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Philip Franklin
Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis. Dr. Franklin received a B.S. in 1918 from City College of New York (who later awarded him its Townsend Harris Medal for the alumnus who achieved notable postgraduate distinction). He received his M.A. in 1920 and Ph.D. in 1921 both from Princeton University. His dissertation, ''The Four Color Problem'', was supervised by Oswald Veblen. After teaching for one year at Princeton and two years at Harvard University (as the Benjamin Peirce Instructor), Franklin joined the Massachusetts Institute of Technology Department of Mathematics, where he stayed until his 1964 retirement. In 1922, Franklin gave the first proof that all planar graphs with at most 25 vertices can be four-colored. In 1928, Franklin gave the first description of an orthonormal basis for ''L''²( ,1 consisting of continuous functions (now known as " Franklin' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York City
New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the List of United States cities by population density, most densely populated major city in the United States, and is more than twice as populous as second-place Los Angeles. New York City lies at the southern tip of New York (state), New York State, and constitutes the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the world by urban area, urban landmass. With over 20.1 million people in its metropolitan statistical area and 23.5 million in its combined statistical area as of 2020, New York is one of the world's most populous Megacity, megacities, and over 58 million people live within of the city. New York City is a global city, global Culture of New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Graph
In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs. A bicubic graph is a cubic bipartite graph. Symmetry In 1932, Ronald M. Foster began collecting examples of cubic symmetric graphs, forming the start of the Foster census.. Many well-known individual graphs are cubic and symmetric, including the utility graph, the Petersen graph, the Heawood graph, the Möbius–Kantor graph, the Pappus graph, the Desargues graph, the Nauru graph, the Coxeter graph, the Tutte–Coxeter graph, the Dyck graph, the Foster graph and the Biggs–Smith graph. W. T. Tutte classified the symmetric cubic graphs by the smallest integer number ''s'' such that each two oriented paths of length ''s'' can be mapped to each other by exactly one symmetry of the graph. He showed that ''s'' is at most 5, and provided examples of graphs with each possible ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University Faculty
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher learning in the United States and one of the most prestigious and highly ranked universities in the world. The university is composed of ten academic faculties plus Harvard Radcliffe Institute. The Faculty of Arts and Sciences offers study in a wide range of undergraduate and graduate academic disciplines, and other faculties offer only graduate degrees, including professional degrees. Harvard has three main campuses: the Cambridge campus centered on Harvard Yard; an adjoining campus immediately across Charles River in the Allston neighborhood of Boston; and the medical campus in Boston's Longwood Medical Area. Harvard's endowment is valued at $50.9 billion, making it the wealthiest academic institution in the world. Endowment inco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Faculty
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. It is one of the highest-ranked universities in the world. The institution moved to Newark, New Jersey, Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. It is a member of the Ivy League. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest List of colleges and universities in the United States by endowment, endowment per student in the United States. Princeton provides undergraduate education, undergraduate and graduate education, graduate in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Alumni
Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution. It is one of the highest-ranked universities in the world. The institution moved to Newark in 1747, and then to the current site nine years later. It officially became a university in 1896 and was subsequently renamed Princeton University. It is a member of the Ivy League. The university is governed by the Trustees of Princeton University and has an endowment of $37.7 billion, the largest endowment per student in the United States. Princeton provides undergraduate and graduate instruction in the humanities, social sciences, natural sciences, and engineering to approximately 8,500 students on its main campus. It offers postgraduate degrees through the Princeton School of Publi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
City College Of New York Alumni
A city is a human settlement of notable size.Goodall, B. (1987) ''The Penguin Dictionary of Human Geography''. London: Penguin.Kuper, A. and Kuper, J., eds (1996) ''The Social Science Encyclopedia''. 2nd edition. London: Routledge. It can be defined as a permanent and densely settled place with administratively defined boundaries whose members work primarily on non-agricultural tasks. Cities generally have extensive systems for housing, transportation, sanitation, utilities, land use, production of goods, and communication. Their density facilitates interaction between people, government organisations and businesses, sometimes benefiting different parties in the process, such as improving efficiency of goods and service distribution. Historically, city-dwellers have been a small proportion of humanity overall, but following two centuries of unprecedented and rapid urbanization, more than half of the world population now lives in cities, which has had profound consequences for g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1965 Deaths
Events January–February * January 14 – The Prime Minister of Northern Ireland and the Taoiseach of the Republic of Ireland meet for the first time in 43 years. * January 20 ** Lyndon B. Johnson is sworn in for a full term as President of the United States. ** Indonesian President Sukarno announces the withdrawal of the Indonesian government from the United Nations. * January 30 – The state funeral of Sir Winston Churchill takes place in London with the largest assembly of dignitaries in the world until the 2005 funeral of Pope John Paul II. * February 4 – Trofim Lysenko is removed from his post as director of the Institute of Genetics at the Academy of Sciences in the Soviet Union. Lysenkoist theories are now treated as pseudoscience. * February 12 ** The African and Malagasy Common Organization ('; OCAM) is formed as successor to the Afro-Malagasy Union for Economic Cooperation ('; UAMCE), formerly the African and Malagasy Union ('; UAM ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1898 Births
Events January–March * January 1 – New York City annexes land from surrounding counties, creating the City of Greater New York as the world's second largest. The city is geographically divided into five boroughs: Manhattan, Brooklyn, Queens, The Bronx and Staten Island. * January 13 – Novelist Émile Zola's open letter to the President of the French Republic on the Dreyfus affair, ''J'Accuse…!'', is published on the front page of the Paris daily newspaper ''L'Aurore'', accusing the government of wrongfully imprisoning Alfred Dreyfus and of antisemitism. * February 12 – The automobile belonging to Henry Lindfield of Brighton rolls out of control down a hill in Purley, London, England, and hits a tree; thus he becomes the world's first fatality from an automobile accident on a public highway. * February 15 – Spanish–American War: The USS ''Maine'' explodes and sinks in Havana Harbor, Cuba, for reasons never fully established, killing 266 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Václav E
Václav () is a Czech male first name of Slavic origin, sometimes translated into English as Wenceslaus or Wenceslas. These forms are derived from the old Slavic/Czech form of this name: Venceslav. Nicknames are: Vašek, Vašík, Venca, Venda For etymology and cognates in other languages, see Wenceslaus. Václav or Vácslav * Saint Wenceslaus I, Duke of Bohemia (907–935 or 929) (svatý Václav) * Václav Noid Bárta, singer, songwriter, and actor *Václav Binovec, Czech film director and screenwriter * Václav Brožík, painter * Václav Hanka, philologist * Václav Havel, last President of Czechoslovakia (1989 – 1992) and first President of the Czech Republic (1993 – 2003) * Václav Holek, Designer of the ZB-26 light machinegun for Zbrojovka Brno and its descendants * Václav Hollar, graphic artist * Vaclav Jelinek, a Czechoslovak spy, who worked in London under the assumed identity of Erwin van Haarlem * Václav Jiráček, Czech actor * Václav Jírů, Czech photograp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Norbert Wiener
Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher in stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems. Wiener is considered the originator of cybernetics, the science of communication as it relates to living things and machines, with implications for engineering, systems control, computer science, biology, neuroscience, philosophy, and the organization of society. Norbert Wiener is credited as being one of the first to theorize that all intelligent behavior was the result of feedback mechanisms, that could possibly be simulated by machines and was an important early step towards the development of modern artificial intelligence. Biography Youth Wiener was born in Columbia, Missouri, the first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Textbook
A textbook is a book containing a comprehensive compilation of content in a branch of study with the intention of explaining it. Textbooks are produced to meet the needs of educators, usually at educational institutions. Schoolbooks are textbooks and other books used in schools. Today, many textbooks are published in both print and digital formats. History The history of textbooks dates back to ancient civilizations. For example, Ancient Greeks wrote educational texts. The modern textbook has its roots in the mass production made possible by the printing press. Johannes Gutenberg himself may have printed editions of ''Ars Minor'', a schoolbook on Latin grammar by Aelius Donatus. Early textbooks were used by tutors and teachers (e.g. alphabet books), as well as by individuals who taught themselves. The Greek philosopher Socrates lamented the loss of knowledge because the media of transmission were changing. Before the invention of the Greek alphabet 2,500 years ago, knowledge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT Journal Of Mathematics And Physics
The journal ''Studies in Applied Mathematics'' is published by Wiley–Blackwell on behalf of the Massachusetts Institute of Technology. It features scholarly articles on mathematical applications in allied fields, notably computer science, mechanics, astrophysics, geophysics, biophysics and high-energy physics. Its pedigree came from the ''Journal of Mathematics and Physics'' which was founded by the MIT Mathematics Department in 1920. The Journal changed to its present name in 1969. The journal was edited from 1969 by David Benney of the Department of Mathematics, Massachusetts Institute of Technology. According to ISI Journal Citation Reports ''Journal Citation Reports'' (''JCR'') is an annual publicationby Clarivate Analytics (previously the intellectual property of Thomson Reuters). It has been integrated with the Web of Science and is accessed from the Web of Science-Core Collect ..., in 2020 it ranked 26th among the 265 journals in the Applied Mathematics categor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
