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Stepping Stone Problem on Graphs 图上的垫脚石问题
IF 0.4
Mathematics Enthusiast Pub Date : 2024-02-01 DOI: 10.54870/1551-3440.1616
Rory O’Dwyer
{"title":"Stepping Stone Problem on Graphs","authors":"Rory O’Dwyer","doi":"10.54870/1551-3440.1616","DOIUrl":"https://doi.org/10.54870/1551-3440.1616","url":null,"abstract":": This paper formalizes the stepping stone problem introduced Ladoucer and Rebenstock [G] to the setting of simple graphs. This paper considers the set of functions from the vertices of our graph to N , which assign a fixed number of 1’s to some vertices and assign higher numbers to other vertices by adding up their neighbors’ assignments. The stepping stone solution is defined as an element obtained from the argmax of the maxima of these functions, and the maxima as its growth. This work is organized into work on the bounded and unbounded degree graph cases. In the bounded case, sufficient conditions are obtained for superlinear and sublinear stepping stone solution growth. Furthermore this paper demonstrates the existence of a basis of graphs which characterizes superlinear growth. In the unbounded case, properly sublinear and superlinear stepping stone solution growth are obtained.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70969739","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
Using Gardner's Three-Squares Problem for a Group Project in a Mathematical Problem Solving Module 运用Gardner的三平方问题在数学解题模块中的小组作业
IF 0.4
Mathematics Enthusiast Pub Date : 2024-02-01 DOI: 10.54870/1551-3440.1638
Jonathan Hoseana
{"title":"Using Gardner's Three-Squares Problem for a Group Project in a Mathematical Problem Solving Module","authors":"Jonathan Hoseana","doi":"10.54870/1551-3440.1638","DOIUrl":"https://doi.org/10.54870/1551-3440.1638","url":null,"abstract":": Consider a 1 × 3 grid whose top-left vertex is connected to the bottom-right vertex of each of the unit squares. What is the sum of the three acute angles formed by the connecting segments with the unit squares’ bases? This is the so-called three-squares problem, often attributed to Gardner. In a recent academic year, the author used a video on this problem, produced by the YouTube channel Numberphile, for a group project in a first-semester undergraduate module: Mathematical Prob-lem Solving. The project involved collaborative writing on the problem and individual completion of a peer-assessment form. We report the outcomes of this project, which give rise to both theoretical and pedagogical discussions. The theoretical discussion comprises seven alternative solutions to the problem, as well as a generalisation to the case of identical parallelograms forming an arbitrary-sized grid whose top-left vertex is connected to the bottom-right vertex of each parallelogram. The pedagogical discussion highlights the peer-assessment form’s effectiveness in detecting unequal group members’ contribution, as well as the students’ inadequate communication skills. The latter, which has consistently raised concerns, subsequently led to the module being developed and renamed as Mathematical Writing and Reasoning, whose realisation commenced the following academic year.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70970468","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
On Convincing Power of Counterexamples 论反例的说服力
IF 0.4
Mathematics Enthusiast Pub Date : 2024-02-01 DOI: 10.54870/1551-3440.1636
Orly Buchbinder, Rina Zazkis
{"title":"On Convincing Power of Counterexamples","authors":"Orly Buchbinder, Rina Zazkis","doi":"10.54870/1551-3440.1636","DOIUrl":"https://doi.org/10.54870/1551-3440.1636","url":null,"abstract":": Despite plethora of research that attends to the convincing power of different types of proofs, research related to the convincing power of counterexamples is rather slim. In this paper we examine how prospective and practicing secondary school mathematics teachers respond to different types of counterexamples. The counterexamples were presented as products of students’ arguments, and the participants were asked to evaluate their correctness and comment on them. The counterexamples varied according to mathematical topic: algebra or geometry, and their explicitness. However, as we analyzed the data, we discovered that these distinctions were insufficient to explain why teachers accepted some counterexamples, but rejected others, with seemingly similar features. As we analyze the participants’ perceived transparency of different counterexamples, we employ various theoretical approaches that can advance our understanding of teachers’ conceptions of conviction with respect to counterexamples.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70970532","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
Encounters With “Love and Math” A Belated Review of Edward Frenkel’s Love and Math: The Heart of Hidden 爱德华·弗兰克尔的《爱与数学:隐藏的心》迟来的评论
IF 0.4
Mathematics Enthusiast Pub Date : 2023-04-01 DOI: 10.54870/1551-3440.1585
Rina Zazkis
{"title":"Encounters With “Love and Math” A Belated Review of Edward Frenkel’s Love and Math: The Heart of Hidden","authors":"Rina Zazkis","doi":"10.54870/1551-3440.1585","DOIUrl":"https://doi.org/10.54870/1551-3440.1585","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70969103","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 Math Ed Take on a Love-Hate Relationship A Review of Reuben Hersh and Vera John-Steiner’s Loving + Hating Mathematics: Challenging the Myths of Mathematical Life 对鲁本·赫什和维拉·约翰·斯坦纳的《爱与恨数学:挑战数学生活的神话》的回顾
IF 0.4
Mathematics Enthusiast Pub Date : 2023-04-01 DOI: 10.54870/1551-3440.1587
J. Holm
{"title":"A Math Ed Take on a Love-Hate Relationship A Review of Reuben Hersh and Vera John-Steiner’s Loving + Hating Mathematics: Challenging the Myths of Mathematical Life","authors":"J. Holm","doi":"10.54870/1551-3440.1587","DOIUrl":"https://doi.org/10.54870/1551-3440.1587","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44784937","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
Algorithms and Mathematics Education A Response and Review of Hannah Fry’s Hello World: Being Human in the Age of Algorithms 算法与数学教育——对Hannah Fry的《你好世界：算法时代的人》的回应与评论
IF 0.4
Mathematics Enthusiast Pub Date : 2023-04-01 DOI: 10.54870/1551-3440.1599
Joshua T. Hertel
{"title":"Algorithms and Mathematics Education A Response and Review of Hannah Fry’s Hello World: Being Human in the Age of Algorithms","authors":"Joshua T. Hertel","doi":"10.54870/1551-3440.1599","DOIUrl":"https://doi.org/10.54870/1551-3440.1599","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49111015","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: 1
Overcoming Misconceptions about Probability A Review of David J. Hand’s The Improbability Principle 克服概率的误区——大卫·J·汉德的不可能性原理述评
IF 0.4
Mathematics Enthusiast Pub Date : 2023-04-01 DOI: 10.54870/1551-3440.1607
Keith Gallagher
{"title":"Overcoming Misconceptions about Probability A Review of David J. Hand’s The Improbability Principle","authors":"Keith Gallagher","doi":"10.54870/1551-3440.1607","DOIUrl":"https://doi.org/10.54870/1551-3440.1607","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43417181","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: 1
Numerate Life for Whom? A Non-book-review of John Allen Paulos’s A Numerate Life: Mathematician Explores the Vagaries of Life, His Own and Probably Yours 为谁计算生命？约翰·艾伦·保洛斯的《数字生活：数学家探索生活的模糊性》非书评
IF 0.4
Mathematics Enthusiast Pub Date : 2023-04-01 DOI: 10.54870/1551-3440.1590
Ofer Marmur
{"title":"Numerate Life for Whom? A Non-book-review of John Allen Paulos’s A Numerate Life: Mathematician Explores the Vagaries of Life, His Own and Probably Yours","authors":"Ofer Marmur","doi":"10.54870/1551-3440.1590","DOIUrl":"https://doi.org/10.54870/1551-3440.1590","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41627246","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
Queering the Stats A Review of David Spiegelhalter’s The Art of Statistics: Learning from Data 对大卫·斯皮格哈尔特的《统计的艺术:从数据中学习》的评论
IF 0.4
Mathematics Enthusiast Pub Date : 2023-04-01 DOI: 10.54870/1551-3440.1592
N. Radaković
{"title":"Queering the Stats A Review of David Spiegelhalter’s The Art of Statistics: Learning from Data","authors":"N. Radaković","doi":"10.54870/1551-3440.1592","DOIUrl":"https://doi.org/10.54870/1551-3440.1592","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42599538","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
Woo-Hoo! The Mathematics and Education of the D’oh-Nut. A Review of Simon Singh’s The Simpsons and Their Mathematical Secrets 呜呜！D’oh-Nut的数学与教育。西蒙·辛格的《辛普森一家》及其数学秘密述评
IF 0.4
Mathematics Enthusiast Pub Date : 2023-04-01 DOI: 10.54870/1551-3440.1591
Jamie S. Pyper
{"title":"Woo-Hoo! The Mathematics and Education of the D’oh-Nut. A Review of Simon Singh’s The Simpsons and Their Mathematical Secrets","authors":"Jamie S. Pyper","doi":"10.54870/1551-3440.1591","DOIUrl":"https://doi.org/10.54870/1551-3440.1591","url":null,"abstract":"","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47098433","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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