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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''. 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 welcomed Dickson as a Ph.D. student, and Dickson initially accepted Harvard's offer, but chose to attend Chicago in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence, Iowa
Independence is a city in, and the county seat of, Buchanan County, Iowa, United States. The population was 6,064 in the 2020 census, an increase from 6,014 in 2000. History Independence was founded in 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 (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 in 1864, a short-lived neighboring village, called New Haven, had grown up on the west side of the river, hence the name New Haven Mill.) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Ross
Arnold Ephraim Ross (August 24, 1906 – September 25, 2002) was a mathematician and educator who founded the Ross Mathematics Program, a number theory summer program for gifted high school students. He was born in Chicago, but spent his youth in Odessa, Ukraine, where he studied with Samuil Shatunovsky. Ross returned to Chicago and enrolled in University of Chicago graduate coursework under E. H. Moore, despite his lack of formal academic training. He received his Ph.D. and married his wife, Bee, in 1931. Ross taught at several institutions including St. Louis University before becoming chair of University of Notre Dame's mathematics department in 1946. He started a teacher training program in mathematics that evolved into the Ross Mathematics Program in 1957 with the addition of high school students. The program moved with him to Ohio State University when he became their department chair in 1963. Though forced to retire in 1976, Ross ran the summer program until 2000. He had ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers. Many other fields, such as fields of rational functions, algebraic function fields, algebraic number fields, and ''p''-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry. Most cryptographic protocols rely on finite fields, i.e., fields with finitely many elements. The relation of two fields is expressed by the notion of a field extension. Galois theory, initiated by Évariste Galois in the 1830s, is devoted to understanding the symmetries of field extensions. Among other results, thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the ''variety of groups''. History Before the nineteenth century, algebra meant ... [...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, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); 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' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) 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 mathematician recorded by history was Hypati ... [...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.. To be eligible for the Cole prize, the author must be a member of the American Mathematical Society or the paper should appear in a recognized North American journal. The first award for algebra was made in 1928 to L. E. 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 reme ... [...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''. 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 session, sectional or societal, during the AAAS Annual Meeting. It is now sponsored by the Fodor Family Trust and includes a prize of $25,000. Recipients List of winners Current rules Previous rules See also * AAAS Award for Science Diplomacy * AAA ... [...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 poly ... [...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 . Dicks ... [...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 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 only fini ... [...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). Dickson's conjecture is further extended by Schinzel's hypothesis H. 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 infi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
