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Leonard Eugene Dickson
Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remembered for a three-volume history of number theory, '' History of the Theory of Numbers''. The L. E. Dickson instructorships at the University of Chicago Department of Mathematics are named after him. Life Dickson considered himself a Texan by virtue of having grown up in Cleburne, where his father was a banker, merchant, and real estate investor. He attended the University of Texas at Austin, where George Bruce Halsted encouraged his study of mathematics. Dickson earned a B.S. in 1893 and an M.S. in 1894, under Halsted's supervision. Dickson first specialised in Halsted's own specialty, geometry. A. A. Albert (1955Leonard Eugene Dickson 1874–1954from National Academy of Sciences Both the University of Chicago and Harvard University ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence, Iowa
Independence is a city in, and the county seat of, Buchanan County, Iowa, Buchanan County, Iowa, United States. The population was 6,064 at the 2020 United States census, 2020 census. History Independence was founded on June 15, 1847 near the center of present-day Buchanan County. The original town plat was a simple nine-block grid on the east side of the Wapsipinicon River. The town was intended as an alternative to Quasqueton, Iowa, Quasqueton (then called Quasequetuk), which was the county seat prior to 1847. The village of Independence had fewer than 15 persons when the county seat was transferred there. On Main Street, on the west bank of the Wapsipinicon, a six-story grist mill was built in 1867. Some of its foundation stones were taken from that of an earlier mill, the New Haven Mill, built in 1854, that was used for wool processing. (Prior to the incorporation of Independence on October 15, 1864, a short-lived neighboring village, called New Haven, had grown up on th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mina Rees
Mina Spiegel Rees (August 2, 1902 – October 25, 1997) was an American mathematician. She is known for her assistance to the US Government during WWII, as well as making several breakthroughs for women in science. Her most notable accomplishments include becoming the first female President of the American Association for the Advancement of Science (1971) and head of the mathematics department of the Office of Naval Research of the US. Rees was a pioneer in the history of computing and helped establish funding streams and institutional infrastructure for research. She also helped other women succeed in mathematics with her involvement in the Association for Women in Mathematics as well as her life-long career as a professor at Hunter College. Personal life Rees was the daughter of Moses and Alice Louise (née Stackhouse) Rees. Her mother (Alice Louise) emigrated from Germany in 1882. Mina Rees grew up with four siblings: Elsie Isabella Rees, Albert L Rees, Clyde Harvey Rees, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's 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", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory.. The prize is named after Frank Nelson Cole, who served the Society for 25 years. The Cole Prize in algebra was funded by Cole himself, from funds given to him as a retirement gift; the prize fund was later augmented by his son, leading to the double award.. The prizes recognize a notable research work in algebra (given every three years) or number theory (given every three years) that has appeared in the last six years. The work must be published in a recognized, peer-reviewed venue. The first award for algebra was made in 1928 to L. E. Dickson, while the first award for number theory was made in 1931 to H. S. Vandiver. Frank Nelson Cole Prize in Algebra Frank Nelson Cole Prize in Number Theory For full citations, see exter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newcomb Cleveland Prize
The Newcomb Cleveland Prize of the American Association for the Advancement of Science (AAAS) is annually awarded to author(s) of outstanding scientific paper published in the Research Articles or Reports sections of ''Science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...''. Established in 1923, funded by Newcomb Cleveland who remained anonymous until his death in 1951, and for this period it was known as the AAAS Thousand Dollar Prize. "The prize was inspired by Mr. Cleveland's belief that it was the scientist who counted and who needed the encouragement an unexpected monetary award could give." The present rules were instituted in 1975, previously it had gone to the author(s) of noteworthy papers, representing an outstanding contribution to science, presented in a regular sess ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Invariant Theory
In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic (usually dividing the order of the group). The study of modular invariants was originated in about 1914 by . Dickson invariant When ''G'' is the finite general linear group GL''n''(F''q'') over the finite field F''q'' of order a prime power ''q'' acting on the ring F''q'' 'X''1, ...,''X''''n''in the natural way, found a complete set of invariants as follows. Write 'e''1, ..., ''e''''n''for the determinant of the matrix whose entries are ''X'', where ''e''1, ..., ''e''''n'' are non-negative integers. For example, the Moore determinant ,1,2of order 3 is :\begin x_1 & x_1^q & x_1^\\x_2 & x_2^q & x_2^\\x_3 & x_3^q & x_3^ \end Then under the action of an element ''g'' of GL''n''(F''q'') these determinants are all multiplied by det(''g''), so they are all invariants of SL''n''(F''q'') and the ratios 'e''1, ...,''e''''n''thinsp;/ , 1,&nb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dickson Polynomial
In mathematics, the Dickson polynomials, denoted , form a polynomial sequence introduced by . They were rediscovered by in his study of Brewer sums and have at times, although rarely, been referred to as Brewer polynomials. Over the complex numbers, Dickson polynomials are essentially equivalent to Chebyshev polynomials with a change of variable, and, in fact, Dickson polynomials are sometimes called Chebyshev polynomials. Dickson polynomials are generally studied over finite fields, where they sometimes may not be equivalent to Chebyshev polynomials. One of the main reasons for interest in them is that for fixed , they give many examples of '' permutation polynomials''; polynomials acting as permutations of finite fields. Definition First kind For integer and in a commutative ring with identity (often chosen to be the finite field ) the Dickson polynomials (of the first kind) over are given by :D_n(x,\alpha)=\sum_^\frac \binom (-\alpha)^i x^ \,. The first few Dickson pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dickson Invariant (other) studied by Dickson
{{mathdab ...
In mathematics, the Dickson invariant, named after Leonard Eugene Dickson, may mean: *The Dickson invariant of an element of the orthogonal group in characteristic 2 *A modular invariant of a group In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic (usually dividing the order of the group). The study of modular invariants was originated in about 1914 by . Dick ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dickson's Lemma
In mathematics, Dickson's lemma states that every set of n-tuples of natural numbers has finitely many minimal elements. This simple fact from combinatorics has become attributed to the American algebraist L. E. Dickson, who used it to prove a result in number theory about perfect numbers. However, the lemma was certainly known earlier, for example to Paul Gordan in his research on invariant theory.. Example Let K be a fixed natural number, and let S = \ be the set of pairs of numbers whose product is at least K. When defined over the positive real numbers, S has infinitely many minimal elements of the form (x,K/x), one for each positive number x; this set of points forms one of the branches of a hyperbola. The pairs on this hyperbola are minimal, because it is not possible for a different pair that belongs to S to be less than or equal to (x,K/x) in both of its coordinates. However, Dickson's lemma concerns only tuples of natural numbers, and over the natural numbers there are on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dickson's Conjecture
In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by that for a finite set of linear forms , , ..., with , there are infinitely many positive integers for which they are all prime, unless there is a congruence condition preventing this . The case ''k'' = 1 is Dirichlet's theorem. Two other special cases are well-known conjectures: there are infinitely many twin primes (''n'' and 2 + ''n'' are primes), and there are infinitely many Sophie Germain primes (''n'' and 1 + 2''n'' are primes). Generalized Dickson's conjecture Given ''n'' polynomials with positive degrees and integer coefficients (''n'' can be any natural number) that each satisfy all three conditions in the Bunyakovsky conjecture, and for any prime ''p'' there is an integer ''x'' such that the values of all ''n'' polynomials at ''x'' are not divisible by ''p'', then there are infinitely many positive integers ''x'' such that all values of these ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cayley–Dickson Construction
In mathematics, the Cayley–Dickson construction, sometimes also known as the Cayley–Dickson process or the Cayley–Dickson procedure produces a sequence of algebra over a field, algebras over the field (mathematics), field of real numbers, each with twice the dimension of a vector space, dimension of the previous one. It is named after Arthur Cayley and Leonard Eugene Dickson. The algebras produced by this process are known as Cayley–Dickson algebras, for example complex numbers, quaternions, and octonions. These examples are useful composition algebras frequently applied in mathematical physics. The Cayley–Dickson construction defines a new algebra as a Cartesian product of an algebra with itself, with multiplication defined in a specific way (different from the componentwise operation, componentwise multiplication) and an involution (mathematics), involution known as ''conjugation''. The product of an element and its complex conjugate, conjugate (or sometimes the square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Williamson (mathematician)
John Williamson (23 May 1901 – 1949) was a Scottish mathematician who worked in the fields of algebra, invariant theory, and linear algebra. Among other contributions, he is known for the Williamson construction of Hadamard matrices. Williamson graduated from the University of Edinburgh with first-class honours in 1922. Awarded a Commonwealth Fellowship in 1925, he studied at the University of Chicago under the direction of L. E. Dickson and E. H. Moore, receiving the Ph.D. in 1927. He held a Lectureship in Mathematics at the University of St Andrews and an Associate Professorship in Mathematics at Johns Hopkins University The Johns Hopkins University (often abbreviated as Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland, United States. Founded in 1876 based on the European research institution model, J .... See also * Williamson conjecture References External links * * 1901 births 1949 deat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
