University of Modena and Reggio Emilia
The University of Modena and Reggio Emilia, located in Modena and Reggio Emilia, Emilia-Romagna, Italy, is one of the oldest and most prestigious universities in Italy, founded in 1175, with a population of 20,000 students. The medieval university disappeared by 1338 and was replaced by "three public lectureships" which did not award degrees and were suspended in the 1590s "for lack of money"; the university was not reestablished in Modena until the 1680s and did not receive an imperial charter until 1685. Some famous students who attended the University include Ludovico Antonio Muratori, a noted Italian historian and scholar who graduated in 1694, the playwright Carlo Goldoni in the 17th century and, in the last century, Sandro Pertini, who became President of the Italian Republic; the University of Modena dates back to 1175, a few decades after the birth of the University of Bologna, making it one of the oldest universities in Italy and the world. It was established by the city of Modena, which financed professors' contracts through local taxation.
The first to be invited to teach was Pillio da Medicina from Bologna. The School of Law was subsequently made up the nucleus of the University. In the two centuries that followed, the Studium expanded from legal studies to include the training of notaries and the study of medicine as well; the subsequent history of the University was profoundly marked by the changing fortunes of the ruling Este family. Between the sixteenth and seventeenth centuries, when the Court of Este settled in Ferrara, academic titles were no longer awarded, the activities of the Studium were reduced. Only after the Court moved to Modena in 1772 did the University regain its original splendour and academic prestige, receiving an imperial charter from Duke Francis II; the University offered multiple disciplines, including law and surgery, mathematical and natural sciences. The Department of Economics was established in 1968, followed by the Department of Engineering in 1989; the year 1998 was of fundamental importance in the history of the University when the Reggio Emilia site was instituted and the University of Modena and Reggio Emilia was founded, with the support of local institutions.
In fact, Reggio Emilia had an ancient and noble tradition of university studies which ended in 1772 following the reform of Duke Francis II of Este. A School of Law, proposed by the city, is mentioned as early as 1188. In 1532, Emperor Carl V granted the College of Judges the privilege of awarding diplomas and degrees in Law. Duke Alfonse II of Este established a Medical College in 1561 and ten years Emperor Maximilian II authorized the conferral of degrees in medicine. In the seventeenth century, a School of Letters was opened at the Seminary and, in the following century, a chair of Scholastic Theology was established along with schools of grammar and rhetoric. In 1752, the University of Reggio was inaugurated in Palazzo Busetti and consisted of four faculties: Law, Theology and Philosophy. However, its activities continued only until 1772 when, after the reform of Francis II, its right to grant degrees was taken away and given to the University of Modena; the creation of the University of Modena and Reggio Emilia not only combined the ancient traditions of the two cities into one institution, but gave a new and powerful boost to the development of the University, resulting in a substantial growth of scientific and academic activities, which still continues today.
The Department of Engineering and Agriculture was established in Reggio Emilia in 1998, followed in 1999, by the Department of Arts and Humanities in Modena. Subsequently, the University witnessed the birth of the Departments of Communication Sciences and of Education Sciences in Reggio Emilia, while growth continued in Modena with the institution of the Department of Biosciences and Biotechnologies; the university is divided into fourteen Departments: Area: Technology "Enzo Ferrari" Department of Engineering Department of Engineering Sciences and MethodsArea: Life Department of Life SciencesArea: Society Department of Communication and Economics "Marco Biagi" Department of Economics Department of Education and Humanities Department of Law Department of Studies on Language and CultureArea: Health Surgical and Dental Department of Morphological Sciences related to Transplant and Regenerative Medicine Department of Diagnostics and Public Health Medicine Department of Biomedical and Neural Sciences Department of Medical and Surgical SciencesArea: Science Department of Chemical and Geological Sciences Department of Physics and Mathematics Orto Botanico dell'Università di Modena e Reggio Emilia, the university's botanical garden List of early modern universities in Europe List of Italian universities University of Modena and Reggio Emilia website UNIMORE's website for International Students
Évariste Galois was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem standing for 350 years, his work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, the subfield of Galois connections. He died at age 20 from wounds suffered in a duel. Galois was born on 25 October 1811 to Nicolas-Gabriel Adélaïde-Marie, his father was head of Bourg-la-Reine's liberal party. His father became mayor of the village after Louis XVIII returned to the throne in 1814, his mother, the daughter of a jurist, was a fluent reader of Latin and classical literature and was responsible for her son's education for his first twelve years. In October 1823, he entered the Lycée Louis-le-Grand, At the age of 14, he began to take a serious interest in mathematics, he found a copy of Adrien-Marie Legendre's Éléments de Géométrie, which, it is said, he read "like a novel" and mastered at the first reading.
At 15, he was reading the original papers of Joseph-Louis Lagrange, such as the Réflexions sur la résolution algébrique des équations which motivated his work on equation theory, Leçons sur le calcul des fonctions, work intended for professional mathematicians, yet his classwork remained uninspired, his teachers accused him of affecting ambition and originality in a negative way. In 1828, he attempted the entrance examination for the École Polytechnique, the most prestigious institution for mathematics in France at the time, without the usual preparation in mathematics, failed for lack of explanations on the oral examination. In that same year, he entered the École Normale, a far inferior institution for mathematical studies at that time, where he found some professors sympathetic to him. In the following year Galois' first paper, on continued fractions, was published, it was at around the same time that he began making fundamental discoveries in the theory of polynomial equations. He submitted two papers on this topic to the Academy of Sciences.
Augustin-Louis Cauchy refereed these papers, but refused to accept them for publication for reasons that still remain unclear. However, in spite of many claims to the contrary, it is held that Cauchy recognized the importance of Galois' work, that he suggested combining the two papers into one in order to enter it in the competition for the Academy's Grand Prize in Mathematics. Cauchy, an eminent mathematician of the time, though with political views that were at the opposite end from Galois', considered Galois' work to be a winner. On 28 July 1829, Galois' father committed suicide after a bitter political dispute with the village priest. A couple of days Galois made his second and last attempt to enter the Polytechnique, failed yet again, it is undisputed. More plausible accounts state that Galois made too many logical leaps and baffled the incompetent examiner, which enraged Galois; the recent death of his father may have influenced his behavior. Having been denied admission to the Polytechnique, Galois took the Baccalaureate examinations in order to enter the École Normale.
He passed, receiving his degree on 29 December 1829. His examiner in mathematics reported, "This pupil is sometimes obscure in expressing his ideas, but he is intelligent and shows a remarkable spirit of research." He submitted his memoir on equation theory several times, but it was never published in his lifetime due to various events. Though his first attempt was refused by Cauchy, in February 1830 following Cauchy's suggestion he submitted it to the Academy's secretary Joseph Fourier, to be considered for the Grand Prix of the Academy. Fourier died soon after, the memoir was lost; the prize would be awarded that year to Niels Henrik Abel posthumously and to Carl Gustav Jacob Jacobi. Despite the lost memoir, Galois published three papers that year, one of which laid the foundations for Galois theory; the second one was about the numerical resolution of equations. The third was an important one in number theory, in which the concept of a finite field was first articulated. Galois lived during a time of political turmoil in France.
Charles X had succeeded Louis XVIII in 1824, but in 1827 his party suffered a major electoral setback and by 1830 the opposition liberal party became the majority. Charles, faced with abdication, staged a coup d'état, issued his notorious July Ordinances, touching off the July Revolution which ended with Louis-Philippe becoming king. While their counterparts at the Polytechnique were making history in the streets during les Trois Glorieuses and all the other students at the École Normale were locked in by the school's director. Galois was incensed and wrote a blistering letter criticizing the director, which he submitted to the Gazette des Écoles, signing the letter with his full name. Although the Gazette's editor omitted the signature for publication, Galois was expelled. Although his expulsion would have formally taken effect on 4 January 1831, Galois quit school and joined the staunchly Republican artillery unit of the National Guard, he divided his time between his political affiliations.
Due to controversy surrounding the unit, soon after Galois became a member, on 31 December 1830, the artillery of the National Guard was disbanded out of fear that they might destabilize the government. At around the same time, nineteen officers of Galois' former unit were arrested and charged with c
Joseph-Louis Lagrange was an Italian Enlightenment Era mathematician and astronomer. He made significant contributions to the fields of analysis, number theory, both classical and celestial mechanics. In 1766, on the recommendation of Leonhard Euler and d'Alembert, Lagrange succeeded Euler as the director of mathematics at the Prussian Academy of Sciences in Berlin, where he stayed for over twenty years, producing volumes of work and winning several prizes of the French Academy of Sciences. Lagrange's treatise on analytical mechanics, written in Berlin and first published in 1788, offered the most comprehensive treatment of classical mechanics since Newton and formed a basis for the development of mathematical physics in the nineteenth century. In 1787, at age 51, he moved from Berlin to Paris and became a member of the French Academy of Sciences, he remained in France until the end of his life. He was involved in the decimalisation in Revolutionary France, became the first professor of analysis at the École Polytechnique upon its opening in 1794, was a founding member of the Bureau des Longitudes, became Senator in 1799.
Lagrange was one of the creators of the calculus of variations, deriving the Euler–Lagrange equations for extrema of functionals. He extended the method to take into account possible constraints, arriving at the method of Lagrange multipliers. Lagrange invented the method of solving differential equations known as variation of parameters, applied differential calculus to the theory of probabilities and attained notable work on the solution of equations, he proved. His treatise Theorie des fonctions analytiques laid some of the foundations of group theory, anticipating Galois. In calculus, Lagrange developed a novel approach to interpolation and Taylor series, he studied the three-body problem for the Earth and Moon and the movement of Jupiter's satellites, in 1772 found the special-case solutions to this problem that yield what are now known as Lagrangian points. But above all, he is best known for his work on mechanics, where he transformed Newtonian mechanics into a branch of analysis, Lagrangian mechanics as it is now called, presented the so-called mechanical "principles" as simple results of the variational calculus.
Born as Giuseppe Lodovico Lagrangia, Lagrange was of French descent. His paternal great-grandfather was a French army officer who had moved to Turin, the de facto capital of the kingdom of Piedmont-Sardinia at Lagrange's time, married an Italian, his mother was from the countryside of Turin. He was raised as a Roman Catholic, his father, who had charge of the king's military chest and was Treasurer of the Office of Public Works and Fortifications in Turin, should have maintained a good social position and wealth, but before his son grew up he had lost most of his property in speculations. A career as a lawyer was planned out for Lagrange by his father, Lagrange seems to have accepted this willingly, he studied at the University of Turin and his favourite subject was classical Latin. At first he had no great enthusiasm for mathematics, it was not until he was seventeen that he showed any taste for mathematics – his interest in the subject being first excited by a paper by Edmond Halley which he came across by accident.
Alone and unaided he threw himself into mathematical studies. Charles Emmanuel III appointed Lagrange to serve as the "Sostituto del Maestro di Matematica" at the Royal Military Academy of the Theory and Practice of Artillery in 1755, where he taught courses in calculus and mechanics to support the Piedmontese army's early adoption of the ballistics theories of Benjamin Robins and Leonhard Euler. In that capacity, Lagrange was the first to teach calculus in an engineering school. According to Alessandro Papacino D'Antoni, the academy's military commander and famous artillery theorist, Lagrange proved to be a problematic professor with his oblivious teaching style, abstract reasoning, impatience with artillery and fortification-engineering applications. In this Academy one of his students was François Daviet de Foncenex. Lagrange is one of the founders of the calculus of variations. Starting in 1754, he worked on the problem of tautochrone, discovering a method of maximising and minimising functionals in a way similar to finding extrema of functions.
Lagrange wrote several letters to Leonhard Euler between 1756 describing his results. He outlined his "δ-algorithm", leading to the Euler–Lagrange equations of variational calculus and simplifying Euler's earlier analysis. Lagrange applied his ideas to problems of classical mechanics, generalising the results of Euler and Maupertuis. Euler was impressed with Lagrange's results, it has been stated that "with characteristic courtesy he withheld a paper he had written, which covered some of the same ground, in order that the young Italian might have time to complete his work, claim the undisputed invention of the new calculus". Lagrange published his method in two memoirs of the Turin Society in 1762 and 1773. In 1758, with the aid of his pupils, Lagrange established a society, subsequently incorporated as the Turin Aca
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Biblioteca Nacional de España
The Biblioteca Nacional de España is a major public library, the largest in Spain, one of the largest in the world. It is located on the Paseo de Recoletos; the library was founded by King Philip V in 1712 as the Palace Public Library. The Royal Letters Patent that he granted, the predecessor of the current legal deposit requirement, made it mandatory for printers to submit a copy of every book printed in Spain to the library. In 1836, the library's status as Crown property was revoked and ownership was transferred to the Ministry of Governance. At the same time, it was renamed the Biblioteca Nacional. During the 19th century, confiscations and donations enabled the Biblioteca Nacional to acquire the majority of the antique and valuable books that it holds. In 1892 the building was used to host the Historical American Exposition. On March 16, 1896, the Biblioteca Nacional opened to the public in the same building in which it is housed and included a vast Reading Room on the main floor designed to hold 320 readers.
In 1931 the Reading Room was reorganised, providing it with a major collection of reference works, the General Reading Room was created to cater for students and general readers. During the Spanish Civil War close to 500,000 volumes were collected by the Confiscation Committee and stored in the Biblioteca Nacional to safeguard works of art and books held until in religious establishments and private houses. During the 20th century numerous modifications were made to the building to adapt its rooms and repositories to its expanding collections, to the growing volume of material received following the modification to the Legal Deposit requirement in 1958, to the numerous works purchased by the library. Among this building work, some of the most noteworthy changes were the alterations made in 1955 to triple the capacity of the library's repositories, those started in 1986 and completed in 2000, which led to the creation of the new building in Alcalá de Henares and complete remodelling of the building on Paseo de Recoletos, Madrid.
In 1986, when Spain's main bibliographic institutions - the National Newspaper Library, the Spanish Bibliographic Institute and the Centre for Documentary and Bibliographic Treasures - were incorporated into the Biblioteca Nacional, the library was established as the State Repository of Spain's Cultural Memory, making all of Spain's bibliographic output on any media available to the Spanish Library System and national and international researchers and cultural and educational institutions. In 1990 it was made an Autonomous Entity attached to the Ministry of Culture; the Madrid premises are shared with the National Archaeological Museum. The Biblioteca Nacional is Spain's highest library institution and is head of the Spanish Library System; as the country's national library, it is the centre responsible for identifying, preserving and disseminating information about Spain's documentary heritage, it aspires to be an essential point of reference for research into Spanish culture. In accordance with its Articles of Association, passed by Royal Decree 1581/1991 of October 31, 1991, its principal functions are to: Compile and conserve bibliographic archives produced in any language of the Spanish state, or any other language, for the purposes of research and information.
Promote research through the study and reproduction of its bibliographic archive. Disseminate information on Spain's bibliographic output based on the entries received through the legal deposit requirement; the library's collection consists of more than 26,000,000 items, including 15,000,000 books and other printed materials, 4,500,000 graphic materials, 600,000 sound recordings, 510,000 music scores, more than 500,000 microforms, 500,000 maps, 143,000 newspapers and serials, 90,000 audiovisuals, 90,000 electronic documents, 30,000 manuscripts. The current director of the Biblioteca Nacional is Ana Santos Aramburo, appointed in 2013. Former directors include her predecessors Glòria Pérez-Salmerón and Milagros del Corral as well as historian Juan Pablo Fusi and author Rosa Regàs. Given its role as the legal deposit for the whole of Spain, since 1991 it has kept most of the overflowing collection at a secondary site in Alcalá de Henares, near Madrid; the Biblioteca Nacional provides access to its collections through the following library services: Guidance and general information on the institution and other libraries.
Bibliographic information about its collection and those held by other libraries or library systems. Access to its automated catalogue, which contains close to 3,000,000 bibliographic records encompassing all of its collections. Archive consultation in the library's reading rooms. Interlibrary loans. Archive reproduction. Biblioteca Digital Hispánica, digital library launched in 2008 by the Biblioteca Nacional de España List of libraries in Spain Media related to Biblioteca Nacional de España at Wikimedia Commons Official site Official web catalog