Pub Date : 2015-02-20DOI: 10.1007/978-3-319-47337-6_1
O. A. Agust'in-Aquino
{"title":"Extended Counterpoint Symmetries and Continuous Counterpoint","authors":"O. A. Agust'in-Aquino","doi":"10.1007/978-3-319-47337-6_1","DOIUrl":"https://doi.org/10.1007/978-3-319-47337-6_1","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128410680","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}
Pub Date : 2015-02-01DOI: 10.4310/ICCM.2015.V3.N2.A6
G. Sinkevich
This is the history of translating Cantor's works into Russian from 1892 to 1985 in Odessa, Moscow, Tomsk, Kazan, S.-Petersburg, Leningrad. Mathematicians and philosophers in Russia took the ideas of the theory of sets enthusiastically. Such renowned scholars and scientists as Timchenko, Shatunovsky, Vasiliev, Florensky, Mlodzeevsky, Nekrasov, Zhegalkin, Yushkevich Sr., Fet, Yushkevich Jr., Kolmogorov, and Medvedev took part in their popularisation. In 1970 Academician Pontryagin rated the theory of sets as useless for young mathematicians, and the translated works of Cantor were not published. This article first describes the tragic fate of this translation.
{"title":"The Fate of Russian Translations of Cantor","authors":"G. Sinkevich","doi":"10.4310/ICCM.2015.V3.N2.A6","DOIUrl":"https://doi.org/10.4310/ICCM.2015.V3.N2.A6","url":null,"abstract":"This is the history of translating Cantor's works into Russian from 1892 to 1985 in Odessa, Moscow, Tomsk, Kazan, S.-Petersburg, Leningrad. Mathematicians and philosophers in Russia took the ideas of the theory of sets enthusiastically. Such renowned scholars and scientists as Timchenko, Shatunovsky, Vasiliev, Florensky, Mlodzeevsky, Nekrasov, Zhegalkin, Yushkevich Sr., Fet, Yushkevich Jr., Kolmogorov, and Medvedev took part in their popularisation. In 1970 Academician Pontryagin rated the theory of sets as useless for young mathematicians, and the translated works of Cantor were not published. This article first describes the tragic fate of this translation.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122358890","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}
Pub Date : 2015-01-21DOI: 10.1007/978-3-319-16856-2_2
E. Baake, A. Wakolbinger
{"title":"Feller's Contributions to Mathematical Biology","authors":"E. Baake, A. Wakolbinger","doi":"10.1007/978-3-319-16856-2_2","DOIUrl":"https://doi.org/10.1007/978-3-319-16856-2_2","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125040129","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}
Pub Date : 2015-01-01DOI: 10.17323/1609-4514-2015-15-4-741-748
Y. Manin
This note is a brief survey of some results of the recent collaboration of neurobiologists and mathematicians dedicated to stimulus reconstruction from neuronal spiking activity. This collaboration, in particular, led to the consideration of binary codes used by brain for encoding a stimuli domain such as a rodent's territory through the combinatorics of its covering by local neighborhoods. The survey is addressed to mathematicians (cf. [DeSch01]) and focuses on the idea that stimuli spaces are represented by the relevant neural codes as simplicial sets and thus encode say, the homotopy type of space if local neighborhoods are convex (see [CuIt08], [CuItVCYo13], [Yo14], [SiGh07]).}
{"title":"Neural codes and homotopy types: mathematical models of place field recognition","authors":"Y. Manin","doi":"10.17323/1609-4514-2015-15-4-741-748","DOIUrl":"https://doi.org/10.17323/1609-4514-2015-15-4-741-748","url":null,"abstract":"This note is a brief survey of some results of the recent collaboration of neurobiologists and mathematicians dedicated to stimulus reconstruction from neuronal spiking activity. This collaboration, in particular, led to the consideration of binary codes used by brain for encoding a stimuli domain such as a rodent's territory through the combinatorics of its covering by local neighborhoods. \u0000The survey is addressed to mathematicians (cf. [DeSch01]) and focuses on the idea that stimuli spaces are represented by the relevant neural codes as simplicial sets and thus encode say, the homotopy type of space if local neighborhoods are convex (see [CuIt08], [CuItVCYo13], [Yo14], [SiGh07]).}","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132008296","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}
In this paper we investigate the evolution of the concept of area in Peano's works, taking into account the main role played by Grassmann's geometric-vector calculus and Peano's theory on derivative of measures. Geometric (1887) and bi-vectorial (1888) Peano's approaches to surface area mark the development of this topic during the first half of the last century. In the sequel we will present some significative contributions on surface area that are inspired and/or closely related to Peano's definition.
{"title":"Peano on definition of surface area","authors":"G. H. Greco, S. Mazzucchi, Enrico Pagani","doi":"10.4171/RLM/734","DOIUrl":"https://doi.org/10.4171/RLM/734","url":null,"abstract":"In this paper we investigate the evolution of the concept of area in Peano's works, taking into account the main role played by Grassmann's geometric-vector calculus and Peano's theory on derivative of measures. Geometric (1887) and bi-vectorial (1888) Peano's approaches to surface area mark the development of this topic during the first half of the last century. In the sequel we will present some significative contributions on surface area that are inspired and/or closely related to Peano's definition.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115867804","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}
We show that for any bounded function $f:[a,b]rightarrow{mathbb R}$ and $epsilon>0$ there is a partition $P$ of $[a,b]$ with respect to which the Riemann sum of $f$ using right endpoints is within $epsilon$ of the upper Darboux sum of $f$. This leads to an elementary proof of the theorem of Gillespie cite{G} showing that Cauchy's and Riemann's definitions of integrability coincide.
{"title":"A note on Cauchy integrability","authors":"S. Schneider","doi":"10.12988/IMF.2014.49162","DOIUrl":"https://doi.org/10.12988/IMF.2014.49162","url":null,"abstract":"We show that for any bounded function $f:[a,b]rightarrow{mathbb R}$ and $epsilon>0$ there is a partition $P$ of $[a,b]$ with respect to which the Riemann sum of $f$ using right endpoints is within $epsilon$ of the upper Darboux sum of $f$. This leads to an elementary proof of the theorem of Gillespie cite{G} showing that Cauchy's and Riemann's definitions of integrability coincide.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116344064","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}
Pub Date : 2014-07-24DOI: 10.1007/978-3-658-23090-6
H. Burscheid, Horst Struve
{"title":"Empirische Theorien im Kontext der Mathematikdidaktik","authors":"H. Burscheid, Horst Struve","doi":"10.1007/978-3-658-23090-6","DOIUrl":"https://doi.org/10.1007/978-3-658-23090-6","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122767608","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}
In this brief essay we succinctly comment on the historical origin of Hilbert geometry. In particular, we give a summary of the letter in which David Hilbert informs his friend and colleague Felix Klein about his discovery of this geometry. The present paper is to appear in the Handbook of Hilbert geometry, (ed. A. Papadopoulos and M. Troyanov), European Mathematical Society, Z"urich, 2014.
在这篇简短的文章中，我们对希尔伯特几何的历史起源作了简要的评述。特别地，我们给出了大卫·希尔伯特告诉他的朋友和同事菲利克斯·克莱因他发现这个几何的信的摘要。本文将发表在《希尔伯特几何手册》(A. Papadopoulos and M. Troyanov)，欧洲数学学会学报，2014。
{"title":"On the origin of Hilbert Geometry","authors":"M. Troyanov","doi":"10.4171/147-1/14","DOIUrl":"https://doi.org/10.4171/147-1/14","url":null,"abstract":"In this brief essay we succinctly comment on the historical origin of Hilbert geometry. In particular, we give a summary of the letter in which David Hilbert informs his friend and colleague Felix Klein about his discovery of this geometry. The present paper is to appear in the Handbook of Hilbert geometry, (ed. A. Papadopoulos and M. Troyanov), European Mathematical Society, Z\"urich, 2014.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132056348","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}
Pub Date : 2014-07-08DOI: 10.1007/978-3-319-28582-5_20
A. Borovik
{"title":"Calling a Spade a Spade: Mathematics in the New Pattern of Division of Labour","authors":"A. Borovik","doi":"10.1007/978-3-319-28582-5_20","DOIUrl":"https://doi.org/10.1007/978-3-319-28582-5_20","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"128 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121522068","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}
Tiziana Bascelli, E. Bottazzi, Frederik S. Herzberg, V. Kanovei, Karin U. Katz, M. Katz, Tahl Nowik, David Sherry, S. Shnider
Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.
{"title":"Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow","authors":"Tiziana Bascelli, E. Bottazzi, Frederik S. Herzberg, V. Kanovei, Karin U. Katz, M. Katz, Tahl Nowik, David Sherry, S. Shnider","doi":"10.1090/NOTI1149","DOIUrl":"https://doi.org/10.1090/NOTI1149","url":null,"abstract":"Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding \"negligible\" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129586439","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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