{"title":"CONSISTENCIA, NO TRIVIALIDAD Y REDUNDANCIA EN MATEMÁTICA","authors":"Eleonora Catsigeras","doi":"10.18270/rcfc.v17i34.2085","DOIUrl":"https://doi.org/10.18270/rcfc.v17i34.2085","url":null,"abstract":"We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria, from the logic-formal ones to the non formal ones (but still rational criteria).We illustrate the discussion with concrete examples obtained form the mathematical reseach, particularly from the results that were published in the last 50 years in the mathematical theory of deterministic dynamical systems.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126494410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Remembering Victor Petrovich Havin","authors":"Konstantin M. Dyakonov","doi":"10.1007/978-3-319-59078-3_3","DOIUrl":"https://doi.org/10.1007/978-3-319-59078-3_3","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128314869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Useful Solution of the Coupon Collector's Problem","authors":"Niklas Braband, Sonja Braband, Malte Braunschweig, Technische Universitat Braunschweig","doi":"10.7795/320.201908","DOIUrl":"https://doi.org/10.7795/320.201908","url":null,"abstract":"The Coupon Collector's Problem is one of the few mathematical problems that make news headlines regularly. The reasons for this are on one hand the immense popularity of soccer albums (called Paninimania) and on the other hand that no solution is known that is able to take into account all effects such as replacement (limited purchasing of missing stickers) or swapping. In previous papers we have proven that the classical assumptions are not fulfilled in practice. Therefore we define new assumptions that match reality. Based on these assumptions we are able to derive formulae for the mean number of stickers needed (and the associated standard deviation) that are able to take into account all effects that occur in practical collecting. Thus collectors can estimate the average cost of completion of an album and its standard deviation just based on elementary calculations. From a practical point of view we consider the Coupon Collector's problem as solved. \u0000----- \u0000Das Sammelbilderproblem ist eines der wenigen mathematischen Probleme, die regelmasig in den Schlagzeilen der Nachrichten vorkommen. Dies liegt einerseits an der grosen Popularitat von Fusball-Sammelbildern (Paninimania genannt) und andererseits daran, dass es bisher keine Losung gibt, die alle relevanten Effekte wie Nachkaufen oder Tauschen berucksichtigt. Wir haben bereits nachgewiesen, dass die klassischen Annahmen nicht der Realitat entsprechen. Deshalb stellen wir neue Annahmen auf, die die Praxis besser abbilden. Darauf aufbauend konnen wir Formeln fur die mittlere Anzahl benotigter Bilder (sowie deren Standardabweichung) ableiten, die alle in der Praxis relevanten Effekte berucksichtigen. Damit konnen Sammler die mittleren Kosten eines Albums sowie deren Standardabweichung nur mit Hilfe von elementaren Rechnungen bestimmen. Fur praktische Zwecke ist das Sammelbilderproblem damit gelost.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133771706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The liar paradox is a real problem","authors":"N. Weaver","doi":"10.4288/JAFPOS.25.0_89","DOIUrl":"https://doi.org/10.4288/JAFPOS.25.0_89","url":null,"abstract":"The liar paradox is widely seen as not a serious problem. I try to explain why this view is mistaken.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124242634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Solving Sangaku: A Traditional Solution to a Nineteenth Century Japanese Temple Problem","authors":"Rosalie Hosking","doi":"10.14477/JHM.2017.30.2.053","DOIUrl":"https://doi.org/10.14477/JHM.2017.30.2.053","url":null,"abstract":"This paper demonstrates how a nineteenth century Japanese votive temple problem known as a sangaku from Okayama prefecture can be solved using traditional mathematical methods of the Japanese Edo (1603-1868 CE). We compare a modern solution to a sangaku problem from Sacred Geometry: Japanese Temple Problems of Tony Rothman and Hidetoshi Fukagawa with a traditional solution of =Ohara Toshiaki (?-1828). Our investigation into the solution of =Ohara provides an example of traditional Edo period mathematics using the tenzan jutsu symbolic manipulation method, as well as producing new insights regarding the contextual nature of the rules of this technique.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132796023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generalized Riemann Sums","authors":"T. Sunada","doi":"10.1007/978-3-319-60039-0_15","DOIUrl":"https://doi.org/10.1007/978-3-319-60039-0_15","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121109287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Probability, propensity and probability of propensities (and of probabilities)","authors":"G. D'Agostini","doi":"10.1063/1.4985350","DOIUrl":"https://doi.org/10.1063/1.4985350","url":null,"abstract":"The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real life applications, arise quite naturally and the resulting discussion among non-ideologized, free-minded people offers an opportunity for clarifications.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133246013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fibonacci numbers and the golden ratio","authors":"R. Schneider","doi":"10.3840/08003775","DOIUrl":"https://doi.org/10.3840/08003775","url":null,"abstract":"In this expository paper written to commemorate Fibonacci Day 2016, we discuss famous relations involving the Fibonacci sequence, the golden ratio, continued fractions and nested radicals, and show how these fit into a more general framework stemming from the quadratic formula.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129299223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On History of Epsilontics","authors":"Galina Iwanowna Sinkiewicz","doi":"10.14708/AM.V10I0.805","DOIUrl":"https://doi.org/10.14708/AM.V10I0.805","url":null,"abstract":"This is a review of genesis of „e-δ\" language in works of mathematicians of the 19th century. It shows that although the symbols e and δ were initially introduced in 1823 by Cauchy, no functional relationship for δ as a function of e was ever ever specified by Cauchy. It was only in 1861 that the epsilon-delta method manifested itself to the full in Weierstrass de_nition of a limit. The article gives various interpretations of these issues later provided by mathematicians. This article presents the text [ Sinkevich, 2012d ] of the same author which is slightly redone and translated into English. Normal 0 21 false false false PL X-NONE X-NONE /* Style Definitions */ \u0000 table.MsoNormalTable \u0000 {mso-style-name:Standardowy; \u0000 mso-tstyle-rowband-size:0; \u0000 mso-tstyle-colband-size:0; \u0000 mso-style-noshow:yes; \u0000 mso-style-priority:99; \u0000 mso-style-parent:\"\"; \u0000 mso-padding-alt:0cm 5.4pt 0cm 5.4pt; \u0000 mso-para-margin-top:0cm; \u0000 mso-para-margin-right:0cm; \u0000 mso-para-margin-bottom:10.0pt; \u0000 mso-para-margin-left:0cm; \u0000 line-height:115%; \u0000 mso-pagination:widow-orphan; \u0000 font-size:11.0pt; \u0000 font-family:\"Calibri\",\"sans-serif\"; \u0000 mso-ascii-font-family:Calibri; \u0000 mso-ascii-theme-font:minor-latin; \u0000 mso-hansi-font-family:Calibri; \u0000 mso-hansi-theme-font:minor-latin; \u0000 mso-bidi-font-family:\"Times New Roman\"; \u0000 mso-bidi-theme-font:minor-bidi; \u0000 mso-fareast-language:EN-US;}","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133659926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Paley and the Paley Graphs","authors":"G. Jones","doi":"10.1007/978-3-030-32808-5_5","DOIUrl":"https://doi.org/10.1007/978-3-030-32808-5_5","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121892778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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