In 1804 the chair of Elementary Mathematics at Prague University became vacant and a selection procedure, which consisted of a written and an oral examination, was announced. Only Bernard Bolzano and ...Ladislav Jandera took part in it. Jandera was appointed to the chair, whereas Bolzano became Professor of “Religious Doctrine.” In this paper we examine the context of this Concursprüfung, the performance of both candidates and the outcome, based on a number of related papers preserved at the Czech National Archives. In addition to this, we publish for the first time, albeit only in the online version of this paper, the transcription and English translation of Bolzano's written examination.
Im Jahr 1804 wurde die Lehrkanzel der Elementarmathematik an der Prager Carl-Ferdinand-Universität durch die Pensionierung von Stanislav Vydra vakant. Die Concursprüfung, an der nur Bernard Bolzano und Ladislav Jandera teilnahmen, bestand aus einem schriftlichen und einem mündlichen Teil. Der Lehrstuhl ging an Jandera, während Bolzano Professor für “Religionslehre” wurde. Der vorliegende Aufsatz untersucht den Kontext der Concursprüfung, die Antworten der beiden Kandidaten und das Ergebnis, basierend auf einer Reihe von verwandten Papieren, die im Nationalarchiv in Prag aufbewahrt werden. Zusätzlich veröffentlichen wir als Anhang erstmals –wenn auch nur in der Online-Version dieses Aufsatzes– die englische Übersetzung und Transkription von Bolzanos schriftlichen Antworten.
There is a growing awareness among researchers in the humanities
and social sciences of the rhetorical force of mathematical
discourse-whether in regard to gerrymandering, facial recognition
...technologies, or racial biases in algorithmic automation. This book
proposes a novel way to engage with and understand mathematics via
a theoretical framework that highlights how math transforms the
social-material world.
In this study, G. Mitchell Reyes applies contemporary rhetorical
analysis to mathematical discourse, calling into question the
commonly held view that math equals truth. Examining mathematics in
historical context, Reyes traces its development from Plato's
teaching about abstract numbers to Euclidian geometry and the
emergence of calculus and infinitesimals, imaginary numbers, and
algorithms. This history reveals that mathematical innovation has
always relied on rhetorical practices of making meaning, such as
analogy, metaphor, and invention. Far from expressing truth hidden
deep in reality, mathematics is dynamic and evolving, shaping
reality and our experience of it.
By bringing mathematics back down to the material-social world,
Reyes makes it possible for scholars of the rhetoric and sociology
of science, technology, and math to collaborate with mathematicians
themselves in order to better understand our material world and
public culture.
History of ematics textbook Dejene Girma Denbel
Cogent education,
12/2023, Volume:
10, Issue:
2
Journal Article
Peer reviewed
Open access
AbstractThe purpose of this study was to investigate elements of the history of mathematics in secondary school mathematics textbooks in Ethiopia. In line with this, the study also identified the ...extent to which mathematics is seen as a social construct in textbooks. To achieve these four mathematics textbooks from Grades 9 to Grade 12 were selected for this purpose. The document review method used to determine the extent of use of elements of the history of mathematics, the stage in the unit it used, and the learning domains of mathematics it covered in these textbooks are considered. For document analysis purposes Erdoğan et al.’s (2015) classification of elements of the history of mathematics was adopted. This distribution involves historical notes, notes on usage areas of mathematics, applications with historical notes, and historical elements in students’ extracurricular activities. The result has indicated that it has found 26 elements of the history of mathematics and the highest number found in the grade 11 Mathematics textbook. The learning domain algebra in the form of historical notes also received the highest coverage than others. Moreover, the result has indicated most elements of the history of mathematics were used at the beginning stage of the unit. Finally, the study has concluded that elements of the history of mathematics are not sufficiently integrated with the contents of mathematics textbooks. Several elements of the history of mathematics are far from the social context of the learner, as indicated in the textbooks.
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory ...is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Old mathematics books and textbooks have focused different researchers onto the history of mathematics and mathematics education. However, books are not the only information source for this field; ...for example, researchers can also study periodical-type publications from the past (such as diaries, weeklies, newspapers, etc.). Considering this, this study developed an instrument to analyze publications about mathematics and mathematics education included in newspapers, weeklies, journals, etc., which were not exclusively devoted to science, from the perspective of the history of mathematics and mathematics education. In order to do so, a descriptive research focused on the analysis of historical texts was carried out using the content analysis technique. The different labels and categories of this instrument are here exemplified by the categorization of some entries included in several periodical publications published in the 18th century in Spain.
W artykule przedstawimy działalność Komisji Historii Matematyki powołanej przez Zarząd Główny PTM. Od 1997 do 2000 roku nieprzerwanie przewodniczyła Komisji dr Zofia Pawlikowska-Brożek – dr ...matematyki UJ w zakresie historii matematyki – uczennica wielce zasłużonego dla upowszechniania i badań nad historią matematyki wybitnego matematyka oraz cenionego dydaktyka prof. dra hab. Zdzisława Opiala (1930–1974).
Na podstawie dokumentów, które autor otrzymał do dyspozycji od Przewodniczącej Komisji, przedstawimy w jaki, sposób działalność Komisji przyczyniła się do inicjonowania badań nad historią matematyki i do powstania profesjonalnego środowiska historyków matematyki w Polsce.
Historia matematyki w Krakowie jest dyscypliną dobrze znaną od czasów Ludwika A. Birkenmajera (1855–1929). Jego działania z powodzeniem kontynuował Z. Opial. Problematyka krakowskiego ośrodka historyków matematyki została przedstawiona m.in. w pracach (Domoradzki 2020; Kokowski 2020). Istotną inspiracją dla działań Komisji były inicjatywy podejmowane przez Zakład Historii Nauki, Oświaty i Techniki PAN w porozumieniu z Komitetem Historii Nauki i Techniki PAN, w pracach wspomnianych gremiów aktywnie uczestniczyła Przewodnicząca Komisji.
Materiały prezentowane w pracy obejmują także okres przed powołaniem Komisji.
In the article, we present operation of the Commission for the History of Mathematics appointed by the Main Board of the Polish Mathematical Society. From 1997 to 2000, the Committee was continuously ...chaired by Dr. Zofia Pawlikowska-Brożek, PhD in mathematics at the Jagiellonian University in the field of History of Mathematics, a student of an outstanding mathematician and respected teacher, Professor Dr hab. Zdzisław Opial (1930–1974). Based on the documents, that the author received from the Chair of the Commission, we present how the activities of the Commission contributed to initiation of research on the history of mathematics, and to e creation of a professional community of historians of mathematics in Poland. The history of mathematics has been a discipline well known in Kraków since the times of Ludwik A. Birkenmajer (1855–1929). His activities were successfully continued by Z. Opial. The issues of Kraków center for history of mathematics were presented by Domoradzki 2020; and Kokowski 2020, among others. An important inspiration for the activities of the Committee were initiatives undertaken by the Department of History of Science, Education, and Technology of the Polish Academy of Sciences in agreement with the Committee of the History of Science and Technology of the Polish Academy of Sciences, in which the Chairwoman of the Committee actively participated. The materials presented in the work cover also the period before the establishment of the Commission for the History of Mathematics.
According to Jaina cosmology, the non-universe is a hollow sphere beyond and exists all round the universe, whose middle region is the horizontal universe resting on a circular disc. The Bhagavatī ...Sūtra and the Sthānāṅga Sūtra each mention that there is the core of the horizontal universe where a cube of eight space-points is and from those eight space-points ten directions originate. This paper presents a conjectural explanation for understanding that cube. The core of the non-universe is the core of a core-sphere when the core-sphere is formed using n core-circles such that they are stacked up and down in the same order from the nth core-circle to the first core-circle. The upper four points of the cube of eight points form the core of the horizontal universe and the cube of eight points is the core of the non-universe. The nth core-circle becomes the horizontal universe when n is innumerable and the nth core-sphere forms the non-universe when n approaches infinity. This paper also shows that the intermediate and cardinal directions are linear and planar respectively while the zenith and nadir ones are three-dimensional.
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