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Number bond Summary Number_bond The term "number bond" is also used to refer to a pictorial representation of part-part-whole relationships, often found in the Singapore mathematics curriculum. Number bonds consist of a minimum of 3 circles that are connected by lines. The “whole” is written in the first circle and its... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chunking (division) Summary Chunking_(division) In mathematics education at the primary school level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple division questions by repeated subtraction. It is also known as the hangman method with the addition of a line ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chunking (division) Summary Chunking_(division) As a result, it is often considered to be a more intuitive, but a less systematic approach to divisions – where the efficiency is highly dependent upon one's numeracy skills. To calculate the whole number quotient of dividing a large number by a small number, the student ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chunking (division) Summary Chunking_(division) At the same time the student is generating a list of the multiples of the small number (i.e., partial quotients) that have so far been taken away, which when added up together would then become the whole number quotient itself. For example, to calculate 132 ÷ 8, one might... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Chunking (division) Summary Chunking_(division) However, it is argued that chunking, rather than moving straight to short division, gives a better introduction to division, in part because the focus is always holistic, focusing throughout on the whole calculation and its meaning, rather than just rules for generating s... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Finite mathematics Summary Finite_mathematics In mathematics education, Finite Mathematics is a syllabus in college and university mathematics that is independent of calculus. A course in precalculus may be a prerequisite for Finite Mathematics. Contents of the course include an eclectic selection of topics often appli... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Finite mathematics Summary Finite_mathematics These topics were used in Finite Mathematics courses at Dartmouth College as developed by John G. Kemeny, Gerald L. Thompson, and J. Laurie Snell and published by Prentice-Hall. Other publishers followed with their own topics. With the arrival of software to facilitate comp... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical manipulative Summary Manipulative_(mathematics_education) In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through devel... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical manipulative Summary Manipulative_(mathematics_education) The second and third steps are representational and abstract, respectively. Mathematical manipulatives can be purchased or constructed by the teacher. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical manipulative Summary Manipulative_(mathematics_education) Examples of common manipulatives include number lines, Cuisenaire rods; fraction strips, blocks, or stacks; base ten blocks (also known as Dienes or multibase blocks); interlocking linking cubes (such as Unifix); construction sets (such as Polydron ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mathematical manipulative Summary Manipulative_(mathematics_education) Notable collections of virtual manipulatives include The National Library of Virtual Manipulatives and the Ubersketch. Multiple experiences with manipulatives provide children with the conceptual foundation to understand mathematics at a conceptual ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Number sentence Summary Number_sentence In mathematics education, a number sentence is an equation or inequality expressed using numbers and mathematical symbols. The term is used in primary level mathematics teaching in the US, Canada, UK, Australia, New Zealand and South Africa. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Procept Summary Procept In mathematics education, a procept is an amalgam of three components: a "process" which produces a mathematical "object" and a "symbol" which is used to represent either process or object. It derives from the work of Eddie Gray and David O. Tall. The notion was first published in a paper in the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Procept Summary Procept Examples of such notations are: 3 + 4 {\displaystyle 3+4}: refers to the process of adding as well as the outcome of the process. ∑ n = 0 ∞ ( a n ) {\displaystyle \sum _{n=0}^{\infty }(a_{n})}: refers to the process of summing an infinite sequence, and to the outcome of the process. f ( x ) = 3 ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiple representations (mathematics education) Summary Multiple_representations_(mathematics_education) In mathematics education, a representation is a way of encoding an idea or a relationship, and can be both internal (e.g., mental construct) and external (e.g., graph). Thus multiple representations are ways to sym... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Differential and integral calculus Etymology Differential_and_integral_calculus > Etymology In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word calculus is Latin for "small pebble" (the diminutive of calx, meanin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
History of calculus Etymology History_of_calculus > Etymology In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word calculus is Latin for "small pebble" (the diminutive of calx, meaning "stone"), a meaning which st... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Concept image and concept definition Summary Concept_image_and_concept_definition In mathematics education, concept image and concept definition are two ways of understanding a mathematical concept. The terms were introduced by Tall & Vinner (1981). They define a concept image as such: "We shall use the term concept im... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Ethnomathematics Summary Ethnomathematics In mathematics education, ethnomathematics is the study of the relationship between mathematics and culture. Often associated with "cultures without written expression", it may also be defined as "the mathematics which is practised among identifiable cultural groups". It refers... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Precalculus Summary Precalculus In mathematics education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus, thus the name precalculus. Schools often distinguish between algebra and trigonometry as two separate... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Van Hiele model Summary Van_Hiele_model In mathematics education, the Van Hiele model is a theory that describes how students learn geometry. The theory originated in 1957 in the doctoral dissertations of Dina van Hiele-Geldof and Pierre van Hiele (wife and husband) at Utrecht University, in the Netherlands. The Soviet... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Van Hiele model Summary Van_Hiele_model Pierre van Hiele published Structure and Insight in 1986, further describing his theory. The model has greatly influenced geometry curricula throughout the world through emphasis on analyzing properties and classification of shapes at early grade levels. In the United States, the... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Multiplication and repeated addition Summary Multiplication_and_repeated_addition In mathematics education, there was a debate on the issue of whether the operation of multiplication should be taught as being a form of repeated addition. Participants in the debate brought up multiple perspectives, including axioms of a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Unit fraction Fair division and mathematics education Unit_fractions > Applications > Fair division and mathematics education In mathematics education, unit fractions are often introduced earlier than other kinds of fractions, because of the ease of explaining them visually as equal parts of a whole. A common practical... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Process graph Summary Process_graph In mathematics graph theory a process graph or P-graph is a directed bipartite graph used in workflow modeling. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Single-entry single-exit Summary Single-entry_single-exit In mathematics graph theory, a single-entry single-exit (SESE) region in a given graph is an ordered edge pair. For example, with the ordered edge pair, (a, b) of distinct control-flow edges a and b where: a dominates b b postdominates a Every cycle containing a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Holomorphic separability Summary Holomorphic_separability In mathematics in complex analysis, the concept of holomorphic separability is a measure of the richness of the set of holomorphic functions on a complex manifold or complex-analytic space. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characterization of probability distributions Summary Characterization_of_probability_distributions In mathematics in general, a characterization theorem says that a particular object – a function, a space, etc. – is the only one that possesses properties specified in the theorem. A characterization of a probability di... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characterization of probability distributions Summary Characterization_of_probability_distributions On the probability space we define the space X = { X } {\displaystyle {\mathcal {X}}=\{X\}} of random variables with values in measurable metric space ( U , d u ) {\displaystyle (U,d_{u})} and the space Y = { Y } {\displ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characterization of probability distributions Summary Characterization_of_probability_distributions So, the set which interests us appears therefore in the following form: X ∈ A , F X ∈ B ⇔ X ∈ C , i . e . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characterization of probability distributions Summary Characterization_of_probability_distributions C = F − 1 B , {\displaystyle X\in {\mathcal {A}},\mathbf {F} X\in {\mathcal {B}}\Leftrightarrow X\in {\mathcal {C}},i.e.{\mathcal {C}}=\mathbf {F} ^{-1}{\mathcal {B}},} where F − 1 B {\displaystyle \mathbf {F} ^{-1}{\mat... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characterization of probability distributions Summary Characterization_of_probability_distributions "Memoryless" means that if X {\displaystyle X} is a random variable with such a distribution, then for any numbers 0 < y < x {\displaystyle 0 x ∣ X > y ) = Pr ( X > x − y ) {\displaystyle \Pr(X>x\mid X>y)=\Pr(X>x-y)} . V... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Characterization of probability distributions Summary Characterization_of_probability_distributions That is why there arises the following natural question. Suppose that the conditions of the characterization theorem are fulfilled not exactly but only approximately. May we assert that the conclusion of the theorem is a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cocurvature Summary Cocurvature In mathematics in the branch of differential geometry, the cocurvature of a connection on a manifold is the obstruction to the integrability of the vertical bundle. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Bracket ring Summary Bracket_ring In mathematics invariant theory, the bracket ring is the subring of the ring of polynomials k generated by the d-by-d minors of a generic d-by-n matrix (xij). The bracket ring may be regarded as the ring of polynomials on the image of a Grassmannian under the Plücker embedding.For give... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Normal convergence Summary Normal_convergence In mathematics normal convergence is a type of convergence for series of functions. Like absolute-convergence, it has the useful property that it is preserved when the order of summation is changed. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nyström method Summary Nyström_method In mathematics numerical analysis, the Nyström method or quadrature method seeks the numerical solution of an integral equation by replacing the integral with a representative weighted sum. The continuous problem is broken into n {\displaystyle n} discrete intervals; quadrature or ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Nyström method Summary Nyström_method This discrete problem may be ill-conditioned, depending on the original problem and the chosen quadrature rule. Since the linear equations require O ( n 3 ) {\displaystyle O(n^{3})} operations to solve, high-order quadrature rules perform better because low-order quadrature rules r... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Neuman–Sándor mean Summary Neuman–Sándor_mean In mathematics of special functions, the Neuman–Sándor mean M, of two positive and unequal numbers a and b, is defined as: M ( a , b ) = a − b 2 arsinh ( a − b a + b ) {\displaystyle M(a,b)={\frac {a-b}{2\operatorname {arsinh} \left({\frac {a-b}{a+b}}\right)}}} This mean ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parity bit Parity Parity_check > Parity In mathematics parity can refer to the evenness or oddness of an integer, which, when written in its binary form, can be determined just by examining only its least significant bit. In information technology parity refers to the evenness or oddness, given any set of binary digits... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parity bit Parity Parity_check > Parity The transmission medium is preset, at both end points, to agree on either odd parity or even parity. For each string of bits ready to transmit (data packet) the sender calculates its parity bit, zero or one, to make it conform to the agreed parity, even or odd. The receiver of th... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parity bit Parity Parity_check > Parity In computer science the parity stripe or parity disk in a RAID provides error-correction. Parity bits are written at the rate of one parity bit per n bits, where n is the number of disks in the array. When a read error occurs, each bit in the error region is recalculated from its... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Parity bit Parity Parity_check > Parity In this way, using one parity bit creates "redundancy" for a region from the size of one bit to the size of one disk. See § Redundant Array of Independent Disks below. In electronics, transcoding data with parity can be very efficient, as XOR gates output what is equivalent to a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cycle shape Definition Circular_notation > Definition In mathematics texts it is customary to denote permutations using lowercase Greek letters. Commonly, either α {\displaystyle \alpha } and β , {\displaystyle \beta ,} or σ , τ {\displaystyle \sigma ,\tau } and π {\displaystyle \pi } are used.Permutations can be defin... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cycle shape Definition Circular_notation > Definition {\displaystyle \pi \sigma .} Associativity: For any three permutations π , σ , τ ∈ S n {\displaystyle \pi ,\sigma ,\tau \in S_{n}} , ( π σ ) τ = π ( σ τ ) . {\displaystyle (\pi \sigma )\tau =\pi (\sigma \tau ).} | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cycle shape Definition Circular_notation > Definition Identity: There is an identity permutation, denoted id {\displaystyle \operatorname {id} } and defined by id ( x ) = x {\displaystyle \operatorname {id} (x)=x} for all x ∈ S {\displaystyle x\in S} . For any σ ∈ S n {\displaystyle \sigma \in S_{n}} , id σ = σ id ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cycle shape Definition Circular_notation > Definition Invertibility: For every permutation π ∈ S n {\displaystyle \pi \in S_{n}} , there exists an inverse permutation π − 1 ∈ S n {\displaystyle \pi ^{-1}\in S_{n}} , so that π π − 1 = π − 1 π = id . {\displaystyle \pi \pi ^{-1}=\pi ^{-1}\pi =\operatorname {id} .} In gen... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cycle shape Definition Circular_notation > Definition {\displaystyle \pi \sigma \neq \sigma \pi .} As a bijection from a set to itself, a permutation is a function that performs a rearrangement of a set, and is not an arrangement itself. An older and more elementary viewpoint is that permutations are the arrangements t... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cycle shape Definition Circular_notation > Definition To distinguish between these two, the identifiers active and passive are sometimes prefixed to the term permutation, whereas in older terminology substitutions and permutations are used.A permutation can be decomposed into one or more disjoint cycles, that is, the o... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Cycle shape Definition Circular_notation > Definition An element in a 1-cycle ( x ) {\displaystyle (\,x\,)} is called a fixed point of the permutation. A permutation with no fixed points is called a derangement. 2-cycles are called transpositions; such permutations merely exchange two elements, leaving the others fixed... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Baum–Sweet sequence Summary Baum–Sweet_sequence In mathematics the Baum–Sweet sequence is an infinite automatic sequence of 0s and 1s defined by the rule: bn = 1 if the binary representation of n contains no block of consecutive 0s of odd length; bn = 0 otherwise;for n ≥ 0.For example, b4 = 1 because the binary represe... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Function field sieve Summary Function_field_sieve In mathematics the Function Field Sieve is one of the most efficient algorithms to solve the Discrete Logarithm Problem (DLP) in a finite field. It has heuristic subexponential complexity. Leonard Adleman developed it in 1994 and then elaborated it together with M. D. H... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Function field sieve Summary Function_field_sieve Previous work includes the work of D. Coppersmith about the DLP in fields of characteristic two. The discrete logarithm problem in a finite field consists of solving the equation a x = b {\displaystyle a^{x}=b} for a , b ∈ F p n {\displaystyle a,b\in \mathbb {F} _{p^{n}... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Goodwin–Staton integral Summary Goodwin–Staton_integral In mathematics the Goodwin–Staton integral is defined as: G ( z ) = ∫ 0 ∞ e − t 2 t + z d t {\displaystyle G(z)=\int _{0}^{\infty }{\frac {e^{-t^{2}}}{t+z}}\,dt} It satisfies the following third-order nonlinear differential equation： 4 w ( z ) + 8 z d d z w ( z ) ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Gould polynomials Summary Gould_polynomials In mathematics the Gould polynomials Gn(x; a,b) are polynomials introduced by H. W. Gould and named by Roman in 1984. They are given by exp ( x f − 1 ( t ) ) = ∑ n = 0 ∞ G n ( x ; a , b ) t n n ! {\displaystyle \displaystyle \exp(xf^{-1}(t))=\sum _{n=0}^{\infty }G_{n}(x;a,b... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Jacobian ideal Summary Jacobian_ideal In mathematics the Jacobian ideal or gradient ideal is the ideal generated by the Jacobian of a function or function germ. Let O ( x 1 , … , x n ) {\displaystyle {\mathcal {O}}(x_{1},\ldots ,x_{n})} denote the ring of smooth functions in n {\displaystyle n} variables and f {\displa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Split idempotent Summary Karoubi_envelope In mathematics the Karoubi envelope (or Cauchy completion or idempotent completion) of a category C is a classification of the idempotents of C, by means of an auxiliary category. Taking the Karoubi envelope of a preadditive category gives a pseudo-abelian category, hence the c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Split idempotent Summary Karoubi_envelope Given a category C, an idempotent of C is an endomorphism e: A → A {\displaystyle e:A\rightarrow A} with e ∘ e = e {\displaystyle e\circ e=e} .An idempotent e: A → A is said to split if there is an object B and morphisms f: A → B, g: B → A such that e = g f and 1B = f g. The Ka... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Split idempotent Summary Karoubi_envelope In Split(C) every idempotent splits, and Split(C) is the universal category with this property. The Karoubi envelope of a category C can therefore be considered as the "completion" of C which splits idempotents. The Karoubi envelope of a category C can equivalently be defined a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Korovkin approximation Summary Korovkin_approximation In mathematics the Korovkin approximation is a convergence statement in which the approximation of a function is given by a certain sequence of functions. In practice a continuous function can be approximated by polynomials. With Korovkin approximations one comes a ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Lawrence–Krammer representation Summary Lawrence–Krammer_representation In mathematics the Lawrence–Krammer representation is a representation of the braid groups. It fits into a family of representations called the Lawrence representations. The first Lawrence representation is the Burau representation and the second i... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Markov theorem Summary Markov_theorem In mathematics the Markov theorem gives necessary and sufficient conditions for two braids to have closures that are equivalent knots or links. The conditions are stated in terms of the group structures on braids. Braids are algebraic objects described by diagrams; the relation to ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Markov theorem Summary Markov_theorem describes the elementary moves generating the equivalence relation on braids given by the equivalence of their closures. More precisely Markov's theorem can be stated as follows: given two braids represented by elements β n , β m ′ {\displaystyle \beta _{n},\beta _{m}'} in the brai... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Montgomery curve Summary Montgomery_curve In mathematics the Montgomery curve is a form of elliptic curve introduced by Peter L. Montgomery in 1987, different from the usual Weierstrass form. It is used for certain computations, and in particular in different cryptography applications. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mott polynomials Summary Mott_polynomials In mathematics the Mott polynomials sn(x) are polynomials introduced by N. F. Mott (1932, p. 442) who applied them to a problem in the theory of electrons. They are given by the exponential generating function e x ( 1 − t 2 − 1 ) / t = ∑ n s n ( x ) t n / n ! . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mott polynomials Summary Mott_polynomials {\displaystyle e^{x({\sqrt {1-t^{2}}}-1)/t}=\sum _{n}s_{n}(x)t^{n}/n!.} Because the factor in the exponential has the power series 1 − t 2 − 1 t = − ∑ k ≥ 0 C k ( t 2 ) 2 k + 1 {\displaystyle {\frac {{\sqrt {1-t^{2}}}-1}{t}}=-\sum _{k\geq 0}C_{k}\left({\frac {t}{2}}\right)^{2k+... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mott polynomials Summary Mott_polynomials 2 n ∑ n = l 1 + l 2 + ⋯ + l k C ( l 1 − 1 ) / 2 C ( l 2 − 1 ) / 2 ⋯ C ( l k − 1 ) / 2 {\displaystyle s_{n}(x)=(-1)^{k}{\frac {n! }{k!2^{n}}}\sum _{n=l_{1}+l_{2}+\cdots +l_{k}}C_{(l_{1}-1)/2}C_{(l_{2}-1)/2}\cdots C_{(l_{k}-1)/2}} ,according to the general formula for generalized... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mott polynomials Summary Mott_polynomials Special values, where all contributing Catalan numbers equal 1, are s n ( x ) = ( − 1 ) n 2 n . {\displaystyle s_{n}(x)={\frac {(-1)^{n}}{2^{n}}}.} s n ( x ) = ( − 1 ) n n ( n − 1 ) ( n − 2 ) 2 n . | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Mott polynomials Summary Mott_polynomials {\displaystyle s_{n}(x)={\frac {(-1)^{n}n(n-1)(n-2)}{2^{n}}}.} By differentiation the recurrence for the first derivative becomes s ′ ( x ) = − ∑ k = 0 ⌊ ( n − 1 ) / 2 ⌋ n ! ( n − 1 − 2 k ) ! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Padovan cuboid spiral Summary Padovan_cuboid_spiral In mathematics the Padovan cuboid spiral is the spiral created by joining the diagonals of faces of successive cuboids added to a unit cube. The cuboids are added sequentially so that the resulting cuboid has dimensions that are successive Padovan numbers.The first cu... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Padovan cuboid spiral Summary Padovan_cuboid_spiral This pattern continues, forming in succession a 2x2x3 cuboid, a 2x3x4 cuboid etc. Joining the diagonals of the exposed end of each new added cuboid creates a spiral (seen as the black line in the figure). The points on this spiral all lie in the same plane.The cuboids... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Petersson inner product Summary Petersson_inner_product In mathematics the Petersson inner product is an inner product defined on the space of entire modular forms. It was introduced by the German mathematician Hans Petersson. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Vicsek fractal Summary Vicsek_fractal In mathematics the Vicsek fractal, also known as Vicsek snowflake or box fractal, is a fractal arising from a construction similar to that of the Sierpinski carpet, proposed by Tamás Vicsek. It has applications including as compact antennas, particularly in cellular phones. Box fra... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Quintuple product identity Summary Quintuple_product_identity In mathematics the Watson quintuple product identity is an infinite product identity introduced by Watson (1929) and rediscovered by Bailey (1951) and Gordon (1961). It is analogous to the Jacobi triple product identity, and is the Macdonald identity for a c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Differential calculus over commutative algebras Summary Differential_calculus_over_commutative_algebras In mathematics the differential calculus over commutative algebras is a part of commutative algebra based on the observation that most concepts known from classical differential calculus can be formulated in purely a... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Differential calculus over commutative algebras Summary Differential_calculus_over_commutative_algebras More generally, a linear differential operator of order k, sending sections of a vector bundle E → M {\displaystyle E\rightarrow M} to sections of another bundle F → M {\displaystyle F\rightarrow M} is seen to be an ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Differential calculus over commutative algebras Summary Differential_calculus_over_commutative_algebras Replacing the real numbers R {\displaystyle \mathbb {R} } with any commutative ring, and the algebra C ∞ ( M ) {\displaystyle C^{\infty }(M)} with any commutative algebra the above said remains meaningful, hence diff... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Discrete least squares meshless method Summary Discrete_least_squares_meshless_method In mathematics the discrete least squares meshless (DLSM) method is a meshless method based on the least squares concept. The method is based on the minimization of a least squares functional, defined as the weighted summation of the ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Division polynomial Summary Division_polynomial In mathematics the division polynomials provide a way to calculate multiples of points on elliptic curves and to study the fields generated by torsion points. They play a central role in the study of counting points on elliptic curves in Schoof's algorithm. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic rational function Summary Elliptic_rational_function In mathematics the elliptic rational functions are a sequence of rational functions with real coefficients. Elliptic rational functions are extensively used in the design of elliptic electronic filters. (These functions are sometimes called Chebyshev rationa... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Elliptic rational function Summary Elliptic_rational_function Rational elliptic functions are identified by a positive integer order n and include a parameter ξ ≥ 1 called the selectivity factor. A rational elliptic function of degree n in x with selectivity factor ξ is generally defined as: R n ( ξ , x ) ≡ c d ( n K (... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Estimation lemma Summary Estimation_lemma In mathematics the estimation lemma, also known as the ML inequality, gives an upper bound for a contour integral. If f is a complex-valued, continuous function on the contour Γ and if its absolute value |f (z)| is bounded by a constant M for all z on Γ, then | ∫ Γ f ( z ) d z ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Estimation lemma Summary Estimation_lemma Out of all the maximum |f (z)|s for the segments, there will be an overall largest one. Hence, if the overall largest |f (z)| is summed over the entire path then the integral of f (z) over the path must be less than or equal to it. Formally, the inequality can be shown to hold ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Finite Fourier transform Summary Finite_Fourier_transform In mathematics the finite Fourier transform may refer to either another name for discrete-time Fourier transform (DTFT) of a finite-length series. E.g., F.J.Harris (pp. 52–53) describes the finite Fourier transform as a "continuous periodic function" and the dis... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Finite Fourier transform Summary Finite_Fourier_transform In actual implementation, that is not two separate steps; the DFT replaces the DTFT. So J.Cooley (pp. 77–78) describes the implementation as discrete finite Fourier transform.or another name for the Fourier series coefficients.or another name for one snapshot of... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let expression Let definition in mathematics Let_expression > Definition > Let definition in mathematics In mathematics the let expression is described as the conjunction of expressions. In functional languages the let expression is also used to limit scope. In mathematics scope is described by quantifiers. | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let expression Let definition in mathematics Let_expression > Definition > Let definition in mathematics The let expression is a conjunction within an existential quantifier. ( ∃ x E ∧ F ) ⟺ let x: E in F {\displaystyle (\exists xE\land F)\iff \operatorname {let} x:E\operatorname {in} F} where E and F are of type B... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let expression Let definition in mathematics Let_expression > Definition > Let definition in mathematics This substitution may be applied within a restricted scope, to a sub expression. The natural use of the let expression is in application to a restricted scope (called lambda dropping). These rules define how the sco... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Let expression Let definition in mathematics Let_expression > Definition > Let definition in mathematics From this definition the following standard definition of a let expression, as used in a functional language may be derived. x ∉ FV ( y ) ⟹ ( let x: x = y in z ) = z = ( λ x . z ) y {\displaystyle x\not \in \... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Polynomial basis Summary Monomial_form In mathematics the monomial basis of a polynomial ring is its basis (as a vector space or free module over the field or ring of coefficients) that consists of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Central binomial coefficient Summary Central_binomial_coefficient In mathematics the nth central binomial coefficient is the particular binomial coefficient ( 2 n n ) = ( 2 n ) ! ( n ! ) 2 = ∏ k = 1 n n + k k for all n ≥ 0. {\displaystyle {2n \choose n}={\frac {(2n)!}{(n! | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Central binomial coefficient Summary Central_binomial_coefficient )^{2}}}=\prod \limits _{k=1}^{n}{\frac {n+k}{k}}{\text{ for all }}n\geq 0.} They are called central since they show up exactly in the middle of the even-numbered rows in Pascal's triangle. The first few central binomial coefficients starting at n = 0 are... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Negative sign Mathematics Positive_sign > Use as a qualifier > Mathematics In mathematics the one-sided limit x → a+ means x approaches a from the right (i.e., right-sided limit), and x → a− means x approaches a from the left (i.e., left-sided limit). For example, 1/x → + ∞ {\displaystyle \infty } as x → 0+ but 1/x → −... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Regular paperfolding sequence Summary Regular_paperfolding_sequence In mathematics the regular paperfolding sequence, also known as the dragon curve sequence, is an infinite sequence of 0s and 1s. It is obtained from the repeating partial sequence by filling in the question marks by another copy of the whole sequence. ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Signal-to-noise statistic Summary Signal-to-noise_statistic In mathematics the signal-to-noise statistic distance between two vectors a and b with mean values μ a {\displaystyle \mu _{a}} and μ b {\displaystyle \mu _{b}} and standard deviation σ a {\displaystyle \sigma _{a}} and σ b {\displaystyle \sigma _{b}} respecti... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spin group Summary Spinor_group In mathematics the spin group Spin(n) is a Lie group whose underlying manifold is the double cover of the special orthogonal group SO(n) = SO(n, R), such that there exists a short exact sequence of Lie groups (when n ≠ 2) 1 → Z 2 → Spin ( n ) → SO ( n ) → 1. {\displaystyle 1\to \math... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Spin group Summary Spinor_group As a Lie group, Spin(n) therefore shares its dimension, n(n − 1)/2, and its Lie algebra with the special orthogonal group. For n > 2, Spin(n) is simply connected and so coincides with the universal cover of SO(n). The non-trivial element of the kernel is denoted −1, which should not be c... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symmetrization methods Summary Symmetrization_methods In mathematics the symmetrization methods are algorithms of transforming a set A ⊂ R n {\displaystyle A\subset \mathbb {R} ^{n}} to a ball B ⊂ R n {\displaystyle B\subset \mathbb {R} ^{n}} with equal volume vol ( B ) = vol ( A ) {\displaystyle \operatorname {vol... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Symmetrization methods Summary Symmetrization_methods From this many other isoperimetric problems sprung and other symmetrization algorithms. For example, Rayleigh's conjecture is that the first eigenvalue of the Dirichlet problem is minimized for the ball (see Rayleigh–Faber–Krahn inequality for details). Another prob... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
Synchrotron function Summary Synchrotron_function In mathematics the synchrotron functions are defined as follows (for x ≥ 0): First synchrotron function F ( x ) = x ∫ x ∞ K 5 3 ( t ) d t {\displaystyle F(x)=x\int _{x}^{\infty }K_{\frac {5}{3}}(t)\,dt} Second synchrotron function G ( x ) = x K 2 3 ( x ) {\displaystyle ... | https://www.kaggle.com/datasets/conjuring92/wiki-stem-corpus |
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