\begin{pmatrix} 1 & 1 & 1 & 14 \\ 0 & 1 & 3 & 8 \\ 0 & 2 & 8 & 18\end{pmatrix}$$ $$\approx$$ $$f_3-2f_2\quad y\quad f_1-f_2$$

$$\begin{pmatrix} 1 & 0 & -2 & 6 \\ 0 & 1 & 3 & 8 \\ 0 & 0 & 2 & 2\end{pmatrix}$$ $$\approx$$ $$\frac {1}{2}f_3$$

$$\begin{pmatrix} 1 & 0 & -2 & 6 \\ 0 & 1 & 3 & 8 \\ 0 & 0 & 1 & 1\end{pmatrix}$$ $$\approx$$ $$f_1+2f_3\quad y\quad f_2-3f_3$$

$$\begin{pmatrix} 1 & 0 & 0 & 8 \\ 0 & 1 & 0 & 5 \\ 0 & 0 & 1 & 1\end{pmatrix}$$

 * $$\ a_0+0+0 = 8$$
 * $$\ a_1+0 = 5$$
 * $$\ a_2 = 1$$

 * $$\ y = x^2+5x+8$$

4. (1,8) (3,26) (5,60)

 * $$\ a_0+a_1+a_2 = 8$$
 * $$\ a_0+3a_1+9a_2 = 26$$
 * $$\ a_0+5a_1+25a_2 = 60$$

$$\begin{pmatrix} 1 & 1 & 1 & 8 \\ 1 & 3 & 9 & 26 \\ 1 & 5 & 25 & 60\end{pmatrix}$$ $$\approx$$ $$f_2-f_1\quad y\quad f_3-f_1$$

$$\begin{pmatrix} 1 & 1 & 1 & 8 \\ 0 & 2 & 8 & 18 \\ 0 & 4 & 24 & 52\end{pmatrix}$$ $$\approx$$ $$\frac {1}{3}f_3\quad y\quad \frac {1}{2}f_2$$

$$\begin{pmatrix} 1 & 1 & 1 & 8 \\ 0 & 1 & 4 & 9 \\ 0 & 1 & 6 & 13\end{pmatrix}$$ $$\approx$$ $$f_3-f_2$$

$$\begin{pmatrix} 1 & 1 & 1 & 8 \\ 0 & 1 & 4 & 9 \\ 0 & 0 & 2 & 4\end{pmatrix}$$ $$\approx$$ $$\frac {1}{2}f_3\quad y\quad f_1-f_2$$

$$\begin{pmatrix} 1 & 0 & -3 & -1 \\ 0 & 1 & 4 & 9 \\ 0 & 0 & 1 & 2\end{pmatrix}$$ $$\approx$$ $$f_1+3f_3\quad y\quad f_2-4f_3$$

$$\begin{pmatrix} 1 & 0 & 0 & 5 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 2\end{pmatrix}$$

 * $$\ a_0 =5 $$
 * $$\ a_1 = 1$$
 * $$\ a_2 = 2$$

 * $$\ y = 2x^2+x+5$$

cuando x=2

 * $$\ y = (2)2^2+2+5$$
 * $$\ y = 5+2+2(4)$$
 * $$\ y = 2+8+5$$
 * $$\ y = 15$$

6. (1,-3), (2,-1), (3,9), (4,33)

 * $$\ a_0+a_1+a_2+a_3 = -3$$
 * $$\ a_0+2a_1+4a_2+8a_3 = -1$$
 * $$\ a_0+3a_1+9a_2+27a_3 = 9$$
 * $$\ a_0+4a_1+16a_2+64a_3 = -3$$

$$\begin{pmatrix} 1 & 1 & 1 & 1 & -3 \\ 1 & 2 & 4 & 8 & -1 \\ 1 & 3 & 9 & 27 & 9 \\ 1 & 4 & 16 & 64 & 33\end{pmatrix}$$ $$\approx$$ $$f_2-f_1 \quad y\quad f_3-f_1 \quad y\quad f_4 - f_1$$

$$\begin{pmatrix} 1 & 1 & 1 & 1 & -3 \\ 0 & 1 & 3 & 7 & 2 \\ 0 & 2 & 8 & 26 & 12 \\ 0 & 3 & 15 & 63 & 36\end{pmatrix}$$ $$\approx$$ $$\frac{1}{2}f_3 \quad y\quad \frac {1}{3}f_4$$

$$\begin{pmatrix} 1 & 1 & 1 & 1 & -3 \\ 0 & 1 & 3 & 7 & 2 \\ 0 & 1 & 4 & 13 & 6 \\ 0 & 1 & 5 & 21 & 12\end{pmatrix}$$ $$\approx$$ $$f_1-f_2 \quad y\quad f_3-f_2 \quad y\quad f_4 - f_2$$

$$\begin{pmatrix} 1 & 0 & -2 & -6 & -5 \\ 0 & 1 & 3 & 7 & 2 \\ 0 & 0 & 1 & 6 & 4 \\ 0 & 0 & 2 & 14 & 10\end{pmatrix}$$ $$\approx$$ $$\frac{1}{2}f_4$$

$$\begin{pmatrix} 1 & 0 & -2 & -6 & -5 \\ 0 & 1 & 3 & 7 & 2 \\ 0 & 0 & 1 & 6 & 4 \\ 0 & 0 & 1 & 7 & 5\end{pmatrix}$$ $$\approx$$ $$f_1+2f_3 \quad y\quad f_2-3f_3 \quad y\quad f_4 - f_3$$

$$\begin{pmatrix} 1 & 0 & 0 & 6 & 3 \\ 0 & 1 & 0 & -11 & -10 \\ 0 & 0 & 1 & 6 & 4 \\ 0 & 0 & 0 & 1 & 1\end{pmatrix}$$ $$\approx$$ $$f_1-6f_4 \quad y\quad f_2+11f_4 \quad y\quad f_3 - 6f_4$$

$$\begin{pmatrix} 1 & 0 & 0 & 0 & -3 \\ 0 & 1 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 & -2 \\ 0 & 0 & 0 & 1 & 1\end{pmatrix}$$

 * $$\ a_0 =-3 $$
 * $$\ a_1 =1 $$
 * $$\ a_2 =-2 $$
 * $$\ a_3 =1 $$

 * $$\ y = 2x^2+x+5$$

8.

 * $$\ union B: I_1+ I_2= I_3$$
 * $$\ union D: I_3= I_1+I_3$$

 * $$\ I_1+ I_2- I_3= 0$$
 * $$\ I_1+ 2I_3)= 9$$
 * $$\ I_1- 3(I_2)= 9- 17 $$
 * $$\ I_1- 3I_2 = -8 $$

$$\begin{pmatrix} 1 & 1 & -1 & 0 \\ 1 & 0 & 2 & 9 \\ 1 & -3 & 0 & -8\end{pmatrix}$$ $$\approx$$ $$f_2-f_1 \quad y\quad f_3-f_1 $$

$$\begin{pmatrix} 1 & 1 & -1 & 0 \\ 0 & -1 & 3 & 9 \\ 0 & -4 & 1 & -8\end{pmatrix}$$ $$\approx$$ $$f_1+f_2 \quad y\quad f_3-4f_2 $$

$$\begin{pmatrix} 1 & 0 & 2 & 9 \\ 0 & -1 & 3 & 9 \\ 0 & 0 & -11 & -44\end{pmatrix}$$ $$\approx$$ $$-f_2\quad y\quad -\frac {1}{11} $$

$$\begin{pmatrix} 1 & 0 & 2 & 9 \\ 0 & 1 & -3 & -9 \\ 0 & 0 & 1 & 4\end{pmatrix}$$ $$\approx$$ $$f_1-2f_3 \quad y\quad f_2+3f_3 $$

$$\begin{pmatrix} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 3 \\ 0 & 0 & 1 & 4\end{pmatrix}$$

 * $$\ I_1 = 1$$
 * $$\ I_2 = 3$$
 * $$\ I_3 = 4 $$

10.

 * $$\ union B: I_1+ I_2= I_3$$
 * $$\ union D: I_3= I_1+I_2$$

 * $$\ I_1+ I_2- I_3= 0$$
 * $$\ 2I_1+ 2I_3= 4$$
 * $$\ I_2+ 2I_3 + 3I_2= 2 $$

 * $$\ I_1+ I_2- I_3= 0$$
 * $$\ 2I_1+ 2I_3= 4$$
 * $$\ 4I_2+ 2I_3 = 2 $$

$$\begin{pmatrix} 1 & 1 & -1 & 0 \\ 2 & 0 & 2 & 4 \\ 0 & 4 & 2 & 2\end{pmatrix}$$ $$\approx$$ $$\ f_2-2f_1 \quad y\quad \frac {1}{2}f_3 $$

$$\begin{pmatrix} 1 & 1 & -1 & 0 \\ 0 & -2 & 4 & 4 \\ 0 & 2 & 1 & 1\end{pmatrix}$$ $$\approx$$ $$\ -\frac {1}{2}f_2 $$

$$\begin{pmatrix} 1 & 1 & -1 & 0 \\ 0 & 1 & -2 & -2 \\ 0 & 2 & 1 & 1\end{pmatrix}$$ $$\approx$$ $$\ f_1-2f_2 \quad y\quad f_3-2f_2 $$

$$\begin{pmatrix} 1 & 0 & 1 & 2 \\ 0 & 1 & -2 & -2 \\ 0 & 0 & 5 & 5\end{pmatrix}$$ $$\approx$$ $$\ \frac{1}{5}f_3 $$

$$\begin{pmatrix} 1 & 0 & 1 & 2 \\ 0 & 1 & -2 & -2 \\ 0 & 0 & 1 & 1\end{pmatrix}$$ $$\approx$$ $$\ f_2+2f_3 $$

$$\begin{pmatrix} 1 & 0 & 1 & 2 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1\end{pmatrix}$$

 * $$\ I_1 = 1$$
 * $$\ I_2 = 0$$
 * $$\ I_3 = 1 $$

16.
 * $$\ A. 100 + 200 = x_1 + x_4$$
 * $$\ B. x_1 + x_2 = 100 + 50$$
 * $$\ C. 50 + 50 = x_3 + x_2$$
 * $$\ D. x_3 + x_4 = 100 + 50 $$

 * $$\ A. x_1 + x_4 = 300$$
 * $$\ B. x_1 + x_2 = 150$$
 * $$\ C. x_2 + x_3 = 100$$
 * $$\ D. x_3 + x_4 = 150 $$

$$\begin{pmatrix} 1 & 0 & 0 & 1 & 300 \\ 1 & 1 & 0 & 0 & 250 \\ 0 & 1 & 1 & 0 & 100 \\ 0 & 0 & 1 & 1 & 150\end{pmatrix}$$ $$\approx$$ $$\ f_2-f_1 $$

$$\begin{pmatrix} 1 & 0 & 0 & 1 & 300 \\ 0 & 1 & 0 & -1 & -50 \\ 0 & 1 & 1 & 0 & 100 \\ 0 & 0 & 1 & 1 & 150\end{pmatrix}$$ $$\approx$$ $$\ f_3-f_2 $$

$$\begin{pmatrix} 1 & 0 & 0 & 1 & 300 \\ 0 & 1 & 0 & -1 & -50 \\ 0 & 0 & 1 & 1 & 150 \\ 0 & 0 & 1 & 1 & 150\end{pmatrix}$$ $$\approx$$ $$\ f_4-f_3 $$

$$\begin{pmatrix} 1 & 0 & 0 & 1 & 300 \\ 0 & 1 & 0 & -1 & -50 \\ 0 & 0 & 1 & 1 & 150 \\ 0 & 0 & 0 & 0 & 0\end{pmatrix}$$

 * $$\ x_1 + x_4 = 300$$
 * $$\ x_2 - x_4 = -50$$
 * $$\ x_3 + x_4 = 150$$

 * $$\ x_1 = 300 - x_4$$
 * $$\ x_2 = x_4 - 50$$
 * $$\ x_3 = 150 - x_4$$

Flujo AB

 * $$\ x_1 = 300 - x_4$$
 * $$\ x_4 = 300 - x_1$$

 * $$\ 300 - x_1 \ge 0$$
 * $$\ 300 \ge x_1$$

La afluencia mínima es de 300 entre A y B

17.

 * $$\ A. x_4 + 100 = x_1$$
 * $$\ B. x_1 = 200 + x_2$$
 * $$\ C. 150 + x_2 = x_3$$
 * $$\ D. x_3 = 50 + x_4$$

 * $$\ x_1 - x_4 = 100$$
 * $$\ x_1 - x_2 = 200$$
 * $$\ x_3 - x_2 = 150$$
 * $$\ x_3 - x_4 = 50$$

$$\begin{pmatrix} 1 & 0 & 0 & -1 & 100 \\ 1 & -1 & 0 & 0 & 200 \\ 0 & -1 & 1 & 0 & 150 \\ 0 & 0 & 1 & -1 & 50\end{pmatrix}$$ $$\approx$$ $$\ f_2-f_1 $$

$$\begin{pmatrix} 1 & 0 & 0 & -1 & 100 \\ 0 & -1 & 0 & 1 & 100 \\ 0 & -1 & 1 & 0 & 150 \\ 0 & 0 & 1 & -1 & 50\end{pmatrix}$$ $$\approx$$ $$\ -f_2 $$

$$\begin{pmatrix} 1 & 0 & 0 & -1 & 100 \\ 0 & 1 & 0 & -1 & -100 \\ 0 & -1 & 1 & 0 & 150 \\ 0 & 0 & 1 & -1 & 50\end{pmatrix}$$ $$\approx$$ $$\ f_3 + f_2 $$

$$\begin{pmatrix} 1 & 0 & 0 & -1 & 100 \\ 0 & 1 & 0 & -1 & -100 \\ 0 & 0 & 1 & -1 & 50 \\ 0 & 0 & 1 & -1 & 50\end{pmatrix}$$ $$\approx$$ $$\ f_4 - f_3 $$

$$\begin{pmatrix} 1 & 0 & 0 & -1 & 100 \\ 0 & 1 & 0 & -1 & -100 \\ 0 & 0 & 1 & -1 & 50 \\ 0 & 0 & 0 & 0 & 0\end{pmatrix}$$

 * $$\ x_1 - x_4 = 100$$
 * $$\ x_2 - x_4 = -100$$
 * $$\ x_3 - x_4 = 50$$

 * $$\ - x_4 = -100 - x_2$$
 * $$\ x_4 = 100 + x_2$$
 * $$\ x_2 + 100 \ge 0 $$
 * $$\ x_2 \ge -100 $$

 * No es posible porque no puede haber una vía negativa

Ejercicio de la matriz de entradas y salidas

a) La cantidad de electricidad que se consume en la producción del valor de $1 de acero

 * $$\ 1 / 0.25 $$
 * $$\ 4$$

b) La cantidad de acero que se consume en la producción del valor de $1 en la industria automotriz

 * $$\ 1 / 0.40 $$
 * $$\ 2.5 $$

c) El mayor consumo de carbón

Es 0.3 que equivale a la electricidad

d) El mayor consumo de electricidad

Es 0.25 que equivale al acero

e) La industria de la que depende más la industria automotriz

Es 0.10 que equivale al acero y 0.10 que equivale a la química

7.

$$ A = \begin{pmatrix} 0.20 & 0.40 \\ 0.50 & 0.10 \end{pmatrix}$$ $$ X = \begin{pmatrix} 8 \\ 10 \end{pmatrix}$$

 * $$ X = AX + D$$
 * $$ X - AX = D$$

$$ D = \begin{pmatrix} 8 \\ 10 \end{pmatrix} - \begin{pmatrix} 0.20 & 0.40 \\ 0.50 & 0.10 \end{pmatrix}\begin{pmatrix} 8 \\ 10 \end{pmatrix}$$

$$ D = \begin{pmatrix} 8 \\ 10 \end{pmatrix} - \begin{pmatrix} 9.6 \\ 5 \end{pmatrix}$$

$$ D = \begin{pmatrix} 2.4 \\ 5 \end{pmatrix}$$

Es la cantidad disponible de cada industria para el sector público

8.

$$ A = \begin{pmatrix} 0.10 & 0.20 & 0.30 \\ 0 & 0.10 & 0.40 \\ 0.50 & 0.40 & 0.20 \end{pmatrix}$$ $$ X = \begin{pmatrix} 10 \\ 10 \\ 20\end{pmatrix}$$

 * $$ X = AX + D$$
 * $$ X - AX = D$$

$$ D = \begin{pmatrix} 10 \\ 10 \\ 20\end{pmatrix} - \begin{pmatrix} 0.10 & 0.20 & 0.30 \\ 0 & 0.10 & 0.40 \\ 0.50 & 0.40 & 0.20 \end{pmatrix}\begin{pmatrix} 10 \\ 10 \\ 20\end{pmatrix}$$

$$ D = \begin{pmatrix} 10 \\ 10 \\ 20\end{pmatrix} - \begin{pmatrix} 9 \\ 9 \\ 13\end{pmatrix}$$

$$ D = \begin{pmatrix} 1 \\ 1 \\ 7\end{pmatrix}$$

Es la cantidad disponible de cada industria para el sector público

title: User:Margebtk


text:
Talk:Swedish/Vocabulary

(W)
(heading inserted by Rursus (talk) 13:28, 19 March 2009 (UTC))

There are no swedish words beginning with the letter "W", actually it is not used in swedish at all. It is only in names for persons an older place-names you can find it. It should not be in the list. // Solkoll 18:21, 15 Sep 2004 (UTC)

 * It shouldn't. In a Swedish telephone catalogue list, the name of the V entry "V, W" could be used, since personal names can be spelled to contain W, but never in dictionaries, nor name lists of places in Sweden. The entry should be "V" only. Rursus (talk) 13:28, 19 March 2009 (UTC)

Nice list...
...but it lacks two fundamental things: conjugations and genders.

The list is just telling that "apple" is äpple but it doesn't tell that it's ett äpple and that it is conjugated as ett äpple, äpplet, äpplen, äpplena. If you're ever going to get people to understand Swedish, you have to teach them how to conjugate all the verbs, nouns and adjectives. Conjugating is not a hard thing to grasp even for a beginner.

Just some advice from a passer-by, I hope someone listens to me. --84.239.157.217 10:52, 17 September 2006 (UTC)

Statisticallity?
Now, are there any principles for choosing words for the vocabulary? Or, have you ever considered asking:
 * Have you seen any berserkers around lately?

And other things: Rursus (talk) 13:41, 19 March 2009 (UTC)
 * since verbs are weak and strong, the three standard forms, infinitive, preterite and supinum should be listed, such as skriva, skrev, skrivit, or hitta, -de, -t.
 * all entries should be lowercase, Sw. don't use the standard of setting the first letter of nouns uppercase.

 * Most entries should be lowercase, in particular anything but geographical names and other names. Swedish don't use initial capital for the name of a people, so that Swedes = svenskar, nor languages, so that Swedish = svenska. Rursus (talk) 14:22, 19 March 2009 (UTC)

Wiktionary?
The german vocabulary is much better structured regarding tutoring purposes. A straight vocabulary like this one, could better reside on Wiktionary. I propose reworking this vocabulary to look like the German one. Rursus (talk) 14:32, 19 March 2009 (UTC)

title: Talk:Swedish/Vocabulary


text:
Statistics/Introduction/Statistics Subjects

A remarkable amount of today's modern statistics comes from the original work of R.A. Fisher in the early 20th Century. Although there are a dizzying number of minor disciplines in the field, there are some basic, fundamental studies.

The beginning student of statistics will be more interested in one topic or another depending on his or her outside interest. The following is a list of some of the primary branches of statistics.

Probability Theory and Mathematical Statistics
Those of us who are purists and philosophers may be interested in the intersection between pure mathematics and the messy realities of the world. A rigorous study of probability — especially the probability distributions and the distribution of errors — can provide an understanding of where all these statistical procedures and equations come from. Although this sort of rigor is likely to get in the way of a psychologist (for example) learning and using statistics effectively, it is important if one wants to do serious (i.e. graduate-level) work in the field.

That being said, there is good reason for all students to have a fundamental understanding of where all these "statistical techniques and equations" are coming from! We're always more adept at using a tool if we can understand why we're using that tool. The challenge is getting these important ideas to the non-mathematician without the student's eyes glazing over. One can take this argument a step further to claim that a vast number of students will never actually use a t-test—he or she will never plug those numbers into a calculator and churn through some esoteric equations—but by having a fundamental understanding of such a test, he or she will be able to understand (and question) the results of someone else's findings.

Design of Experiments
One of the most neglected aspects of statistics—and maybe the single greatest reason that Statisticians drink—is Experimental Design. So often a scientist will bring the results of an important experiment to a statistician and ask for help analyzing results only to find that a flaw in the experimental design rendered the results useless. So often we statisticians have researchers come to us hoping that we will somehow magically "rescue" their experiments.

A friend provided me with a classic example of this. In his psychology class he was required to conduct an experiment and summarize its results. He decided to study whether music had an impact on problem solving. He had a large number of subjects (myself included) solve a puzzle first in silence, then while listening to classical music and finally listening to rock and roll, and finally in silence. He measured how long it would take to complete each of the tasks and then summarized the results.

What my friend failed to consider was that the results were highly impacted by a learning effect he hadn't considered. The first puzzle always took longer because the subjects were first learning how to work the puzzle. By the third try (when subjected to rock and roll) the subjects were much more adept at solving the puzzle, thus the results of the experiment would seem to suggest that people were much better at solving problems while listening to rock and roll!

The simple act of randomizing the order of the tests would have isolated the "learning effect" and in fact, a well-designed experiment would have allowed him to measure both the effects of each type of music and the effect of learning. Instead, his results were meaningless. A careful experimental design can help preserve the results of an experiment, and in fact some designs can save huge amounts of time and money, maximize the results of an experiment, and sometimes yield additional information the researcher had never even considered!

Sampling
Similar to the Design of Experiments, the study of sampling allows us to find a most effective statistical design that will optimize the amount of information we can collect while minimizing the level of effort. Sampling is very different from experimental design however. In a laboratory we can design an experiment and control it from start to finish. But often we want to study something outside of the laboratory, over which we have much less control.

If we wanted to measure the population of some harmful beetle and its effect on trees, we would be forced to travel into some forest land and make observations, for example: measuring the population of the beetles in different locations, noting which trees they were infesting, measuring the health and size of these trees, etc.

Sampling design gets involved in questions like "How many measurements do I have to take?" or "How do I select the locations from which I take my measurements?" Without planning for these issues, researchers might spend a lot of time and money only to discover that they really have to sample ten times as many points to get meaningful results or that some of their sample points were in some landscape (like a marsh) where the beetles thrived more or the trees grew better.

Modern Regression
Regression models relate variables to each other in a linear fashion. For example, if you recorded the heights and weights of several people and plotted them against each other, you would find that as height increases, weight tends to increase too. You would probably also see that a straight line through the data is about as good a way of approximating the relationship as you will be able to find, though there will be some variability about the line. Such linear models are possibly the most important tool available to statisticians. They have a long history and many of the more detailed theoretical aspects were discovered in the 1970s. The usual method for fitting such models is by "least squares" estimation, though other methods are available and are often more appropriate, especially when the data are not normally distributed.

What happens, though, if the relationship is not a straight line? How can a curve be fit to the data? There are many answers to this question. One simple solution is to fit a quadratic relationship, but in practice such a curve is often not flexible enough. Also, what if you have many variables and relationships between them are dissimilar and complicated?

Modern regression methods aim at addressing these problems. Methods such as generalized additive models, projection pursuit regression, neural networks and boosting allow for very general relationships between explanatory variables and response variables, and modern computing power makes these methods a practical option for many applications

Classification
Some things are different from others. How? That is, how are objects classified into their respective groups? Consider a bank that is hoping to lend money to customers. Some customers who borrow money will be unable or unwilling to pay it back, though most will pay it back as regular repayments. How is the bank to classify customers into these two groups when deciding which ones to lend money to?

The answer to this question no doubt is influenced by many things, including a customer's income, credit history, assets, already existing debt, age and profession. There may be other influential, measurable characteristics that can be used to predict what kind of customer a particular individual is. How should the bank decide which characteristics are important, and how should it combine this information into a rule that tells it whether or not to lend the money?

This is an example of a classification problem, and statistical classification is a large field containing methods such as linear discriminant analysis, classification trees, neural networks and other methods.

Time Series
Many types of research look at data that are gathered over time, where an observation taken today may have some correlation with the observation taken tomorrow. Two prominent examples of this are the fields of finance (the stock market) and atmospheric science.

We've all seen those line graphs of stock prices as they meander up and down over time. Investors are interested in predicting which stocks are likely to keep climbing (i.e. when to buy) and when a stock in their portfolio is falling. It is easy to be misled by a sudden jolt of good news or a simple "market correction" into inferring—incorrectly—that one or the other is taking place!

In meteorology scientists are concerned with the venerable science of predicting the weather. Whether trying to predict if tomorrow will be sunny or determining whether we are experiencing true climate changes (i.e. global warming) it is important to analyze weather data over time.

Survival Analysis
Suppose that a pharmaceutical company is studying a new drug which it is hoped will cause people to live longer (whether by curing them of cancer, reducing their blood pressure or cholesterol and thereby their risk of heart disease, or by some other mechanism). The company will recruit patients into a clinical trial, give some patients the drug and others a placebo, and follow them until they have amassed enough data to answer the question of whether, and by how long, the new drug extends life expectancy.

Such data present problems for analysis. Some patients will have died earlier than others, and often some patients will not have died before the clinical trial completes. Clearly, patients who live longer contribute informative data about the ability (or not) of the drug to extend life expectancy. So how should such data be analyzed?

Survival analysis provides answers to this question and gives statisticians the tools necessary to make full use of the available data to correctly interpret the treatment effect.

Categorical Analysis
In laboratories we can measure the weight of fruit that a plant bears, or the temperature of a chemical reaction. These data points are easily measured with a yardstick or a thermometer, but what about the color of a person's eyes or her attitudes regarding the taste of broccoli? Psychologists can't measure someone's anger with a measuring stick, but they can ask their patients if they feel "very angry" or "a little angry" or "indifferent". Entirely different methodologies must be used in statistical analysis from these sorts of experiments. Categorical Analysis is used in a myriad of places, from political polls to analysis of census data to genetics and medicine.

Clinical Trials
In the United States, the FDA requires that pharmaceutical companies undergo rigorous procedures called Clinical Trials and statistical analyses to assure public safety before allowing the sale or use of new drugs. In fact, the pharmaceutical industry employs more statisticians than any other business!


text:
Statistics/Summary

Summary Statistics
The most simple example of statistics "in practice" is in the generation of summary statistics. Let us consider the example where we are interested in the weight of eighth graders in a school. (Maybe we're looking at the growing epidemic of child obesity in America!) Our school has 200 eighth graders, so we gather all their weights. What we have are 200 positive real numbers.

If an administrator asked you what the weight was of this eighth grade class, you wouldn't grab your list and start reading off all the individual weights; it's just too much information. That same administrator wouldn't learn anything except that she shouldn't ask you any questions in the future! What you want to do is to distill the information — these 200 numbers — into something concise.

What might we express about these 200 numbers that would be of interest? The most obvious thing to do is to calculate the average or mean value so we know how much the "typical eighth grader" in the school weighs. It would also be useful to express how much this number varies; after all, eighth graders come in a wide variety of shapes and sizes! In reality, we can probably reduce this set of 200 weights into at most four or five numbers that give us a firm comprehension of the data set.

title: Statistics/Summary


text:
User:MichaelBurns

Currently working on the autobiography.

title: User:MichaelBurns


text:
Statistics/Distributions/Binomial

Where the Bernoulli Distribution asks the question of "Will this single event succeed?" the Binomial is associated with the question "Out of a given number of trials, how many will succeed?" Some example questions that are modeled with a Binomial distribution are:

 * Out of ten tosses, how many times will this coin land heads?
 * From the children born in a given hospital on a given day, how many of them will be girls?
 * How many students in a given classroom will have green eyes?
 * How many mosquitos, out of a swarm, will die when sprayed with insecticide?

The relation between the Bernoulli and binomial distributions is intuitive: The binomial distribution is composed of multiple Bernoulli trials. We conduct $$n$$ repeated experiments where the probability of success is given by the parameter $$p$$ and add up the number of successes. This number of successes is represented by the random variable X. The value of X is then between 0 and $$n$$.

When a random variable X has a binomial distribution with parameters $$p$$ and $$n$$ we write it as X ~ Bin(n,p) or X ~ B(n,p) and the probability mass function is given by the equation:

 * $$ P\left[X = k\right] = \begin{cases} {n \choose k} p^k \left(1-p\right)^{n-k}\ & 0 \le k \le n \\ 0 & \mbox{otherwise} \end{cases} \quad 0 \leq p \leq 1, \quad n \in \mathbb{N}$$

where $${n \choose k}={n! \over k!(n-k)!}$$

For a refresher on factorials (n!), go back to the Refresher Course earlier in this wiki book.

An example
Let's walk through a simple example of the binomial distribution. We're going to use some pretty small numbers because factorials can be hard to compute. We are going to ask five random people if they believe there is life on other planets. We are going to assume in this example that we know 30% of people believe this to be true. We want to ask the question: "How many people will say they believe in extraterrestrial life?" Actually, we want to be more specific than that: "What is the probability that exactly 2 people will say they believe in extraterrestrial life?"

We know all the values that we need to plug into the equation. The number of people asked, n=5. The probability of any given person answering "yes", p=0.3. (Remember, I said that 30% of people believe in life on other planets!) Finally, we're asking for the probability that exactly 2 people answer "yes" so k=2. This yields the equation:

 * $$ P \left[X = 2 \right] = {5 \choose 2} \cdot {{0.3^2 \cdot} {\left( 1 - 0.3 \right)^{3}}} = {10} \cdot {{0.3^2} \cdot {\left( 1-0.3 \right)^{3}}} = 0.3087$$ since $${5 \choose 2}={5! \over 2! \cdot 3!}={5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 \over (2 \cdot 1) \cdot (3 \cdot 2 \cdot 1)}={120 \over 12}=10$$

Here are the probabilities for all the possible values of X. You can get these values by replacing the k=2 in the above equation with all values from 0 to 5.

What can we learn from these results? Well, first of all we'll see that it's just a little more likely that only one person will confess to believing in life on other planets. There's a distinct chance (about 17%) that nobody will believe it, and there's only a 0.24% (a little over 2 in 1000) that all five people will be believers.

Explanation of the equation
Take the above example. Let's consider each of the five people one by one.

The probability that any one person believes in extraterrestrial life is 30%, or 0.3. So the probability that any two people both believe in extraterrestrial life is 0.3 squared. Similarly, the probability that any one person does not believe in extraterrestrial life is 70%, or 0.7, so the probability that any three people do not believe in extraterrestrial life is 0.7 cubed.

Now, for two out of five people to believe in extraterrestrial life, two conditions must be satisfied: two people believe in extraterrestrial life, and three do not. The probability of two out of five people believing in extraterrestrial life would thus appear to be 0.3 squared (two believers) times 0.7 cubed (three non-believers), or 0.03087.

However, in doing this, we are only considering the case whereby the first two selected people are believers. How do we consider cases such as that in which the third and fifth people are believers, which would also mean a total of two believers out of five?

The answer lies in combinatorics. Bearing in mind that the probability that the first two out of five people believe in extraterrestrial life is 0.03087, we note that there are C(5,2), or 10, ways of selecting a set of two people from out of a set of five, i.e. there are ten ways of considering two people out of the five to be the "first two". This is why we multiply by C(n,k). The probability of having any two of the five people be believers is ten times 0.03087, or 0.3087.

feruzi
The mean can be derived as follow.
 * $$\operatorname{E}[X] = \sum_i f(x_i) \cdot x_i = \sum_{x=0}^n {n \choose x} p^x \left(1-p\right)^{n-x} \cdot x$$
 * $$\operatorname{E}[X] = \sum_{x=0}^n {n! \over x!(n-x)!} p^x \left(1-p\right)^{n-x} x$$
 * $$\operatorname{E}[X] = {n! \over 0!(n-0)!} p^0 \left(1-p\right)^{n-0} \cdot 0 + \sum_{x=1}^n {n! \over x!(n-x)!} p^x \left(1-p\right)^{n-x} x$$
 * $$\operatorname{E}[X] = 0 + \sum_{x=1}^n {n(n-1)! \over x(x-1)!(n-x)!} p \cdot p^{x-1} \left(1-p\right)^{n-x} x$$
 * $$\operatorname{E}[X] = np\sum_{x=1}^n {(n-1)! \over (x-1)!(n-x)!} p^{x-1} \left(1-p\right)^{n-x}$$

Now let w=x-1 and m=n-1. We see that m-w=n-x. We can now rewrite the summation as
 * $$\operatorname{E}[X] = np \left[\sum_{w=0}^m {m! \over w!(m-w)!} p^{w} \left(1-p\right)^{m-w}\right]$$

We now see that the summation is the sum over the complete pmf of a binomial random variable distributed Bin(m, p). This is equal to 1 (and can be easily verified using the Binomial theorem). Therefore, we have
 * $$\operatorname{E}[X] = np \left[1\right]=np$$

Variance
We derive the variance using the following formula:

 * $$\operatorname{Var}[X] = \operatorname{E}[X^2] - (\operatorname{E}[X])^2.$$

We have already calculated E[X] above, so now we will calculate E[X2] and then return to this variance formula:

 * $$\operatorname{E}[X^2] = \sum_i f(x_i) \cdot x^2

= \sum_{x=0}^n x^2 \cdot {n\choose x}p^x(1-p)^{n-x}.$$

We can use our experience gained above in deriving the mean. We use the same definitions of m and w.

 * $$\operatorname{E}[X^2] = \sum_{x=0}^n {n! \over x!(n-x)!} p^x \left(1-p\right)^{n-x} x^2$$

 * $$\operatorname{E}[X^2] = 0 + \sum_{x=1}^n {n! \over x!(n-x)!} p^x \left(1-p\right)^{n-x} x^2$$

 * $$\operatorname{E}[X^2] = np\sum_{x=1}^n {(n-1)! \over (x-1)!(n-x)!} p^{x-1} \left(1-p\right)^{n-x}x$$

 * $$\operatorname{E}[X^2] = np \sum_{w=0}^m {m\choose w} p^{w} \left(1-p\right)^{m-w}(w+1)$$
 * $$\operatorname{E}[X^2] = np \left[\sum_{w=0}^m {m\choose w} p^{w} \left(1-p\right)^{m-w}w+\sum_{w=0}^m {m\choose w} p^{w} \left(1-p\right)^{m-w} \right] $$

The first sum is identical in form to the one we calculated in the Mean (above). It sums to mp. The second sum is 1.

 * $$\operatorname{E}[X^2] = np \cdot ( mp + 1) = np((n-1)p + 1) = np(np - p + 1).$$

Using this result in the expression for the variance, along with the Mean (E(X) = np), we get

 * $$\operatorname{Var}(X) = \operatorname{E}[X^2] - (\operatorname{E}[X])^2 = np(np - p + 1) - (np)^2 = np(1-p).$$

title: Statistics/Distributions/Binomial


text:
Statistics/Distributions/Bernoulli

Bernoulli Distribution: The coin toss
There is no more basic random event than the flipping of a coin. Heads or tails. It's as simple as you can get! The "Bernoulli Trial" refers to a single event which can have one of two possible outcomes with a fixed probability of each occurring. You can describe these events as "yes or no" questions. For example:

 * Will the coin land heads?
 * Will the newborn child be a girl?
 * Are a random person's eyes green?
 * Will a mosquito die after the area was sprayed with insecticide?
 * Will a potential customer decide to buy my product?
 * Will a citizen vote for a specific candidate?
 * Is an employee going to vote pro-union?
 * Will this person be abducted by aliens in their lifetime?

The Bernoulli Distribution has one controlling parameter: the probability of success. A "fair coin" or an experiment where success and failure are equally likely will have a probability of 0.5 (50%). Typically the variable p is used to represent this parameter.

If a random variable X is distributed with a Bernoulli Distribution with a parameter p we write its probability mass function as:

 * $$f(x) = \begin{cases}p, & \mbox{if } x = 1\\1-p, & \mbox{if } x = 0\end{cases}\quad 0\leq p \leq 1$$

Where the event X=1 represents the "yes."

This distribution may seem trivial, but it is still a very important building block in probability. The Binomial distribution extends the Bernoulli distribution to encompass multiple "yes" or "no" cases with a fixed probability. Take a close look at the examples cited above. Some similar questions will be presented in the next section which might give an understanding of how these distributions are related.

Mean
The mean (E[X]) can be derived:

 * $$\operatorname{E}[X] = \sum_i f(x_i) \cdot x_i$$
 * $$\operatorname{E}[X] = p \cdot 1 + (1-p) \cdot 0$$
 * $$\operatorname{E}[X]= p \,$$

Variance

 * $$\operatorname{Var}(X) = \operatorname{E}[(X-\operatorname{E}[X])^2] = \sum_i f(x_i) \cdot (x_i - \operatorname{E}[X])^2$$
 * $$\operatorname{Var}(X)= p \cdot (1-p)^2 + (1-p) \cdot (0-p)^2 $$
 * $$\operatorname{Var}(X)= [p(1-p) + p^2](1-p) \,$$
 * $$\operatorname{Var}(X)= p(1-p) \,$$

title: Statistics/Distributions/Bernoulli


text:
Statistics/Distributions/Poisson

Poisson Distribution
Any French speaker will notice that "Poisson" means "fish", but really there's nothing fishy about this distribution. It's actually pretty straightforward. The name comes from the mathematician Siméon-Denis Poisson (1781-1840).

The Poisson Distribution is very similar to the Binomial Distribution. We are examining the number of times an event happens. The difference is subtle. Whereas the Binomial Distribution looks at how many times we register a success over a fixed total number of trials, the Poisson Distribution measures how many times a discrete event occurs, over a period of continuous space or time. There isn't a "total" value n. As with the previous sections, let's examine a couple of experiments or questions that might have an underlying Poisson nature.

 * How many pennies will I encounter on my walk home?
 * How many children will be delivered at the hospital today?
 * How many mosquito bites did you get today after having sprayed with insecticide?
 * How many angry phone calls did I get after airing a particularly distasteful political ad?
 * How many products will I sell after airing a new television commercial?
 * How many people, per hour, will cross a picket line into my store?
 * How many alien abduction reports will be filed this year?
 * How many defects will there be per 100 metres of rope sold?

What's a little different about this distribution is that the random variable X which counts the number of events can take on any non-negative integer value. In other words, I could walk home and find no pennies on the street. I could also find one penny. It's also possible (although unlikely, short of an armored-car exploding nearby) that I would find 10 or 100 or 10,000 pennies.

Instead of having a parameter p that represents a component probability like in the Bernoulli and Binomial distributions, this time we have the parameter "lambda" or λ which represents the "average or expected" number of events to happen within our experiment. The probability mass function of the Poisson is given by

 * $$P(N=k)=\frac{e^{-\lambda}\lambda^k}{k!}$$.

An example
We run a restaurant and our signature dish (which is very expensive) gets ordered on average 4 times per day. What is the probability of having this dish ordered exactly 3 times tomorrow? If we only have the ingredients to prepare 3 of these dishes, what is the probability that it will get sold out and we'll have to turn some orders away?

The probability of having the dish ordered 3 times exactly is given if we set k=3 in the above equation. Remember that we've already determined that we sell on average 4 dishes per day, so λ=4.

 * $$P(N=k)=\frac{e^{-\lambda}\lambda^k}{k!} = \frac{e^{-4} 4^3}{3!} = 0.195$$

Here's a table of the probabilities for all values from k=0..6:

Now for the big question: Will we run out of food by the end of the day tomorrow? In other words, we're asking if the random variable X>3. In order to compute this we would have to add the probabilities that X=4, X=5, X=6,... all the way to infinity! But wait, there's a better way!

The probability that we run out of food P(X>3) is the same as 1 minus the probability that we don't run out of food, or 1-P(X≤3). So if we total the probability that we sell zero, one, two and three dishes and subtract that from 1, we'll have our answer. So,

 * 1 - P(X≤3) = 1 - ( P(X=0) + P(X=1) + P(X=2) + P(X=3) ) = 1 - 0.4335 = 0.5665

In other words, we have a 56.65% chance of selling out of our wonderful signature dish. I guess crossing our fingers is in order!

de:Statistik: Poissonverteilung

Mean
We calculate the mean as follows:
 * $$\operatorname{E}[X] = \sum_i f(x_i) \cdot x_i = \sum^{\infin}_{x=0} \frac{e^{-\lambda}\lambda^x}{x!}x$$
 * $$\operatorname{E}[X] = \frac{e^{-\lambda}\lambda^0}{0!}\cdot 0 + \sum^{\infin}_{x=1} \frac{e^{-\lambda}\lambda^x}{x!}x$$
 * $$\operatorname{E}[X] = 0 + e^{-\lambda} \sum^{\infin}_{x=1} \frac{\lambda \lambda^{x-1}}{(x-1)!}$$
 * $$\operatorname{E}[X] = \lambda e^{-\lambda}\sum^{\infin}_{x=1} \frac{\lambda^{x-1}}{(x-1)!}$$
 * $$\operatorname{E}[X] = \lambda e^{-\lambda}\sum^{\infin}_{x=0} \frac{\lambda^x}{x!}$$

Remember that $$\mathrm{e}^{\lambda} = \sum^{\infin}_{x=0} \frac{\lambda^x}{x!}$$
 * $$\operatorname{E}[X] = \lambda e^{-\lambda}e^{\lambda}=\lambda$$

Variance
We derive the variance using the following formula:

 * $$\operatorname{Var}[X] = \operatorname{E}[X^2] - (\operatorname{E}[X])^2$$

We have already calculated E[X] above, so now we will calculate E[X2] and then return to this variance formula:

 * $$\operatorname{E}[X^2] = \sum_i f(x_i) \cdot x^2$$
 * $$\operatorname{E}[X^2] = \sum^{\infin}_{x=0} \frac{e^{-\lambda}\lambda^x}{x!}x^2$$
 * $$\operatorname{E}[X^2] = 0+\sum^{\infin}_{x=1} \frac{e^{-\lambda}\lambda \lambda^{x-1}}{(x-1)!}x$$
 * $$\operatorname{E}[X^2] = \lambda\sum^{\infin}_{x=0} \frac{e^{-\lambda}\lambda^x}{x!}(x+1)$$ ....replacing $$x$$ with $$x+1$$
 * $$\operatorname{E}[X^2] = \lambda\left[\sum^{\infin}_{x=0} \frac{e^{-\lambda}\lambda^x}{x!}x+\sum^{\infin}_{x=0} \frac{e^{-\lambda}\lambda^x}{x!}\right]$$

The first sum is E[X]=λ and the second we also calculated above to be 1.
 * $$\operatorname{E}[X^2] = \lambda\left[\lambda+1\right]=\lambda^2+\lambda$$

Returning to the variance formula we find that

 * $$\operatorname{Var}[X] = (\lambda^2+\lambda) - (\lambda)^2=\lambda$$

title: Statistics/Distributions/Poisson


text:
Talk:Calculus/Summation notation

 * $$\sum_{j=2}^7 i^2 = 2^2 + 3^2 + 4^2 + 5^2 + 6^2+7^2$$

Here, the dummy variable is j, the lower limit of summation is 2, and the uppper limit is 7.

>> is this correct? yes, except upper is spelled wrong

=induction= hey this seems like it would be a very nice place to put a discussion on Induction. anyone disagree?--Stranger104 13:04, 15 Jun 2005 (UTC)

=moved= this page needs to be moved as it is so short (compared to say the entire topic of differentiation). Either into the integration page, or as an appendix.

title: Talk:Calculus/Summation notation


text:
Management Strategy

Management Strategy is about determining where you want an organization to go and how you want it to get there. Activities that fall into the category of strategy affect a significant portion of the organization for a considerable time, distinguished from tactics which are activities in response to particular situations and are unlikely to ruin the organization if they fail.

There are competing theories as to how to determine what goals and actions are required. All of them boil down to analyzing the current situation, developing goals and a plan of action, and then driving towards those goals.

 * Michael Porter's /Five Forces/
 * Jay Barney's /Sustainable Competitive Advantage/
 * David A. Aaker's /Strategic Market Management/
 * Main Text: Henry Mintzberg's The Strategy Process 4th Ed.
 * /Analyzing Resources and Capabilities/
 * /Cost Advantage/

title: Management Strategy


text:
User:Murraytodd

[Murray Todd Williams] (born: March 18, 1970) is a 34 year-old Coloradan, born and raised in Fort Collins. His interests are varied enough to suggest schizophrenia or multiple-personality disorder. Part of his brain belongs to the sciences—he has a B.A. in Mathematics from Pomona College and an M.S. in Statistics from Colorado State University. Despite that he has spent five years in New York City and two in Los Angeles pursuing acting, dance, voice and writing.

Murray has been an avid computer enthusiast since age eight. His computers of influence were (in order) the HP 85 and HP 9845/C, CDC Cyber, Apple II, TI 99/4A, "PC", IBM 4341, and various models of DEC VAX before he fell in love with Apple after the unveiling of OS X. He is co-author of the book "Early Adopter Mac OS X Java" ISBN 186100611X.

Recently Murray has become involved in Politics, motivated equally by his opposition to George W. Bush and the inspiration of Howard Dean. He helped establish the [Stonewall Young Democrats] in Los Angeles.

title: User:Murraytodd


text:
User:Sublium

I am Sublium. I spend a lot of free time editing articles at (mainly) Wikipedia. Figured I would drop by and see what was up over here.

title: User:Sublium


text:
Tamil/Introduction

Tamil is the oldest of the Dravidian languages. Along with Chinese, Greek, Sanskrit and others, it is one of the world's classical languages. Tamil literature spans 4000 years. This language was the first to develop a distinct prose form of writing among the classical languages of the world. Tamil is the only language among the old languages that has a history of 2000 or more years of existence. With slight variation in scripts and usage, the language still thrives. The literatures written in 200 BC are still learnt and used in normal speeches. The Tamil Thirukkural is second only to the Bible in number of published translations. Over the course of the language's development, many words from other languages have been absorbed. For instance, Tamil spoken in Tamil Nadu has a significant number of words from Sanskrit, English, Dutch, French and Urdu.

The letter 'ழ' of 'தமிழ்' (Tamil) is pronounced like a retroflex 'r', and is often transliterated as "zh".

Local usages of Tamil vary. There are differences in its usage not only among countries but even within Tamil Nadu, a region of India where Tamil is the predominantly spoken language.

Tamil is one of the recognized languages for official correspondence in four countries viz, India, Sri Lanka, Singapore and Malaysia. In both Canada and Myanmar, the Tamil speaking population is about one million. There are about 80 million Tamil speakers worldwide.

Tamil is a Dravidian language, like most south Indian languages. Other Dravidian languages include Telugu, Kannada, Malayalam and Tulu.

History
Tamil's origins are independent of Sanskrit (which is from the Indo-European language family and the ancestor of many Indian languages), but it has been flexible in allowing other languages to blend in seamlessly giving the non-speaker a sense of ease while trying to learn the language. This is one of the specialties of the language since it does not modify the structural integrity of the language. The oldest Tamil text Tolkaappiyam is a grammar of Tamil.

Quite significantly for its age, Tamil seems to have undergone minimal changes and adaptations over the years. Classical Tamil is quite comprehensible to speakers of the modern language. The ancient Tamil book Tirukkural is an example. The verses from the book are often taught to young students of the language at the primary level, and they pick up the lines in the ancient dialect with little difficulty.

Tamil Literature
Tamil literature is literature in the Tamil language which most prominently includes the contributions of the historic Tamil country or Tamizhagam, a large part of which constitutes the modern state of Tamil Nadu in India. Because of the antiquity of the Tamil language, Tamil literature has a rich tradition spanning more than 5000 years and is particularly famous for its poetic tradition as well as for its epics, philosophical works and secular flavour.

The works of the Sangam period, known as Sangam literature, at the turn of the first millennium are the most ancient and considered very important. The word Sangam refers to an academy. Tolkaappiyam, Akananaru and Purananaru are important works from this period.

In the post-Sangam period, there were many notable works. Silapadhigaaram by Ilangovadigal tells the tale of Kannagi, Kovalan and Maadhavi. Thirukkural by Thiruvalluvar consists of 1330 couplets which discuss about various aspects of life and is widely known even today. Aathichoodi, a collection of single-line sayings was written by Auvaiyaar, a young poetess who became prematurely old according to folklore. The first word in each saying is based on alphabetical order. Kambaramayanam was a version of the Ramayana by the poet Kamban (Kambar). Periya puranaam, Divya Prabhandham ,Thiruppavai, Thiruvempaavai and Dhevaaram were written in the Bhakti cult. Manimegalai, Seevaga sindhamani, Valayaapathi, Kundalakesi are other important works.

In the modern period, the works of poet Subramanya Bharathy, (better known as Bharathiar) who was also a great freedom fighter, are particularly stimulating in their progressive themes- emancipation of women, freedom, etc.,

As far as modern fiction is concerned, Prathapa Mudaliar Charithram was the first novel in Tamil.

In the early twentieth century, Kalki Krishnamurthy is one of the most renowned and respected writers. Sivagamiyin Sabhadham and Ponniyin Selvan constitute some of his greatest works, both based on historical themes.

Some famous contemporary writers include Pudhumaipiththan, Jayakanthan, Thi. Janakiraman, La.Sa.Ramamrutham, Sujatha, Jayamohan, and S.Ramakrishnan.

title: Tamil/Introduction


text:
Tamil/Tamil Script

In Tamil, there are 30 characters. The Tamil alphabet has 12 vowels and 18 consonants. (The practise of taking the cartesian product of the vowels and consonants is widely seen. Their supporting argument is that when a consonant is used with a vowel it is a separate letter. But one cannot of course use any consonant without suffixing it with vowel!)

The vowels are divided into short and long (five of each type) and two dipthongs (ஐ and ஒள). The consonants are classified into three categories with 6 in each category: vallinam - hard, mellinam - soft or nasal, and idayinam - medium. Unlike Devanagari, Tamil has neither conjunct consonants nor aspirated and voiced stops. Some scholars have suggested that in Sentamil (which refers to Tamil as it existed before Sanskrit words were borrowed), stops were voiceless when at the start of a word and unvoiced otherwise. However, no such distinction is observed by modern Tamil speakers.

The script is sometimes called Vattezhuthu, literally "round writing". This characterstic has partly to do with the fact that in ancient times, writing involved carving with a sharp point on palm leaves (olaichuvadi) and it was apparently easier to produce curves than straight lines by this method. The script is syllabic, in the sense that each letter is a syllable. However, the signs for the syllables are derived from that of the inherent consonant; thus it is of the abugida type. Some syllables are written by modifying the shape of the consonant in a way that is inherent to the vowel, others are written by adding vowel-inherent suffix to the consonant, yet others a prefix, and finally some vowels require adding both a prefix and a suffix to the consonant. In every case the vowel symbol is different from the vowel standing alone. An overdot (see image) - equivalent to Devanagari sign virama - suppresses the inherent trailing a sound of the consonant sign - that is, it is a pure consonant.

There are some lexical rules for formation of words. Some examples: a word cannot end in certain consonants, and cannot begin with some consonants including 'r' 'l' and 'll'; there are two consonants for the dental 'n' - which one should be used depends on whether the 'n' occurs at the start of the word and on the letters around it.

Basic Consonants
Consonants are also called the 'body' letters.

Borrowed consonants
Also called Grantha letters, these are used exclusively for writing words borrowed from Sanskrit, English, and other languages. Of course, not all such words include these letters.

Vowels
Vowels are also called the 'life' or 'soul' letters. Together with the consonants (which are called 'body' letters, they form compound, syllabic (abugida) letters that are called 'living' letters (ie. letters that have both 'body' and 'soul').

Compound Form
Using the consonant 'k' as an example.

Special letter ஃ (pronounced 'akh') is rarely used by itself - normally serves purely grammatical function as independent vowel form of the dot on consonants that suppresses the inherent 'a' sound in plain consonants.

The long ('nedil') vowels are about twice as long as the short ('kuRil') vowels. The diphthongs are usually pronounced about 1.5 times as long as the short vowels, though some grammatical texts place them with the long ('nedil') vowels.

As can be seen in the compound form, the vowel sign can be added to the right, left or both sides of the consonants. It can also form a ligature. These rules are evolving and older use has more ligatures than modern use. What you actually see on this page depends on your font selection. 'Code 2000' will show more ligatures than 'Latha'.

There are proponents of script reform who want to eliminate all ligatures and let all vowel signs appear on the right side.

Unicode encodes the character in logical order (always the consonant first), whereas legacy 8-bit encodings (like TSCII) prefer the written order. This is a problem in trans-coding these.

Tamil in Unicode
The Unicode range for Tamil is U+0B80 ... U+0BFF.

title: Tamil/Tamil Script


text:
Tamil/History

History
Tamil's origins are independent of Sanskrit (which is from the Indo-European language family and the ancestor of many Indian languages), but it has borrowed a number of words from Sanskrit in recent centuries. The oldest Tamil text Tolkaappiyam is a grammar of Tamil.

Quite significantly for its age, Tamil seems to have undergone minimal changes and adaptations over the years. Classical Tamil is quite comprehensible to speakers of the modern language. The ancient Tamil book Tirukkural is an example. The verses from the book are often taught to young students of the language at the primary level, and they pick up the lines in the ancient dialect with little difficulty.

title: Tamil/History


text:
Tamil/Tamil literature

Tamil literature is literature in the Tamil language which most prominently includes the contributions of the historic Tamil country or Tamizhagam, a large part of which constitutes the modern state of Tamil Nadu in India. Because of the antiquity of the Tamil language, Tamil literature has a rich tradition spanning more than 5000 years and is particularly famous for its poetic tradition as well as for its epics, philosophical works and secular flavour.

The works of the Sangam period, known as Sangam literature, at the turn of the first millennium are the most ancient and considered very important. The word Sangam refers to an academy. Tolkaappiyam, Akananaru and Purananaru are important works from this period.

In the post-Sangam period, there were many notable works. Silapadhigaaram by Ilangovadigal tells the tale of Kannagi, Kovalan and Maadhavi. Thirukkural by Thiruvalluvar consists of 1330 couplets which discuss about various aspects of life and is widely known even today. Aathichoodi, a collection of single-line sayings was written by Auvaiyaar, a young poetess who became prematurely old according to folklore. The first word in each saying is based on alphabetical order. Kambaramayanam was a version of the Ramayana by the poet Kamban (Kambar). Periya puranaam, Divya Prabhandham ,Thiruppavai, Thiruvempaavai and Dhevaaram were written in the Bhakti cult. Manimegalai, Seevaga sindhamani, Valayaapathi, Kundalakesi are other important works.

In the modern period, the works of poet Subramanya Bharathy, (better known as Bharathiar) who was also a great freedom fighter, are particularly stimulating in their progressive themes- emancipation of women, freedom, etc.,

As far as modern fiction is concerned, Prathapa Mudaliar Charithram was the first novel in Tamil.

In the early twentieth century, Kalki Krishnamurthy is one of the most renowned and respected writers. Sivagamiyin Sabhadham and Ponniyin Selvan constitute some of his greatest works, both based on historical themes.

Some famous contemporary writers include Pudhumaipiththan, Jayakanthan, Thi. Janakiraman, La.Sa.Ramamrutham, Sujatha, Jayamohan, and S.Ramakrishnan.

Mobile Books in Tamil

 * MobileVeda Tamil Mobile Books - Tamil Literature now available as mobile books.

title: Tamil/Tamil literature