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Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory
In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures.Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects y i conform, in some consistent way, to ...
Univalent foundations are an approach to the foundations of mathematics in which mathematical structures are built out of objects called types.Types in univalent foundations do not correspond exactly to anything in set-theoretic foundations, but they may be thought of as spaces, with equal types corresponding to homotopy equivalent spaces and with equal elements of a type corresponding to ...
Lebesgue greatly improved measure theory, and introduced his own theory of integration, now known as Lebesgue integration, which proved to be a big improvement over Riemann's. Hilbert introduced Hilbert spaces to solve integral equations. The idea of normed vector space was in the air, and in the 1920s Banach created functional analysis.
The method of forcing is employed in set theory, model theory, and recursion theory, as well as in the study of intuitionistic mathematics. The mathematical field of category theory uses many formal axiomatic methods, and includes the study of categorical logic , but category theory is not ordinarily considered a subfield of mathematical logic.
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite . The order of an element of a group (also called period length or period ) is the order of the subgroup generated by the element.