Results 171 to 180 of about 30,508 (216)
Some of the next articles are maybe not open access.
Formal Representation of Mathematics in a Dependently Typed Set Theory
2007We have formalized material from an introductory real analysis textbook in the proof assistant Scunak. Scunak is a system based on set theory encoded in a dependent type theory. We use the formalized material to illustrate some interesting aspects of the relationship between informal presentations of mathematics and their formal representation.
Feryal Fulya Horozal, Chad E. Brown
openaire +1 more source
Comparing the theory of representations and constructive mathematics
2005The paper explores the analogy between reducibility statements of Weihrauch's theory of representations and theorems of constructive mathematics which can be reformulated as inclusions between sets. Kleene's function-realizability is the key to understanding of the analogy, and suggests an alternative way of looking at the theory of reducibilities.
openaire +1 more source
A comprehensive theory of representation for mathematics education
The Journal of Mathematical Behavior, 1998Representation is a difficult concept. Behaviorists wanted to get rid of it; many researchers prefer other terms like “conception” or “reasoning” or even “encoding;” and many cognitive science resarchers have tried to avoid the problem by reducing thinking to production rules.There are at least two simple and naive reasons for considering ...
openaire +1 more source
2022
The textbook presents in the most simplified form the basic theoretical provisions of set theory, number representation, combinatorics and mathematical logic, as well as ways to solve practical problems using their methods. A large number of examples are considered.
I. Blagoveschenskiy +2 more
openaire +1 more source
The textbook presents in the most simplified form the basic theoretical provisions of set theory, number representation, combinatorics and mathematical logic, as well as ways to solve practical problems using their methods. A large number of examples are considered.
I. Blagoveschenskiy +2 more
openaire +1 more source
Knowledge representation for mathematical discovery: Three experiments in graph theory
Applied Intelligence, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Susan L. Epstein, N. S. Sridharan
openaire +2 more sources
Mathematical Representation for Wald’s Compartment Theory*
Journal of the Optical Society of America, 1963G. Wald has suggested a compartment theory for the functioning of the rods which corresponds mathematically to that of the Geiger–Muller counter. In this paper a discussion is given as to how the compartment theory fits various models for Geiger–Muller counters. Numerical examples are given to illustrate how the mathematical models can be compared with
openaire +1 more source
To the mathematical theory of representation of information in neural nets
Ukrainian Mathematical Journal, 1995We study irreducible nonorthogonal resolutions of the identity. The results obtained show that, in contrast to traditional requirements of “independent measurements” type, the noncommutative approach gives a more precise description of information systems.
openaire +1 more source
Mathematical representation of articular surfaces using influence surface theory
KSME International Journal, 1998Many mathematical techniques have been developed to determine the geometry of articular joint surfaces, because of its so importance to the study of human joint biomechanics. However, a three-dimensional geometric model of the articular joint, which is essential to solid modelling, contact area measurement, and load bearing analyses, has not been well ...
Jung Soo Han, Hak Soo Han
openaire +1 more source
Linear representation of tree structure - a mathematical theory of parenthesis-free notations
Proceedings of the third annual ACM symposium on Theory of computing - STOC '71, 1971In this paper we present a substantially general theory of parenthesis-free notations for finite plane trees. We obtain stronger one-to-oneness results, including a characterization of one-to-oneness for a large class of notations, and a quite general sufficient condition for one-to-oneness that involves the recursive structure of plane trees in what ...
openaire +1 more source
Knowledge Representation in Mathematics a Case Study in Graph Theory
1983In this dissertation we present our work on representational languages for graph theory. We have shown that a knowledge representation can be structured to provide both expressive and procedural power. Our major research contributions are three. First we have defined representations of infinite sets and recommended that mathematical concepts be ...
openaire +1 more source