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In mathematics, a Dedekind cut, named after Richard Dedekind, is a partition of the rational numbers into two non-empty parts A and B, such that all elements of A are less than all elements of B, and A contains no greatest element.
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mathematics and Dedekind
In mathematics, the extent to which unique factorization fails in the ring of integers of an algebraic number field ( or more generally any Dedekind domain ) can be described by a certain group known as an ideal class group ( or class group ).
Although the formalisation of logic was much advanced by the work of such figures as Gottlob Frege, Giuseppe Peano, Bertrand Russell, and Richard Dedekind, the story of modern proof theory is often seen as being established by David Hilbert, who initiated what is called Hilbert's program in the foundations of mathematics.
Dedekind, who felt that there were significant gaps at the time in his mathematics education, considered that the occasion to study with Dirichlet made him " a new human being ".
The use of multisets in mathematics predates the name " multiset " by nearly 90 years: Richard Dedekind used multisets in a paper published in 1888.
In mathematics, in particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study of Dedekind domains.
In mathematics, the Chowla – Selberg formula is the evaluation of a certain product of values of the Gamma function at rational values in terms of values of the Dedekind eta function at imaginary quadratic irrational numbers.
In mathematics, Dedekind sums, named after Richard Dedekind, are certain sums of products of a sawtooth function, and are given by a function D of three integer variables.
In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζ < sub > K </ sub >( s ), is a generalization of the Riemann zeta function — which is obtained by specializing to the case where K is the rational numbers Q.
mathematics and cut
Having studied Peter for so long, I decided he was quite unfitted for any career except art, so I cut Latin, Algebra, high mathematics and substituted dramatics instead.
In algebraic topology, a branch of mathematics, the excision theorem is a useful theorem about relative homology — given topological spaces X and subspaces A and U such that U is also a subspace of A, the theorem says that under certain circumstances, we can cut out ( excise ) U from both spaces such that the relative homologies of the pairs ( X, A ) and ( X
Secant is a term in mathematics derived from the Latin secare (" to cut ").
The resulting document sets forth a set of six principles ( Equity, Curriculum, Teaching, Learning, Assessment, and Technology ) that describe NCTM's recommended framework for mathematics programs, and ten general strands or standards that cut across the school mathematics curriculum.
Ten general strands or standards of mathematics content and processes were defined that cut across the school mathematics curriculum.
mathematics and named
In mathematics, the Borsuk – Ulam theorem, named after Stanisław Ulam and Karol Borsuk, states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point.
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.
In mathematics, a Cauchy sequence ( pronounced ), named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses.
* In Canadian junior high schools, an annual national mathematics competition ( Gauss Mathematics Competition ) administered by the Centre for Education in Mathematics and Computing is named in honour of Gauss,
In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.
In the essay a blind English mathematician named Saunderson argues that since knowledge derives from the senses, then mathematics is the only form of knowledge that both he and a sighted person can agree about.
In pure mathematics, the magnitude of a googolplex could be related to other forms of large-number notation such as tetration, Knuth's up-arrow notation, Steinhaus-Moser notation, or Conway chained arrow notation, though neither googol nor googolplex are anywhere near the largest representable or even specifically named numbers.
A mathematics center has been named in his honor at the University of Idaho in Moscow, Idaho.
In mathematics, a generalized mean, also known as power mean or Hölder mean ( named after Otto Hölder ), is an abstraction of the Pythagorean means including arithmetic, geometric, and harmonic means.
In 2006, Harvey Mudd was also named one of the " new Ivy leagues " by Kaplan and Newsweek, while the mathematics department won the first American Mathematical Society Award for Exemplary Program.
In mathematics, a Mersenne number, named after Marin Mersenne ( a French monk who began the study of these numbers in the early 17th century ), is a positive integer that is one less than a power of two:
He returned to Alexandria, and began determinedly studying the works of Aristotle under Olympiodorus the Elder ( he also began studying mathematics during this period as well with a teacher named Heron ( no relation to Hero of Alexandria who was also known as Heron ).
Descartes ' influence in mathematics is equally apparent ; the Cartesian coordinate system — allowing reference to a point in space as a set of numbers, and allowing algebraic equations to be expressed as geometric shapes in a two-dimensional coordinate system ( and conversely, shapes to be described as equations ) — was named after him.
In combinatorial mathematics, a Steiner system ( named after Jakob Steiner ) is a type of block design, specifically a t-design with λ = 1 and t ≥ 2.
Bertrand Russell is credited with noticing the existence of such paradoxes even in the best symbolic formalizations of mathematics in his day, in particular the paradox that came to be named after him, Russell's paradox.
The award is named after Alan Turing, mathematician and reader in mathematics at the University of Manchester.
Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order ( number of elements ) of every subgroup H of G divides the order of G. The theorem is named after Joseph Lagrange.
In mathematics, specifically in real analysis, the Bolzano – Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space R < sup > n </ sup >.
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937.
There are three programming languages named after him, Haskell, Brooks and Curry, as well as the concept of currying, a technique used for transforming functions in mathematics and computer science.
Dalton's early life was highly influenced by a prominent Eaglesfield Quaker named Elihu Robinson, a competent meteorologist and instrument maker, who got him interested in problems of mathematics and meteorology.
In mathematics, a Hurwitz polynomial, named after Adolf Hurwitz, is a polynomial whose coefficients are positive real numbers and whose zeros are located in the left half-plane of the complex plane, that is, the real part of every zero is negative.
In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Ludwig Sylow (
mathematics and after
Next September, after receiving a degree from Yale's Master of Arts in Teaching Program, I will be teaching somewhere -- that much is guaranteed by the present shortage of mathematics teachers.
From the ages of 6 to 9, Alexei was educated by his tutor Vyazemsky, but after the removal of his mother by Peter the Great to the Suzdal Intercession Convent, Alexei was confined to the care of educated foreigners, who taught him history, geography, mathematics and French.
Grothendieck ’ s way of thinking has influenced generations of mathematicians long after his departure from mathematics.
This program culminated in the proofs of the Weil conjectures, the last of which was settled by Grothendieck's student Pierre Deligne in the early 1970s after Grothendieck had largely withdrawn from mathematics.
More than a decade after Richardson completed his work, Benoît Mandelbrot developed a new branch of mathematics, fractal geometry, to describe just such non-rectifiable complexes in nature as the infinite coastline.
Galois returned to mathematics after his expulsion from the École Normale, although he continued to spend time in political activities.
He was educated at Northampton Grammar School and, after the age of 14, Mill Hill School in London ( on scholarship ), where he studied mathematics, physics, and chemistry with his best friend John Shilston.
Writing decades after Cantor's death, Wittgenstein lamented that mathematics is " ridden through and through with the pernicious idioms of set theory ," which he dismissed as " utter nonsense " that is " laughable " and " wrong ".
Soon after that second hospitalization, Cantor's youngest son Rudolph died suddenly ( while Cantor was delivering a lecture on his views on Baconian theory and William Shakespeare ), and this tragedy drained Cantor of much of his passion for mathematics.
Quite unhappy with the lack of formal science education at Eton College, Maynard Smith took it upon himself to develop an interest in Darwinian evolutionary theory and mathematics, after having read the work of old Etonian J. B. S.
On July 10, 1726, Nicolas died of appendicitis after spending a year in Russia, and when Daniel assumed his brother's position in the mathematics / physics division, he recommended that the post in physiology that he had vacated be filled by his friend Euler.
He studied law, history and mathematics at Graz University, and after graduating moved back to Lemberg where he became a professor.
He won a football scholarship to Prairie View A & M University, where he majored in mathematics, but was expelled after his first year.
Menger did not embrace this hedonic conception, explained diminishing marginal utility in terms of subjective prioritization of possible uses, and emphasized disequilibrium and the discrete ; further Menger had an objection to the use of mathematics in economics, while the other two modeled their theories after 19th century mechanics.
But this increase in mathematics was accompanied by greater dominance of neoclassical economics in Anglo-American universities after World War II.
Initially beginning his career as a chemistry and mathematics teacher after leaving school at the age of 15, Anderson soon entered the Swedish popular music scene, becoming a music producer, manager and also occasional performer.
When night came, they would deny her warm clothes and a fire for her bedroom to try to keep her from studying, but after they left she would take out candles, wrap herself in quilts and do mathematics.
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