BIBSYS is an administrative agency set up and organized by the Ministry of Education and Research in Norway. They are a service provider, focusing on the exchange and retrieval of data pertaining to research and learning – metadata related to library resources. BIBSYS are collaborating with all Norwegian universities and university colleges as well as research institutions and the National Library of Norway. 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 Research. BIBSYS offer researchers and others an easy access to library resources by providing the unified search service Oria.no and other library services. They deliver integrated products for the internal operation for research and special libraries as well as open educational resources; as a DataCite member BIBSYS act as a national DataCite representative in Norway and thereby allow all of Norway's higher education and research institutions to use DOI on their research data.
All their products and services are developed in cooperation with their member institutions. BIBSYS began in 1972 as a collaborative project between the Royal Norwegian Society of Sciences and Letters Library, the Norwegian Institute of Technology Library and the Computer Centre at the Norwegian Institute of Technology; 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, by providing them easy access to library resources. BIBSYS is a public administrative agency answerable to the Ministry of Education and Research, administratively organised as a unit at NTNU. In addition to BIBSYS Library System, the product portfolio consists of BISBYS Ask, BIBSYS Brage, BIBSYS Galleri and BIBSYS Tyr. All operation of applications and databases is performed centrally by BIBSYS.
BIBSYS offer a range of services, both in connection with their products and separate services independent of the products they supply. Open access in Norway Om Bibsys
Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
Kurt Friedrich Gödel was an Austrian, American, logician and philosopher. Considered along with Aristotle, Alfred Tarski and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor. Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna; the first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
He showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted axioms of set theory, assuming these axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs, he made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, modal logic. Gödel was born April 28, 1906, in Brünn, Austria-Hungary into the German family of Rudolf Gödel, the manager of a textile factory, Marianne Gödel. Throughout his life, Gödel would remain close to his mother. At the time of his birth the city had a German-speaking majority, his father was Catholic and his mother was Protestant and the children were raised Protestant. The ancestors of Kurt Gödel were active in Brünn's cultural life. For example, his grandfather Joseph Gödel was a famous singer of that time and for some years a member of the Brünner Männergesangverein. Gödel automatically became a Czechoslovak citizen at age 12 when the Austro-Hungarian Empire broke up at the end of World War I.
In his family, young Kurt was known as Herr Warum because of his insatiable curiosity. According to his brother Rudolf, at the age of six or seven Kurt suffered from rheumatic fever. Beginning at age four, Gödel suffered from "frequent episodes of poor health," which would continue for his entire life. Gödel attended the Evangelische Volksschule, a Lutheran school in Brünn from 1912 to 1916, was enrolled in the Deutsches Staats-Realgymnasium from 1916 to 1924, excelling with honors in all his subjects in mathematics and religion. Although Kurt had first excelled in languages, he became more interested in history and mathematics, his interest in mathematics increased when in 1920 his older brother Rudolf left for Vienna to go to medical school at the University of Vienna. During his teens, Kurt studied Gabelsberger shorthand, Goethe's Theory of Colours and criticisms of Isaac Newton, the writings of Immanuel Kant. At the age of 18, Gödel entered the University of Vienna. By that time, he had mastered university-level mathematics.
Although intending to study theoretical physics, he attended courses on mathematics and philosophy. During this time, he adopted ideas of mathematical realism, he read Kant's Metaphysische Anfangsgründe der Naturwissenschaft, participated in the Vienna Circle with Moritz Schlick, Hans Hahn, Rudolf Carnap. Gödel studied number theory, but when he took part in a seminar run by Moritz Schlick which studied Bertrand Russell's book Introduction to Mathematical Philosophy, he became interested in mathematical logic. According to Gödel, mathematical logic was "a science prior to all others, which contains the ideas and principles underlying all sciences."Attending a lecture by David Hilbert in Bologna on completeness and consistency of mathematical systems may have set Gödel's life course. In 1928, Hilbert and Wilhelm Ackermann published Grundzüge der theoretischen Logik, an introduction to first-order logic in which the problem of completeness was posed: Are the axioms of a formal system sufficient to derive every statement, true in all models of the system?
This problem became the topic. In 1929, at the age of 23, he completed his doctoral dissertation under Hans Hahn's supervision. In it, he established his eponymous completeness theorem regarding the first-order predicate calculus, he was awarded his doctorate in 1930, his thesis was published by the Vienna Academy of Science. Kurt Gödel's achievement in modern logic is singular and monumental—indeed it is more than a monument, it is a landmark which will remain visible far in space and time.... The subject of logic has completely changed its nature and possibilities with Gödel's achievement. In 1931 and while still in Vienna, Gödel published
Saunders Mac Lane
Saunders Mac Lane was an American mathematician who co-founded category theory with Samuel Eilenberg. Mac Lane was born in Norwich, near where his family lived in Taftville, he was christened "Leslie Saunders MacLane", but "Leslie" fell into disuse because his parents, Donald MacLane and Winifred Saunders, came to dislike it. He began inserting a space into his surname because his first wife found it difficult to type the name without a space, he was the oldest of three brothers. Another sister died as a baby, his father and grandfather were both ministers. His mother, née Winifred Saunders, studied at Mount Holyoke College and taught English and mathematics. In high school, Mac Lane's favorite subject was chemistry. While in high school, his father died, he came under his grandfather's care, his half-uncle, a lawyer, determined to send him to Yale University, where many of his relatives had been educated, paid his way there beginning in 1926. As a freshman, he became disillusioned with chemistry.
His mathematics instructor, Lester S. Hill, coached him for a local mathematics competition which he won, setting the direction for his future work, he went on to study mathematics and physics as a double major, taking courses from Jesse Beams, Ernest William Brown, Ernest Lawrence, F. S. C. Northrop, Øystein Ore, among others, he graduated from Yale with a B. A. in 1930. During this period, he published his first scientific paper, in physics and co-authored with Irving Langmuir. In 1929, at a party of Yale football supporters in Montclair, New Jersey, Mac Lane had met Robert Maynard Hutchins, the new president of the University of Chicago, who encouraged him to go there for his graduate studies and soon afterwards offered him a scholarship. Mac Lane neglected to apply to the program, but showed up and was admitted anyway. At Chicago, the subjects he studied included set theory with E. H. Moore, number theory with Leonard Eugene Dickson, the calculus of variations with Gilbert Ames Bliss, logic with Mortimer J. Adler.
In 1931, having earned his master's degree and feeling restless at Chicago, he earned a fellowship from the Institute of International Education and became one of the last Americans to study at the University of Göttingen prior to its decline under the Nazis. His greatest influences there were Paul Bernays and Hermann Weyl. By the time he finished his doctorate in 1934, Bernays had been forced to leave because he was Jewish, Weyl became his main examiner. At Göttingen, Mac Lane studied with Gustav Herglotz and Emmy Noether. Within days of finishing his degree, he married Dorothy Jones, from Chicago, soon returned to the U. S. From 1934 through 1938, Mac Lane held short term appointments at Yale University, Harvard University, Cornell University, the University of Chicago, he held a tenure track appointment at Harvard from 1938 to 1947. In 1941, while giving a series of visiting lectures at the University of Michigan, he met Samuel Eilenberg and began what would become a fruitful collaboration on the interplay between algebra and topology.
In 1944 and 1945, he directed Columbia University's Applied Mathematics Group, involved in the war effort as a contractor for the Applied Mathematics Panel. In 1947, he accepted an offer to return to Chicago, where many other famous mathematicians and physicists had recently moved, he traveled as a Guggenheim Fellow to ETH Zurich for the 1947–1948 term, where he worked with Heinz Hopf. Mac Lane succeeded Stone as department chair in 1952, served for six years. Mac Lane was vice president of the National Academy of Sciences and the American Philosophical Society, president of the American Mathematical Society. While presiding over the Mathematical Association of America in the 1950s, he initiated its activities aimed at improving the teaching of modern mathematics, he was a member of 1974 -- 1980, advising the American government. In 1976, he led a delegation of mathematicians to China to study the conditions affecting mathematics there. Mac Lane was elected to the National Academy of Sciences in 1949, received the National Medal of Science in 1989.
After a thesis in mathematical logic, his early work was in valuation theory. He wrote on valuation rings and Witt vectors, separability in infinite field extensions, he started writing on group extensions in 1942, in 1943 began his research on what are now called Eilenberg–MacLane spaces K, having a single non-trivial homotopy group G in dimension n. This work opened the way to group cohomology in general. After introducing, via the Eilenberg–Steenrod axioms, the abstract approach to homology theory, he and Eilenberg originated category theory in 1945, he is known for his work on coherence theorems. A recurring feature of category theory, abstract algebra, of some other mathematics as well, is the use of diagrams, consisting of arrows linking objects, such as products and coproducts. According to McLarty, this diagrammatic approach to contemporary mathematics stems from Mac Lane. Mac Lane coined the term Yoneda lemma for a lemma, an essential background to many central conc
National Library of the Czech Republic
The National Library of the Czech Republic is the central library of the Czech Republic. It is directed by the Ministry of Culture; the library's main building is located in the historical Clementinum building in Prague, where 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 stores older material from Turkey and India. The library 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 library building on Letna plain, between Hradčanská metro station and Sparta Prague's football ground, Letná stadium. In March 2007, following a request for tender, Czech architect Jan Kaplický was selected by a jury to undertake the project, with a projected completion date of 2011. In 2007 the project was delayed following objections regarding its proposed location from government officials including Prague Mayor Pavel Bém and President Václav Klaus. Plans for the building had still not been decided in February 2008, with the matter being referred to the Office for the Protection of Competition in order to determine if the tender had been won fairly. In 2008, Minister of Culture Václav Jehlička announced the end of the project, following a ruling from the European Commission that the tender process had not been carried out legally; 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. List of national and state libraries Official website