1.
The Hague
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The Hague is a city on the western coast of the Netherlands, and the capital city of the province of South Holland. With a population of 520,704 inhabitants and more than one million including the suburbs, it is the third-largest city of the Netherlands. The Rotterdam The Hague Metropolitan Area, with a population of approximately 2.7 million, is the 12th-largest in the European Union and the most populous in the country. Located in the west of the Netherlands, The Hague is in the centre of the Haaglanden conurbation and lies at the southwest corner of the larger Randstad conurbation. The Hague is the seat of the Dutch government, parliament, the Supreme Court, and the Council of State, but the city is not the capital of the Netherlands, which constitutionally is Amsterdam. King Willem-Alexander of the Netherlands plans to live at Huis ten Bosch and works at Noordeinde Palace in The Hague, the Hague is also home to the world headquarters of Royal Dutch Shell and numerous other major Dutch companies. The Hague originated around 1230, when Count Floris IV of Holland purchased land alongside a pond, in 1248, his son and successor William II, King of the Romans, decided to extend the residence to a palace, which would later be called the Binnenhof. He died in 1256 before this palace was completed but parts of it were finished by his son Floris V, of which the Ridderzaal and it is still used for political events, such as the annual speech from the throne by the Dutch monarch. From the 13th century onwards, the counts of Holland used The Hague as their administrative centre, the village that originated around the Binnenhof was first mentioned as Haga in a charter dating from 1242. In the 15th century, the smarter des Graven hage came into use, literally The Counts Wood, with connotations like The Counts Hedge, s-Gravenhage was officially used for the city from the 17th century onwards. Today, this name is used in some official documents like birth. The city itself uses Den Haag in all its communication and their seat was located in The Hague. At the beginning of the Eighty Years War, the absence of city walls proved disastrous, in 1575, the States of Holland even considered demolishing the city but this proposal was abandoned, after mediation by William of Orange. From 1588, The Hague also became the seat of the government of the Dutch Republic, in order for the administration to maintain control over city matters, The Hague never received official city status, although it did have many of the privileges normally granted only to cities. In modern administrative law, city rights have no place anymore, only in 1806, when the Kingdom of Holland was a puppet state of the First French Empire, was the settlement granted city rights by Louis Bonaparte. After the Napoleonic Wars, modern-day Belgium and the Netherlands were combined in the United Kingdom of the Netherlands to form a buffer against France, as a compromise, Brussels and Amsterdam alternated as capital every two years, with the government remaining in The Hague. After the separation of Belgium in 1830, Amsterdam remained the capital of the Netherlands, when the government started to play a more prominent role in Dutch society after 1850, The Hague quickly expanded. The growing city annexed the rural municipality of Loosduinen partly in 1903, the city sustained heavy damage during World War II
2.
Nuenen
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Nuenen is a town in the municipality of Nuenen, Gerwen en Nederwetten in the Netherlands. From 1883 to 1885, Vincent van Gogh lived and worked in Nuenen, in 1944, the town was a battle scene during Operation Market Garden. The local dialect is called Peellands, in 2009, Nuenen had a population of 22,437. Nuenen is listed in the 1792 Gazetteer of the Netherlands, which lists it as a village of Brabant, the British lost two tanks, and four American and three British soldiers were killed. The fight is dramatised in episode 4 Replacements of the television series Band of Brothers, in 1882 Van Goghs father became a pastor in Nuenen and the family lived at the vicarage there. After a stay in Drenthe for several months, Van Gogh moved to live with his parents in December 1883, Vincent van Gogh resided in Nuenen from 1883 to 1885. During that time he painted many studies of peasants and weavers that culminated in The Potato Eaters. This painting was stolen from the Van Gogh Museum in December 2002, there is a street named after it in the town, as well as a cafe, college and bar. A statue of Van Gogh is located in the park of the town. Theoretical computer scientist Edsger W. Dijkstra lived in Nuenen later in his life, the following year, the ACM PODC Influential Paper Award in distributed computing was renamed the Dijkstra Prize in his honour. Episode Four of TV World War II mini-series Band of Brothers is partly set in Nuenen, media related to Nuenen at Wikimedia Commons Nuenen travel guide from Wikivoyage
3.
Netherlands
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The Netherlands, also informally known as Holland is the main constituent country of the Kingdom of the Netherlands. It is a densely populated country located in Western Europe with three territories in the Caribbean. The European part of the Netherlands borders Germany to the east, Belgium to the south, and the North Sea to the northwest, sharing borders with Belgium, the United Kingdom. The three largest cities in the Netherlands are Amsterdam, Rotterdam and The Hague, Amsterdam is the countrys capital, while The Hague holds the Dutch seat of parliament and government. The port of Rotterdam is the worlds largest port outside East-Asia, the name Holland is used informally to refer to the whole of the country of the Netherlands. Netherlands literally means lower countries, influenced by its low land and flat geography, most of the areas below sea level are artificial. Since the late 16th century, large areas have been reclaimed from the sea and lakes, with a population density of 412 people per km2 –507 if water is excluded – the Netherlands is classified as a very densely populated country. Only Bangladesh, South Korea, and Taiwan have both a population and higher population density. Nevertheless, the Netherlands is the worlds second-largest exporter of food and agricultural products and this is partly due to the fertility of the soil and the mild climate. In 2001, it became the worlds first country to legalise same-sex marriage, the Netherlands is a founding member of the EU, Eurozone, G-10, NATO, OECD and WTO, as well as being a part of the Schengen Area and the trilateral Benelux Union. The first four are situated in The Hague, as is the EUs criminal intelligence agency Europol and this has led to the city being dubbed the worlds legal capital. The country also ranks second highest in the worlds 2016 Press Freedom Index, the Netherlands has a market-based mixed economy, ranking 17th of 177 countries according to the Index of Economic Freedom. It had the thirteenth-highest per capita income in the world in 2013 according to the International Monetary Fund, in 2013, the United Nations World Happiness Report ranked the Netherlands as the seventh-happiest country in the world, reflecting its high quality of life. The Netherlands also ranks joint second highest in the Inequality-adjusted Human Development Index, the region called Low Countries and the country of the Netherlands have the same toponymy. Place names with Neder, Nieder, Nether and Nedre and Bas or Inferior are in use in all over Europe. They are sometimes used in a relation to a higher ground that consecutively is indicated as Upper, Boven, Oben. In the case of the Low Countries / the Netherlands the geographical location of the region has been more or less downstream. The geographical location of the region, however, changed over time tremendously
4.
Vrije Universiteit Amsterdam
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Vrije Universiteit Amsterdam is a university in Amsterdam, Netherlands, founded in 1880. VU is one of two large, publicly funded universities in the city, the other being the University of Amsterdam. The literal translation of the Dutch name Vrije Universiteit is Free University. Free refers to independence of the university from both the State and Church, both within and outside the university, the institution is commonly referred to as the VU. Although founded as an institution, VU has received government funding on a parity basis with public universities since 1970. Over the past decades, VU has transformed from an institution into a broad. While the Netherlands does not have a ranking system, according to the CWTS Leiden Ranking. The university is located on an urban campus in the southern Buitenveldert neighbourhood of Amsterdam. In 2014, VU had 23,656 registered students, most of whom were full-time students and that year, the university had 2,263 faculty members and researchers, and 1,410 administrative, clerical and technical employees, based on FTE units. The universitys annual endowment for 2014 was circa €480 million, about three quarters of this endowment is government funding, the remainder is made up of tuition fees, research grants, and private funding. The official university seal is entitled The Virgin in the Garden, in 1990, the university adopted the mythical griffin as its common emblem. The position of its wings symbolizes the freedom in the name from both the State and Church. The bright and blue postmodern symbol has been the point of the universitys Main Building ever since. The VU was founded in 1880 by a group of orthodox-Protestant Christians led by Abraham Kuyper as the first orthodox-Protestant university in the Netherlands, Kuyper was a theologian, journalist, politician, and prime minister of the Netherlands from 1901 to 1905. He was a professor of theology at VU as well as the universitys first rector magnificus, kuypers worldview and philosophy is referred to as Neo-Calvinism. As a reflection of his beliefs, Vrije Universiteit literally means Free University to signify independence from government and church. Teaching at the Vrije Universiteit started in 1880 in a few rooms rented at the Scottish Missionary Church, here, Kuyper and four fellow professors began lecturing in three faculties, theology, law, and the arts. By the turn of the 20th century, the Scottish Missionary Church became too small for the number of students. In the following years, the university acquired more buildings throughout the city, in 1905, VU was formally accredited and granted the legal right to award academic degrees
5.
De Bruijn sequence
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In combinatorial mathematics, a de Bruijn sequence of order n on a size-k alphabet A is a cyclic sequence in which every possible length-n string on A occurs exactly once as a substring. Such a sequence is denoted by B and has length kn, there are k n −1 k n distinct de Bruijn sequences B. The sequences are named after the Dutch mathematician Nicolaas Govert de Bruijn, the problem was solved, along with the count 22 n −1 − n, by C. Flye Sainte-Marie in the same year and this was largely forgotten, and Martin proved the existence of such cycles for general alphabet size in place of 2, with an algorithm for constructing them. Finally, when in 1944 Kees Posthumus conjectured the count 22 n −1 − n for binary sequences, de Bruijn proved the conjecture in 1946, karl Popper independently describes these objects in his The Logic of Scientific Discovery, calling them shortest random-like sequences. Taking A =, there are two distinct B,00010111 and 11101000, one being the reverse or negation of the other, two of the 2048 possible B in the same alphabet are 00000100011001010011101011011111 and 00000101001000111110111001101011. The de Bruijn sequences can be constructed by taking a Hamiltonian path of an n-dimensional de Bruijn graph over k symbols, an alternative construction involves concatenating together, in lexicographic order, all the Lyndon words whose length divides n. An inverse Burrows—Wheeler transform can be used to generate the required Lyndon words in lexicographic order, De Bruijn sequences can also be constructed using shift registers or via finite fields. Goal, to construct a B de Bruijn sequence of length 24 =16 using Eulerian 3-D de Bruijn graph cycle. Each edge in this 3-dimensional de Bruijn graph corresponds to a sequence of four digits, if one traverses the edge labeled 1 from 000, one arrives at 001, thereby indicating the presence of the subsequence 0001 in the de Bruijn sequence. To traverse each edge exactly once is to use each of the 16 four-digit sequences exactly once. For example, suppose we follow the following Eulerian path through these nodes,000,000,001,011,111,111,110,101,011,110,100,001,010,101,010,100,000. 0}00011110110010011110110010 {1. each of the eight 3-digit sequences appears exactly twice, and each of the sixteen 4-digit sequences appears exactly once. Mathematically, an inverse Burrows—Wheeler transform on a word w generates a multi-set of equivalence classes consisting of strings and these equivalence classes of strings each contain a Lyndon word as a unique minimum element, so the inverse Burrows—Wheeler transform can be considered to generate a set of Lyndon words. It follows that arranging these Lyndon words in order will yield a de Bruijn sequence B. This process defines the standard permutation, write this permutation in cycle notation with the smallest position in each cycle first, and the cycles sorted in increasing order. For each cycle, replace each number with the letter from string w in that position. Each cycle has now become a Lyndon word, and they are arranged in lexicographic order, for example, to construct the smallest B de Bruijn sequence of length 24 =16, repeat the alphabet 8 times yielding w=abababababababab
6.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
7.
Eindhoven University of Technology
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The Eindhoven University of Technology is a university of technology located in Eindhoven, Netherlands. Its motto is Mens agitat molem, the university was the second of its kind in the Netherlands, only Delft University of Technology existed previously. Until mid-1980 it was known as the Technische Hogeschool Eindhoven, in 2011 QS World University Rankings placed Eindhoven at 146th internationally, but 61st globally for Engineering & IT. In 2003 a European Commission report ranked TU/e at third place among all European research universities, the Eindhoven University of Technology was founded as the Technische Hogeschool Eindhoven on 23 June 1956 by the Dutch government. The University was acknowledged for its research in Automobile sector and it was the second institute of its kind in the Netherlands, preceded only by the Delft University of Technology. It is located on its own campus in the center of Eindhoven and it is currently home to about 240 professors,7200 students,250 PDEng-students,600 Ph. D. students,200 post-doc students and 3000 regular employees. It supports about 100 student associations and 15 alumni associations, yearly, the Eindhoven University of Technology produces almost 3000 scientific publications,140 PhD-awards, and 40 patents. The Eindhoven University of Technology is main participant in the top institutes DPI. One of its students is Gerard Kleisterlee, a former CEO of Philips. The university is in an area where several companies active in technology are doing their research, like Philips, ASML, the university maintains close contacts with most of these companies. As of 29 April 2005, Prof. dr. ir, C. J. van Duijn has the position of rector magnificus. In 2006, the university celebrated its 50th birthday, in a 2003 European Commission report, TU/e was ranked as 3rd among European research universities, based on the impact of its scientific research. In The Times Higher Education Supplement World University Ranking 2005 and it was ranked 74th among world universities, and 67th in 2006. Also, the university maintains partnerships with several Dutch universities and announced a partnership with the Universiteit Utrecht on 3 January 2011. Arno Peels presented the universitys strategic vision document for the period up to 2020, particularly the science park of the vision is costly, with an expected 700 million euro investment in the campus needed for realization of the plan. The Eindhoven University of Technology is a university of the Netherlands. As such its structure and management is determined by the Wet op het Hoger Onderwijs en Wetenschappelijk Onderzoek. The College provides oversight for the departments, the service organizations, the College consists of three people, plus a secretary, The chairman The chairman is the chairman of the college and the main face of the university to the outside world
8.
Jurjen Ferdinand Koksma
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Jurjen Ferdinand Koksma was a Dutch mathematician who specialized in analytic number theory. Koksma received his Ph. D. degree in 1930 at the University of Groningen under supervision of Johannes van der Corput, around the same time, aged 26, he was invited to become full professor at the Vrije Universiteit Amsterdam. He accepted and in 1930 became the first professor in mathematics at this university, Koksma is also one of the founders of the Dutch Mathematisch Centrum. One of Koksmas main works was the book Diophantische Approximationen, published in 1936 by Springer and he also wrote several papers with Paul Erdős. In 1950 he became member of the Royal Netherlands Academy of Arts, Koksma had two brothers who were also mathematicians, Jan Koksma and Marten Koksma. Denjoy–Koksma inequality Low-discrepancy sequence Arie van Deursen, The distinctive character of the Free University in Amsterdam, 1880-2005, Eerdmans Publishing
9.
Stan Ackermans
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Stanislaus Thomas Maria Ackermans was a Dutch mathematician, and the seventh rector magnificus of the Eindhoven University of Technology. He was also one of the founders, the namesake and the first director of the Stan Ackermans Instituut, Ackermans was the son of Rie A. G. Schonk and Anton J. J. M. Ackermans, a school teacher in Amsterdam. Following his secondary education, Ackermans attended the University of Amsterdam, in 1961 he followed his professor to Eindhoven to work under him again, this time on his Ph. D. In the period of 1967–68 he worked at UCLA and he was appointed full professor of mathematics back in Eindhoven in 1972, for the chairs of algebra and functional analysis. Ackermans became dean of the department in 1978, he remained as the dean until 1981. In 1982 he succeeded Professor Hans Erkelens as rector magnificus, Ackermans completed one term as rector. In 1986 he took the initiative in founding the Institute for Continuing Education, algebra en Analyse together with Professor Jack Van Lint — textbook used for decades at the university. An Asymptomatic Method in the Theory of Series, Ackermans 1964 PhD dissertation
10.
Mathematician
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A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems. Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, 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, and 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 works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. 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 working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe. As time passed, many gravitated towards universities. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking. ”Thus, seminars, overall, science became the focus of universities in the 19th and 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. ”Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education, and then 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 an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation. Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology. With professional focus on a variety of problems, theoretical systems
11.
Mathematical analysis
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Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions. These theories are studied in the context of real and complex numbers. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis, analysis may be distinguished from geometry, however, it can be applied to any space of mathematical objects that has a definition of nearness or specific distances between objects. Mathematical analysis formally developed in the 17th century during the Scientific Revolution, early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, a geometric sum is implicit in Zenos paradox of the dichotomy. The explicit use of infinitesimals appears in Archimedes The Method of Mechanical Theorems, in Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle. Zu Chongzhi established a method that would later be called Cavalieris principle to find the volume of a sphere in the 5th century, the Indian mathematician Bhāskara II gave examples of the derivative and used what is now known as Rolles theorem in the 12th century. In the 14th century, Madhava of Sangamagrama developed infinite series expansions, like the power series and his followers at the Kerala school of astronomy and mathematics further expanded his works, up to the 16th century. The modern foundations of analysis were established in 17th century Europe. During this period, calculus techniques were applied to approximate discrete problems by continuous ones, in the 18th century, Euler introduced the notion of mathematical function. Real analysis began to emerge as an independent subject when Bernard Bolzano introduced the definition of continuity in 1816. In 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra widely used in earlier work, instead, Cauchy formulated calculus in terms of geometric ideas and infinitesimals. Thus, his definition of continuity required a change in x to correspond to an infinitesimal change in y. He also introduced the concept of the Cauchy sequence, and started the theory of complex analysis. Poisson, Liouville, Fourier and others studied partial differential equations, the contributions of these mathematicians and others, such as Weierstrass, developed the -definition of limit approach, thus founding the modern field of mathematical analysis. In the middle of the 19th century Riemann introduced his theory of integration, the last third of the century saw the arithmetization of analysis by Weierstrass, who thought that geometric reasoning was inherently misleading, and introduced the epsilon-delta definition of limit. Then, mathematicians started worrying that they were assuming the existence of a continuum of numbers without proof. Around that time, the attempts to refine the theorems of Riemann integration led to the study of the size of the set of discontinuities of real functions, also, monsters began to be investigated
12.
Number theory
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Number theory or, in older usage, arithmetic is a branch of pure mathematics devoted primarily to the study of the integers. It is sometimes called The Queen of Mathematics because of its place in the discipline. Number theorists study prime numbers as well as the properties of objects out of integers or defined as generalizations of the integers. Integers can be considered either in themselves or as solutions to equations, questions in number theory are often best understood through the study of analytical objects that encode properties of the integers, primes or other number-theoretic objects in some fashion. One may also study real numbers in relation to rational numbers, the older term for number theory is arithmetic. By the early century, it had been superseded by number theory. The use of the arithmetic for number theory regained some ground in the second half of the 20th century. In particular, arithmetical is preferred as an adjective to number-theoretic. The first historical find of a nature is a fragment of a table. The triples are too many and too large to have been obtained by brute force, the heading over the first column reads, The takiltum of the diagonal which has been subtracted such that the width. The tables layout suggests that it was constructed by means of what amounts, in language, to the identity 2 +1 =2. If some other method was used, the triples were first constructed and then reordered by c / a, presumably for use as a table. It is not known what these applications may have been, or whether there could have any, Babylonian astronomy, for example. It has been suggested instead that the table was a source of examples for school problems. While Babylonian number theory—or what survives of Babylonian mathematics that can be called thus—consists of this single, striking fragment, late Neoplatonic sources state that Pythagoras learned mathematics from the Babylonians. Much earlier sources state that Thales and Pythagoras traveled and studied in Egypt, Euclid IX 21—34 is very probably Pythagorean, it is very simple material, but it is all that is needed to prove that 2 is irrational. Pythagorean mystics gave great importance to the odd and the even, the discovery that 2 is irrational is credited to the early Pythagoreans. This forced a distinction between numbers, on the one hand, and lengths and proportions, on the other hand, the Pythagorean tradition spoke also of so-called polygonal or figurate numbers
13.
Combinatorics
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Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Many combinatorial questions have historically been considered in isolation, giving an ad hoc solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general methods were developed. One of the oldest and most accessible parts of combinatorics is graph theory, Combinatorics is used frequently in computer science to obtain formulas and estimates in the analysis of algorithms. A mathematician who studies combinatorics is called a combinatorialist or a combinatorist, basic combinatorial concepts and enumerative results appeared throughout the ancient world. Greek historian Plutarch discusses an argument between Chrysippus and Hipparchus of a rather delicate enumerative problem, which was shown to be related to Schröder–Hipparchus numbers. In the Ostomachion, Archimedes considers a tiling puzzle, in the Middle Ages, combinatorics continued to be studied, largely outside of the European civilization. The Indian mathematician Mahāvīra provided formulae for the number of permutations and combinations, later, in Medieval England, campanology provided examples of what is now known as Hamiltonian cycles in certain Cayley graphs on permutations. During the Renaissance, together with the rest of mathematics and the sciences, works of Pascal, Newton, Jacob Bernoulli and Euler became foundational in the emerging field. In modern times, the works of J. J. Sylvester and Percy MacMahon helped lay the foundation for enumerative, graph theory also enjoyed an explosion of interest at the same time, especially in connection with the four color problem. In the second half of the 20th century, combinatorics enjoyed a rapid growth, in part, the growth was spurred by new connections and applications to other fields, ranging from algebra to probability, from functional analysis to number theory, etc. These connections shed the boundaries between combinatorics and parts of mathematics and theoretical science, but at the same time led to a partial fragmentation of the field. Enumerative combinatorics is the most classical area of combinatorics and concentrates on counting the number of combinatorial objects. Although counting the number of elements in a set is a rather broad mathematical problem, fibonacci numbers is the basic example of a problem in enumerative combinatorics. The twelvefold way provides a framework for counting permutations, combinations and partitions. Analytic combinatorics concerns the enumeration of combinatorial structures using tools from complex analysis, in contrast with enumerative combinatorics, which uses explicit combinatorial formulae and generating functions to describe the results, analytic combinatorics aims at obtaining asymptotic formulae. Partition theory studies various enumeration and asymptotic problems related to integer partitions, originally a part of number theory and analysis, it is now considered a part of combinatorics or an independent field. It incorporates the bijective approach and various tools in analysis and analytic number theory, graphs are basic objects in combinatorics
14.
Logic
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Logic, originally meaning the word or what is spoken, is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a relation of logical support between the assumptions of the argument and its conclusion. Historically, logic has been studied in philosophy and mathematics, and recently logic has been studied in science, linguistics, psychology. The concept of form is central to logic. The validity of an argument is determined by its logical form, traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic. Informal logic is the study of natural language arguments, the study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive, on some conceptions of logic, formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as an application of a wholly abstract rule, that is. The works of Aristotle contain the earliest known study of logic. Modern formal logic follows and expands on Aristotle, in many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language, Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is divided into two main branches, propositional logic and predicate logic. Mathematical logic is an extension of logic into other areas, in particular to the study of model theory, proof theory, set theory. Logic is generally considered formal when it analyzes and represents the form of any valid argument type, the form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. Simply put, formalising simply means translating English sentences into the language of logic and this is called showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a variety of form. Second, certain parts of the sentence must be replaced with schematic letters, thus, for example, the expression all Ps are Qs shows the logical form common to the sentences all men are mortals, all cats are carnivores, all Greeks are philosophers, and so on. The schema can further be condensed into the formula A, where the letter A indicates the judgement all - are -, the importance of form was recognised from ancient times
15.
Leiden University
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Leiden University, located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, the Dutch Royal Family and Leiden University still have a close relationship, Queens Juliana and Beatrix and King Willem-Alexander are all former students. Leiden University has seven faculties, over 50 departments and enjoys an international reputation. Shanghai Jiao Tong Universitys 2011 Academic Ranking of World Universities ranked Leiden University as the 29th best university worldwide, the Times Higher Education World University Rankings consistently rank Leiden University as the best university in Continental Europe for Arts and Humanities. During this time Leiden was home to figures as René Descartes, Rembrandt, Christiaan Huygens, Hugo Grotius, Baruch Spinoza. The university is a member of the Coimbra Group, the Europaeum, Leiden University houses more than 40 national and international research institutes. In 1575, the emerging Dutch Republic did not have any universities in its northern heartland, the only other university in the Habsburg Netherlands was the University of Leuven in southern Leuven, firmly under Spanish control. It is said the choice fell on Leiden as a reward for the defence of Leiden against Spanish attacks in the previous year. Ironically, the name of Philip II of Spain, Williams adversary, appears on the foundation certificate. Philip II replied by forbidding any subject to study in Leiden, renowned philosopher Baruch Spinoza was based close to Leiden during this period and interacted with numerous scholars at the university. At the end of the century, Leiden University again became one of Europes leading universities. At the world’s first university low-temperature laboratory, professor Heike Kamerlingh Onnes achieved temperatures of one degree above absolute zero of −273 degrees Celsius. In 1908 he was also the first to succeed in liquifying helium, Kamerlingh Onnes was awarded the Nobel Prize for Physics in 1913. In 2005 the manuscript of Einstein on the theory of the monatomic ideal gas was discovered in one of Leidens libraries. Of the seventy-seven Spinozapremie, nineteen were granted to professors of the Universiteit Leiden, literary historian Frits van Oostrom was the first professor of Leiden to be granted the Spinoza award for his work on developing the NLCM centre into a top research centre. Among other leading professors are Wim Blockmans, professor of Medieval History, the portraits of many famous professors since the earliest days hang in the university aula, one of the most memorable places, as Niebuhr called it, in the history of science. The University Library, which has more than 5 and it houses the largest collections worldwide on Indonesia and the Caribbean. Scholars from all over the world visit Leiden University Library, the oldest in the Netherlands, the anatomical and pathological laboratories of the university are modern, and the museums of geology and mineralogy have been restored
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University of Amsterdam
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The University of Amsterdam is a public university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities and later renamed for the city of Amsterdam and it is one of the largest research universities in Europe with 31,186 students,4,794 staff,1,340 PhD students and an annual budget of €600 million. It is the largest university in the Netherlands by enrollment, the main campus is located in central Amsterdam, with a few faculties located in adjacent boroughs. The university is organised into seven faculties, Humanities, Social and Behavioural Sciences, Economics and Business, Science, Law, Medicine, the University of Amsterdam has produced six Nobel Laureates and five prime ministers of the Netherlands. In 2014, it was ranked 50th in the world, 15th in Europe, in January 1632, the Athenaeum Illustre of Amsterdam was founded by the municipal authorities in Amsterdam. It was mainly devoted to medical teaching, the first two professors were Gerardus Vossius and Caspar Barlaeus. The Athenaeum Illustre provided education comparable to higher education institutions. After training at the Athenaeum, students could complete their education at a university in another town, Amsterdams large degree of religious freedom allowed for the establishment of these institutions. Students of the Colegium Chirugicum and the institutions regularly attended classes at the Athenaeum Illustre. ”The Athenaeum began offering classes for students attending non-academic professional training in pharmacy. The Athenaeum remained an institution until the 19th century, with no more than 250 students. Alumni of the Athenaeum include Cornelis Petrus Tiele, in 1877, the Athenuem Illustre became the Municipal University of Amsterdam and received the right to confer doctoral degrees. This gave the university the same privileges as national universities while being funded by the city of Amsterdam, the professors and lecturers were appointed by the municipal council. This resulted in a staff that was in ways more colorful than the staffs of national universities. The University of Amsterdams municipal status brought about the relatively early addition of the faculties of Economics, after the World War II the dramatic rise in the cost of university education put a constraint on the university’s growth. In 1961 the national government made the university a national university, giving it its current name, funding was now given by the national government instead of the city and the appointment of professors was transferred to the Board of Governors. The city of Amsterdam retained a limited influence until 1971, when the appointment was handed over to the Executive Board, the protest lasted for days and was eventually broken up by the police. During the 1970s and 1980s, the university was often the target of nationwide student actions, the university saw considerable expansion since becoming a national university, from 7,500 students in 1960 to over 32,000 in 2010. In 2007, UvA undertook the construction of the Science Park Amsterdam, much of the park has now been completed
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Royal Netherlands Academy of Arts and Sciences
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The Royal Netherlands Academy of Arts and Sciences is an organization dedicated to the advancement of science and literature in the Netherlands. The Academy is housed in the Trippenhuis in Amsterdam, the Academy advises the Dutch government on scientific matters. The Academy offers solicited and unsolicited advice to parliament, ministries, universities and research institutes, funding agencies, nominations for candidate membership by persons or organizations outside the Academy are accepted. The acceptance criterion is delivered scientific achievements, Academy membership is therefore regarded as a great honor, and prestigious. Besides regular members, there are members and corresponding members. Since a new system was introduced in 2011 there will be no new corresponding members. Each year a maximum of sixteen members is appointed to the Academy, the Royal Netherlands Academy of Arts and Sciences has long embraced the entire field of learning. The Royal Academy comprises two departments, consisting of around 500 members, Science Humanities and Social Sciences Both departments have their own board, the departments, in turn, are divided into sections. The highest organ in the Academy is the meeting of members. The president was Frits van Oostrom until 1 May 2008, after which he was succeeded by Robbert Dijkgraaf, in March 2012, Hans Clevers was elected president and took office in June 2012. In 2015 he was succeeded by José van Dijck, during the French occupation of the Dutch Republic, it was founded as the Koninklijk Instituut van Wetenschappen, Letterkunde en Schoone Kunsten by Lodewijk Napoleon on May 4,1808. In 1816, after the occupation had ended, it was renamed to Koninklijk-Nederlandsch Instituut van Wetenschappen, Letteren en Schoone Kunsten, in 1851 it was disbanded and re-established as the Koninklijke Akademie van Wetenschappen and in 1938 obtained its present name. Since 1812 the Academy has resided in the Trippenhuis in Amsterdam, the institute was awarded the Gouden Ganzenveer in 1955. De Jonge Akademie is a society of younger researchers, founded in 2005 as part of the KNAW. Ten members are elected each year for a term of five years, members are scientists between 25 and 45 years old and are selected for a record of excellence in their research. It was modelled after the similar German Junge Akademie, and both of these academies in turn were used as models for the Global Young Academy, Netherlands Organisation for Applied Scientific Research Netherlands Organisation for Scientific Research Royal Netherlands Academy of Arts and Sciences, official website
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Order of the Netherlands Lion
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The Order of the Netherlands Lion, also referred to as the Order of the Lion of the Netherlands is a Dutch order of chivalry founded by King William I of the Netherlands on 29 September 1815. Since 1980 the Order has been used to recognise merit in the arts, science, sport and literature. The Order ranks after the Military William Order, which is awarded for military merit. The second and third class of the Order are not awarded to foreigners, the King of the Netherlands is the Grand Master of the Order. The Order is issued in three classes, there was also a Medal for Brothers which had not been conferred since 1960. The Brothers became extinct and the grade was abolished in 1994, Wears the badge on a sash on the right shoulder, plus the star on the left chest. Commander - Usually conferred upon Dutch Nobel Prize winners, a few distinguished artists, writers, Wears the badge on a necklet, plus an identical breast cross on the left chest. Knight - Wears the badge on a ribbon on the left chest, Brother - No longer issued, see section below. Wore the medal on a ribbon on the left chest, the badge of the Order is a gilt, white-enamelled Maltese Cross, with the monogram W between the arms of the cross. The obverse central disc is in blue enamel, bearing the motto Virtus Nobilitat, the reverse central disc is plain golden, with the lion from the Netherlands coat-of-arms. The badge hangs from a royal crown, as with all honours awarded by the Netherlands, the insignia comprises a decoration, a miniature and optionally a breast star. The decoration and breast stars are worn at formal occasions or while in state office. While wearing a smoking, it is allowed to wear the miniature, decorations are not worn on any other type of clothing. The decoration hangs from a ribbon and this is tied as a sash, which is worn from the right shoulder to the left hip. The star, consisting of the decoration without crown, is attached to a slightly rounded golden star consisting of forty-eight rays. The rays of the star are alternately scaled and all tied at the ends, the star is worn directly above the waist on the left-hand side of the clothing. The star and the described above are always worn together. The miniature is a ribbon tied as a rosette, behind which a bar of gold braid is attached and this is all attached to a bow
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Penrose tiling
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A Penrose tiling is an example of non-periodic tiling generated by an aperiodic set of prototiles. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated these sets in the 1970s, the aperiodicity of prototiles implies that a shifted copy of a tiling will never match the original. A Penrose tiling may be constructed so as to both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right. A Penrose tiling has many properties, most notably, It is non-periodic. It is self-similar, so the same patterns occur at larger and larger scales, thus, the tiling can be obtained through inflation and every finite patch from the tiling occurs infinitely many times. It is a quasicrystal, implemented as a structure a Penrose tiling will produce Bragg diffraction. Various methods to construct Penrose tilings have been discovered, including matching rules, substitutions or subdivision rules, cut and project schemes, Penrose tilings are simple examples of aperiodic tilings of the plane. The most familiar tilings are periodic, a copy of the tiling can be obtained by translating all of the tiles by a fixed distance in a given direction. Such a translation is called a period of the tiling, more informally, if a tiling has no periods it is said to be non-periodic. A set of prototiles is said to be if it tiles the plane but every such tiling is non-periodic. The subject of aperiodic tilings received new interest in the 1960s when logician Hao Wang noted connections between decision problems and tilings and he observed that if this problem were undecidable, then there would have to exist an aperiodic set of Wang dominoes. At the time, this implausible, so Wang conjectured no such set could exist. Wangs student Robert Berger proved that the Domino Problem was undecidable in his 1964 thesis, raphael Robinson, in a 1971 paper which simplified Bergers techniques and undecidability proof, used this technique to obtain an aperiodic set of just six prototiles. The first Penrose tiling is a set of six prototiles, introduced by Roger Penrose in a 1974 paper. Traces of these ideas can also be found in the work of Albrecht Dürer, acknowledging inspiration from Kepler, Penrose found matching rules for these shapes, obtaining an aperiodic set. His tiling can be viewed as a completion of Keplers finite Aa pattern, Penrose subsequently reduced the number of prototiles to two, discovering the kite and dart tiling and the rhombus tiling. The rhombus tiling was discovered by Robert Ammann in 1976. In this approach, the Penrose tiling is viewed as a set of points, its vertices, the three types of Penrose tiling, P1–P3, are described individually below
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Wayback Machine
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The Internet Archive launched the Wayback Machine in October 2001. It was set up by Brewster Kahle and Bruce Gilliat, and is maintained with content from Alexa Internet, the service enables users to see archived versions of web pages across time, which the archive calls a three dimensional index. Since 1996, the Wayback Machine has been archiving cached pages of websites onto its large cluster of Linux nodes and it revisits sites every few weeks or months and archives a new version. Sites can also be captured on the fly by visitors who enter the sites URL into a search box, the intent is to capture and archive content that otherwise would be lost whenever a site is changed or closed down. The overall vision of the machines creators is to archive the entire Internet, the name Wayback Machine was chosen as a reference to the WABAC machine, a time-traveling device used by the characters Mr. Peabody and Sherman in The Rocky and Bullwinkle Show, an animated cartoon. These crawlers also respect the robots exclusion standard for websites whose owners opt for them not to appear in search results or be cached, to overcome inconsistencies in partially cached websites, Archive-It. Information had been kept on digital tape for five years, with Kahle occasionally allowing researchers, when the archive reached its fifth anniversary, it was unveiled and opened to the public in a ceremony at the University of California, Berkeley. Snapshots usually become more than six months after they are archived or, in some cases, even later. The frequency of snapshots is variable, so not all tracked website updates are recorded, Sometimes there are intervals of several weeks or years between snapshots. After August 2008 sites had to be listed on the Open Directory in order to be included. As of 2009, the Wayback Machine contained approximately three petabytes of data and was growing at a rate of 100 terabytes each month, the growth rate reported in 2003 was 12 terabytes/month, the data is stored on PetaBox rack systems manufactured by Capricorn Technologies. In 2009, the Internet Archive migrated its customized storage architecture to Sun Open Storage, in 2011 a new, improved version of the Wayback Machine, with an updated interface and fresher index of archived content, was made available for public testing. The index driving the classic Wayback Machine only has a bit of material past 2008. In January 2013, the company announced a ground-breaking milestone of 240 billion URLs, in October 2013, the company announced the Save a Page feature which allows any Internet user to archive the contents of a URL. This became a threat of abuse by the service for hosting malicious binaries, as of December 2014, the Wayback Machine contained almost nine petabytes of data and was growing at a rate of about 20 terabytes each week. Between October 2013 and March 2015 the websites global Alexa rank changed from 162 to 208, in a 2009 case, Netbula, LLC v. Chordiant Software Inc. defendant Chordiant filed a motion to compel Netbula to disable the robots. Netbula objected to the motion on the ground that defendants were asking to alter Netbulas website, in an October 2004 case, Telewizja Polska USA, Inc. v. Echostar Satellite, No.02 C3293,65 Fed. 673, a litigant attempted to use the Wayback Machine archives as a source of admissible evidence, Telewizja Polska is the provider of TVP Polonia and EchoStar operates the Dish Network
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Integrated Authority File
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The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly for documentation in libraries and increasingly also by archives, the GND is managed by the German National Library in cooperation with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license, the GND specification provides a hierarchy of high-level entities and sub-classes, useful in library classification, and an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format
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Virtual International Authority File
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The Virtual International Authority File is an international authority file. It is a joint project of national libraries and operated by the Online Computer Library Center. The project was initiated by the US Library of Congress, the German National Library, the National Library of France joined the project on October 5,2007. The project transitions to 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, and refers to the original authority records. The data are available online and are available for research and data exchange. Reciprocal updating uses the Open Archives Initiative Protocol for Metadata Harvesting protocol, the file numbers are also being added to Wikipedia biographical articles and are incorporated into Wikidata. VIAFs 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