Alexandria is the capital city of the Teleorman County, Romania. It is located south-west of Bucharest, towards the Bulgarian border; the city has over 45,000 inhabitants. Alexandria was named after its founder, Alexandru D. Ghica, Prince of Wallachia from April 1834 to 7 October 1842, its population in 1900 was 1,675. Its chief trade was in grain, dispatched by rail to the Danubian port of Zimnicea, or by river to Giurgiu. In 1989, the city had more than six large factories. Cătălin Botezatu, fashion creator Alexandru Colfescu, lawyer, writer Anghel Demetriescu, historian Alexandria travel guide from Wikivoyage Media related to Alexandria, Romania at Wikimedia Commons
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number", it was the Pythagoreans who coined the term "mathematics", with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria, she succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; as these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, proceed to specialize in topics of their own choice at the graduate level.
In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns
In mathematics, topology generalizes the notion of triangulation in a natural way as follows: A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h: K → X. Triangulation is useful in determining the properties of a topological space. For example, one can compute homology and cohomology groups of a triangulated space using simplicial homology and cohomology theories instead of more complicated homology and cohomology theories. For topological manifolds, there is a stronger notion of triangulation: a piecewise-linear triangulation is a triangulation with the extra property – defined for dimensions 0, 1, 2... inductively – that the link of any simplex is a piecewise-linear sphere. The link of a simplex s in a simplicial complex K is a subcomplex of K consisting of the simplices t that are disjoint from s and such that both s and t are faces of some higher-dimensional simplex in K. For instance, in a two-dimensional piecewise-linear manifold formed by a set of vertices and triangles, the link of a vertex s consists of the cycle of vertices and edges surrounding s: if t is a vertex in this cycle, t and s are both endpoints of an edge of K, if t is an edge in this cycle, it and s are both faces of a triangle of K.
This cycle is homeomorphic to a circle, a 1-dimensional sphere. But in this article the word "triangulation" is just used to mean homeomorphic to a simplicial complex. For manifolds of dimension at most 4, any triangulation of a manifold is a piecewise linear triangulation: In any simplicial complex homeomorphic to a manifold, the link of any simplex can only be homeomorphic to a sphere, but in dimension n ≥ 5 the -fold suspension of the Poincaré sphere is a topological manifold with a triangulation, not piecewise-linear: it has a simplex whose link is the Poincaré sphere, a three-dimensional manifold, not homeomorphic to a sphere. This is the double suspension theorem, due to R. D. Edwards in the 1970s; the question of which manifolds have piecewise-linear triangulations has led to much research in topology. Differentiable manifolds and subanalytic sets admit a piecewise-linear triangulation, technically by passing via the PDIFF category. Topological manifolds of dimensions 2 and 3 are always triangulable by an unique triangulation.
As shown independently by James Munkres, Steve Smale and J. H. C. Whitehead, each of these manifolds admits a smooth structure, unique up to diffeomorphism. In dimension 4, the E8 manifold does not admit a triangulation, some compact 4-manifolds have an infinite number of triangulations, all piecewise-linear inequivalent. In dimension greater than 4, Rob Kirby and Larry Siebenmann constructed manifolds that do not have piecewise-linear triangulations. Further, Ciprian Manolescu proved that there exist compact manifolds of dimension 5 that are not homeomorphic to a simplicial complex, i.e. that do not admit a triangulation. An important special case of topological triangulation is that of two-dimensional surfaces, or closed 2-manifolds. There is a standard proof. Indeed, if the surface is given a Riemannian metric, each point x is contained inside a small convex geodesic triangle lying inside a normal ball with centre x; the interiors of finitely many of the triangles will cover the surface. Another simple procedure for triangulating differentiable manifolds was given by Hassler Whitney in 1957, based on his embedding theorem.
In fact, if X is a closed n-submanifold of Rm, subdivide a cubical lattice in Rm into simplices to give a triangulation of Rm. By taking the mesh of the lattice small enough and moving finitely many of the vertices, the triangulation will be in general position with respect to X: thus no simplices of dimension < s = m − n intersect X and each s-simplex intersecting X does so in one interior point. These points of intersection and their barycentres generate an n-dimensional simplicial subcomplex in Rm, lying wholly inside the tubular neighbourhood; the triangulation is given by the projection of this simplicial complex onto X. A Whitney triangulation or clean triangulation of a surface is an embedding of a graph onto the surface in such a way that the faces of the embedding are the cliques of the graph. Equivalently, every face is a triangle, every triangle is a face, the graph is not itself a clique; the clique complex of the graph is homeomorphic to the surface. The 1-skeletons of Whitney triangulations are the locally cyclic graphs other than K4.
Whitehead, J. H. C.. "On C1-Complexes". Annals of Mathematics. Second Series. 41: 809–824. Doi:10.2307/1968861. JSTOR 1968861. Whitehead, J. H. C.. "Manifolds with Transverse Fields in Euclidean Space". The Annals of Mathematics. 73: 154–212. Doi:10.2307/1970
A thesis or dissertation is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings. In some contexts, the word "thesis" or a cognate is used for part of a bachelor's or master's course, while "dissertation" is applied to a doctorate, while in other contexts, the reverse is true; the term graduate thesis is sometimes used to refer to both master's theses and doctoral dissertations. The required complexity or quality of research of a thesis or dissertation can vary by country, university, or program, the required minimum study period may thus vary in duration; the word "dissertation" can at times be used to describe a treatise without relation to obtaining an academic degree. The term "thesis" is used to refer to the general claim of an essay or similar work; the term "thesis" comes from the Greek θέσις, meaning "something put forth", refers to an intellectual proposition. "Dissertation" comes from the Latin dissertātiō, meaning "discussion".
Aristotle was the first philosopher to define the term thesis. "A'thesis' is a supposition of some eminent philosopher that conflicts with the general opinion...for to take notice when any ordinary person expresses views contrary to men's usual opinions would be silly". For Aristotle, a thesis would therefore be a supposition, stated in contradiction with general opinion or express disagreement with other philosophers. A supposition is a statement or opinion that may or may not be true depending on the evidence and/or proof, offered; the purpose of the dissertation is thus to outline the proofs of why the author disagrees with other philosophers or the general opinion. A thesis may be arranged as a thesis by publication or a monograph, with or without appended papers though many graduate programs allow candidates to submit a curated collection of published papers. An ordinary monograph has a title page, an abstract, a table of contents, comprising the various chapters, a bibliography or a references section.
They differ in their structure in accordance with the many different areas of study and the differences between them. In a thesis by publication, the chapters constitute an introductory and comprehensive review of the appended published and unpublished article documents. Dissertations report on a research project or study, or an extended analysis of a topic; the structure of a thesis or dissertation explains the purpose, the previous research literature impinging on the topic of the study, the methods used, the findings of the project. Most world universities use a multiple chapter format: a) an introduction, which introduces the research topic, the methodology, as well as its scope and significance. Degree-awarding institutions define their own house style that candidates have to follow when preparing a thesis document. In addition to institution-specific house styles, there exist a number of field-specific and international standards and recommendations for the presentation of theses, for instance ISO 7144.
Other applicable international standards include ISO 2145 on section numbers, ISO 690 on bibliographic references, ISO 31 on quantities or units. Some older house styles specify that front matter must use a separate page number sequence from the main text, using Roman numerals; the relevant international standard and many newer style guides recognize that this book design practice can cause confusion where electronic document viewers number all pages of a document continuously from the first page, independent of any printed page numbers. They, avoid the traditional separate number sequence for front matter and require a single sequence of Arabic numerals starting with 1 for the first printed page. Presentation requirements, including pagination, layout and color of paper, use of acid-free paper, paper size, order of components, citation style, will be checked page by page by the accepting officer before the thesis is accepted and a receipt is issued. However, strict standards are not always required.
Most Italian universities, for example, have only general requirements on the character size and the page formatting, leave much freedom for the actual typographic details. A thesis or dissertation committee is a committee. In the US, these committees consist of a primary supervisor or advisor and two or more committee members, who supervise the progress of the dissertation and may act as the examining committee, or jury, at the oral examination of the thesis. At most universities, the committee is chosen by the student in conjunction with his or her primary adviser after completion of the comprehensive examinations or prospectus meeting, may consist of members of the comps committee; the committee members are doctors in their field (whether a PhD or other des
Socialist Republic of Romania
The Socialist Republic of Romania refers to Romania under Marxist-Leninist one-party communist rule that existed from 1947 to 1989. From 1947 to 1965, the state was known as the Romanian People's Republic; the country was a Soviet-aligned Eastern Bloc state with a dominant role for the Romanian Communist Party enshrined in its constitutions. As World War II ended, Romania, a former Axis member, was occupied by the Soviet Union, the sole representative of the Allies. On 6 March 1945, after mass demonstrations by communist sympathizers and political pressure from the Soviet representative of the Allied Control Commission, a new pro-Soviet government that included members of the outlawed Romanian Workers' Party was installed. More members of the Workers' Party and communist-aligned parties gained control of the administration and pre-war political leaders were eliminated from political life. In December 1947, King Michael was coerced to abdicate and the People's Republic of Romania was declared.
At first, Romania's scarce post-war resources were drained by the "SovRoms", new tax-exempt Soviet-Romanian companies that allowed the Soviet Union to control Romania's major sources of income. Another drain was the war reparations paid to the Soviet Union. In the 1950s, Romania's communist government began to assert more independence, for example, the withdrawal of all Soviet troops from Romania by 1958. In the 1960s and 1970s, Nicolae Ceaușescu became General Secretary of the Communist Party, Chairman of the State Council and assumed the newly established role of President in 1974. Ceaușescu's denunciation of the 1968 Soviet invasion of Czechoslovakia and a brief relaxation in internal repression helped give him a positive image both at home and in the West. However, rapid economic growth fueled in part by foreign credits gave way to an austerity and political repression that led to the fall of his totalitarian government in December 1989. A large number of people were executed or died in custody during communist Romania's existence, most during the Stalinist era of the 1950s.
While judicial executions between 1945 and 1964 numbered 137, deaths in custody are estimated in the tens or hundreds of thousands. Many more were imprisoned for political, economical or other reasons and suffered abuse, torture and/or death. Geographically, Romania bordered the Black Sea to the east; when King Michael, supported by the main political parties, overthrew Ion Antonescu in August 1944, breaking Romania away from the Axis and bringing it over to the Allied side, Michael could do nothing to erase the memory of his country's recent active participation in the German invasion of the Soviet Union. Romanian forces fought under Soviet command, driving through Northern Transylvania into Hungary proper, on into Czechoslovakia and Austria. However, the Soviets treated Romania as conquered territory, Soviet troops remained in the country as occupying forces under the pretext that Romanian authorities could not guarantee the security and stability of Northern Transylvania; the Yalta Conference had granted the Soviet Union a predominant interest in Romania, the Paris Peace Treaties failed to acknowledge Romania as a co-belligerent, the Red Army was sitting on Romanian soil.
The Communists, as all political parties, played only a minor role in the first Michael's wartime governments, headed by General Constantin Sănătescu, though their presence increased in the one led by Nicolae Rădescu. This changed in March 1945, when Dr. Petru Groza of the Ploughmen's Front, a party associated with the Communists, became prime minister, his government was broad-based on paper, including members of most major prewar parties except the Iron Guard. However, the Communists held the key ministries, most of the ministers nominally representing non-Communist parties were, like Groza himself, fellow travelers; the King was not happy with the direction of this government, but when he attempted to force Groza's resignation by refusing to sign any legislation, Groza chose to enact laws without bothering to obtain Michael's signature. On 8 November 1945, King Michael's name day, a pro-monarchy demonstration in front of the Royal Palace in Bucharest escalated into street fights between opposition supporters and soldiers and pro-government workers, resulting in dozens of killed and wounded.
Despite the King's disapproval, the first Groza government brought women's suffrage. However, it brought the beginnings of Soviet domination of Romania. In the elections of 19 November 1946, the Communist-led Bloc of Democratic Parties claimed 84% of the votes; these elections were characterized by widespread irregularities, including intimidation, electoral fraud, assassinations Archives confirm suspicions at the time that the election results were, in fact, falsified. After forming a government, the Communists moved to eliminate the role of the centrist parties. A show trial of their leadership was arranged, they were put in jail. Other parties were forced to "merge" with the Communists. In 1946 and 1947, several high-ranking members in the pro-Axis government were executed as war criminals for their involvement in the Holocaust and for attacking the Soviet Union. Ant
Columbia University is a private Ivy League research university in Upper Manhattan, New York City. Established in 1754, Columbia is the oldest institution of higher education in New York and the fifth-oldest institution of higher learning in the United States, it is one of nine colonial colleges founded prior to the Declaration of Independence, seven of which belong to the Ivy League. It has been ranked by numerous major education publications as among the top ten universities in the world. Columbia was established as King's College by royal charter of George II of Great Britain in reaction to the founding of Princeton University in New Jersey, it was renamed Columbia College in 1784 following the Revolutionary War and in 1787 was placed under a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved from Madison Avenue to its current location in Morningside Heights and renamed Columbia University. Columbia scientists and scholars have played an important role in the development of notable scientific fields and breakthroughs including: brain-computer interface.
The Columbia University Physics Department has been affiliated with 33 Nobel Prize winners as alumni, faculty or research staff, the third most of any American institution behind MIT and Harvard. In addition, 22 Nobel Prize winners in Physiology and Medicine have been affiliated with Columbia, the third most of any American institution; the university's research efforts include the Lamont-Doherty Earth Observatory, Goddard Institute for Space Studies and accelerator laboratories with major technology firms such as IBM. Columbia is one of the fourteen founding members of the Association of American Universities and was the first school in the United States to grant the M. D. degree. The university administers the Pulitzer Prize annually. Columbia is organized into twenty schools, including three undergraduate schools and numerous graduate schools, it maintains research centers outside of the United States known as Columbia Global Centers. In 2018, Columbia's undergraduate acceptance rate was 5.1%, making it one of the most selective colleges in the United States, the second most selective in the Ivy League after Harvard.
Columbia is ranked as the 3rd best university in the United States by U. S. News & World Report behind Princeton and Harvard. In athletics, the Lions field varsity teams in 29 sports as a member of the NCAA Division I Ivy League conference; the university's endowment stood at $10.9 billion in 2018, among the largest of any academic institution. As of 2018, Columbia's alumni and affiliates include: five Founding Fathers of the United States — among them an author of the United States Constitution and co-author of the Declaration of Independence. S. presidents. Discussions regarding the founding of a college in the Province of New York began as early as 1704, at which time Colonel Lewis Morris wrote to the Society for the Propagation of the Gospel in Foreign Parts, the missionary arm of the Church of England, persuading the society that New York City was an ideal community in which to establish a college. However, it was not until the founding of the College of New Jersey across the Hudson River in New Jersey that the City of New York considered founding a college.
In 1746, an act was passed by the general assembly of New York to raise funds for the foundation of a new college. In 1751, the assembly appointed a commission of ten New York residents, seven of whom were members of the Church of England, to direct the funds accrued by the state lottery towards the foundation of a college. Classes were held in July 1754 and were presided over by the college's first president, Dr. Samuel Johnson. Dr. Johnson was the only instructor of the college's first class, which consisted of a mere eight students. Instruction was held in a new schoolhouse adjoining Trinity Church, located on what is now lower Broadway in Manhattan; the college was founded on October 31, 1754, as King's College by royal charter of King George II, making it the oldest institution of higher learning in the state of New York and the fifth oldest in the United States. In 1763, Dr. Johnson was succeeded in the presidency by Myles Cooper, a graduate of The Queen's College, an ardent Tory. In the charged political climate of the American Revolution, his chief opponent in discussions at the college was an undergraduate of the class of 1777, Alexander Hamilton.
The American Revolutionary War broke out in 1776, was catastrophic for the operation of King's College, which suspended instruction for eight years beginning in 1776 with the arrival of the Continental Army. The suspension continued through the military occupation of New York City by British troops until their departure in 1783; the college's library was looted and its sole building requisitioned for use as a military hospital first by American and British forces. Loyalists were forced to abandon their King's College in New York, seized by the rebels and renamed Columbia College; the Loyalists, led by Bishop Charles Inglis fled to Windsor, Nova Scotia, where the
Harvard University is a private Ivy League research university in Cambridge, with about 6,700 undergraduate students and about 15,250 postgraduate students. Established in 1636 and named for its first benefactor, clergyman John Harvard, Harvard is the United States' oldest institution of higher learning, its history and wealth have made it one of the world's most prestigious universities; the Harvard Corporation is its first chartered corporation. Although never formally affiliated with any denomination, the early College trained Congregational and Unitarian clergy, its curriculum and student body were secularized during the 18th century, by the 19th century, Harvard had emerged as the central cultural establishment among Boston elites. Following the American Civil War, President Charles W. Eliot's long tenure transformed the college and affiliated professional schools into a modern research university. A. Lawrence Lowell, who followed Eliot, further reformed the undergraduate curriculum and undertook aggressive expansion of Harvard's land holdings and physical plant.
James Bryant Conant led the university through the Great Depression and World War II and began to reform the curriculum and liberalize admissions after the war. The undergraduate college became coeducational after its 1977 merger with Radcliffe College; the university is organized into eleven separate academic units—ten faculties and the Radcliffe Institute for Advanced Study—with campuses throughout the Boston metropolitan area: its 209-acre main campus is centered on Harvard Yard in Cambridge 3 miles northwest of Boston. Harvard's endowment is worth $39.2 billion, making it the largest of any academic institution. Harvard is a large residential research university; the nominal cost of attendance is high, but the university's large endowment allows it to offer generous financial aid packages. The Harvard Library is the world's largest academic and private library system, comprising 79 individual libraries holding over 18 million items; the University is cited as one of the world's top tertiary institutions by various organizations.
Harvard's alumni include eight U. S. presidents, more than thirty foreign heads of state, 62 living billionaires, 359 Rhodes Scholars, 242 Marshall Scholars. As of October 2018, 158 Nobel laureates, 18 Fields Medalists, 14 Turing Award winners have been affiliated as students, faculty, or researchers. In addition, Harvard students and alumni have won 10 Academy Awards, 48 Pulitzer Prizes and 108 Olympic medals, have founded a large number of companies worldwide. Harvard was established in 1636 by vote of the Great and General Court of the Massachusetts Bay Colony. In 1638, it acquired British North America's first known printing press. In 1639, it was named Harvard College after deceased clergyman John Harvard, an alumnus of the University of Cambridge, who had left the school £779 and his scholar's library of some 400 volumes; the charter creating the Harvard Corporation was granted in 1650. A 1643 publication gave the school's purpose as "to advance learning and perpetuate it to posterity, dreading to leave an illiterate ministry to the churches when our present ministers shall lie in the dust".
It offered a classic curriculum on the English university model—many leaders in the colony had attended the University of Cambridge—but conformed to the tenets of Puritanism. It was never affiliated with any particular denomination, but many of its earliest graduates went on to become clergymen in Congregational and Unitarian churches; the leading Boston divine Increase Mather served as president from 1685 to 1701. In 1708, John Leverett became the first president, not a clergyman, marking a turning of the college from Puritanism and toward intellectual independence. Throughout the 18th century, Enlightenment ideas of the power of reason and free will became widespread among Congregational ministers, putting those ministers and their congregations in tension with more traditionalist, Calvinist parties; when the Hollis Professor of Divinity David Tappan died in 1803 and the president of Harvard Joseph Willard died a year in 1804, a struggle broke out over their replacements. Henry Ware was elected to the chair in 1805, the liberal Samuel Webber was appointed to the presidency of Harvard two years which signaled the changing of the tide from the dominance of traditional ideas at Harvard to the dominance of liberal, Arminian ideas.
In 1846, the natural history lectures of Louis Agassiz were acclaimed both in New York and on the campus at Harvard College. Agassiz's approach was distinctly idealist and posited Americans' "participation in the Divine Nature" and the possibility of understanding "intellectual existences". Agassiz's perspective on science combined observation with intuition and the assumption that a person can grasp the "divine plan" in all phenomena; when it came to explaining life-forms, Agassiz resorted to matters of shape based on a presumed archetype for his evidence. This dual view of knowledge was in concert with the teachings of Common Sense Realism derived from Scottish philosophers Thomas Reid and Dugald Stewart, whose works were part of the Harvard curriculum at the time; the popularity of Agassiz's efforts to "soar with Plato" also derived from other writings to which Harvard students