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Andrew Gleason
Andrew Mattei Gleason (19212008) was an American mathematician who made fundamental contributions to widely varied areas of mathematics, including the solution of Hilbert's fifth problem, and was a leader in reform and innovation in teaching at all levels.. Gleason's theorem in quantum logic and the Greenwood–Gleason graph, an important example in Ramsey theory, are named for him. As a young World War II naval officer, Gleason broke German and Japanese military codes. After the war he spent his entire academic career at Harvard University, from which he retired in 1992. His numerous academic and scholarly leadership posts included chairmanship of the Harvard Mathematics Department and the Harvard Society of Fellows, and presidency of the American Mathematical Society. He continued to advise the United States government on cryptographic security, and the Commonwealth of Massachusetts on education for children, almost until the end of his life. Gleason won the Newcomb Clevela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gleason–Prange Theorem
A quadratic residue code is a type of cyclic code. Examples Examples of quadratic residue codes include the (7,4) Hamming code over GF(2), the (23,12) binary Golay code over GF(2) and the (11,6) ternary Golay code over GF(3). Constructions There is a quadratic residue code of length p over the finite field GF(l) whenever p and l are primes, p is odd, and l is a quadratic residue modulo p. Its generator polynomial as a cyclic code is given by :f(x)=\prod_(x-\zeta^j) where Q is the set of quadratic residues of p in the set \ and \zeta is a primitive pth root of unity in some finite extension field of GF(l). The condition that l is a quadratic residue of p ensures that the coefficients of f lie in GF(l). The dimension of the code is (p+1)/2. Replacing \zeta by another primitive p-th root of unity \zeta^r either results in the same code or an equivalent code, according to whether or not r is a quadratic residue of p. An alternative construction avoids roots of unity. Define :g(x)=c+ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notices Of The American Mathematical Society
''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since January 1995 is available in its entirety on the journal web site. Articles are peer-reviewed by an editorial board of mathematical experts. Since 2019, the editor-in-chief is Erica Flapan. The cover regularly features mathematical visualization Mathematical phenomena can be understood and explored via visualization. Classically this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century), while today it ...s. The ''Notices'' is self-described to be the world's most widely read mathematical journal. As the membership journal of the American Mathematical Society, the ''Notices'' is sent to the approximately 30,000 AMS members worldwide, one-third of whom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hollis Chair Of Mathematics And Natural Philosophy
The Hollis Chair of Mathematicks and Natural Philosophy is an endowed professorship established at Harvard College in 1727 by Thomas Hollis. The chair, now part of the Physics Department, is the second oldest at Harvard, and the oldest professorship in science in the United States. The spelling of the title of the chair has been retained since its establishment. The original Rules and Orders relating to the chair are still extant. The incumbents have been: * Isaac Greenwood (1727–1737) * John Winthrop (1737–1779) * Samuel Williams (1779–1789) * Samuel Webber (1789–1806) * John Farrar (1807–1838) * Joseph Lovering (1838–1888) * Benjamin Osgood Peirce (1888–1914) * Wallace Clement Sabine (1914–1919) * vacated (January 1919–September 1921) Sabine died in January 1919, and Lyman was not appointed until September 1921. * Theodore Lyman (1921–1926) * Percy Williams Bridgman (1926–1950) * John Hasbrouck Van Vleck (1951–1969) * Andrew Gleason (1969–1992) * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Philosophical Society
The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and community outreach. Considered the first learned society in the United States, it has about 1,000 elected members, and by April 2020 had had only 5,710 members since its creation. Through research grants, published journals, the American Philosophical Society Museum, an extensive library, and regular meetings, the society supports a variety of disciplines in the humanities and the sciences. Philosophical Hall, now a museum, is just east of Independence Hall in Independence National Historical Park; it was designated a National Historic Landmark in 1965. History The Philosophical Society, as it was originally called, was founded in 1743 by Benjamin Franklin, James Alexander, Francis Hopkinson, John Bartram, Philip Syng, Jr. and others as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Academy Of Sciences
The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the National Academy of Medicine (NAM). As a national academy, new members of the organization are elected annually by current members, based on their distinguished and continuing achievements in original research. Election to the National Academy is one of the highest honors in the scientific field. Members of the National Academy of Sciences serve ''pro bono'' as "advisers to the nation" on science, engineering, and medicine. The group holds a congressional charter under Title 36 of the United States Code. Founded in 1863 as a result of an Act of Congress that was approved by Abraham Lincoln, the NAS is charged with "providing independent, objective advice to the nation on matters related to science and technology. ... to provide scien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the '' Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard Society Of Fellows
The Society of Fellows is a group of scholars selected at the beginnings of their careers by Harvard University for their potential to advance academic wisdom, upon whom are bestowed distinctive opportunities to foster their individual and intellectual growth. Junior fellows are appointed by senior fellows based upon previous academic accomplishments and receive generous financial support for three years while they conduct independent research at Harvard University in any discipline, without being required to meet formal degree requirements or to be graded in any way. The only stipulation is that they maintain primary residence in Cambridge, Massachusetts, for the duration of their fellowship. Membership in the society is for life. The society has contributed numerous scholars to the Harvard faculty and thus significantly influenced the tenor of discourse at the university. Among its best-known members are philosopher W. V. O. Quine, Jf '36; behaviorist B. F. Skinner, Jf '36; do ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramsey Theory
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a question of the form: "how big must some structure be to guarantee that a particular property holds?" More specifically, Ron Graham described Ramsey theory as a "branch of combinatorics". Examples A typical result in Ramsey theory starts with some mathematical structure that is then cut into pieces. How big must the original structure be in order to ensure that at least one of the pieces has a given interesting property? This idea can be defined as partition regularity. For example, consider a complete graph of order ''n''; that is, there are ''n'' vertices and each vertex is connected to every other vertex by an edge. A complete graph of order 3 is called a triangle. Now colour each edge either red or blue. How large must ''n'' be i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Logic
In the mathematical study of logic and the physical analysis of quantum foundations, quantum logic is a set of rules for manipulation of propositions inspired by the structure of quantum theory. The field takes as its starting point an observation of Garrett Birkhoff and John von Neumann, that the structure of experimental tests in classical mechanics forms a Boolean algebra, but the structure of experimental tests in quantum mechanics forms a much more complicated structure. Quantum logic has been proposed as the correct logic for propositional inference generally, most notably by the philosopher Hilary Putnam, at least at one point in his career. This thesis was an important ingredient in Putnam's 1968 paper " Is Logic Empirical?" in which he analysed the epistemological status of the rules of propositional logic. Modern philosophers reject quantum logic as a basis for reasoning, because it lacks a material conditional; a common alternative is the system of linear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boston Globe
''The Boston Globe'' is an American daily newspaper founded and based in Boston, Massachusetts. The newspaper has won a total of 27 Pulitzer Prizes, and has a total circulation of close to 300,000 print and digital subscribers. ''The Boston Globe'' is the oldest and largest daily newspaper in Boston. Founded in 1872, the paper was mainly controlled by Irish Catholic interests before being sold to Charles H. Taylor and his family. After being privately held until 1973, it was sold to ''The New York Times'' in 1993 for $1.1billion, making it one of the most expensive print purchases in U.S. history. The newspaper was purchased in 2013 by Boston Red Sox and Liverpool owner John W. Henry for $70million from The New York Times Company, having lost over 90% of its value in 20 years. The newspaper has been noted as "one of the nation's most prestigious papers." In 1967, ''The Boston Globe'' became the first major paper in the U.S. to come out against the Vietnam War. The paper's 2002 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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