Prague is the capital and largest city in the Czech Republic, the 14th largest city in the European Union and the historical capital of Bohemia. Situated in the north-west of the country on the Vltava river, the city is home to about 1.3 million people, while its metropolitan area is estimated to have a population of 2.6 million. The city has a temperate climate, with chilly winters. Prague has been a political and economic centre of central Europe complete with a rich history. Founded during the Romanesque and flourishing by the Gothic and Baroque eras, Prague was the capital of the Kingdom of Bohemia and the main residence of several Holy Roman Emperors, most notably of Charles IV, it was an important city to its Austro-Hungarian Empire. The city played major roles in the Bohemian and Protestant Reformation, the Thirty Years' War and in 20th-century history as the capital of Czechoslovakia, during both World Wars and the post-war Communist era. Prague is home to a number of well-known cultural attractions, many of which survived the violence and destruction of 20th-century Europe.
Main attractions include Prague Castle, Charles Bridge, Old Town Square with the Prague astronomical clock, the Jewish Quarter, Petřín hill and Vyšehrad. Since 1992, the extensive historic centre of Prague has been included in the UNESCO list of World Heritage Sites; the city has more than ten major museums, along with numerous theatres, galleries and other historical exhibits. An extensive modern public transportation system connects the city, it is home to a wide range of public and private schools, including Charles University in Prague, the oldest university in Central Europe. Prague is classified as an "Alpha −" global city according to GaWC studies and ranked sixth in the Tripadvisor world list of best destinations in 2016, its rich history makes it a popular tourist destination and as of 2017, the city receives more than 8.5 million international visitors annually. Prague is the fourth most visited European city after London and Rome. During the thousand years of its existence, the city grew from a settlement stretching from Prague Castle in the north to the fort of Vyšehrad in the south, becoming the capital of a modern European country, the Czech Republic, a member state of the European Union.
The region was settled as early as the Paleolithic age. A Jewish chronicler David Solomon Ganz, citing Cyriacus Spangenberg, claimed that the city was founded as Boihaem in c. 1306 BC by an ancient king, Boyya. Around the fifth and fourth century BC, a Celts tribe appeared in the area establishing settlements including an oppidum in Závist, a present-day suburb of Prague, naming the region of Bohemia, which means "home of the Boii people". In the last century BC, the Celts were driven away by Germanic tribes, leading some to place the seat of the Marcomanni king, Maroboduus, in southern Prague in the suburb now called Závist. Around the area where present-day Prague stands, the 2nd century map drawn by Ptolemaios mentioned a Germanic city called Casurgis. In the late 5th century AD, during the great Migration Period following the collapse of the Western Roman Empire, the Germanic tribes living in Bohemia moved westwards and in the 6th century, the Slavic tribes settled the Central Bohemian Region.
In the following three centuries, the Czech tribes built several fortified settlements in the area, most notably in the Šárka valley and Levý Hradec. The construction of what came to be known as Prague Castle began near the end of the 9th century, growing a fortified settlement that existed on the site since the year 800; the first masonry under Prague Castle dates from the year 885 at the latest. The other prominent Prague fort, the Přemyslid fort Vyšehrad, was founded in the 10th century, some 70 years than Prague Castle. Prague Castle is dominated by the cathedral, which began construction in 1344, but wasn't completed until the 20th century; the legendary origins of Prague attribute its foundation to the 8th century Czech duchess and prophetess Libuše and her husband, Přemysl, founder of the Přemyslid dynasty. Legend says that Libuše came out on a rocky cliff high above the Vltava and prophesied: "I see a great city whose glory will touch the stars." She ordered a town called Praha to be built on the site.
The region became the seat of the dukes, kings of Bohemia. Under Holy Roman Emperor Otto II the area became a bishopric in 973; until Prague was elevated to archbishopric in 1344, it was under the jurisdiction of the Archbishopric of Mainz. Prague was an important seat for trading where merchants from all of Europe settled, including many Jews, as recalled in 965 by the Hispano-Jewish merchant and traveller Ibrahim ibn Ya'qub; the Old New Synagogue of 1270 still stands in the city. Prague was once home to an important slave market. At the site of the ford in the Vltava river, King Vladislaus I had the first bridge built in 1170, the Judith Bridge, named in honour of his wife Judith of Thuringia; this bridge was destroyed by a flood in 1342, but some of the original foundation stones of that bridge remain in the river. It was named the Charles Bridge. In 1257, under King Ottokar II, Malá Strana was founded in Prague on the site of an older village in what would become the Hradčany area; this was the district of the German people, who had the right to administer the law autonomously, pursuant to Magdeburg rights.
The new district was on the bank opposite of the Staré Město, which had borough status and was bordered by a line of walls and fortifications. Prague flourished dur
Virtual International Authority File
The Virtual International Authority File is an international authority file. It is a joint project of several national libraries and operated by the Online Computer Library Center. Discussion about having a common international authority started in the late 1990s. After a series of failed attempts to come up with a unique common authority file, the new idea was to link existing national authorities; this would present all the benefits of a common file without requiring a large investment of time and expense in the process. The project was initiated by the US Library of Congress, the German National Library and the OCLC on August 6, 2003; the Bibliothèque nationale de France joined the project on October 5, 2007. The project transitioned to being a service of the OCLC on April 4, 2012; the aim is to link the national authority files to a single virtual authority file. In this file, identical records from the different data sets are linked together. A VIAF record receives a standard data number, contains the primary "see" and "see also" records from the original records, refers to the original authority records.
The data are available for research and data exchange and sharing. Reciprocal updating uses the Open Archives Initiative Protocol for Metadata Harvesting protocol; the file numbers are being added to Wikipedia biographical articles and are incorporated into Wikidata. VIAF's clustering algorithm is run every month; as more data are added from participating libraries, clusters of authority records may coalesce or split, leading to some fluctuation in the VIAF identifier of certain authority records. Authority control Faceted Application of Subject Terminology Integrated Authority File International Standard Authority Data Number International Standard Name Identifier Wikipedia's authority control template for articles Official website VIAF at OCLC
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis. Numerical analysis finds application in all fields of engineering and the physical sciences, but in the 21st century the life sciences, social sciences, medicine and the arts have adopted elements of scientific computations; as an aspect of mathematics and computer science that generates and implements algorithms, the growth in power and the revolution in computing has raised the use of realistic mathematical models in science and engineering, complex numerical analysis is required to provide solutions to these more involved models of the world. Ordinary differential equations appear in celestial mechanics. Before the advent of modern computers, numerical methods depended on hand interpolation in large printed tables. Since the mid 20th century, computers calculate the required functions instead; these same interpolation formulas continue to be used as part of the software algorithms for solving differential equations.
One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian Collection, which gives a sexagesimal numerical approximation of the square root of 2, the length of the diagonal in a unit square. Being able to compute the sides of a triangle is important, for instance, in astronomy and construction. Numerical analysis continues this long tradition of practical mathematical calculations. Much like the Babylonian approximation of the square root of 2, modern numerical analysis does not seek exact answers, because exact answers are impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors; the overall goal of the field of numerical analysis is the design and analysis of techniques to give approximate but accurate solutions to hard problems, the variety of, suggested by the following: Advanced numerical methods are essential in making numerical weather prediction feasible.
Computing the trajectory of a spacecraft requires the accurate numerical solution of a system of ordinary differential equations. Car companies can improve the crash safety of their vehicles by using computer simulations of car crashes; such simulations consist of solving partial differential equations numerically. Hedge funds use tools from all fields of numerical analysis to attempt to calculate the value of stocks and derivatives more than other market participants. Airlines use sophisticated optimization algorithms to decide ticket prices and crew assignments and fuel needs; such algorithms were developed within the overlapping field of operations research. Insurance companies use numerical programs for actuarial analysis; the rest of this section outlines several important themes of numerical analysis. The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
To facilitate computations by hand, large books were produced with formulas and tables of data such as interpolation points and function coefficients. Using these tables calculated out to 16 decimal places or more for some functions, one could look up values to plug into the formulas given and achieve good numerical estimates of some functions; the canonical work in the field is the NIST publication edited by Abramowitz and Stegun, a 1000-plus page book of a large number of used formulas and functions and their values at many points. The function values are no longer useful when a computer is available, but the large listing of formulas can still be handy; the mechanical calculator was developed as a tool for hand computation. These calculators evolved into electronic computers in the 1940s, it was found that these computers were useful for administrative purposes, but the invention of the computer influenced the field of numerical analysis, since now longer and more complicated calculations could be done.
Direct methods compute the solution to a problem in a finite number of steps. These methods would give the precise answer. Examples include Gaussian elimination, the QR factorization method for solving systems of linear equations, the simplex method of linear programming. In practice, finite precision is used and the result is an approximation of the true solution. In contrast to direct methods, iterative methods are not expected to terminate in a finite number of steps. Starting from an initial guess, iterative methods form successive approximations that converge to the exact solution only in the limit. A convergence test involving the residual, is specified in order to decide when a sufficiently accurate solution has been found. Using infinite precision arithmetic these methods would not reach the solution within a finite number of steps. Examples include Newton's method, the bisection method, Jacobi iteration. In computational matrix algebra, iterative methods are generall
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number", it was the Pythagoreans who coined the term "mathematics", with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria, she succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; as these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, proceed to specialize in topics of their own choice at the graduate level.
In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns
The Czechs or the Czech people, are a West Slavic ethnic group and a nation native to the Czech Republic in Central Europe, who share a common ancestry, culture and Czech language. Ethnic Czechs were called Bohemians in English until the early 20th century, referring to the medieval land of Bohemia which in turn was adapted from late Iron Age tribe of Celtic Boii. During the Migration Period, West Slavic tribes of Bohemians settled in the area, "assimilated the remaining Celtic and Germanic populations", formed a principality in the 9th century, part of Great Moravia, in form of Duchy of Bohemia and Kingdom of Bohemia, the predecessors of the modern republic; the Czech diaspora is found in notable numbers in the United States, Israel, Germany, Switzerland, the United Kingdom, Russia and Brazil, among others. The Czech ethnic group is part of the West Slavic subgroup of the larger Slavic ethno-linguistical group; the West Slavs have their origin in early Slavic tribes which settled in Central Europe after East Germanic tribes had left this area during the migration period.
The West Slavic tribe of Bohemians settled in the area of Bohemia during the migration period, assimilated the remaining Celtic and Germanic populations. They formed a principality in the 9th century, the Duchy of Bohemia, under the Přemyslid dynasty, part of the Great Moravia under Svatopluk I. According to mythology, the founding father of the Czech people were Forefather Čech, who according to legend brought the tribe of Czechs into its land; the Czech are related to the neighbouring Slovaks. The Czech–Slovak languages form a dialect continuum rather than being two distinct languages. Czech cultural influence in Slovak culture is noted as having been much higher than the other way around. Czech people have a long history of coexistence with Germanic people. In the 17th century, German replaced Czech in local administration; the Czech National Revival took place in the 18th and 19th centuries aiming to revive Czech language and national identity. The Czech were the initiators of Pan-Slavism; the Czech ethnonym was the name of a Slavic tribe in central Bohemia that subdued the surrounding tribes in the late 9th century and created the Czech/Bohemian state.
The origin of the name of the tribe itself is unknown. According to legend, it comes from their leader Čech. Research regards Čech as a derivative of the root čel-; the Czech ethnonym was adopted by the Moravians in the 19th century. The population of the Czech lands has been influenced by different human migrations that wide-crossed Europe over time. In their Y-DNA haplogroups, which are inherited along the male line, Czechs have shown a mix of Eastern and Western European traits. According to a 2007 study, 34.2% of Czech males belong to R1a. Within the Czech Republic, the proportion of R1a seems to increase from west to east According to a 2000 study, 35.6% of Czech males have haplogroup R1b, common in Western Europe among Germanic and Celtic nations, but rare among Slavic nations. A mtDNA study of 179 individuals from Western Bohemia showed that 3% had East Eurasian lineages that entered the gene pool through admixture with Central Asian nomadic tribes in the early Middle Ages. A group of scientists suggested that the high frequency of a gene mutation causing cystic fibrosis in Central European and Celtic populations supports the theory of some Celtic ancestry among the Czech population.
The population of the Czech Republic descends from diverse peoples of Slavic and Germanic origin. Presence of West Slavs in the 6th century during the Migration Period has been documented on the Czech territory. Slavs settled in Bohemia and Austria sometime during the 6th or 7th centuries, "assimilated the remaining Celtic and Germanic populations". According to a popular myth, the Slavs came with Forefather Čech. During the 7th century, the Frankish merchant Samo, supporting the Slavs fighting against nearby settled Avars, became the ruler of the first known Slav state in Central Europe, the Samo's Empire; the principality Great Moravia, controlled by the Moymir dynasty, arose in the 8th century and reached its zenith in the 9th when it held off the influence of the Franks. Great Moravia was Christianized, the crucial role played Byzantine mission of Methodius; the Duchy of Bohemia emerged in the late 9th century. In 880, Prague Castle was constructed by Prince Bořivoj, founder of the Přemyslid dynasty and the city of Prague was established.
Vratislav II was the first Czech king in 1085 and the duchy was raised to a hereditary kingdom under Ottokar I in 1198. The second half of the 13th century was a period of advancing German immigration into the Czech lands; the number of Czechs who have at least German ancestry today runs into hundreds of thousands. The Habsburg Monarchy focused much of its power on religious wars against the Protestants. While these religious wars were taking place, the Czech estates revolted against Habsburg from 1546 to 1547 but were defeated. Defenestrations of Prague in 1618, signaled an open revolt by the Bohemian estates against the Habsburgs and started the Thirty Years' War. After the Battle
Royal Library of the Netherlands
The Royal Library of the Netherlands is based in The Hague and was founded in 1798. The mission of the Royal Library of the Netherlands, as presented on the library's web site, is to provide "access to the knowledge and culture of the past and the present by providing high-quality services for research and cultural experience"; the initiative to found a national library was proposed by representative Albert Jan Verbeek on August 17 1798. The collection would be based on the confiscated book collection of William V; the library was founded as the Nationale Bibliotheek on November 8 of the same year, after a committee of representatives had advised the creation of a national library on the same day. The National Library was only open to members of the Representative Body. King Louis Bonaparte gave the national library its name of the Royal Library in 1806. Napoleon Bonaparte transferred the Royal Library to The Hague as property, while allowing the Imperial Library in Paris to expropriate publications from the Royal Library.
In 1815 King William I of the Netherlands confirmed the name of'Royal Library' by royal resolution. It has been known as the National Library of the Netherlands since 1982, when it opened new quarters; the institution became independent of the state in 1996, although it is financed by the Department of Education and Science. In 2004, the National Library of the Netherlands contained 3,300,000 items, equivalent to 67 kilometers of bookshelves. Most items in the collection are books. There are pieces of "grey literature", where the author, publisher, or date may not be apparent but the document has cultural or intellectual significance; the collection contains the entire literature of the Netherlands, from medieval manuscripts to modern scientific publications. For a publication to be accepted, it must be from a registered Dutch publisher; the collection is accessible for members. Any person aged 16 years or older can become a member. One day passes are available. Requests for material take 30 minutes.
The KB hosts several open access websites, including the "Memory of the Netherlands". List of libraries in the Netherlands European Library Nederlandse Centrale Catalogus Books in the Netherlands Media related to Koninklijke Bibliotheek at Wikimedia Commons Official website
Charles University, known as Charles University in Prague or as the University of Prague, is the oldest and largest university in the Czech Republic. Founded in 1348, it was the first university in Central Europe, it is one of the oldest universities in Europe in continuous operation and ranks in the upper 1.5 percent of the world’s best universities. Today, the university consists of 17 faculties located in Hradec Králové and Pilsen, its academic publishing house is Karolinum Press. The university operates several museums and two botanical gardens, its seal shows its protector Emperor Charles IV, with his coats of arms as King of the Romans and King of Bohemia, kneeling in front of St. Wenceslas, the patron saint of Bohemia, it is surrounded by Sigillum Universitatis Scolarium Studii Pragensis. The establishment of a medieval university in Prague was inspired by Holy Roman Emperor Charles IV, he asked Pope Clement VI, to do so. On 26 January 1347 the pope issued the bull establishing a university in Prague, modeled on the University of Paris, with the full number of faculties, including theological.
On 7 April 1348 Charles, the king of Bohemia, gave to the established university privileges and immunities from the secular power in a Golden Bull and on 14 January 1349 he repeated that as the King of the Romans. Most Czech sources since the 19th century—encyclopedias, general histories, materials of the University itself—prefer to give 1348 as the year of the founding of the university, rather than 1347 or 1349; this was caused by an anticlerical shift in the 19th century, shared by both Germans. The university was opened in 1349; the university was sectioned into parts called nations: the Bohemian, Bavarian and Saxon. The Bohemian natio included Bohemians, southern Slavs, Hungarians. Ethnically Czech students made 16–20% of all students. Archbishop Arnošt of Pardubice took an active part in the foundation by obliging the clergy to contribute and became a chancellor of the university; the first graduate was promoted in 1359. The lectures were held in the colleges, of which the oldest was named for the king the Carolinum, established in 1366.
In 1372 the Faculty of Law became an independent university. In 1402 Jerome of Prague in Oxford copied out the Trialogus of John Wycliffe; the dean of the philosophical faculty, Jan Hus, translated Trialogus into the Czech language. In 1403 the university forbade its members to follow the teachings of Wycliffe, but his doctrine continued to gain in popularity. In the Western Schism, the Bohemian natio took the side of king Wenceslaus and supported the Council of Pisa; the other nationes of the university declared their support for the side of Pope Gregory XII, thus the vote was 1:3 against the Bohemians. Hus and other Bohemians, took advantage of Wenceslaus' opposition to Gregory. By the Decree of Kutná Hora on 18 January 1409, the king subverted the university constitution by granting the Bohemian masters three votes. Only a single vote was left for all other three nationes combined, compared to one vote per each natio before; the result of this coup was the emigration of foreign professors and students, founding the University of Leipzig in May 1409.
Before that, in 1408, the university had about 200 doctors and magisters, 500 bachelors, 30,000 students. In the autumn of 1409, Hus was elected rector of the now Czech-dominated rump university. Thus, the Prague university lost the largest part of its students and faculty. From on the university declined to a regional institution with a low status. Soon, in 1419, the faculties of theology and law disappeared, only the faculty of arts remained in existence; the faculty of arts became a centre of the Hussite movement, the chief doctrinal authority of the Utraquists. No degrees were given in the years 1417–30. Emperor Sigismund, son of Charles IV, took what was left into his personal property and some progress was made; the emperor Ferdinand I called the Jesuits to Prague and in 1562 they opened an academy—the Clementinum. From 1541 till 1558 the Czech humanist Mattheus Collinus was a professor of Greek language; some progress was made again. In 1609 the obligatory celibacy of the professors was abolished.
In 1616 the Jesuit Academy became a university. Jesuits were expelled 1618–1621 during the early stages of the Thirty Years' War, started in Prague by anti-Catholic and anti-Imperial Bohemians. By 1622 the Jesuits had a predominant influence over the emperor. An Imperial decree of 19 September 1622 gave the Jesuits supreme control over the entire school system of Bohemia and Silesia; the last four professors at the Carolinum resigned and all of the Carolinum and nine colleges went to the Jesuits. The right of handing out degrees, of holding chancellorships and of appointing the secular professors was granted to the Jesuits. Cardinal Ernst Adalbert von Harrach opposed union of the university with another institution and the withdrawal of the archepiscopal right to the chanc