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In mathematics, a parallelization of a manifold M {\displaystyle M\,} of dimension n is a set of n global smooth linearly independent vector fields. Given
Parallelization_(mathematics)
Didactica Mathematica. 36: 25–40. A.B. Ivanov: Anti-parallel straight lines. In: Encyclopaedia of Mathematics - ISBN 1-4020-0609-8 Weisstein, Eric W. "Antiparallel"
Antiparallel_lines
Field of knowledge
Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical
Mathematics
divisor of the dimension of the ambient manifold. Foliation Parallelization (mathematics) S. Benenti (1997). "Intrinsic characterization of the variable
Web_(differential_geometry)
Topics referred to by the same term
directions Antiparallel (electronics), the polarity of devices run in parallel Antiparallelogram This disambiguation page lists articles associated with
Antiparallel
Mathematical operation modeling parallel resistors
financial mathematics. The name parallel comes from the use of the operator computing the combined resistance of resistors in parallel. The parallel operator
Parallel_(operator)
Reasoning for mathematical statements
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The
Mathematical_proof
Problem easily dividable into parallel tasks
CPU cores, or clusters. "Embarrassingly" is used here to refer to parallelization problems which are "embarrassingly easy". The term may imply embarrassment
Embarrassingly_parallel
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern
History_of_mathematics
2D surface which extends indefinitely
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero
Plane_(mathematics)
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
Relation used in geometry
[September 1928]. "§ 184, § 359, § 368". A History of Mathematical Notations - Notations in Elementary Mathematics. Vol. 1 (two volumes in one unaltered reprint ed
Parallel_(geometry)
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Basic framework of mathematics
Foundations of mathematics are the logical and mathematical frameworks that allow the development of mathematics without generating self-contradictory
Foundations_of_mathematics
Teaching, learning, and scholarly research in mathematics
In contemporary education, mathematics education (known in Europe as the didactics or pedagogy of mathematics) is the practice of teaching, learning, and
Mathematics_education
System of moving vectors in differential geometry
approximate parallelograms. Basic introduction to the mathematics of curved spacetime Connection (mathematics) Development (differential geometry) Affine connection
Parallel_transport
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mathematical concept
infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object. The
Infinity
Algebraic structure with addition, multiplication, and division
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on
Field_(mathematics)
Topics referred to by the same term
never intersect Parallel (operator), mathematical operation named after the composition of electrical resistance in parallel circuits Parallel (latitude),
Parallel
Set with associative invertible operation
In mathematics, a group is a set with an operation that combines any two elements of the set to produce a third element within the same set and the following
Group_(mathematics)
Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly
Philosophy_of_mathematics
Circulation density in a vector field
Hodges. 1880. Earliest Known Uses of Some of the Words of Mathematics tripod.com Mathematical methods for physics and engineering, K.F. Riley, M.P. Hobson
Curl_(mathematics)
Subfield of mathematics
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory
Mathematical_logic
Statement that is taken to be true
used in deduction to build a mathematical theory, and might or might not be self-evident in nature (e.g., the parallel postulate in Euclidean geometry)
Axiom
Used to count, measure, and label
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth. Individual
Number
Tool to track locally defined data attached to the open sets of a topological space
Look up sheaf in Wiktionary, the free dictionary. In mathematics, a sheaf (pl.: sheaves) is a tool for systematically tracking data (such as sets, abelian
Sheaf_(mathematics)
Property that is not changed by mathematical transformations
In mathematics, an invariant is a property of a mathematical object (or a class of mathematical objects) which remains unchanged after operations or transformations
Invariant_(mathematics)
Branch of mathematics
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is
Geometry
Broad concept generalizing scalars in mathematics and physics
In mathematics and physics, a vector is a generalization of a single number. It may denote a vector quantity, i.e., physical quantity that cannot be expressed
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Geometric axiom
Lewis (Jan 1920), "History of the Parallel Postulate", The American Mathematical Monthly, 27 (1), The American Mathematical Monthly, vol. 27, no. 1: 16–23
Parallel_postulate
Branch of applied mathematics
development of mathematical ideas inspired by physics, known as physical mathematics. There are several distinct branches of mathematical physics, and these
Mathematical_physics
Volume space bounded by a sphere
In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. It may be a closed ball (including the boundary points
Ball_(mathematics)
Mathematical set with some added structure
In mathematics, a space is a set (sometimes known as a universe) endowed with a structure defining the relationships among the elements of the set. A
Space_(mathematics)
Greek mathematician and physicist (c. 287 – 212 BC)
expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, working on statics and hydrostatics. Archimedes'
Archimedes
Proof that is not easily verified by hand
especially of computer-assisted proofs. Among early suggestions was that of parallelization: the verification task could be split across many readers, each of
Non-surveyable_proof
Form of realism that suggests that mathematical entities are abstract
Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and
Mathematical_Platonism
Mapping equal to its square under mapping composition
In mathematics, a projection is a mapping from a set to itself—or an endomorphism of a mathematical structure—that is idempotent, that is, equals its composition
Projection_(mathematics)
Natural number
is a determiner for singular nouns and a gender-neutral pronoun. In mathematics, 1 is the multiplicative identity, meaning that any number multiplied
1
Basic notion of sameness in mathematics
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical
Equality_(mathematics)
Function in mathematics
Connection (composite bundle) Connection (algebraic framework) Gauge theory (mathematics) Connes connection Levi-Civita, T.; Ricci, G. (1900), "Méthodes de calcul
Connection_(mathematics)
Algorithmic technique
computed independently of each other, binary splitting lends well to parallelization and checkpointing. In a less specific sense, binary splitting may also
Binary_splitting
Minimum spanning forest algorithm that greedily adds edges
Filter-Kruskal lends itself better to parallelization as sorting, filtering, and partitioning can easily be performed in parallel by distributing the edges between
Kruskal's_algorithm
Umbrella term for technical disciplines
mathematics (STEM) is an umbrella term used to group together the related technical disciplines of science, technology, engineering, and mathematics.
Science, technology, engineering, and mathematics
Science,_technology,_engineering,_and_mathematics
Emerging field of applied ethics
Ethics in mathematics is an emerging field of applied ethics, the inquiry into ethical aspects of the practice and applications of mathematics. It deals
Ethics_in_mathematics
Limiting case which is different from the rest of the class
In mathematics, a degenerate case is a limiting case of a class of objects which appears to be qualitatively different from (and usually simpler than)
Degeneracy_(mathematics)
Mathematics is a broad subject that is commonly divided in many areas or branches that may be defined by their objects of study, by the used methods,
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Subfield of computer science and mathematics
obstacles to getting good parallel program performance. The maximum possible speed-up of a single program as a result of parallelization is known as Amdahl's
Theoretical_computer_science
American mathematician
(2008), "Large scale ab initio calculations based on three levels of parallelization", Computational Materials Science, 42 (2): 329–336, arXiv:0707.3405
Andrei Knyazev (mathematician)
Andrei_Knyazev_(mathematician)
Two geometries based on axioms closely related to those specifying Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean
Non-Euclidean_geometry
Type of differentiable manifold
of such a basis of vector fields on M {\displaystyle M} is called a parallelization (or an absolute parallelism) of M {\displaystyle M} . An example with
Parallelizable_manifold
Algebraic structure associated with a topological space
In mathematics, the term homology, originally introduced in algebraic topology, has three primary, closely related usages. First, there is the homology
Homology_(mathematics)
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the
Ancient_Greek_mathematics
Calculating tool
David Eugene (1958). History of Mathematics. Dover Books on Mathematics. Vol. 2: Special Topics of Elementary Mathematics. Courier Dover Publications.
Abacus
Sequence in computer science
item. An implementation of a parallel prefix sum algorithm, like other parallel algorithms, has to take the parallelization architecture of the platform
Prefix_sum
This is a list of axioms as that term is understood in mathematics. In epistemology, the word axiom is understood differently; see axiom and self-evidence
List_of_axioms
Branch of applied mathematics
Example applications of mathematical linguistics Mathematical linguistics is the application of mathematics to model phenomena and solve problems in general
Mathematical_linguistics
Mathematics used in Ancient China
Mathematics emerged independently in China by the 11th century BCE. The Chinese independently developed a real number system that includes significantly
Chinese_mathematics
Arithmetic operation
numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects
Addition
Robotics and planning computational problem
"Optimal paths for a car that goes both forwards and backwards" (PDF), Pacific Journal of Mathematics, 145 (2): 367–393, doi:10.2140/pjm.1990.145.367. v t e
Parallel_parking_problem
Form of mathematical proof
Mathematical induction is a method for proving that a statement P ( n ) {\displaystyle P(n)} is true for every natural number n {\displaystyle n} , that
Mathematical_induction
Branch of mathematics
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems
Algebra
When a closed manifold embedded in M has an isotopy onto a boundary component of M
In mathematics, a connected submanifold of a compact manifold with boundary is said to be boundary parallel, ∂-parallel, or peripheral if it can be continuously
Boundary_parallel
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
in any theory that relies on the mathematics of plane parallel layers, there is a set of definitions and mathematics, some old and some new, which have
Representative_layer_theory
Property of a mathematical space
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify
Dimension
Topics referred to by the same term
for great circle, a geodesic on the sphere Orthographic projection, a parallel projection onto a perpendicular plane Orthomyxovirus, a family of viruses
Ortho
Convex quadrilateral with at least one pair of parallel sides
trapezoids with exactly one pair of parallel sides, analogous to uses of the word proper in some other mathematical objects. In the ancient Greek geometry
Trapezoid
American foundation
The Clay Mathematics Institute (CMI) is a private, non-profit foundation dedicated to increasing and disseminating mathematical knowledge. It was established
Clay_Mathematics_Institute
Quadrilateral with two pairs of parallel sides
neither a rectangle nor a rhombus). This term is not used in modern mathematics but it does survive in some contexts in biology in names like the rhomboid
Parallelogram
Use of mathematics as a philosophical framework
Mathematicism is 'the effort to employ the formal structure and rigorous method of mathematics as a model for the conduct of philosophy', or the epistemological
Mathematicism
Topics referred to by the same term
longitude 12th meridian west, a line of longitude 12th parallel north, a circle of latitude 12th parallel south, a circle of latitude 12th Avenue (disambiguation)
Twelfth
International mathematics conference
The European Congress of Mathematics (ECM) is the second largest international conference of the mathematics community, after the International Congresses
European Congress of Mathematics
European_Congress_of_Mathematics
Flextensional Hydrophones"; Journal of Lightwave Technology 1995-2002 (1989); "Parallelization of the Naval Space Surveillance Satellite Motion Model", Journal of
Donald_A._Danielson
Mathematical term
In mathematics, the slope or gradient of a line is a number that describes the direction of the line on a plane. It is commonly denoted by the letter
Slope
Software used in mathematical applications
Mathematical software is software used to model, analyze or calculate numeric, symbolic or geometric data. Numerical analysis and symbolic computation
Mathematical_software
Mapping from a Euclidean space to itself
In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of
Reflection_(mathematics)
Country in South Asia
ISBN 978-0-14-056102-9. Stillwell, John (2004). Mathematics and its History. Undergraduate Texts in Mathematics (2 ed.). Springer, Berlin and New York, 568
India
Mathematics education in the United States varies considerably from one state to the next, and even within a single state. With the adoption of the Common
Mathematics education in the United States
Mathematics_education_in_the_United_States
Shape with three sides
Greitzer, S. L. (1967). Geometry Revisited. Anneli Lax New Mathematical Library. Vol. 19. Mathematical Association of America. ISBN 978-0-88385-619-2. Devadoss
Triangle
Recursively-formed graph with two terminal vertices
1016/0890-5401(92)90041-D. Duffin, R. J. (1965). "Topology of Series–Parallel Networks". Journal of Mathematical Analysis and Applications. 10 (2): 303–313. doi:10
Series–parallel_graph
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Mathematical concept
In mathematics, when the elements of some set S {\displaystyle S} have a notion of equivalence (formalized as an equivalence relation), then one may naturally
Equivalence_class
Topics referred to by the same term
mirroring Smartphone ad hoc network Critical path length in analysis of parallel algorithms Span (band), a Norwegian rock band Span (design firm), an American
Span
Sequence of operations for a task
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is a finite sequence of mathematically rigorous instructions, typically used to solve
Algorithm
Punctuation mark
forms of brackets are used in mathematics, with specific mathematical meanings, often for denoting specific mathematical functions and subformulas. Angle
Bracket
Measure of similarity between two graphs
in parallel. To handle tables of different sizes, X-TED further adopts a dynamic parallelization strategy that allocates different levels of parallel resources
Graph_edit_distance
Australian and American mathematician (born 1975)
harmonic analysis, and additive number theory. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the
Terence_Tao
American inventor and author (b. 1957)
an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity. For many years, he was
Clifford_A._Pickover
Mathematical modeling of psychological theories and phenomena
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes
Mathematical_psychology
Generalization of perpendicularity
In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity to linear algebra of bilinear forms. Two elements u and
Orthogonality_(mathematics)
Topological space that locally resembles Euclidean space
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional
Manifold
Mathematical formula expressing equality
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =. The word
Equation
Convex polyhedron property
In mathematics, a convex polyhedron is defined to be k {\displaystyle k} -equiprojective if every orthogonal projection of the polygon onto a plane, in
Equiprojective_polyhedra
Type of non-Euclidean geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate
Hyperbolic_geometry
Problem of finding obscured edges in a wire-frame 3D model
efficient output-sensitive hidden surface removal algorithm and its parallelization. In Proc. 4th Annual Symp. on Computational Geometry, SCG ’88, pp.
Hidden-line_removal
Quantity of a three-dimensional space
evidence of volume calculation came from ancient Egypt and Mesopotamia as mathematical problems, approximating volume of simple shapes such as cuboids, cylinders
Volume
Straight figure with zero width and depth
\theta =\alpha \quad {\text{or}}\quad \theta =\alpha +\pi .} In modern mathematics, given the multitude of geometries, the concept of a line is closely
Line_(geometry)
Study of mathematical algorithms for optimization problems
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria
Mathematical_optimization
Mathematical symbol of equality
equal sign (American English), also known as the equality sign, is the mathematical symbol =, which is used to indicate equality. In an equation it is placed
Equals_sign
PARALLELIZATION MATHEMATICS
PARALLELIZATION MATHEMATICS
PARALLELIZATION MATHEMATICS
Surname or Lastname
English
English : of uncertain origin; perhaps derived from the vocabulary word soul as a term of affection.French (Soulé) : variant of Soulier 1.George Soule (1600–80), one of the passengers on the Mayflower in 1620, was one of the founders of Duxbury, MA, where he became comparatively wealthy. He left eight children.
Boy/Male
American, Australian, British, Christian, Dutch, English, French, German, Greek, Irish, Latin, Portuguese
Constant; Steadfast; Firm
Boy/Male
Gujarati, Hindu, Indian, Kannada
Who Loves Everyone
Boy/Male
Hindu, Indian, Malayalam, Tamil, Telugu
Sun
Boy/Male
German
Bear-strength
Boy/Male
Indian
Who's Soul is Joyous.
Girl/Female
Indian
Good
Girl/Female
Christian, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Tree that Grow from Root
Girl/Female
Scandinavian American
Abbreviation of Katherine. Pure.
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Strengthening
PARALLELIZATION MATHEMATICS
PARALLELIZATION MATHEMATICS
PARALLELIZATION MATHEMATICS
PARALLELIZATION MATHEMATICS
PARALLELIZATION MATHEMATICS
n.
Mixed mathematics.
n.
One of a school of physicians in Italy, about the middle of the 17th century, who tried to apply the laws of mechanics and mathematics to the human body, and hence were eager student of anatomy; -- opposed to the iatrochemists.
n.
That branch of mathematics which treats of the relations of the sides and angles of triangles, which the methods of deducing from certain given parts other required parts, and also of the general relations which exist between the trigonometrical functions of arcs or angles.
n.
That science, or class of sciences, which treats of the exact relations existing between quantities or magnitudes, and of the methods by which, in accordance with these relations, quantities sought are deducible from other quantities known or supposed; the science of spatial and quantitative relations.
n.
That branch of applied mathematics which teaches the art of determining the area of any portion of the earth's surface, the length and directions of the bounding lines, the contour of the surface, etc., with an accurate delineation of the whole on paper; the act or occupation of making surveys.
a.
Presenting themselves simultaneously and having reciprocal properties; -- frequently used in pure and applied mathematics with reference to two quantities, points, lines, axes, curves, etc.
n.
A preliminary or auxiliary proposition demonstrated or accepted for immediate use in the demonstration of some other proposition, as in mathematics or logic.
n.
That science, or branch of applied mathematics, which treats of the action of forces on bodies.
n.
The act of solving, or the state of being solved; the disentanglement of any intricate problem or difficult question; explanation; clearing up; -- used especially in mathematics, either of the process of solving an equation or problem, or the result of the process.
n.
A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation.
n.
One versed in mathematics.
n.
One who has made considerable advances in any business, art, science, or branch of learning; an expert; an adept; as, proficient in a trade; a proficient in mathematics, music, etc.
v. i.
To surpass others in good qualities, laudable actions, or acquirements; to be distinguished by superiority; as, to excel in mathematics, or classics.
a.
Of or pertaining to mathematics; according to mathematics; hence, theoretically precise; accurate; as, mathematical geography; mathematical instruments; mathematical exactness.
n.
The branch of mathematics which studies methods for the calculation of probabilities.
n.
Learning; especially, mathematics.
n.
One who professed, or publicly teaches, any science or branch of learning; especially, an officer in a university, college, or other seminary, whose business it is to read lectures, or instruct students, in a particular branch of learning; as a professor of theology, of botany, of mathematics, or of political economy.