...it serves the needs of both mathematical logic itself and related areas of mathematics.
...in connection with the program of D. Hilbert of providing a foundation for mathematics (see [[Formalism|Formalism]]).
3 KB (392 words) - 12:21, 19 August 2014
...d by [[Interval analysis|interval analysis]] (or, more generally, interval mathematics). The interval approach allows one to obtain guaranteed estimates for unkno
...ubsumed under the term "reliable computation" . The following branches of mathematics also belong here: symbolic computations that permit reformulation of the pr
2 KB (270 words) - 17:01, 7 February 2011
...s, unfortunately, itself a broad notion in mathematics and logic). In this connection it is possible either to give a list of the elements of the set, an enumera
...R><TD valign="top">[4]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Theory of sets" , Addison-Wesley (1968) (Translated from French)</TD></T
4 KB (645 words) - 16:57, 7 February 2011
From the point of view of the foundations of mathematics it is important that $ T _ {2} $
...itionism or constructive mathematics. Moreover, outside the foundations of mathematics this restriction is superfluous. If one is interested not in the question o
4 KB (627 words) - 08:00, 6 June 2020
The concept of non-predicativity arose in connection with the discovery of set-theoretical paradoxes, and the term itself is due
...all sets. In this formula $R$ is a possible value of the variable $x$. In mathematics non-predicative definitions are widely used. For example, the union $S$ of
4 KB (713 words) - 17:07, 14 February 2020
The traditional name of the part of mathematics studying tensors and tensor fields (see [[Tensor on a vector space|Tensor o
...ortant constituent part of the apparatus of differential geometry. In this connection it was first systematically developed by G. Ricci and T. Levi-Civita (see [
2 KB (243 words) - 16:39, 21 August 2014
An obsolete name for the branch of mathematics dealing with the properties of operations carried out on vectors (cf. [[Vec
Vector calculus originated in the 19th century in connection with the needs of mechanics and physics, when operations on vectors began t
2 KB (301 words) - 16:54, 7 February 2011
...ndom variable. The concept of a random graph is highly useful in modelling connection networks which are subject to certain random changes or of logical networks
...can be interpreted as characteristics of the reliability of the respective connection network or logical network. In such a case the number $ 1 - q ( e) $
6 KB (999 words) - 20:05, 15 March 2023
Many results in the theory of ordinary Lie groups (the connection between Lie groups and Lie algebras, the construction and properties of the
<TR><TD valign="top">[1]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Lie groups and Lie algebras" , Addison-Wesley (1975) (Translated from Fr
2 KB (327 words) - 11:17, 9 April 2023
...thematical models of physical events; it holds a special position, both in mathematics and physics, being found at the junction of the two sciences.
...construction of mathematical models and, at the same time, is a branch of mathematics, since the methods of investigation of these models are mathematical. Inclu
13 KB (1,857 words) - 21:26, 8 November 2014
...lly infinite (unboundedly extendable), then it terminates. In constructive mathematics several concrete versions of this principle are used which are equivalent i
...hin the framework of the system of abstractions applicable in constructive mathematics consists in the following: If the impossibility of potential infinity of a
7 KB (1,033 words) - 17:48, 1 November 2014
Ideal numbers were introduced in connection with the absence of uniqueness of factorization into prime factors in the r
The concept of an ideal number was introduced by E. Kummer in connection with his investigation of the arithmetic of cyclotomic fields (see , [[#Ref
5 KB (853 words) - 12:16, 22 August 2014
...and came to include certain concepts in and problems of other branches of mathematics. The theory of automata is most closely connected with the theory of algori
...nimization of]]). In addition, there arises the problem of completeness in connection with classes of initialized automata or mappings of automata (cf. [[Functio
7 KB (975 words) - 18:49, 5 April 2020
$#C+1 = 198 : ~/encyclopedia/old_files/data/C025/C.0205140 Connection
...connections on a manifold]], in particular, for example, the [[Levi-Civita connection]] in Riemannian geometry. Let $ p : E \rightarrow B $
17 KB (2,530 words) - 19:28, 17 January 2024
...tems are one of the basic objects of mathematical cybernetics and discrete mathematics, and reflect the following principal features of real and abstract control
...ubstantial connection with real cybernetic models of control systems. This connection, on the one hand, determines a number of essential requirements that are im
7 KB (1,087 words) - 19:40, 5 June 2020
...are stated in [[#References|[a1]]]; see also [[#References|[a4]]]. For the connection with other topological fields (cf. [[Topological field|Topological field]])
...ign="top">[a5]</TD> <TD valign="top"> S. Warner, "Topological fields" , ''Mathematics Studies'' , '''157''' , North-Holland (1989)</TD></TR>
3 KB (406 words) - 05:56, 16 July 2024
...up endowed with a two-sidedly invariant pseudo-Riemannian metric or affine connection, then the one-parameter subgroups of $ G $
...><TD valign="top">[a1]</TD> <TD valign="top"> N. Bourbaki, "Elements of mathematics. Lie groups and Lie algebras" , Addison-Wesley (1975) (Translated from Fr
3 KB (397 words) - 08:04, 6 June 2020
A branch of mathematics and computer science concerned with finding efficient algorithms, or comput
There is an interesting connection between Voronoi diagrams and convex hulls, dating back to G.F. Voronoi. Thr
6 KB (957 words) - 17:46, 4 June 2020
is the [[Levi-Civita connection|Levi-Civita connection]] on $ M $
.... Blair, "Contact manifolds in Riemannian geometry" , ''Lecture Notes in Mathematics'' , '''509''' , Springer (1976)</TD></TR><TR><TD valign="top">[a3]</TD> <T
6 KB (891 words) - 01:08, 8 May 2022
...[[#References|[3]]]. Most algorithmic problems considered in logic and in mathematics are expressible as problems of membership in enumerable sets of constructiv
...character of combinatorial optimization problems from various branches of mathematics [[#References|[5]]]; for more details on this subject see [[#References|[1]
6 KB (862 words) - 19:26, 22 January 2016