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Singularity: a Seventh Memo? 奇点：第七次备忘录？
arXiv - MATH - History and Overview Pub Date : 2024-03-27 DOI: arxiv-2403.18487
Matteo Gallone, Sandra Lucente
{"title":"Singularity: a Seventh Memo?","authors":"Matteo Gallone, Sandra Lucente","doi":"arxiv-2403.18487","DOIUrl":"https://doi.org/arxiv-2403.18487","url":null,"abstract":"In this paper we explore the relationships between Calvino's memos and\u0000Mathematics. In the first part, we discuss how Lightness, Quickness,\u0000Exactitude, Visibility, Multiplicity are present in the mathematical language,\u0000reasoning and in the work of the mathematician. In addiction, we follow a\u0000similar path for the topics of Calvino's lecture of which we only know the\u0000title or some notes. In the final part, we explain why `Singularity' could be\u0000chosen as topic for Calvino's seventh lecture.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312804","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}
引用次数: 0
Helping students deal with Ethical Reasoning: The Proto-Guidelines for Ethical Practice in Mathematics as a deck of cards 帮助学生处理道德推理问题：将《数学道德实践原指南》作为一副扑克牌
arXiv - MATH - History and Overview Pub Date : 2024-03-25 DOI: arxiv-2403.16849
Stephen M. Walk, Rochelle E. Tractenberg
{"title":"Helping students deal with Ethical Reasoning: The Proto-Guidelines for Ethical Practice in Mathematics as a deck of cards","authors":"Stephen M. Walk, Rochelle E. Tractenberg","doi":"arxiv-2403.16849","DOIUrl":"https://doi.org/arxiv-2403.16849","url":null,"abstract":"Tractenberg, Piercey, and Buell 2024 presented a list of 44 proto-Guidelines\u0000for Ethical Mathematical Practice, developed through examination of codes of\u0000ethics of adjacent disciplines and consultation with members of the mathematics\u0000community, and gave justifications for the use of these proto-Guidelines. We\u0000propose formatting the list as a deck of 44 cards and describe ways to use the\u0000cards in classes at any stage of the undergraduate mathematics program. A\u0000simple game or encounter with the cards can be used exclusively as an\u0000introduction, or the cards can be used repeatedly in order to help students\u0000move to higher levels of achievement with respect to the proto-Guidelines and\u0000ethical reasoning in general. We present, in Appendix A, a sample semester long\u0000sequence of assignments for such a purpose, with activities at various levels\u0000of Blooms taxonomy.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140298818","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}
引用次数: 0
Revisiting the Sleeping Beauty problem 重新审视睡美人问题
arXiv - MATH - History and Overview Pub Date : 2024-03-25 DOI: arxiv-2403.16666
Paulo S. Piva, Gabriel Ruffolo
{"title":"Revisiting the Sleeping Beauty problem","authors":"Paulo S. Piva, Gabriel Ruffolo","doi":"arxiv-2403.16666","DOIUrl":"https://doi.org/arxiv-2403.16666","url":null,"abstract":"The Sleeping Beauty problem is a probability riddle with no definite solution\u0000for more than two decades and its solution is of great interest in many fields\u0000of knowledge. There are two main competing solutions to the problem: the halfer\u0000approach, and the thirder approach. The main reason for disagreement in the\u0000literature is connected to the use of different probability spaces to represent\u0000the same probabilistic riddle. In this work, we analyse the problem from a\u0000mathematical perspective, identifying probability distributions induced\u0000directly from the thought experiment's rules. The precise choices of\u0000probability spaces provide both halfer and thirder solutions to the problem. To\u0000try and decide on which approach to follow, a criterion involving the\u0000information available to Sleeping Beauty is proposed.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140299305","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}
引用次数: 0
Motivated exposition of combinatorial Nullstellensatz 组合无效定理的动机论述
arXiv - MATH - History and Overview Pub Date : 2024-03-23 DOI: arxiv-2404.10778
M. Lozhkin, A. Skopenkov
{"title":"Motivated exposition of combinatorial Nullstellensatz","authors":"M. Lozhkin, A. Skopenkov","doi":"arxiv-2404.10778","DOIUrl":"https://doi.org/arxiv-2404.10778","url":null,"abstract":"In this expository note we show how combinatorial Nullstellensatz by N. Alon\u0000naturally appears in solutions of elementary problems. Simple ideas gradually\u0000and naturally appear in such solutions, thus bringing a reader to\u0000generalizations. The note is accessible to mathematicians not specialized in\u0000the area, and to students familiar with polynomials.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140616967","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}
引用次数: 0
Riemann Integration in the Euclidean Space 欧几里得空间中的黎曼积分
arXiv - MATH - History and Overview Pub Date : 2024-03-21 DOI: arxiv-2403.19703
Akerele Olofin Segun
{"title":"Riemann Integration in the Euclidean Space","authors":"Akerele Olofin Segun","doi":"arxiv-2403.19703","DOIUrl":"https://doi.org/arxiv-2403.19703","url":null,"abstract":"The so-called Riemann sums have their origin in the efforts of Greek\u0000mathematicians to find the center of gravity or the volume of a solid body.\u0000These researches led to the method of exhaustion, discovered by Archimedes and\u0000described using modern ideas by MacLaurin in his textit{Treatise of Fluxions}\u0000in 1742. At this times the sums were only a practical method for computing an\u0000area under a curve, and the existence of this area was considered geometrically\u0000obvious. The method of exhaustion consists in almost covering the space\u0000enclosed by the curve with $n$ geometric objects with well-known areas such as\u0000rectangles or triangles, and finding the limit (though this topic was very\u0000blurry at these early times) when $n$ increases. One of its most remarkable\u0000application is squaring the area $mathcal{A}$ enclosed by a parabola and a\u0000line.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574456","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}
引用次数: 0
Oriented and Non-oriented Cubical Surfaces in The Penteract Penteract 中的定向和无定向立方体表面
arXiv - MATH - History and Overview Pub Date : 2024-03-19 DOI: arxiv-2403.12825
Manuel Estevez, Erika Roldan, Henry Segerman
{"title":"Oriented and Non-oriented Cubical Surfaces in The Penteract","authors":"Manuel Estevez, Erika Roldan, Henry Segerman","doi":"arxiv-2403.12825","DOIUrl":"https://doi.org/arxiv-2403.12825","url":null,"abstract":"Which surfaces can be realized with two-dimensional faces of the\u0000five-dimensional cube (the penteract)? How can we visualize them? In recent\u0000work, Aveni, Govc, and Roldan, show that there exist 2690 connected closed\u0000cubical surfaces up to isomorphism in the 5-cube. They give a classification in\u0000terms of their genus $g$ for closed orientable cubical surfaces and their\u0000demigenus $k$ for a closed non-orientable cubical surface. In this paper, we\u0000explain the main idea behind the exhaustive search and we visualize the\u0000projection to $mathbb{R}^3$ of a torus, a genus two torus, the projective\u0000plane, and the Klein bottle. We use reinforcement learning techniques to obtain\u0000configurations optimized for 3D printing.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168268","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}
引用次数: 0
A review of Pythagorean triples from both classical and modern viewpoints 从古典和现代角度回顾毕达哥拉斯三段论
arXiv - MATH - History and Overview Pub Date : 2024-03-15 DOI: arxiv-2403.17966
Ali Taghavi
{"title":"A review of Pythagorean triples from both classical and modern viewpoints","authors":"Ali Taghavi","doi":"arxiv-2403.17966","DOIUrl":"https://doi.org/arxiv-2403.17966","url":null,"abstract":"In this note we present a survey on some classical and modern approaches on\u0000Pythagorean triples. Some questions are also posed in direction of some\u0000materials under review. In particular some non commutative and operator\u0000theoretical approaches of Pythagorean triples are discussed","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312297","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}
引用次数: 0
Algumas luminescências sobre o jogo Lights Out 熄灯游戏的几个缩影
arXiv - MATH - History and Overview Pub Date : 2024-03-15 DOI: arxiv-2403.17967
Adriano Verdério, Izabele D'Agostin, Mari Sano, Patrícia Massae Kitani
{"title":"Algumas luminescências sobre o jogo Lights Out","authors":"Adriano Verdério, Izabele D'Agostin, Mari Sano, Patrícia Massae Kitani","doi":"arxiv-2403.17967","DOIUrl":"https://doi.org/arxiv-2403.17967","url":null,"abstract":"The theory behind the Lights Out game has been developed by several authors.\u0000The aim of this work is to present some results related to this game using\u0000Linear Algebra. We establish a criterion for the solubility of this game in the\u0000case of an $m$ by $n$ grid, which depends on the invertibility of a matrix, and\u0000we present the conditions for this to occur, easily verifiable from $m$ and\u0000$n$. Furthermore, we explicitly determine the value of the determinant for a\u0000particular case.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312415","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}
引用次数: 0
Emergence of Mathematics in Ancient India: A Reassessment 古印度数学的兴起：重新评估
arXiv - MATH - History and Overview Pub Date : 2024-03-07 DOI: arxiv-2403.04823
Jaidev Dasgupta
{"title":"Emergence of Mathematics in Ancient India: A Reassessment","authors":"Jaidev Dasgupta","doi":"arxiv-2403.04823","DOIUrl":"https://doi.org/arxiv-2403.04823","url":null,"abstract":"This work explores a possible course of evolution of mathematics in ancient\u0000times in India when there was no script, no place-value system, and no zero.\u0000Reviewing examples of time-reckoning, large numbers, sacrificial altar-making,\u0000and astronomy, it investigates the role of concrete objects, natural events,\u0000rituals and names in context-dependent arithmetic, revealing its limited scope\u0000confined to counting, addition and subtraction. Higher operations, namely,\u0000multiplication, division and fractional calculations had to wait until the\u0000advent of symbolic numerals and procedures for computation. It is argued that\u0000the impression of these higher operations in a period usually known as the\u0000Vedic times is caused by inadvertent interpolation of present knowledge of\u0000mathematics in modern readings of the ancient texts.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140100301","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}
引用次数: 0
The legacy of Bletchley Park on UK mathematics 布莱切利公园对英国数学的影响
arXiv - MATH - History and Overview Pub Date : 2024-03-02 DOI: arxiv-2403.01331
Daniel Shiu
{"title":"The legacy of Bletchley Park on UK mathematics","authors":"Daniel Shiu","doi":"arxiv-2403.01331","DOIUrl":"https://doi.org/arxiv-2403.01331","url":null,"abstract":"The second world war saw a major influx of mathematical talent into the areas\u0000of cryptanalysis and cryptography. This was particularly true at the UK's\u0000Government Codes and Cypher School (GCCS) at Bletchley Park. The success of\u0000introducing mathematical thinking into activities previously dominated by\u0000linguists is well-studied, but the reciprocal question of how the cryptologic\u0000effort affected the field of mathematics has been less investigated. Although\u0000their cryptologic achievements are not as celebrated as those of Turing, Tutte\u0000and Welchman, Bletchley Park's effort was supplemented by more eminent\u0000mathematicians, and those who would achieve eminence and provide leadership and\u0000direction for mathematical research in the United Kingdom. Amongst their number\u0000were Ian Cassels, Sandy Green, Philip Hall, Max Newman and Henry Whitehead.\u0000This paper considers how the experience of these and other mathematicians at\u0000Bletchley Park may have informed and influenced the mathematics that was\u0000produced in their post-war careers.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140033704","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}
引用次数: 0
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