Related papers: Karl Weierstrass Bicentenary
The primary aim of this chapter is, commemorating the 150th anniversary of Riemann's death, to explain how the idea of {\it Riemann sum} is linked to other branches of mathematics. The materials I treat are more or less classical and…
In the following, bypassing dynamical systems tools, we propose a simple means of computing the box dimension of the graph of the classical Weierstrass function defined, for any real number~$x$, by~$ {\cal W}(x)=\displaystyle…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
Talk at the meeting of the German Mathematical Society and the Cantor Medal Award Ceremony
The primary sourcebook for developments based on the data of the world components "Theory of Intellectualities and Mathematical Statistics" (TIMS) collections of the Department of Mathematics, Physics and Astronomy of Odessky National…
The first seeds of mathematical intuitionism germinated in Europe over a century ago in the constructive tendencies of Borel, Baire, Lebesque, Poincar\'e, Kronecker and others. The flowering was the work of one man, Luitzen Egbertus Jan…
In the 1850s Weierstrass succeeded in solving the Jacobi inversion problem for the hyper-elliptic case, and claimed he was able to solve the general problem. At about the same time Riemann successfully applied the geometric methods that he…
The influence of Alfred Tarski on computer science was indirect but significant in a number of directions and was in certain respects fundamental. Here surveyed is the work of Tarski on the decision procedure for algebra and geometry, the…
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
Based on M. Grossman in \cite{Grossman83} and Grossman an Katz \cite{GrossmanKatz}, in this paper we discuss about the applications of bigeometric calculus in different branches of mathematics and economics.
A century ago physicists and mathematicians worked in tandem and established quantum mechanism. Indeed, algebras, partial differential equations, group theory, and functional analysis underpin the foundation of quantum mechanism. Currently,…
This talk presents foundations of mathematics as a historically variable set of principles appealing to various modes of human intuition and devoid of any prescriptive/prohibitive power. At each turn of history, foundations crystallize the…
During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to…
$E$-functions were introduced by Siegel in 1929 to generalize Diophantine properties of the exponential function. After developments of Siegel's methods by Shidlovskii, Nesterenko and Andr\'e, Beukers proved in 2006 an optimal result on the…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
Boltzmann's work, ``Ueber die sogenannte H-Curve," discusses his demonstration of the essential characteristics of the H-curve in a clear, concise, and precise style, showcasing his efforts to persuade his peers. To make these findings more…
A history of two Rolle Theorems, about the root of derivative and about root interval from 1690 till the end of XIX century.
This paper aims to give a brief account of the mathematical work of the 7th-century Armenian polymath and natural philosopher Anania Shirakatsi. The three sections of Anania's ``Book of Arithmetic'' -- tables of arithmetic operations, a…
We consider a definition of mathematics as the art of thinking in terms of formalized systems, and the science of relations, structures and algorithms. We also touch upon the relation of mathematics to other sciences, in particular through…