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One celebrated example is Donaldson's theorem, which puts tight restraints on what would otherwise appear to be a large class of manifolds. This (informal) usage reflects the opinion of the mathematical community: not only should such a theorem be strong in the descriptive sense (below) but it should also be definitive in its area.
A geometry: it is equipped with a metric and is flat. A topology: there is a notion of open sets. There are interfaces among these: Its order and, independently, its metric structure induce its topology. Its order and algebraic structure make it into an ordered field.
There are many equivalent definitions of a category. [1] One commonly used definition is as follows. A category C consists of a class ob(C) of objects, a class mor(C) of morphisms or arrows, a domain or source class function dom: mor(C) → ob(C), a codomain or target class function cod: mor(C) → ob(C),
3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.
Also called infinitesimal calculus A foundation of calculus, first developed in the 17th century, that makes use of infinitesimal numbers. Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. Catastrophe theory a ...
class 10, class 100, etc. – a measure of the air quality in a cleanroom; class 10 means fewer than 10 airborne particles of size 0.5 μm or larger are permitted per cubic foot of air; cleanroom (clean room) – a specialized manufacturing environment that maintains extremely low levels of particulates; CMP – see chemical-mechanical polishing
In other words it is a (tri)homogeneous polynomial on SV⊕V⊕V* for some vector space V, where SV is some symmetric power of V and V* its dual, that is invariant under the special linear group of V. In practice V often has dimension 2. The degree, class, and order of a concomitant are its degrees in the three types of variable.
The apparent plural form in English goes back to the Latin neuter plural mathematica , based on the Greek plural ta mathēmatiká (τὰ μαθηματικά) and means roughly "all things mathematical", although it is plausible that English borrowed only the adjective mathematic(al) and formed the noun mathematics anew, after the pattern of ...