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After World War II, Hermann Druckrey and Karl Küpfmüller spent many months in allied internment camps in Germany. In camp Hammelburg, the scholars formed a research collaboration which resulted in two very important publications. Druckrey informed Adolf Butenandt about the co-operation in personal letters which have recently become accessible. Through this new source, the origins of the Druckrey-Küpfmüller papers of 1948-1949 have been confirmed and some further details have been added.

The article informs about case study of a serious and multiple ethical misconduct after an author submitted a paper to five journals for publication and committed some form of plagiarism. Topics include mathematics and in sciences in general, multiple submissions of the same results or parallel papers are prohibited as serious ethical misconduct; and mathematics simultaneous or concurrent submission of a manuscript describing the same research publication in the electronic online systems.

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Copyright of Unterrichtswissenschaft (Springer Science & Business Media B.V.) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The article "How many points does your star have?" by Max Hoffmann describes a guide for folding and cutting a star from a square sheet of paper. By folding and cutting, a star with a specific number of points is created. The author suggests using colored paper and using the star as a decoration for the room. The question is also raised whether it is possible to create stars with more or fewer points. The author, Dr. Max Hoffmann, works at the Institute for Mathematics at the University of Paderborn. [Extracted from the article]

Entry-level prerequisites in mathematics are of paramount importance for success in STEM undergraduate programs. Nevertheless, basic mathematical skills from lower secondary school are often neglected in repetition and support measures. Similarly, there is a lack of appropriate diagnostic, quality-controlled instruments for this purpose. This paper presents a reliable and both content as well as differentially and prognostically valid computer-based instrument for diagnosing these skills. A paper and an online version measure the same construct. The online version includes instant feedback that integrates both performance and improvement feedback. In the outlook, outstanding key development and testing steps are addressed. [ABSTRACT FROM AUTHOR]

A lot of feminist and decolonial critiques of knowledge get confronted with the reference to »hard sciences« or »mathematical reasoning« as examples that supposably showcase that there are epistemic spheres of no political dimensions and complete universality. This paper commits to a deconstruction of exactly such a reasoning in directly arguing to view Mathematics not only as also being knowledge production bearing political dimensions but even claiming it to play a particular role in securing hegemonic structures of knowing. In putting forth this argument I have three main claims: a) What is commonly referred to as »mathematics « is actually a specifically Western way of conceptualizing what it means to »think mathematically« (here referred to as Mathematics). b) The Western concept of Mathematics is conceptually entangled with Western concepts of Rationality and Humanism. c) These three concepts and their entanglement can be understood as a re-establishing epistemically violent structures of knowledge. [ABSTRACT FROM AUTHOR]

Copyright of Zeitschrift für interpretative Schul- und Unterrichtsforschung is the property of Verlag Barbara Budrich GmbH and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Zeitschrift für Pädagogische Psychologie is the property of Hogrefe AG and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Lernen und Lernstörungen is the property of Hogrefe AG and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Unterrichtswissenschaft (Springer Science & Business Media B.V.) is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we continue our investigation concerning the concept of a liken. This notion has been defined as a sequence of non-negative real numbers, tending to infinity and closed with respect to addition in R. The most important examples of likens are clearly the set of natural numbers N with addition and the set of positive natural numbers N* with multiplication, represented by the sequence (ln(n+1))∞ n=0. The set of all likens can be parameterized by the points of some infinite dimensional, complete metric space. In this space of likens we consider elements up to isomorphism and define properties of likens as such that are isomorphism invariant. The main result of this paper is a theorem characterizing the liken N* of natural numbers with multiplication in the space of all likens.

Copyright of Annual Review of the Faculty of Philosophy / Godisnjak Filozofskog Fakulteta is the property of Faculty of Philosophy, University of Novi Sad and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The classic method of solving the cubic and the quartic equations using Tschirnhaus transformation yields true as well as false solutions. Recently some papers on this topic are published, in which methods are given to get only the true solutions of cubic and quartic equations. However these methods have some limitations. In this paper the author presents a method of solving cubic and quartic equations using Tschirnhaus transformation, which yields only the true solutions. The proposed method is much simpler than the methods published earlier.

Copyright of Mitteilungen der DMV is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Zeitschrift für Soziologie is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper deals with the issue of interdisciplinarity in literature, tracing the mathematical influences — and particularly those of the incompleteness theorems by Kurt Gödel — on the literary works of Hans Magnus Enzensberger. Our attention is focused on Enzensberger’s publications in mathematics, on his poem Hommage à Gödel, and his montage epos The Sinking of the Titanic. This paper submits a new, interdisciplinary interpretation of the poem Hommage à Gödel as a kind of art manifesto, and comes to the conclusion that the reason Enzensberger finds the incompleteness theorems so interesting is that they offer a scientific basis for undecidable problems and paradoxes. He applies Gödel’s theorems to literature, where they enable a creative, playful oscillation between two positions or aspects of an undecidable problem and self-reference in literature.

In this paper the current relationship between physics and its philosophy is examined as well as its possibilities of development. The study is largely based on case studies. Although both disciplines have joint roots in pre-christian philosophy, today their teachings and research occur independently from one another. Both communities consider their systematic dialogue as important for each side. Nevertheless, the huge amount of information and the high degree of specialization of these debates renders the mutual dialogue rare events. As a result, associated inputs are missing in both directions and at all levels and debates lose the content stringency required for a continuous exchange. True interdisciplinarity is therefore no longer given. In the external perception, the two territories appear to belong together, but within the professional communities factual alienation is quite noticeable. Nevertheless, physics and philosophy remain intimately connected, both in their common claim to generate positive knowledge of the world, and at the level of concrete questions. In this essay, the transformation of physical concepts - which always have a philosophical core – is illustrated on the basis of several case studies. Mathematics also plays a key role in the recognition of nature, and should be addressed as well in this context. Today's physics has many facets: Depending on the perspective, it appears as a mathematically extremely sophisticated theory-building exercise, or as THE paradigmatic example of an empirical science with an astounding history of application successes, or as a world science that is at least implicitly normative. In fact, the interaction between theory, experiment and interpretation allows for a deeper understanding and successful predictions. Latest at this point, the intrinsic connection between physics and philosophy is revealed. In the philosophicalhistorical perspective, the time-invariant component of physics or its supporting inner structure becomes visible: conceptual leitmotifs and explanatory strategies are preserved, although in a modified form. As an effective and sustainable corrective of the current state, which is perceived as unsatisfactory by both sides, I propose that logical and epistemological basic contents, as well as specific topics of the philosophy of physics becomes part of the curriculum of the physicist's education. [ABSTRACT FROM AUTHOR]

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Copyright of Mitteilungen der DMV is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F(x, y))= f(x) + f(y) on components of the denition of a given associative rational function F. The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.

Copyright of Discourse: Journal of Childhood & Adolescense Research / Diskurs Kindheits- und Jugendforschung is the property of Verlag Barbara Budrich GmbH and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper explores the trend of the early 20th century to consolidate mathematics, natural sciences, medicine and technology under the umbrella of one integrative culture--a tendency which contrasts with the increasing mainstream trend of separating the humanities from the natural sciences. The unifying umbrella was framed by the great encyclopedia Die Kultur der Gegenwart which was published by B. G. Teubner from 1905 to 1925 and was planned to run up to 62 volumes. We analyze the quantitative rate of the parts devoted to the humanities, the natural sciences and technology, respectively, the degree to which these parts were completed in this encyclopedia. In particular, we investigate the role of mathematicians and their reasons to find a classification for the mathematical, natural scientific and engineering parts of culture as well as their reasons, to win Nobel prize winners and other famous scientists to become co-editors and authors. We examine the published volumes in the fields of mathematics, chemistry, physics, astronomy and technology in order to show what type of publication--professional or popular--was intended. Furthermore, we illuminate how the educational reform of mathematics, natural sciences and technology of this period--which included a reform of girls' and women's education--was reflected in the encyclopedia Die Kultur der Gegenwart.

In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we consider the model of a market (with d risky assets), which does not hold the same interest rate assumptions. We introduce two predictable processes for modelling deposits and loans. We propose a new concept of a martingale pair for the market and prove that if there exists a martingale pair for the considered market, then there is no arbitrage opportunity. We also consider special cases in which the existence of a martingale pair is necessary and the sufficient conditions for these markets to be arbitrage free

This paper is devoted to the study of a multi-step method with divided differences for solving nonlinear equations in Banach spaces. In earlier studies, hypotheses on the Fréchet derivative up to the sixth order of the operator under consideration is used to prove the convergence of the method. That restricts the applicability of the method. In this paper we extended the applicability of the sixth-order multi-step method by using only hypotheses on the first derivative of the operator involved. Our convergence conditions are weaker than the conditions used in earlier studies. Numerical examples where earlier results cannot be applied to solve equations but our results can be applied are also given in this study.

The paper discusses the problem of infinity with a special reference to mathematical truth. The roots of this problem, in a sense, go back to early efforts to provide a rational account of the phenomena of change, and the phenomenon of motion in particular, and, in connection with this, to the attempt to cast light on the complex relationship between continuity and discreteness. If mathematics is to serve as a tool of a rational description of the world, is it possible to construct a mathematical model of phenomenal continuity? This question was raised already by Zeno when the Pythagorean hypothesis of the essential ‘granularity’ of the world began to crumble as a result of the discovery of incommensurable magnitudes. The discovery of incommensurable magnitudes, and along with it the discovery of irrational numbers, produced well-known paradoxes and gave rise to the question to what extent, if at all, mathematics can deliver a ‘metaphysical’ description of the world. In more recent times, the idea of infinity was built into the infinitesimal calculus which became the foundation of the mathematical description of nature, but the metaphysical questions have not gone away. The issues surrounding actual and potential infinity continue to be the subject of intense debates. Whereas some recognise only potential infinities, others, like Georg Cantor, accept actually existent infinities. This is directly connected with the question of mathematical truth, which, according to the Platonist tradition exists as objectively given. The paper argues that the Cantorian transfinite set theory cannot withstand criticism, and that rather than providing a (metaphysical) description of reality mathematics merely offers possible models in terms of which the world might be better or more conveniently interpreted. The so-called ‘mathematical truth’ reduces to the question of ‘correctness’, viz. whether a given mathematical proposition does or does not follow from given premises.

Copyright of Mitteilungen der DMV is the property of De Gruyter and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

'Growth' or 'Revolution'? Ernst Cassirer and History of Science. Ernst Cassirer's contributions to history of science have been long time neglected. The aim of this paper is to show the historical and philosophical framework of Cassirer's engagement in this field, starting from his seminal work about the problem of knowledge in science and philosophy of the modern age. Moreover the author suggests that Cassirer's late studies about Galilei and the origins of mathematical science are of some interest in order to comprehend both his commitment to contemporary history of science (from Burtt to Koyré) and his intellectual heritage for our agendas in a post-Kuhnian era. [ABSTRACT FROM AUTHOR]

Student knowledge assessment is a key element of the pedagogical process, as it provides students, parents, and educators with important feedback information on students’ knowledge and skills. Assessment of students’ mathematical knowledge is complex, as several factors are normally included in students’ final grade, and simply calculating the average of students’ achievements may not provide a complete picture of their knowledge. Therefore, in this paper, we aimed to investigate the possibility of using fuzzy logic to assess students’ knowledge and competencies by considering (1) students’ overall academic performance, (2) the quality of students’ project work on a topic from the history of mathematics and (3) the regularity of handing in homework. The study was conducted considering 22 Italian high school students. The results show that students’ academic performance is similar to student grades obtained with fuzzy logic.

The article offers briefs related to Deutsche Mathematiker-Vereinigung (DMV). Topics include Science Council published the position paper impetus from the Covid- 19 crisis for further development of the science system in Germany passed to reorientation of science policy; and response capability in policy advice about a lack of sovereignty and Security in the digital space up to strategic challenges in internationalization.

Gustav Theodor Fechner was one of the outstanding German scientists and thinkers. He is well known as the eminent founder of a new science "psychophysics" - the quantitative study of the relations between physical stimuli and sensations. But it seems that first ideas and first solutions of this new science are not the result of hard experimental work but rather of metaphysical speculations. So we found for the first time the important "Fundamentalformel" in the philosophical book "Zend-Avesta", written by Fechner already in 1851. Therefore this formula may not be the result of his later experimental efforts, put down in writing in the important "Elemente der Psychophysik" (1860). In the present paper it was intended to retrace the so-called "indefinite train of thoughts" (Fechner) that lead him to his strictly mathematical formula.

Copyright of Zeitschrift für Pädagogik is the property of Julius Beltz GmbH & Co. KG Beltz Juventa and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)