Partitions of sets and natural numbers have been a very attractive subject during the recent decades. Partitions play important roles in such diverse areas of mathematics as combinatorics, Lie theory, representation theory, mathematical physics, and the theory of special functions. Because of some applications of this subject, mathematicians have given some formulas in this regard. Up to now, t...

The P versus NP question distinguished itself as the central question of Theoretical Computer Science nearly four decades ago. The quest to resolve it, and more generally, to understand the power and limits of efficient computation, has led to the development of Computational Complexity Theory. While this mathematical discipline in general, and the P vs. NP problem in particular, have gained pr...

The mathematicians for centuries have researched the surfaces theory. In this paper, we consider strophoidal surface in three dimensional Euclidean space E^3. We present notations of a geometry. addition, stating helicoidal surface, define and calculate its Gauss map, Gaussian curvature, mean curvature. Finally, give some relations curvature that kind surfaces.

This article outlines the history of our visualization of the interior of the human body. It throws some light on the emotional context and the underlying idea of man. In order of appearance on the historical stage, the leading characters are: painters, murderers (more precisely: executed persons including thieves driven merely by need, women with illegitimate children, etc.), and mathematician...

Abstract The paper shows how to use the Husserlian phenomenological method in contemporary philosophical approaches mathematical practice and ontology. First, develops approach based on Husserl's writings obtain a for understanding practice. Then, put forward full-fledged ontology of mathematics, is complemented with social ontological considerations. proposed account sees objects as constructi...

THE CLOSE CONNECTION BETWEEN mathematics and philosophy has long been recognized by practitioners of both disciplines. The apparent timelessness of mathematical truth, the exactness and objective nature of its concepts, its applicability to the phenomena of the empirical world—explicating such facts presents philosophy with some of its subtlest problems. We shall discuss some of the attempts ma...

It is argued that the mathematical theory of reliability as a separate discipline began in 1961 with the publication of Multi-component systems and their structures and their reliability by Birnbaum, Esary and Saunders. Prior to this time, mathematicians were just applying standard mathematical techniques such as queueing theory, statistics and probability to engineering reliability problems. W...