The thesis focuses on the reception history of Bernard Bolzano (1781- 1848) in the Czech intellectual culture of the 1945-1989 period. The aim of the thesis is not only to summarize existing studies of Bolzano's life and work or to study some of the partial themes related to Bolzano - but to discover basic features of Bolzano reception that can be found accross the different fields of Bolzano research and that are also connected to intellectual and political history background. The expected merit of the thesis can be considered from two different perspectives: In the context of intellectual history the reception of Bolzano is just a very partial theme, however it can expose some of more general features concerning Czech intellectual history of investigated period. From this point of view Bolzano is just a criterion of historical sources selection that enables to study very complex issue of the Czech intellectual history. In the context of Bolzano research this thesis is also a contribution to the better understanding of Bolzano's life and work. The thesis is pointing out themes which should be researched more thoroughly and, it is more important, it discovers the basic contexts of the potential further studies. Keywords: Bernard Bolzano (1781-1848), Czech history 1945-1989, Czech culture 1945-1989,...

Cryptography fascinates people of all generations and is increasingly presented as an example for the relevance and application of the mathematical sciences. Indeed, many principles of modern cryptography can be described at a secondary school level. In this context, the mathematical background is often only sparingly shown. In the worst case, giving mathematics this character of a tool reduces the application of mathematical insights to the message ”cryptography contains math”. This paper examines the question as to what else cryptography can offer to mathematics education. Using the RSA cryptosystem and related content, specific mathematical competencies are highlighted that complement standard teaching, can be taught with cryptography as an example, and extend and deepen key mathematical concepts.

Made available in DSpace on 2016-04-27T16:58:08Z (GMT). No. of bitstreams: 1 dissertacao_gustavo_miranda.pdf: 594697 bytes, checksum: 12a44cd827b057543633c4cda536191f (MD5) Previous issue date: 2004-12-03 / With the purpose of studying the calculus teaching history and, particularly, the consequences of Calculus Made Easy (1910) in the mathematics education context, this work intends to make an historical analysis to clarify the connections between Silvanus Phillips Thompson (its author) and the education in the early twentieth century, mainly mathematics education. Thompson was concerned about Physics and Radiology, however, at the dawn of the new century, his interests in technical education had also burgeoned. One of his goals was to demystify Calculus, tackling the subject intuitively Calculus Made Easy. The book did not draw much respect from mathematicians and was acridly criticized / Com o intuito de estudar a história do ensino de Cálculo e, mais especificamente, os desdobramentos do livro Calculus Made Easy (1910) no contexto da educação matemática, este trabalho procura fazer uma análise histórica que elucide as relações entre Silvanus Phillips Thompson (autor do livro) e a educação do início do século XX, particularmente a educação matemática. Thompson legou muito às áreas da física e da radiologia, porém, com a chegada do novo século, passou a se dedicar intensamente à educação técnica de seus compatriotas ingleses. Tal dedicação, aliada a preocupações políticas e sociais da época, foi crucial para a publicação do seu texto didático mais polêmico: o Calculus Made Easy (1910). A polêmica estava atrelada às discussões sobre o rigor e a intuição no ensino de matemática, visto que o didático tratava dos conceitos fundamentais do Cálculo de maneira intuitiva e com aplicações. Apesar das críticas e do repúdio dos matemáticos da época, Thompson granjeou a admiração e o respeito de muitos alunos de Cálculo durante o século XX. Tornou-se, assim, parte da história do ensino de Cálculo

Made available in DSpace on 2016-04-28T14:16:43Z (GMT). No. of bitstreams: 1 Alexandre Marcos de Mattos Pires Ferreira.pdf: 6236788 bytes, checksum: 4d3ad3ea20314c747f667d8c94a66e04 (MD5) Previous issue date: 2009-10-09 / The present work refers to a study about creation of Faculty of Philosophy, Sciences and Letters / USP, specifically about the early formation of researchers and teachers of mathematic and physic in Sao Paulo. The objective of the work was to know how was occurred the formation of these professionals in the period from 1934 to 1936. The employed method was constituted in using authorities depositions that are preserved in books, in magazines and in the registered interviews. The most important fountains were: Anuário da Faculdade de Filosofia, Ciências e Letras da USP, years: 1934, 1935, 1936, 1937 and 1938; Anuário do Centro Brasileiro de Pesquisas Físicas and of Sociedade Brasileira de Matemática / O presente trabalho refere-se a um estudo sobre a criação da Faculdade de Filosofia, Ciências e Letras da USP, especificamente sobre a formação inicial de pesquisadores e professores de Matemática e de Física em São Paulo. Seu objetivo consiste em explicitar como ocorreu a formação de pesquisadores e professores de matemática e física no período de 1934 a 1936. O método empregado constituiu em utilizar os depoimentos de autoridades da época que se encontram preservados em livros, em revistas e nas entrevistas documentadas. As fontes mais importantes foram: Anuário da Faculdade de Filosofia, Ciências e Letras da USP, anos: 1934, 1935, 1936, 1937 e 1938; Anais do Centro Brasileiro de Pesquisas Físicas e da Sociedade Brasileira de Matemática

Sonderausgabe des "Dresdner Universitätsjournal" von 2001

Bien que ma dissertation de thèse consiste essentiellement en trois pièces de nature assez distincte (il s'agitde la traduction en tchèque de l'Analyse des infiniment petits, son commentaire et l'étude d'introduction),cependant, je subsume le tout sous une idée unificatrice de la loi de continuité leibnizienne qui régit le systèmede symboles au fondement du calcul différentiel. Quant à la première partie, elle décrit premièrement l'histoire dela vie du marquis de l'Hospital dite « officielle» ou bien « académique » due à l'Éloge de Bernard de Fontenellequi sert de l'arrière-plan de la seconde partie, de l'étude introductrice, du portrait « caché», consistant en l'analysedes succès géométriques du marquis, des solutions de problèmes physico-géométrique célèbres en comparaisonde celles de Jean Bernoulli, son jeune précepteur – fondée bien évidemment sur la correspondance mutuelle. Enraison de la nature du calcul leibnizienne tant physique que géométrique je démontre que c'était précisément lapureté géométrique de son esprit qui faisait obstacle à l’invention géométrique du marquis. En deuxième lieu jeprésente la description des controverses qui ont éclaté entre Leibniz et Nieuwentiijt sur la questions de fondementdu calcul, tout en précisant sur les écrits leibniziennes la nature symbolique ambiguë de différentielles. L'autrecontroverse, entre Rolle et Varignon, sert à décrire les contrainte institutionnelles du développement du calculaussi que les explication fondatrices de la part de Varignon qui indique la futur transformation newtonienne ducalcul infinitésimal. Enfin le commentaire, d'après ladite idée unificatrice, marque sur des exemplesmathématiques la transformation algébrique de la géométrie grecque pendant le XVIIe siècle tout en illustrant lesarticles de l'Analyse et comparant ses sources bernoulliennes. / The basis of my dissertation consists in three rather distinct parts, that is Czech translation, a commentaryand introduction to the famous Analyse des infiniment petitis by marquis the l'Hospital. Nevertheless I unify thewhole in virtue of the leibnizien metaphysical idea of the law of continuity governing the symbolic systemfundamental to the differential calculus of Leibniz. Concerning the first part of the introduction I represent the socalled academical or official picture of marquis de l'Hospital based on the Éloge by Bernard de Fontenelle. I usethis picture as a background to the so called hidden picture of the marquis, which consists in the analysis of thephysico-geometrical problems solved by the marquis de l'Hospital in comparison to those of Johann Bernoulli,based naturally on the correspondence of the two of them. I demonstrate, regarding the nature of the calculusboth physical and geometrical, that it was precisely the geometrical purity of his mind had forbidden him to makeinventions in geometry, unlike Johann Bernoulli. In the third part I describe the controversies that made part ofthe development of the calculus; firstly the controversy between Nieuwentijt and Leibniz concerning thefundamental questions of calculus. I precise on this occasion my views on the nature of leibnizian calculus asstated above, that is ambiguous symbolism of differentials. The second controversy, between Rolle and Varignonputs forward institutional obstacles of the development of the calculus as well as the foundational attempts madeby Varignon that indicated the future transformation of the calculus according to the spirit of Newton. Finally thecommentary, by the symbolic idea above, indicates the algebraical shift of the 17th century geometry; illustratesarticles of the Analyse des infiniment petits and shows the dependence on Bernoulli's inventions. / Práce je věnována přelomové, epochální práci prvního období infinitesimálního počtu, Analyse desinfiniment petits Guillauma, markýze de l'Hospitala. Dělí se na tři podstatné části: překlad, komentář a úvodnístudii. Účelem je představit toto dílo v jeho jedinečných okolnostech jeho vzniku a zároveň určit jeho obecnémísto v dějinách matematických idejí. Úvodní studie je věnována především osobnosti markýze de l'Hospitala.Na pozadí rozvoje infinitesimálního počtu se vykresluje jeho po dlouhou dobu oficiální obraz v dějináchmatematiky. V druhé části se rozebírá blízký lidský i matematický vztah markýze de l'Hospitala s JohannemBernoullim; a na základě rozboru markýzových geometrických úspěchů se ve srovnání s řešeními JohannaBernoulliho, bratra Jakoba a Leibnize se podává obecná charakteristika prvního infinitesimálního počtu cobygeometrické i fyzikální teorie a možností jeho objevitelských cest prostřednictvím analogií založených nanejzazším požadavku harmonie přírody. Třetí část úvodní studie v historických souvislostech sporů a výměnstran základů diferenciálního počtu objasňuje z hlavní ideje Leibnizovy symbolické přírody, totiž zákonakontinuity, povahu diferenciálního znaku dx, jeho radikální novost a argumenty ospravedlnění přesnostiinfinitesimálního počtu. Druhá kontroverze, která je v práci představena, probíhá mezi Rollem a Varignonem;podstatnými rysy jsou institucionální podmínky rozvoje počtu a Varignonovy pokusy o důkazy nekonečněmalých v Newtonově duchu. Komentář Analýzy nekonečně malých slouží k historickému, filologickému afilosofickému objasnění nových metod a dokládá utváření Analýzy nekonečně malých z jejích zdrojů, tj.přednášek Johanna Bernoulliho markýzi de l'Hospitalovi a jejich dopisové výměny

Sonderausgabe des 'Dresdner Universitätsjournal' von 2001:Zum Geleit S. 3 Vorwort S. 4 Inhaltsverzeichnis S. 5 Vom Knopf an der Turmspitze der Annenkirche: Die Geometrie des Gotthelf Fischer (1763–1832) S. 6 Frühe Lehrerbildung in Dresden: Lehrer und Eisenbahner – anfänglich stärkste Absolventengruppen S. 8 Junge Wissenschaftler auf neuen Lehrstühlen: Antimathematische Tendenzen – chancenlos unter Gustav Zeuner (1828–1907) S. 10 Von der Feinmechanik zur Mathematik: Die Verbindung von Technik, Kunst und darstellender Geometrie S. 12 Zwischen Mathematik und Physik: Der 2. Mathematische Lehrstuhl unter Aurel Voss (1845–1931) S. 14 Mathematiker als Bibliothekare: Die Katalogisierung – weiterentwickelt von Mathematikern S. 15 Gebündelte Reformbestrebungen: Neuer Aufschwung nach einem schwierigen Jahrzehnt S. 16 Neues vom Kreuzgymnasium: Einführung der Differential- und Integralrechnung in Mathematiklehrpläne S. 18 Mathematiker in der Gesellschaft ISIS: Wachsendes Interesse an mechanischen Rechengeräten S. 20 Rententafeln und Nettotarife: Zur Geschichte des Versicherungstechnischen Seminars S. 22 Dresdner als Ordinarien in Heidelberg: Erfolgreich auf dem Gebiet der kombinatorischen Topologie S. 24 Ein mitreißender Hochschullehrer: Gerhard Kowalewski (1876–1950) – Lehrer von Generationen Studierender S. 26 Frauen leben für die Mathematik: Dresdner Mathematik-Promovendinnen S. 28 Wissenschaftler und Humanist: Erich Trefftz (1888–1937) – „Motor“ der Akademischen Fliegergruppe Dresden S. 30 Mathematik und Politik: Personelle Veränderungen in der Dresdner Mathematik um 1940 S. 32 Impressum / Bildnachweis S. 34

The first International Congress of Mathematicians (ICM) was held in Zurich in 1897, setting the standards for all future ICMs. Whilst giving an overview of the congress itself, this thesis focuses on the Swiss organisers, who were predominantly university professors and secondary school teachers. As this thesis aims to offer some insight into their lives, it includes their biographies, highlighting their individual contributions to the congress. Furthermore, it explains why Zurich was chosen as the first host city and how the committee proceeded with the congress organisation. Two of the main organisers were the Swiss geometers Carl Friedrich Geiser (1843-1934) and Ferdinand Rudio (1856-1929). In addition to the congress, they also made valuable contributions to mathematical education, and in Rudio's case, the history of mathematics. Therefore, this thesis focuses primarily on these two mathematicians. As for Geiser, the relationship to his great-uncle Jakob Steiner is explained in more detail. Furthermore, his contributions to the administration of the Swiss Federal Institute of Technology are summarised. Due to the overarching theme of mathematical education and collaborations in this thesis, Geiser's schoolbook "Einleitung in die synthetische Geometrie" is considered in more detail and Geiser's methods are highlighted. A selection of Rudio's contributions to the history of mathematics is studied as well. His book "Archimedes, Huygens, Lambert, Legendre" is analysed and compared to E W Hobson's treatise "Squaring the Circle". Furthermore, Rudio's papers relating to the commentary of Simplicius on quadratures by Antiphon and Hippocrates are considered, focusing on Rudio's translation of the commentary and on "Die Möndchen des Hippokrates". The thesis concludes with an analysis of Rudio's popular lectures "Leonhard Euler" and "Über den Antheil der mathematischen Wissenschaften an der Kultur der Renaissance", which are prime examples of his approach to the history of mathematics.

In this thesis I present new insights into aspects of Peter Guthrie Tait's life and work, derived principally from largely-unexplored primary source material: Tait's scrapbook, the Tait–Maxwell school-book and Tait's pocket notebook. By way of associated historical insights, I also come to discuss the innovative and far-reaching mathematics of the elusive Frenchman, C.-V. Mourey. P. G. Tait (1831–1901) F.R.S.E., Professor of Mathematics at the Queen's College, Belfast (1854–1860) and of Natural Philosophy at the University of Edinburgh (1860–1901), was one of the leading physicists and mathematicians in Europe in the nineteenth century. His expertise encompassed the breadth of physical science and mathematics. However, since the nineteenth century he has been unfortunately overlooked—overshadowed, perhaps, by the brilliance of his personal friends, James Clerk Maxwell (1831–1879), Sir William Rowan Hamilton (1805–1865) and William Thomson (1824–1907), later Lord Kelvin. Here I present the results of extensive research into the Tait family history. I explore the spiritual aspect of Tait's life in connection with The Unseen Universe (1875) which Tait co-authored with Balfour Stewart (1828–1887). I also reveal Tait's surprising involvement in statistics and give an account of his introduction to complex numbers, as a schoolboy at the Edinburgh Academy. A highlight of the thesis is a re-evaluation of C.-V. Mourey's 1828 work, La Vraie Théorie des quantités négatives et des quantités prétendues imaginaires, which I consider from the perspective of algebraic reform. The thesis also contains: (i) a transcription of an unpublished paper by Hamilton on the fundamental theorem of algebra which was inspired by Mourey and (ii) new biographical information on Mourey.