发布求助
文献互助 智能选刊 最新文献

American Mathematical Monthly最新文献

筛选
英文 中文
A New Polygonal Number Theorem 一个新的多边形数定理
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-01-09 DOI: 10.1080/00029890.2022.2159256
Benjamin Lee Warren
{"title":"A New Polygonal Number Theorem","authors":"Benjamin Lee Warren","doi":"10.1080/00029890.2022.2159256","DOIUrl":"https://doi.org/10.1080/00029890.2022.2159256","url":null,"abstract":"The polygonal number theorem of Fermat, Cauchy, and Legendre has served as one of the leading results in the history of additive number theory. It states that every positive integer can be written as the sum of m m-gonal numbers, and Legendre improved this to four or five m-gonal numbers for sufficiently large integers. A variation of this problem is to determine the minimal amount of m-gonal numbers needed in order to represent all integers as the sum and difference of these elements infinitely many different ways. Fortunately, a full solution is provided to this problem as the following result.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"334 - 334"},"PeriodicalIF":0.5,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47689342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Basel Problem and the Fundamental Theorem of Calculus 巴塞尔问题与微积分基本定理
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2023-01-01 DOI: 10.1080/00029890.2022.2148760
A. D. Vigna
{"title":"The Basel Problem and the Fundamental Theorem of Calculus","authors":"A. D. Vigna","doi":"10.1080/00029890.2022.2148760","DOIUrl":"https://doi.org/10.1080/00029890.2022.2148760","url":null,"abstract":"","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"126"},"PeriodicalIF":0.5,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"58760844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Letter from the Editor: The Power of Book Reviews 编辑来信:书评的力量
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2022-12-22 DOI: 10.1080/00029890.2023.2131309
Della Dumbaugh
{"title":"Letter from the Editor: The Power of Book Reviews","authors":"Della Dumbaugh","doi":"10.1080/00029890.2023.2131309","DOIUrl":"https://doi.org/10.1080/00029890.2023.2131309","url":null,"abstract":"","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"3 - 4"},"PeriodicalIF":0.5,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46554485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Topology of Punctured Spaces 关于穿孔空间的拓扑
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2022-12-20 DOI: 10.1080/00029890.2022.2151804
Katiuscia C. B. Teixeira
{"title":"On the Topology of Punctured Spaces","authors":"Katiuscia C. B. Teixeira","doi":"10.1080/00029890.2022.2151804","DOIUrl":"https://doi.org/10.1080/00029890.2022.2151804","url":null,"abstract":"Abstract We give a short, elementary proof of the fact that singletons are not topologically negligible for a relevant family of metric spaces. The idea is geometric and, in particular, it offers alternative solutions to some classical theorems of that nature.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"182 - 185"},"PeriodicalIF":0.5,"publicationDate":"2022-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46345265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Minimax Theorem Revisited 对极小极大定理的再认识
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2022-12-16 DOI: 10.1080/00029890.2022.2144085
M. I. Schlesinger, V. Krygin
{"title":"Minimax Theorem Revisited","authors":"M. I. Schlesinger, V. Krygin","doi":"10.1080/00029890.2022.2144085","DOIUrl":"https://doi.org/10.1080/00029890.2022.2144085","url":null,"abstract":"Abstract The article presents a new proof of the minimax theorem. Its novelty is that it uses only elementary concepts within the scope of obligatory mathematical education of engineers. The minimax theorem results in numerous applications and many of them are far from being obvious. Hence the use of such applications has to be based not only on belief in the minimax theorem, but on a transparent understanding of it without need of more complicated concepts. The audience for this article is mathematicians who lecture on convex analysis to nonmathematicians.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"145 - 157"},"PeriodicalIF":0.5,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45245720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Random Walks, Directed Cycles, and Markov Chains 随机漫步，有向环和马尔可夫链
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2022-12-12 DOI: 10.1080/00029890.2022.2144088
K. Gingell, F. Mendivil
{"title":"Random Walks, Directed Cycles, and Markov Chains","authors":"K. Gingell, F. Mendivil","doi":"10.1080/00029890.2022.2144088","DOIUrl":"https://doi.org/10.1080/00029890.2022.2144088","url":null,"abstract":"Abstract A Markov chain is a random process which iteratively travels around in its state space with each transition only depending on the current position and not on the past. When the state space is discrete, we can think of a Markov chain as a special type of random walk on a directed graph. Although a Markov chain normally never settles down but keeps moving around, it does usually have a well-defined limiting behavior in a statistical sense. A given finite directed graph can potentially support many different random walks or Markov chains and each one could have one or more invariant (stationary) distributions. In this paper we explore the question of characterizing the set of all possible invariant distributions. The answer turns out to be quite simple and very natural and involves the cycles on the graph.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"127 - 144"},"PeriodicalIF":0.5,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46987805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Nearly Forgotten Polynomial Result by P. Bohl 关于P. Bohl的一个几乎被遗忘的多项式结果
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2022-12-09 DOI: 10.1080/00029890.2022.2144090
J. Cermák, L. Fedorková
{"title":"On a Nearly Forgotten Polynomial Result by P. Bohl","authors":"J. Cermák, L. Fedorková","doi":"10.1080/00029890.2022.2144090","DOIUrl":"https://doi.org/10.1080/00029890.2022.2144090","url":null,"abstract":"Abstract Piers Bohl (1865–1921) was an outstanding Latvian mathematician whose name is particularly connected with several crucial achievements that were ahead of their time. Unfortunately, the contemporary mathematical community did not recognize their significance. This paper discusses one of Bohl’s results from 1908 that remained nearly unnoticed, even up until the present. It concerns a general complex trinomial and answers the problem of the distribution of its roots with respect to a given modulus. During the last few decades, this and other related problems have been extensively studied in numerous particular cases, without knowledge of this existing answer. This paper recalls the aforementioned Bohl’s result and illustrates how easily it can imply conclusions of recent as well as older works regarding this topic.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"176 - 181"},"PeriodicalIF":0.5,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41870124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Math Games With Bad Drawings: 75 Simple, Challenging, Go-Anywhere Games—And Why They Matter 糟糕绘图的数学游戏：75个简单、有挑战性的随时随地游戏——以及它们的重要性
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2022-12-09 DOI: 10.1080/00029890.2023.2146376
Patrick Honner
{"title":"Math Games With Bad Drawings: 75 Simple, Challenging, Go-Anywhere Games—And Why They Matter","authors":"Patrick Honner","doi":"10.1080/00029890.2023.2146376","DOIUrl":"https://doi.org/10.1080/00029890.2023.2146376","url":null,"abstract":"","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"197 - 200"},"PeriodicalIF":0.5,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42738503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
100 Years Ago This Month in The American Mathematical Monthly 100年前的这个月刊登在美国数学月刊上
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2022-12-06 DOI: 10.1080/00029890.2022.2144668
V. Ponomarenko
{"title":"100 Years Ago This Month in The American Mathematical Monthly","authors":"V. Ponomarenko","doi":"10.1080/00029890.2022.2144668","DOIUrl":"https://doi.org/10.1080/00029890.2022.2144668","url":null,"abstract":"","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"181 - 181"},"PeriodicalIF":0.5,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46521802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
What Do Networks and Elliptic Curves Have in Common? 网络和椭圆曲线有什么共同点？
IF 0.5 4区 数学
American Mathematical Monthly Pub Date : 2022-12-05 DOI: 10.1080/00029890.2022.2141548
J. Chahal
{"title":"What Do Networks and Elliptic Curves Have in Common?","authors":"J. Chahal","doi":"10.1080/00029890.2022.2141548","DOIUrl":"https://doi.org/10.1080/00029890.2022.2141548","url":null,"abstract":"Abstract Graph theory used in networking and the arithmetic of elliptic curves have more in common than meets the eye. We present how their zeta functions fuse them seamlessly.","PeriodicalId":7761,"journal":{"name":"American Mathematical Monthly","volume":"130 1","pages":"158 - 175"},"PeriodicalIF":0.5,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41539015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
首页 上一页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信