Pub Date : 2020-12-05DOI: 10.4169/math.mag.89.4.267
J. Wood
The automorphism group of the Petersen Graph is shown to be isomorphic to the symmetric group on 5 elements. The image represents the Petersen Graph with the ten 3-element subsets of ${1, 2, 3, 4, 5}$ as vertices. Two vertices are adjacent when they have precisely one element in common.
{"title":"The Automorphism Group of the Petersen Graph is Isomorphic to $S_5$.","authors":"J. Wood","doi":"10.4169/math.mag.89.4.267","DOIUrl":"https://doi.org/10.4169/math.mag.89.4.267","url":null,"abstract":"The automorphism group of the Petersen Graph is shown to be isomorphic to the symmetric group on 5 elements. The image represents the Petersen Graph with the ten 3-element subsets of ${1, 2, 3, 4, 5}$ as vertices. Two vertices are adjacent when they have precisely one element in common.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126884942","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 : 2020-11-06DOI: 10.1007/978-3-030-48389-0_9
C. Proust
{"title":"Early-Dynastic Tables from Southern Mesopotamia, or the Multiple Facets of the Quantification of Surfaces","authors":"C. Proust","doi":"10.1007/978-3-030-48389-0_9","DOIUrl":"https://doi.org/10.1007/978-3-030-48389-0_9","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132825839","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 : 2020-10-30DOI: 10.1007/978-3-030-86909-0_12
Jack D. Betteridge, Eunice Y. S. Chan, Robert M Corless, J. Davenport, James Grant
{"title":"Teaching Programming for Mathematical Scientists","authors":"Jack D. Betteridge, Eunice Y. S. Chan, Robert M Corless, J. Davenport, James Grant","doi":"10.1007/978-3-030-86909-0_12","DOIUrl":"https://doi.org/10.1007/978-3-030-86909-0_12","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"203 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116402796","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}
E. Chen, William Du, Tanmay Gupta, T. Khovanova, Alicia Li, Srikar Mallajosyula, Rohit Raghavan, Arkajyoti Sinha, Maya Smith, Matthew Qian, Samuel Wang
A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations and reflections of the square. Under these transformations, there are 21 types of magic SET squares. We calculate the number of squares of each type. In addition, we discuss a game of SET tic-tac-toe.
{"title":"The Classification of Magic SET Squares","authors":"E. Chen, William Du, Tanmay Gupta, T. Khovanova, Alicia Li, Srikar Mallajosyula, Rohit Raghavan, Arkajyoti Sinha, Maya Smith, Matthew Qian, Samuel Wang","doi":"10.2478/rmm-2020-0005","DOIUrl":"https://doi.org/10.2478/rmm-2020-0005","url":null,"abstract":"A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations and reflections of the square. Under these transformations, there are 21 types of magic SET squares. We calculate the number of squares of each type. In addition, we discuss a game of SET tic-tac-toe.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121692705","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 : 2020-04-05DOI: 10.4310/ICCM.2020.V8.N2.A5
S. Ghorpade
This is a slightly revised version of the Presidential address (General) delivered at the 84th Annual Conference of the Indian Mathematical Society held at Jammu, India during November 2018.
这是2018年11月在印度查谟举行的第84届印度数学学会年会上主席致辞(一般性)的略微修改版本。
{"title":"The role of history in learning and teaching mathematics: A personal perspective","authors":"S. Ghorpade","doi":"10.4310/ICCM.2020.V8.N2.A5","DOIUrl":"https://doi.org/10.4310/ICCM.2020.V8.N2.A5","url":null,"abstract":"This is a slightly revised version of the Presidential address (General) delivered at the 84th Annual Conference of the Indian Mathematical Society held at Jammu, India during November 2018.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"43 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130472163","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 : 2020-03-01DOI: 10.14321/realanalexch.45.1.0127
J. Bair, Piotr Błaszczyk, P. Heinig, V. Kanovei, M. Katz, T. Mcgaffey
Like his colleagues de Prony, Petit, and Poisson at the Ecole Polytechnique, Cauchy used infinitesimals in the Leibniz-Euler tradition both in his research and teaching. Cauchy applied infinitesimals in an 1826 work in differential geometry where infinitesimals are used neither as variable quantities nor as sequences but rather as numbers. He also applied infinitesimals in an 1832 article on integral geometry, similarly as numbers. We explore these and other applications of Cauchy's infinitesimals as used in his textbooks and research articles. An attentive reading of Cauchy's work challenges received views on Cauchy's role in the history of analysis and geometry. We demonstrate the viability of Cauchy's infinitesimal techniques in fields as diverse as geometric probability, differential geometry, elasticity, Dirac delta functions, continuity and convergence. Keywords: Cauchy--Crofton formula; center of curvature; continuity; infinitesimals; integral geometry; limite; standard part; de Prony; Poisson
{"title":"Cauchy's Work on Integral Geometry, Centers of Curvature, and Other\u0000 Applications of Infinitesimals","authors":"J. Bair, Piotr Błaszczyk, P. Heinig, V. Kanovei, M. Katz, T. Mcgaffey","doi":"10.14321/realanalexch.45.1.0127","DOIUrl":"https://doi.org/10.14321/realanalexch.45.1.0127","url":null,"abstract":"Like his colleagues de Prony, Petit, and Poisson at the Ecole Polytechnique, Cauchy used infinitesimals in the Leibniz-Euler tradition both in his research and teaching. Cauchy applied infinitesimals in an 1826 work in differential geometry where infinitesimals are used neither as variable quantities nor as sequences but rather as numbers. He also applied infinitesimals in an 1832 article on integral geometry, similarly as numbers. We explore these and other applications of Cauchy's infinitesimals as used in his textbooks and research articles. \u0000An attentive reading of Cauchy's work challenges received views on Cauchy's role in the history of analysis and geometry. We demonstrate the viability of Cauchy's infinitesimal techniques in fields as diverse as geometric probability, differential geometry, elasticity, Dirac delta functions, continuity and convergence. \u0000Keywords: Cauchy--Crofton formula; center of curvature; continuity; infinitesimals; integral geometry; limite; standard part; de Prony; Poisson","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125273308","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 : 2020-02-27DOI: 10.1007/978-3-030-76810-2_1
J. Lang
{"title":"Rosenbrock-Wanner Methods: Construction and Mission","authors":"J. Lang","doi":"10.1007/978-3-030-76810-2_1","DOIUrl":"https://doi.org/10.1007/978-3-030-76810-2_1","url":null,"abstract":"","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"10 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120845407","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 : 2020-02-03DOI: 10.1887/0750303565/b295b8
N. Karjanto
Ordinary differential equations and boundary value problems arise in many aspects of mathematical physics. Chebyshev differential equation is one special case of the Sturm-Liouville boundary value problem. Generating function, recursive formula, orthogonality, and Parseval's identity are some important properties of Chebyshev polynomials. Compared with a Fourier series, an interpolation function using Chebyshev polynomials is more accurate in approximating polynomial functions. -------- Des equations differentielles ordinaires et des problemes de valeurs limites se posent dans de nombreux aspects de la physique mathematique. L'equation differentielle de Chebychev est un cas particulier du probleme de la valeur limite de Sturm-Liouville. La fonction generatrice, la formule recursive, l'orthogonalite et l'identite de Parseval sont quelques proprietes importantes du polynome de Chebyshev. Par rapport a une serie de Fourier, une fonction d'interpolation utilisant des polynomes de Chebyshev est plus precise dans l'approximation des fonctions polynomiales.
{"title":"Properties of Chebyshev polynomials","authors":"N. Karjanto","doi":"10.1887/0750303565/b295b8","DOIUrl":"https://doi.org/10.1887/0750303565/b295b8","url":null,"abstract":"Ordinary differential equations and boundary value problems arise in many aspects of mathematical physics. Chebyshev differential equation is one special case of the Sturm-Liouville boundary value problem. Generating function, recursive formula, orthogonality, and Parseval's identity are some important properties of Chebyshev polynomials. Compared with a Fourier series, an interpolation function using Chebyshev polynomials is more accurate in approximating polynomial functions. \u0000-------- \u0000Des equations differentielles ordinaires et des problemes de valeurs limites se posent dans de nombreux aspects de la physique mathematique. L'equation differentielle de Chebychev est un cas particulier du probleme de la valeur limite de Sturm-Liouville. La fonction generatrice, la formule recursive, l'orthogonalite et l'identite de Parseval sont quelques proprietes importantes du polynome de Chebyshev. Par rapport a une serie de Fourier, une fonction d'interpolation utilisant des polynomes de Chebyshev est plus precise dans l'approximation des fonctions polynomiales.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121724864","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 : 2019-07-09DOI: 10.1393/gdf/i2022-10494-0
P. F. Nali
The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in the limit of small probabilities. The same proof is then applied to the solution of a problem in statistical mechanics. --- Lo scopo di questo articolo e dimostrare direttamente, con un metodo elementare, la legge di probabilita di Poisson. Questa dimostrazione e proposta in alternativa alla piu consueta derivazione dalla distribuzione binomiale nel limite delle piccole probabilita. La stessa dimostrazione viene quindi applicata alla soluzione di un problema di meccanica statistica.
{"title":"Una dimostrazione diretta della legge di probabilit`a di Poisson (A direct proof of the Poisson probability law)","authors":"P. F. Nali","doi":"10.1393/gdf/i2022-10494-0","DOIUrl":"https://doi.org/10.1393/gdf/i2022-10494-0","url":null,"abstract":"The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in the limit of small probabilities. The same proof is then applied to the solution of a problem in statistical mechanics. \u0000--- \u0000Lo scopo di questo articolo e dimostrare direttamente, con un metodo elementare, la legge di probabilita di Poisson. Questa dimostrazione e proposta in alternativa alla piu consueta derivazione dalla distribuzione binomiale nel limite delle piccole probabilita. La stessa dimostrazione viene quindi applicata alla soluzione di un problema di meccanica statistica.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125039147","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 : 2019-06-26DOI: 10.1017/9781108591218.008
T. Hales
This article gives some memories of Thomas Hales of his years at Princeton as a graduate student under Robert Langlands. It has been prepared for the book "The Genesis of Langlands' Program," edited by Dr. Julia Mueller and Dr. Freydoon Shahidi.
{"title":"Reminiscences by a Student of Langlands","authors":"T. Hales","doi":"10.1017/9781108591218.008","DOIUrl":"https://doi.org/10.1017/9781108591218.008","url":null,"abstract":"This article gives some memories of Thomas Hales of his years at Princeton as a graduate student under Robert Langlands. It has been prepared for the book \"The Genesis of Langlands' Program,\" edited by Dr. Julia Mueller and Dr. Freydoon Shahidi.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125161725","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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