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76 relations: Absolute space and time, Abstract algebra, Academic Press, Algebra over a field, Associative algebra, Automatic differentiation, Binary relation, Characteristic (algebra), Coefficient, Commutative property, Commutative ring, Complex number, Complex plane, Cornell University, Corrado Segre, Cylinder, Derivation (differential algebra), Differential form, Dimension (vector space), Division algebra, Division by zero, Dual quaternion, Eduard Study, Embedding, Equivalence class, Equivalence relation, Event (relativity), Exponential map (Lie theory), Exterior algebra, Fermion, Field (mathematics), Galilean transformation, Grassmann number, Hermann Grassmann, Ideal (ring theory), Isaak Yaglom, Kähler differential, Line at infinity, Linear algebra, Local ring, London Mathematical Society, Mathematics Magazine, Matrix (mathematics), Matrix addition, Matrix multiplication, Maximal ideal, National Council of Teachers of Mathematics, Nilpotent, Parabola, Pauli exclusion principle, ..., Perturbation theory, Physics, Point at infinity, Polynomial, Polynomial ring, Principal ideal, Projection (mathematics), Projective line over a ring, Quadratic equation, Quotient ring, Real number, Riemann sphere, Ring (mathematics), Screw theory, Shear mapping, Slope, Smooth infinitesimal analysis, Split-complex number, Superspace, Taylor series, Translation (geometry), Unit (ring theory), Velocity, William Kingdon Clifford, Zero divisor, 2 × 2 real matrices. Expand index (26 more) »
Absolute space and time
Absolute space and time is a concept in physics and philosophy about the properties of the universe.
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Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Academic Press
Academic Press is an academic book publisher.
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Algebra over a field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
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Associative algebra
In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.
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Automatic differentiation
In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational differentiation, is a set of techniques to numerically evaluate the derivative of a function specified by a computer program.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Characteristic (algebra)
In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.
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Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.
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Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
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Cornell University
Cornell University is a private and statutory Ivy League research university located in Ithaca, New York.
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Corrado Segre
Corrado Segre (20 August 1863 – 18 May 1924) was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry.
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Cylinder
A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.
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Derivation (differential algebra)
In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator.
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Differential form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
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Dimension (vector space)
In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.
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Division algebra
In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible.
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Division by zero
In mathematics, division by zero is division where the divisor (denominator) is zero.
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Dual quaternion
In mathematics and mechanics, the set of dual quaternions is a Clifford algebra that can be used to represent spatial rigid body displacements.
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Eduard Study
Eduard Study, more properly Christian Hugo Eduard Study (March 23, 1862 – January 6, 1930), was a German mathematician known for work on invariant theory of ternary forms (1889) and for the study of spherical trigonometry.
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Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
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Equivalence class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set S into equivalence classes.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Event (relativity)
In physics, and in particular relativity, an event is the instantaneous physical situation or occurrence associated with a point in spacetime (that is, a specific place and time).
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Exponential map (Lie theory)
In the theory of Lie groups, the exponential map is a map from the Lie algebra \mathfrak g of a Lie group G to the group, which allows one to recapture the local group structure from the Lie algebra.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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Fermion
In particle physics, a fermion is a particle that follows Fermi–Dirac statistics.
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Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
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Galilean transformation
In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics.
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Grassmann number
In mathematical physics, a Grassmann number, named after Hermann Grassmann (also called an anticommuting number or supernumber), is an element of the exterior algebra over the complex numbers.
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Hermann Grassmann
Hermann Günther Grassmann (Graßmann; April 15, 1809 – September 26, 1877) was a German polymath, known in his day as a linguist and now also as a mathematician.
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Ideal (ring theory)
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.
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Isaak Yaglom
Isaak Moiseevich Yaglom (Исаа́к Моисе́евич Ягло́м; 6 March 1921 – 17 April 1988) was a Soviet mathematician and author of popular mathematics books, some with his twin Akiva Yaglom.
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Kähler differential
In mathematics, Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes.
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Line at infinity
In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane.
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Linear algebra
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
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Local ring
In abstract algebra, more specifically ring theory, local rings are certain rings that are comparatively simple, and serve to describe what is called "local behaviour", in the sense of functions defined on varieties or manifolds, or of algebraic number fields examined at a particular place, or prime.
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London Mathematical Society
The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS) and the Institute of Mathematics and its Applications (IMA)).
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Mathematics Magazine
Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matrix addition
In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together.
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Matrix multiplication
In mathematics, matrix multiplication or matrix product is a binary operation that produces a matrix from two matrices with entries in a field, or, more generally, in a ring or even a semiring.
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Maximal ideal
In mathematics, more specifically in ring theory, a maximal ideal is an ideal that is maximal (with respect to set inclusion) amongst all proper ideals.
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National Council of Teachers of Mathematics
The National Council of Teachers of Mathematics (NCTM) was founded in 1920.
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Nilpotent
In mathematics, an element, x, of a ring, R, is called nilpotent if there exists some positive integer, n, such that xn.
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Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
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Pauli exclusion principle
The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.
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Perturbation theory
Perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Point at infinity
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Polynomial ring
In mathematics, especially in the field of abstract algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.
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Principal ideal
In the mathematical field of ring theory, a principal ideal is an ideal I in a ring R that is generated by a single element a of R through multiplication by every element of R. The term also has another, similar meaning in order theory, where it refers to an (order) ideal in a poset P generated by a single element x of P, which is to say the set of all elements less than or equal to x in P. The remainder of this article addresses the ring-theoretic concept.
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Projection (mathematics)
In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent).
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Projective line over a ring
In mathematics, the projective line over a ring is an extension of the concept of projective line over a field.
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Quadratic equation
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.
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Quotient ring
In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring or residue class ring, is a construction quite similar to the quotient groups of group theory and the quotient spaces of linear algebra.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Riemann sphere
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.
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Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
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Screw theory
Screw theory is the algebra and calculus of pairs of vectors, such as forces and moments and angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies.
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Shear mapping
In plane geometry, a shear mapping is a linear map that displaces each point in fixed direction, by an amount proportional to its signed distance from a line that is parallel to that direction.
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Slope
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
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Smooth infinitesimal analysis
Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals.
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Split-complex number
In abstract algebra, a split complex number (or hyperbolic number, also perplex number, double number) has two real number components x and y, and is written z.
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Superspace
Superspace is the coordinate space of a theory exhibiting supersymmetry.
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Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.
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Translation (geometry)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure or a space by the same distance in a given direction.
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Unit (ring theory)
In mathematics, an invertible element or a unit in a (unital) ring is any element that has an inverse element in the multiplicative monoid of, i.e. an element such that The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.
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Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.
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William Kingdon Clifford
William Kingdon Clifford FRS (4 May 1845 – 3 March 1879) was an English mathematician and philosopher.
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Zero divisor
In abstract algebra, an element of a ring is called a left zero divisor if there exists a nonzero such that, or equivalently if the map from to that sends to is not injective.
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2 × 2 real matrices
In mathematics, the associative algebra of real matrices is denoted by M(2, R).
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References
[1] https://en.wikipedia.org/wiki/Dual_number
