1.
United States
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Forty-eight of the fifty states and the federal district are contiguous and located in North America between Canada and Mexico. The state of Alaska is in the northwest corner of North America, bordered by Canada to the east, the state of Hawaii is an archipelago in the mid-Pacific Ocean. The U. S. territories are scattered about the Pacific Ocean, the geography, climate and wildlife of the country are extremely diverse. At 3.8 million square miles and with over 324 million people, the United States is the worlds third- or fourth-largest country by area, third-largest by land area. It is one of the worlds most ethnically diverse and multicultural nations, paleo-Indians migrated from Asia to the North American mainland at least 15,000 years ago. European colonization began in the 16th century, the United States emerged from 13 British colonies along the East Coast. Numerous disputes between Great Britain and the following the Seven Years War led to the American Revolution. On July 4,1776, during the course of the American Revolutionary War, the war ended in 1783 with recognition of the independence of the United States by Great Britain, representing the first successful war of independence against a European power. The current constitution was adopted in 1788, after the Articles of Confederation, the first ten amendments, collectively named the Bill of Rights, were ratified in 1791 and designed to guarantee many fundamental civil liberties. During the second half of the 19th century, the American Civil War led to the end of slavery in the country. By the end of century, the United States extended into the Pacific Ocean. The Spanish–American War and World War I confirmed the status as a global military power. The end of the Cold War and the dissolution of the Soviet Union in 1991 left the United States as the sole superpower. The U. S. is a member of the United Nations, World Bank, International Monetary Fund, Organization of American States. The United States is a developed country, with the worlds largest economy by nominal GDP. It ranks highly in several measures of performance, including average wage, human development, per capita GDP. While the U. S. economy is considered post-industrial, characterized by the dominance of services and knowledge economy, the United States is a prominent political and cultural force internationally, and a leader in scientific research and technological innovations. In 1507, the German cartographer Martin Waldseemüller produced a map on which he named the lands of the Western Hemisphere America after the Italian explorer and cartographer Amerigo Vespucci
2.
California Institute of Technology
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The California Institute of Technology is a private doctorate-granting university located in Pasadena, California, United States. The vocational and preparatory schools were disbanded and spun off in 1910, the university is one among a small group of Institutes of Technology in the United States which is primarily devoted to the instruction of technical arts and applied sciences. Caltech has six divisions with strong emphasis on science and engineering, managing $332 million in 2011 in sponsored research. Its 124-acre primary campus is located approximately 11 mi northeast of downtown Los Angeles, first-year students are required to live on campus, and 95% of undergraduates remain in the on-campus House System at Caltech. Although Caltech has a tradition of practical jokes and pranks. The Caltech Beavers compete in 13 intercollegiate sports in the NCAA Division IIIs Southern California Intercollegiate Athletic Conference, Caltech is frequently cited as one of the worlds best universities. There are 112 faculty members who have elected to the United States National Academies. In addition, numerous faculty members are associated with the Howard Hughes Medical Institute as well as NASA, according to a 2015 Pomona College study, Caltech ranked number one in the U. S. for the percentage of its graduates who go on to earn a PhD. Caltech started as a school founded in Pasadena in 1891 by local businessman and politician Amos G. Throop. The school was known successively as Throop University, Throop Polytechnic Institute, the vocational school was disbanded and the preparatory program was split off to form an independent Polytechnic School in 1907. At a time when research in the United States was still in its infancy, George Ellery Hale. He joined Throops board of trustees in 1907, and soon began developing it and he engineered the appointment of James A. B. Scherer, a literary scholar untutored in science but a capable administrator and fund raiser, scherer persuaded retired businessman and trustee Charles W. Gates to donate $25,000 in seed money to build Gates Laboratory, the first science building on campus. In 1910, Throop moved to its current site, arther Fleming donated the land for the permanent campus site. The promise of Throop attracted physical chemist Arthur Amos Noyes from MIT to develop the institution and assist in establishing it as a center for science, with the onset of World War I, Hale organized the National Research Council to coordinate and support scientific work on military problems. This institution, with its able investigators and excellent research laboratories, through the National Research Council, Hale simultaneously lobbied for science to play a larger role in national affairs, and for Throop to play a national role in science. During the course of the war, Hale, Noyes and Millikan worked together in Washington on the NRC, subsequently, they continued their partnership in developing Caltech. Under the leadership of Hale, Noyes and Millikan, Caltech grew to prominence in the 1920s
3.
Stanford University
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Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California, adjacent to Palo Alto and between San Jose and San Francisco. Its 8, 180-acre campus is one of the largest in the United States, Stanford also has land and facilities elsewhere. The university was founded in 1885 by Leland and Jane Stanford in memory of their only child, Stanford was a former Governor of California and U. S. Senator, he made his fortune as a railroad tycoon. The school admitted its first students 125 years ago on October 1,1891, Stanford University struggled financially after Leland Stanfords death in 1893 and again after much of the campus was damaged by the 1906 San Francisco earthquake. Following World War II, Provost Frederick Terman supported faculty and graduates entrepreneurialism to build self-sufficient local industry in what would later be known as Silicon Valley. The university is one of the top fundraising institutions in the country. There are three schools that have both undergraduate and graduate students and another four professional schools. Students compete in 36 varsity sports, and the university is one of two institutions in the Division I FBS Pac-12 Conference. Stanford faculty and alumni have founded a number of companies that produce more than $2.7 trillion in annual revenue. It is the alma mater of 30 living billionaires,17 astronauts and it is also one of the leading producers of members of the United States Congress. Sixty Nobel laureates and seven Fields Medalists have been affiliated with Stanford as students, alumni, Stanford University was founded in 1885 by Leland and Jane Stanford, dedicated to Leland Stanford Jr, their only child. The institution opened in 1891 on Stanfords previous Palo Alto farm, despite being impacted by earthquakes in both 1906 and 1989, the campus was rebuilt each time. In 1919, The Hoover Institution on War, Revolution and Peace was started by Herbert Hoover to preserve artifacts related to World War I, the Stanford Medical Center, completed in 1959, is a teaching hospital with over 800 beds. The SLAC National Accelerator Laboratory, which was established in 1962, in 2008, 60% of this land remained undeveloped. Besides the central campus described below, the university also operates at more remote locations, some elsewhere on the main campus. Stanfords main campus includes a place within unincorporated Santa Clara County. The campus also includes land in unincorporated San Mateo County, as well as in the city limits of Menlo Park, Woodside. The academic central campus is adjacent to Palo Alto, bounded by El Camino Real, Stanford Avenue, Junipero Serra Boulevard, the United States Postal Service has assigned it two ZIP codes,94305 for campus mail and 94309 for P. O. box mail
4.
Set theory
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Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics, the language of set theory can be used in the definitions of nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor, Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals. Mathematical topics typically emerge and evolve through interactions among many researchers, Set theory, however, was founded by a single paper in 1874 by Georg Cantor, On a Property of the Collection of All Real Algebraic Numbers. Since the 5th century BC, beginning with Greek mathematician Zeno of Elea in the West and early Indian mathematicians in the East, especially notable is the work of Bernard Bolzano in the first half of the 19th century. Modern understanding of infinity began in 1867–71, with Cantors work on number theory, an 1872 meeting between Cantor and Richard Dedekind influenced Cantors thinking and culminated in Cantors 1874 paper. Cantors work initially polarized the mathematicians of his day, while Karl Weierstrass and Dedekind supported Cantor, Leopold Kronecker, now seen as a founder of mathematical constructivism, did not. This utility of set theory led to the article Mengenlehre contributed in 1898 by Arthur Schoenflies to Kleins encyclopedia, in 1899 Cantor had himself posed the question What is the cardinal number of the set of all sets. Russell used his paradox as a theme in his 1903 review of continental mathematics in his The Principles of Mathematics, in 1906 English readers gained the book Theory of Sets of Points by William Henry Young and his wife Grace Chisholm Young, published by Cambridge University Press. The momentum of set theory was such that debate on the paradoxes did not lead to its abandonment, the work of Zermelo in 1908 and Abraham Fraenkel in 1922 resulted in the set of axioms ZFC, which became the most commonly used set of axioms for set theory. The work of such as Henri Lebesgue demonstrated the great mathematical utility of set theory. Set theory is used as a foundational system, although in some areas category theory is thought to be a preferred foundation. Set theory begins with a binary relation between an object o and a set A. If o is a member of A, the notation o ∈ A is used, since sets are objects, the membership relation can relate sets as well. A derived binary relation between two sets is the relation, also called set inclusion. If all the members of set A are also members of set B, then A is a subset of B, for example, is a subset of, and so is but is not. As insinuated from this definition, a set is a subset of itself, for cases where this possibility is unsuitable or would make sense to be rejected, the term proper subset is defined
5.
Topology
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In mathematics, topology is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing. This can be studied by considering a collection of subsets, called open sets, important topological properties include connectedness and compactness. Topology developed as a field of study out of geometry and set theory, through analysis of such as space, dimension. Such ideas go back to Gottfried Leibniz, who in the 17th century envisioned the geometria situs, Leonhard Eulers Seven Bridges of Königsberg Problem and Polyhedron Formula are arguably the fields first theorems. The term topology was introduced by Johann Benedict Listing in the 19th century, by the middle of the 20th century, topology had become a major branch of mathematics. It defines the basic notions used in all branches of topology. Algebraic topology tries to measure degrees of connectivity using algebraic constructs such as homology, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to geometry and together they make up the geometric theory of differentiable manifolds. Geometric topology primarily studies manifolds and their embeddings in other manifolds, a particularly active area is low-dimensional topology, which studies manifolds of four or fewer dimensions. This includes knot theory, the study of mathematical knots, Topology, as a well-defined mathematical discipline, originates in the early part of the twentieth century, but some isolated results can be traced back several centuries. Among these are certain questions in geometry investigated by Leonhard Euler and his 1736 paper on the Seven Bridges of Königsberg is regarded as one of the first practical applications of topology. On 14 November 1750 Euler wrote to a friend that he had realised the importance of the edges of a polyhedron and this led to his polyhedron formula, V − E + F =2. Some authorities regard this analysis as the first theorem, signalling the birth of topology, further contributions were made by Augustin-Louis Cauchy, Ludwig Schläfli, Johann Benedict Listing, Bernhard Riemann and Enrico Betti. Listing introduced the term Topologie in Vorstudien zur Topologie, written in his native German, in 1847, the term topologist in the sense of a specialist in topology was used in 1905 in the magazine Spectator. Their work was corrected, consolidated and greatly extended by Henri Poincaré, in 1895 he published his ground-breaking paper on Analysis Situs, which introduced the concepts now known as homotopy and homology, which are now considered part of algebraic topology. Unifying the work on function spaces of Georg Cantor, Vito Volterra, Cesare Arzelà, Jacques Hadamard, Giulio Ascoli and others, Maurice Fréchet introduced the metric space in 1906. A metric space is now considered a case of a general topological space. In 1914, Felix Hausdorff coined the term topological space and gave the definition for what is now called a Hausdorff space, currently, a topological space is a slight generalization of Hausdorff spaces, given in 1922 by Kazimierz Kuratowski
6.
Associative property
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In mathematics, the associative property is a property of some binary operations. In propositional logic, associativity is a rule of replacement for expressions in logical proofs. That is, rearranging the parentheses in such an expression will not change its value, consider the following equations, +4 =2 + =92 × = ×4 =24. Even though the parentheses were rearranged on each line, the values of the expressions were not altered, since this holds true when performing addition and multiplication on any real numbers, it can be said that addition and multiplication of real numbers are associative operations. Associativity is not to be confused with commutativity, which addresses whether or not the order of two operands changes the result. For example, the order doesnt matter in the multiplication of numbers, that is. Associative operations are abundant in mathematics, in fact, many algebraic structures explicitly require their binary operations to be associative, however, many important and interesting operations are non-associative, some examples include subtraction, exponentiation and the vector cross product. Z = x = xyz for all x, y, z in S, the associative law can also be expressed in functional notation thus, f = f. If a binary operation is associative, repeated application of the produces the same result regardless how valid pairs of parenthesis are inserted in the expression. This is called the generalized associative law, thus the product can be written unambiguously as abcd. As the number of elements increases, the number of ways to insert parentheses grows quickly. Some examples of associative operations include the following, the two methods produce the same result, string concatenation is associative. In arithmetic, addition and multiplication of numbers are associative, i. e. + z = x + = x + y + z z = x = x y z } for all x, y, z ∈ R. x, y, z\in \mathbb. }Because of associativity. Addition and multiplication of numbers and quaternions are associative. Addition of octonions is also associative, but multiplication of octonions is non-associative, the greatest common divisor and least common multiple functions act associatively. Gcd = gcd = gcd lcm = lcm = lcm } for all x, y, z ∈ Z. x, y, z\in \mathbb. }Taking the intersection or the union of sets, ∩ C = A ∩ = A ∩ B ∩ C ∪ C = A ∪ = A ∪ B ∪ C } for all sets A, B, C. Slightly more generally, given four sets M, N, P and Q, with h, M to N, g, N to P, in short, composition of maps is always associative. Consider a set with three elements, A, B, and C, thus, for example, A=C = A
7.
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
8.
Dana Scott
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His research career involved computer science, mathematics, and philosophy. He has worked also on modal logic, topology, and category theory and he received his BA in Mathematics from the University of California, Berkeley, in 1954. He wrote his Ph. D. thesis on Convergent Sequences of Complete Theories under the supervision of Alonzo Church while at Princeton, solomon Feferman writes of this period, Scott began his studies in logic at Berkeley in the early 50s while still an undergraduate. Scott was clearly in line to do a Ph. D. with Tarski, upset by that, Scott left for Princeton where he finished with a Ph. D. under Alonzo Church. But it was not long before the relationship between them was mended to the point that Tarski could say to him, I hope I can call you my student. After completing his Ph. D. studies, he moved to the University of Chicago and this work led to the joint bestowal of the Turing Award on the two, for the introduction of this fundamental concept of computational complexity theory. During this period he started supervising Ph. D. students, such as James Halpern, Scott also began working on modal logic in this period, beginning a collaboration with John Lemmon, who moved to Claremont, California, in 1963. Later, Scott and Montague independently discovered an important generalisation of Kripke semantics for modal and tense logic, John Lemmon and Scott began work on a modal-logic textbook that was interrupted by Lemmons death in 1966. Scott eventually published the work as An Introduction to Modal Logic, following an initial observation of Robert Solovay, Scott formulated the concept of Boolean-valued model, as Solovay and Petr Vopěnka did likewise at around the same time. This work led to the award of the Leroy P. Steele Prize in 1972, Scott took up a post as Professor of Mathematical Logic on the Philosophy faculty of Oxford University in 1972. He was member of Merton College while at Oxford and is now an Honorary Fellow of the college, one of Scotts contributions is his formulation of domain theory, allowing programs involving recursive functions and looping-control constructs to be given denotational semantics. Additionally, he provided a foundation for the understanding of infinitary and continuous information through domain theory, the 2007 EATCS Award for his contribution to theoretical computer science. In 1994, he was inducted as a Fellow of the Association for Computing Machinery, in 2012 he became a fellow of the American Mathematical Society. Finite Automata and Their Decision Problem, a proof of the independence of the continuum hypothesis. In Philosophical Problems in Logic, ed. K. Lambert, gierz, G. Hofmann, K. H. Keimel, K. Lawson, J. D. Mislove, M. W. Scott, D. S. Encyclopedia of Mathematics and its Applications, Scotts trick Scott–Potter set theory Blackburn, de Rijke and Venema. In the Stanford Encyclopedia of Philosophy, solomon Feferman and Anita Burdman Feferman. Cambridge University Press, ISBN 0-521-80240-7, ISBN 978-0-521-80240-6, denotational Semantics, The Scott-Strachey Approach to Programming Language Theory
9.
Measure (mathematics)
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In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, for instance, the Lebesgue measure of the interval in the real numbers is its length in the everyday sense of the word – specifically,1. Technically, a measure is a function that assigns a real number or +∞ to subsets of a set X. It must further be countably additive, the measure of a subset that can be decomposed into a finite number of smaller disjoint subsets, is the sum of the measures of the smaller subsets. In general, if one wants to associate a consistent size to each subset of a set while satisfying the other axioms of a measure. This problem was resolved by defining measure only on a sub-collection of all subsets, the so-called measurable subsets and this means that countable unions, countable intersections and complements of measurable subsets are measurable. Non-measurable sets in a Euclidean space, on which the Lebesgue measure cannot be defined consistently, are complicated in the sense of being badly mixed up with their complement. Indeed, their existence is a consequence of the axiom of choice. Measure theory was developed in stages during the late 19th and early 20th centuries by Émile Borel, Henri Lebesgue, Johann Radon. The main applications of measures are in the foundations of the Lebesgue integral, in Andrey Kolmogorovs axiomatisation of probability theory, probability theory considers measures that assign to the whole set the size 1, and considers measurable subsets to be events whose probability is given by the measure. Ergodic theory considers measures that are invariant under, or arise naturally from, let X be a set and Σ a σ-algebra over X. A function μ from Σ to the real number line is called a measure if it satisfies the following properties, Non-negativity. Countable additivity, For all countable collections i =1 ∞ of pairwise disjoint sets in Σ, μ = ∑ k =1 ∞ μ One may require that at least one set E has finite measure. Then the empty set automatically has measure zero because of countable additivity, because μ = μ = μ + μ + μ + …, which implies that μ =0. If only the second and third conditions of the definition of measure above are met, the pair is called a measurable space, the members of Σ are called measurable sets. If and are two spaces, then a function f, X → Y is called measurable if for every Y-measurable set B ∈ Σ Y. See also Measurable function#Caveat about another setup, a triple is called a measure space. A probability measure is a measure with total measure one – i. e, a probability space is a measure space with a probability measure
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Quasigroup
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In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that division is always possible. Quasigroups differ from groups mainly in that they need not be associative, a quasigroup with an identity element is called a loop. There are at least two structurally equivalent formal definitions of quasigroup, one defines a quasigroup as a set with one binary operation, and the other, from universal algebra, defines a quasigroup as having three primitive operations. The homomorphic image of a quasigroup defined with a binary operation, however. We begin with the first definition, a quasigroup is a set, Q, with a binary operation, ∗, obeying the Latin square property. This states that, for each a and b in Q, the uniqueness requirement can be replaced by the requirement that the magma be cancellative. The unique solutions to these equations are written x = a \ b and y = b / a, the operations \ and / are called, respectively, left and right division. The empty set equipped with the empty binary operation satisfies this definition of a quasigroup, some authors accept the empty quasigroup but others explicitly exclude it. Algebraic structures axiomatized solely by identities are called varieties, many standard results in universal algebra hold only for varieties. Quasigroups are varieties if left and right division are taken as primitive, a quasigroup is a type algebra satisfying the identities, y = x ∗, y = x \, y = ∗ x, y = / x. In other words, Multiplication and division in order, one after the other. Hence if is a quasigroup according to the first definition, then is the same quasigroup in the sense of universal algebra. A loop is a quasigroup with an identity element, that is and it follows that the identity element, e, is unique, and that every element of Q has a unique left and right inverse. Since the presence of an identity element is essential, a loop cannot be empty. e, a loop that is associative is a group. A group can have a non-associative pique isotope, but it cannot have a nonassociative loop isotope, there are also some weaker associativity-like properties which have been given special names. A Bol loop is a loop that either, x ∗ = ∗ z for each x, y and z in Q. A loop that is both a left and right Bol loop is a Moufang loop, a narrower class that is a total symmetric quasigroup in which all conjugates coincide as one operation, xy = x / y = x \ y. Another way to define totally symmetric quasigroup is as a quasigroup which additionally is commutative
11.
Doctor of Philosophy
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A Doctor of Philosophy is a type of doctoral degree awarded by universities in many countries. Ph. D. s are awarded for a range of programs in the sciences, engineering. The Ph. D. is a degree in many fields. The completion of a Ph. D. is often a requirement for employment as a university professor, researcher, individuals with an earned doctorate can use the title of Doctor with their name and use the post-nominal letters Ph. D. The requirements to earn a Ph. D. degree vary considerably according to the country, institution, a person who attains a doctorate of philosophy is automatically awarded the academic title of doctor. A student attaining this level may be granted a Candidate of Philosophy degree at some institutions. A Ph. D. candidate must submit a project, thesis or dissertation often consisting of a body of academic research. In many countries, a candidate must defend this work before a panel of examiners appointed by the university. Universities award other types of doctorates besides the Ph. D. such as the Doctor of Musical Arts, a degree for music performers and the Doctor of Education, in 2016, ELIA launched The Florence Principles on the Doctorate in the Arts. The Florence Principles have been endorsed are supported also by AEC, CILECT, CUMULUS, the degree is abbreviated PhD, from the Latin Philosophiae Doctor, pronounced as three separate letters. In the universities of Medieval Europe, study was organized in four faculties, the faculty of arts. All of these faculties awarded intermediate degrees and final degrees, the doctorates in the higher faculties were quite different from the current Ph. D. degree in that they were awarded for advanced scholarship, not original research. No dissertation or original work was required, only lengthy residency requirements, besides these degrees, there was the licentiate. According to Keith Allan Noble, the first doctoral degree was awarded in medieval Paris around 1150, the doctorate of philosophy developed in Germany as the terminal Teachers credential in the 17th century. Typically, upon completion, the candidate undergoes an oral examination, always public, starting in 2016, in Ukraine Doctor of Philosophy is the highest education level and the first science degree. PhD is awarded in recognition of a contribution to scientific knowledge. A PhD degree is a prerequisite for heading a university department in Ukraine, upon completion of a PhD, a PhD holder can elect to continue his studies and get a post-doctoral degree called Doctor of Sciences, which is the second and the highest science degree in Ukraine. Scandinavian countries were among the early adopters of a known as a doctorate of philosophy
12.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
13.
JSTOR
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JSTOR is a digital library founded in 1995. Originally containing digitized back issues of journals, it now also includes books and primary sources. It provides full-text searches of almost 2,000 journals, more than 8,000 institutions in more than 160 countries have access to JSTOR, most access is by subscription, but some older public domain content is freely available to anyone. William G. Bowen, president of Princeton University from 1972 to 1988, JSTOR originally was conceived as a solution to one of the problems faced by libraries, especially research and university libraries, due to the increasing number of academic journals in existence. Most libraries found it prohibitively expensive in terms of cost and space to maintain a collection of journals. By digitizing many journal titles, JSTOR allowed libraries to outsource the storage of journals with the confidence that they would remain available long-term, online access and full-text search ability improved access dramatically. Bowen initially considered using CD-ROMs for distribution, JSTOR was initiated in 1995 at seven different library sites, and originally encompassed ten economics and history journals. JSTOR access improved based on feedback from its sites. Special software was put in place to make pictures and graphs clear, with the success of this limited project, Bowen and Kevin Guthrie, then-president of JSTOR, wanted to expand the number of participating journals. They met with representatives of the Royal Society of London and an agreement was made to digitize the Philosophical Transactions of the Royal Society dating from its beginning in 1665, the work of adding these volumes to JSTOR was completed by December 2000. The Andrew W. Mellon Foundation funded JSTOR initially, until January 2009 JSTOR operated as an independent, self-sustaining nonprofit organization with offices in New York City and in Ann Arbor, Michigan. JSTOR content is provided by more than 900 publishers, the database contains more than 1,900 journal titles, in more than 50 disciplines. Each object is identified by an integer value, starting at 1. In addition to the site, the JSTOR labs group operates an open service that allows access to the contents of the archives for the purposes of corpus analysis at its Data for Research service. This site offers a facility with graphical indication of the article coverage. Users may create focused sets of articles and then request a dataset containing word and n-gram frequencies and they are notified when the dataset is ready and may download it in either XML or CSV formats. The service does not offer full-text, although academics may request that from JSTOR, JSTOR Plant Science is available in addition to the main site. The materials on JSTOR Plant Science are contributed through the Global Plants Initiative and are only to JSTOR
14.
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
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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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Bibsys
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BIBSYS is an administrative agency set up and organized by the Ministry of Education and Research in Norway. They are a provider, focusing on the exchange, storage and retrieval of data pertaining to research. BIBSYS are collaborating with all Norwegian universities and university colleges as well as research institutions, Bibsys is formally organized as a unit at the Norwegian University of Science and Technology, located in Trondheim, Norway. The board of directors is appointed by Norwegian Ministry of Education, BIBSYS offer researchers, students and others an easy access to library resources by providing the unified search service Oria. no and other library services. They also deliver integrated products for the operation for research. As a DataCite member BIBSYS act as a national DataCite representative in Norway and thereby allow all of Norways higher education, all their products and services are developed in cooperation with their member institutions. The purpose of the project was to automate internal library routines, since 1972 Bibsys has evolved from a library system supplier for two libraries in Trondheim, to developing and operating a national library system for Norwegian research and special libraries. The target group has expanded to include the customers of research and special libraries. BIBSYS is an administrative agency answerable to the Ministry of Education and Research. In addition to BIBSYS Library System, the product consists of BISBYS Ask, BIBSYS Brage, BIBSYS Galleri. All operation of applications and databases is performed centrally by BIBSYS, BIBSYS also offer a range of services, both in connection with their products and separate services independent of the products they supply
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National Diet Library
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The National Diet Library is the only national library in Japan. It was established in 1948 for the purpose of assisting members of the National Diet of Japan in researching matters of public policy, the library is similar in purpose and scope to the United States Library of Congress. The National Diet Library consists of two facilities in Tokyo and Kyoto, and several other branch libraries throughout Japan. The Diets power in prewar Japan was limited, and its need for information was correspondingly small, the original Diet libraries never developed either the collections or the services which might have made them vital adjuncts of genuinely responsible legislative activity. Until Japans defeat, moreover, the executive had controlled all political documents, depriving the people and the Diet of access to vital information. The U. S. occupation forces under General Douglas MacArthur deemed reform of the Diet library system to be an important part of the democratization of Japan after its defeat in World War II. In 1946, each house of the Diet formed its own National Diet Library Standing Committee, hani Gorō, a Marxist historian who had been imprisoned during the war for thought crimes and had been elected to the House of Councillors after the war, spearheaded the reform efforts. Hani envisioned the new body as both a citadel of popular sovereignty, and the means of realizing a peaceful revolution, the National Diet Library opened in June 1948 in the present-day State Guest-House with an initial collection of 100,000 volumes. The first Librarian of the Diet Library was the politician Tokujirō Kanamori, the philosopher Masakazu Nakai served as the first Vice Librarian. In 1949, the NDL merged with the National Library and became the national library in Japan. At this time the collection gained a million volumes previously housed in the former National Library in Ueno. In 1961, the NDL opened at its present location in Nagatachō, in 1986, the NDLs Annex was completed to accommodate a combined total of 12 million books and periodicals. The Kansai-kan, which opened in October 2002 in the Kansai Science City, has a collection of 6 million items, in May 2002, the NDL opened a new branch, the International Library of Childrens Literature, in the former building of the Imperial Library in Ueno. This branch contains some 400,000 items of literature from around the world. Though the NDLs original mandate was to be a library for the National Diet. In the fiscal year ending March 2004, for example, the library reported more than 250,000 reference inquiries, in contrast, as Japans national library, the NDL collects copies of all publications published in Japan. The NDL has an extensive collection of some 30 million pages of documents relating to the Occupation of Japan after World War II. This collection include the documents prepared by General Headquarters and the Supreme Commander of the Allied Powers, the Far Eastern Commission, the NDL maintains a collection of some 530,000 books and booklets and 2 million microform titles relating to the sciences
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National Library of the Czech Republic
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The National Library of the Czech Republic is the central library of the Czech Republic. It is directed by the Ministry of Culture, the librarys main building is located in the historical Clementinum building in Prague, where approximately half of its books are kept. The other half of the collection is stored in the district of Hostivař, the National Library is the biggest library in the Czech Republic, in its funds there are around 6 million documents. The library has around 60,000 registered readers, as well as Czech texts, the library also stores older material from Turkey, Iran and India. The library also houses books for Charles University in Prague, the library won international recognition in 2005 as it received the inaugural Jikji Prize from UNESCO via the Memory of the World Programme for its efforts in digitising old texts. The project, which commenced in 1992, involved the digitisation of 1,700 documents in its first 13 years, the most precious medieval manuscripts preserved in the National Library are the Codex Vyssegradensis and the Passional of Abbes Kunigunde. In 2006 the Czech parliament approved funding for the construction of a new building on Letna plain. In March 2007, following a request for tender, Czech architect Jan Kaplický was selected by a jury to undertake the project, later in 2007 the project was delayed following objections regarding its proposed location from government officials including Prague Mayor Pavel Bém and President Václav Klaus. Later in 2008, Minister of Culture Václav Jehlička announced the end of the project, the library was affected by the 2002 European floods, with some documents moved to upper levels to avoid the excess water. Over 4,000 books were removed from the library in July 2011 following flooding in parts of the main building, there was a fire at the library in December 2012, but nobody was injured in the event. List of national and state libraries Official website