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Raymond Smullyan
Raymond Merrill Smullyan (; May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher. Born in Far Rockaway, New York, Smullyan's first career choice was in stage magic. He earned a BSc from the University of Chicago in 1955 and his PhD from Princeton University in 1959. Smullyan is one of many logicians to have studied with Alonzo Church. Life Smullyan was born on May 25, 1919, in Far Rockaway, Queens, New York, to an Ashkenazi Jewish family. His father was Isidore Smullyan, a Russian-born businessman who emigrated to Belgium when young and graduated from the University of Antwerp, his native language being French. His mother was Rosina Smullyan (née Freeman), a painter and actress born and raised in London. Both parents were musical, his father playing the violin and his mother playing the piano. Smullyan was the youngest of three children. His eldest brother, Emile Benoit Smullyan, later became an econ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Far Rockaway, Queens
Far Rockaway is a neighborhood on the eastern part of the Rockaway peninsula in the New York City borough of Queens. It is the easternmost section of the Rockaways. The neighborhood extends from Beach 32nd Street east to the Nassau County line. Its southern boundary is the Atlantic Ocean; it is one of the neighborhoods along Rockaway Beach. Far Rockaway is located in Queens Community District 14 and its ZIP Codes are 11691 and 11693. It is patrolled by the New York City Police Department's 101st Precinct. History Precolonial and colonial era The indigenous inhabitants of the Rockaways were the Canarsie Indians, a band of Mohegan, whose name was associated with the geography. By 1639, the Mohegan tribe sold most of the Rockaways to the Dutch West India Company. In 1664, the English defeated the Dutch colony and took over their lands in present-day New York.See New Amsterdam In 1685, the band chief, ''Tackapoucha'', and the English governor of the province agreed to s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grace Hofheimer
Grace M. Hofheimer (August 27, 1891 – September 1965) was an American pianist, composer, and educator, author of ''Teaching Techniques For The Piano'' (1954). Early life and education Hofheimer was born in New York City, the daughter of Justinian Alman Hofheimer and Rose Clare Leonard Hofheimer. Her father was a physician. She studied piano with , and Isidor Philipp. At Columbia University she studied music theory under Daniel Gregory Mason. Career Hofheimer was a concert pianist, based in New York City. In 1918, the ''Brooklyn Daily Eagle'' reported that "Miss Hofheimer, who has devoted her time to teaching, possesses an abundant technique and a straightforwardness of interpretation," while noting "a mechanical lack of variety of tone and color, that precluded the expression of the inner essesnce of the compositions." Hofheimer toured for the Edison Company during the 1920-1921 season. She was head of the piano department at the Chase School in Brooklyn, and gave pri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Wisconsin-Madison
A university () is an institution of tertiary education and research which awards academic degrees in several academic disciplines. ''University'' is derived from the Latin phrase , which roughly means "community of teachers and scholars". Universities typically offer both undergraduate and postgraduate programs. The first universities in Europe were established by Catholic monks. The University of Bologna (), Italy, which was founded in 1088, is the first university in the sense of: *being a high degree-awarding institute. *using the word (which was coined at its foundation). *having independence from the ecclesiastic schools and issuing secular as well as non-secular degrees (with teaching conducted by both clergy and non-clergy): grammar, rhetoric, logic, theology, canon law and notarial law.Hunt Janin: "The university in medieval life, 1179–1499", McFarland, 2008, , p. 55f.de Ridder-Symoens, Hilde''A History of the University in Europe: Volume 1, Universities in the M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after the Anglo-Irish philosopher George Berkeley, it is the state's first land-grant university and is the founding campus of the University of California system. Berkeley has an enrollment of more than 45,000 students. The university is organized around fifteen schools of study on the same campus, including the UC Berkeley College of Chemistry, College of Chemistry, the UC Berkeley College of Engineering, College of Engineering, UC Berkeley College of Letters and Science, College of Letters and Science, and the Haas School of Business. It is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". Lawrence Berkeley National Laboratory was originally founded as par ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reed College
Reed College is a Private college, private Liberal arts colleges in the United States, liberal arts college in Portland, Oregon, United States. Founded in 1908, Reed is a residential college with a campus in the Eastmoreland, Portland, Oregon, Eastmoreland neighborhood, Tudor style architecture, Tudor-Gothic Revival architecture, Gothic style architecture, and a forested canyon nature preserve at its center. Reed List of Reed College people, alumni include 123 Fulbright Scholars, 73 Thomas J. Watson Fellowship, Watson Fellows, and three Churchill Scholarship, Churchill Scholars. Its 32 Rhodes Scholars are the second-most for a liberal arts college. Reed is ranked fourth in the United States for the percentage of its graduates who earn a PhD. History The Reed Institute (the legal name of the college) was founded in 1908 and held its first classes in 1911. Reed is named for Oregon pioneers Simeon Gannett Reed (1830–1895) and Amanda Reed (died 1904). Simeon was an entrepreneur in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pacific University
Pacific University is a private university in Forest Grove, Oregon, United States. Founded in 1849 as the Tualatin Academy, the original Forest Grove campus is west of Portland. Affiliated with the United Church of Christ, the school maintains three other campuses in Eugene, Hillsboro, and Woodburn, and has an enrollment of more than 3,000 students. The university has Oregon's only optometry school, and offers doctorates in 14 programs. Pacific competes in NCAA Division III as part of the Northwest Conference, with its teams known as the Boxers. History Tabitha Moffatt Brown immigrated to the Oregon Country over the new Applegate Trail in 1846. She and Harvey L. Clark started a school and orphanage in Forest Grove in 1847 to care for the orphans of Applegate Trail party.Horner, John B''Oregon: Her History, Her Great Men, Her Literature'' Corvallis, OR: Gazette-Times, 1919; pp. 159-160.Carey, Charles Henry. (1922) ''History of Oregon'' Pioneer Historical Publishing Co. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge Rindge And Latin School
The Cambridge Rindge and Latin School, also known as "CRLS" or "Rindge", is a public high school in Cambridge, Massachusetts, United States. It is a part of the Cambridge Public School District. In 1977, two separate schools, Rindge Technical School and Cambridge High and Latin School, merged to form the Cambridge Rindge and Latin School. The newly built high school at the time increased its capacity to more than 2,000 students in all four grades. History Precursors In 1642, the year Harvard College's first class of nine young men was graduated, the General Court made it the duty of Cambridge to require that parents and masters properly educate their children or be fined if they neglected to do so. In 1648, Cambridge set up a public grammar school, Master Elijah Corlett's "lattin schoole," making Cambridge the fifth town (after Boston, Charlestown, Dorchester, and Salem) in the Massachusetts Bay Colony to do so. Corlett's schoolhouse came into the possession of Old Cambridge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Rings
In mathematics, a Boolean ring is a ring for which for all in , that is, a ring that consists of only idempotent elements. An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction or meet , and ring addition to exclusive disjunction or symmetric difference (not disjunction , which would constitute a semiring). Conversely, every Boolean algebra gives rise to a Boolean ring. Boolean rings are named after the founder of Boolean algebra, George Boole. Notation There are at least four different and incompatible systems of notation for Boolean rings and algebras: * In commutative algebra the standard notation is to use for the ring sum of and , and use for their product. * In logic, a common notation is to use for the meet (same as the ring product) and use for the join, given in terms of ring notation (given just above) by . * In set theory and logic it is also common to use fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernest Nagel
Ernest Nagel (; ; November 16, 1901 – September 20, 1985) was an American philosopher of science. Suppes, Patrick (1999)Biographical memoir of Ernest Nagel In '' American National Biograph''y (Vol. 16, pp. 216-218). New York: Oxford University Press. uthor eprint, archived/ref> Along with Rudolf Carnap, Hans Reichenbach, and Carl Hempel, he is sometimes seen as one of the major figures of the logical positivist movement. His 1961 book '' The Structure of Science'' is considered a foundational work in the logic of scientific explanation. Life and career Nagel was born in Nové Mesto nad Váhom (now in Slovakia, then Vágújhely and part of the Austro-Hungarian Empire) to Jewish parents. His mother, Frida Weiss, was from the nearby town of Vrbové (or Verbo). He emigrated to the United States at the age of 10 and became a U.S. citizen in 1919. He received a BSc from the City College of New York (CCNY) in 1923, and earned his PhD from Columbia University in 1931, with a di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Galois Theory
In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to group theory, which makes them simpler and easier to understand. Galois introduced the subject for studying root of a function, roots of polynomials. This allowed him to characterize the polynomial equations that are solvable by radicals in terms of properties of the permutation group of their roots—an equation is by definition ''solvable by radicals'' if its roots may be expressed by a formula involving only integers, nth root, th roots, and the four basic arithmetic operations. This widely generalizes the Abel–Ruffini theorem, which asserts that a general polynomial of degree at least five cannot be solved by radicals. Galois theory has been used to solve classic problems including showing that two problems of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Bronx
The Bronx ( ) is the northernmost of the five Boroughs of New York City, boroughs of New York City, coextensive with Bronx County, in the U.S. state of New York (state), New York. It shares a land border with Westchester County, New York, Westchester County to its north; to its south and west, the New York City borough of Manhattan is across the Harlem River; and to its south and east is the borough of Queens, across the East River. The Bronx, the only New York City borough not primarily located on an island, has a land area of and a population of 1,472,654 at the 2020 United States census, 2020 census. It has the fourth-largest area, fourth-highest population, and third-highest population density of the boroughs.New York State Department of Health''Population, Land Area, and Population Density by County, New York State – 2010'' retrieved on August 8, 2015. The Bronx is divided by the Bronx River into a hillier section in the West Bronx, west, and a flatter East Bronx, easte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
