Related papers: Richard Dedekind: Style and Influence
We carry out a thorough bibliometric analysis of recent publications in mathematics based on the database Web of Science. The individual relations between various features and the citations are provided, and the importance of the features…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
In this paper, we reveal an internal structure within Dedekind numbers, demonstrating that they can be expressed as polynomials of powers of 2. This discovery is based on innovative concepts and methods, offering a new perspective on the…
We present here our introduction to the contributed volume "Quantum Theory: Informational Foundations and Foils", Springer Netherlands (2016). It highlights recent trends in quantum foundations and offers an overview of the contributions…
Following the processing of individual topics of elementary school mathematics as content of empirical theories the question is adressed wether the associated conception of mathematics finds itself under established concepts, and how it can…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
This is my working paper on a proposed logical framework for the practice of mathematics, which is paralleled by philosophical considerations and a computer implementation (a variant of Automath). Updated 10/27/2016 with a version from…
We review some of Olivier Messiaen's use of mathematics in his composition and his theoretical writings. The final version of this paper appeared in the book Twentieth-Century Music and Mathematics, R. Illiano (ed.), Brepols, Turnhout,…
The main purpose of this article is using the analytic mathods and the quadratic residual transformation technique, and properties of Dedekind sums to study the calculating problem of two kinds hybrid power mean involving the two-term…
Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
Academic biography of Karl Weierstrass, his basic works, influence of his doctrine on the development of mathematics.
This book is devoted to an informal discussion of patterns constructed for treating physical problems. Such patterns, when sufficiently formalized, are usually referred as "models", and tents to be applied not only in physics, but conquer…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
Based on Plato's Timaeus, we present some reflections on music, cosmology and mathematics and their mutual influence.The article is dedicated to the composer Walter Zimmermann. The final version of this article will appear in the volume…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
The purpose of this manuscript is to gather together a large amount of source material pertaining to women in mathematics, from studies of girls in elementary school through data on females winning prizes for mathematical research. Along…
We present and discuss a curated selection of recent literature related to the application of quantitative techniques, tools, and topics from mathematics and data science that have been used to analyze the mathematical sciences community.…