Pub Date : 2024-03-04DOI: 10.1080/00029890.2024.2316587
Wagner Oliveira Costa Filho
Published in The American Mathematical Monthly (Ahead of Print, 2024)
发表于《美国数学月刊》（2024 年提前出版）
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Pub Date : 2024-02-23DOI: 10.1080/00029890.2024.2309110
Yusuf Z. Gürtaş
Discriminants of quadratics have been recently generalized as Δk=k(n−k)cn−k2−(k+1)(n−k+1)cn−k−1cn−k+1 for a polynomial f(x)=cnxn+⋯+c1x+c0 of degree n≥2 for 1≤k≤n−1 and it has been shown that Δ1≥0 i...
{"title":"On Nonnegativity of the Generalized Discriminants of Quadratics","authors":"Yusuf Z. Gürtaş","doi":"10.1080/00029890.2024.2309110","DOIUrl":"https://doi.org/10.1080/00029890.2024.2309110","url":null,"abstract":"Discriminants of quadratics have been recently generalized as Δk=k(n−k)cn−k2−(k+1)(n−k+1)cn−k−1cn−k+1 for a polynomial f(x)=cnxn+⋯+c1x+c0 of degree n≥2 for 1≤k≤n−1 and it has been shown that Δ1≥0 i...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139968633","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 : 2024-02-23DOI: 10.1080/00029890.2024.2308457
David M. Bradley, Albert Natian, Seán M. Stewart
{"title":"Integration using Schwinger Parametrization","authors":"David M. Bradley, Albert Natian, Seán M. Stewart","doi":"10.1080/00029890.2024.2308457","DOIUrl":"https://doi.org/10.1080/00029890.2024.2308457","url":null,"abstract":"","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"3 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139957635","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 : 2024-02-22DOI: 10.1080/00029890.2024.2313900
Daniel E. Otero
{"title":"Reviews\u0000 \u0000 Number Theory Through the Eyes of Sophie Germain: An Inquiry Course\u0000 \u0000 . By David Pengelley, MAA Press, Providence, RI, 2023. ISBN 9781470472207, $79.00.","authors":"Daniel E. Otero","doi":"10.1080/00029890.2024.2313900","DOIUrl":"https://doi.org/10.1080/00029890.2024.2313900","url":null,"abstract":"","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"10 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140439550","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 : 2024-02-22DOI: 10.1080/00029890.2024.2309099
Zachary P. Bradshaw, Christophe Vignat
We contribute to the zoo of dubious identities established by J.M. and P.B. Borwein in their 1992 paper, “Strange Series and High Precision Fraud” with five new entries, each of a different variety...
{"title":"Dubious Identities: A Visit to the Borwein Zoo","authors":"Zachary P. Bradshaw, Christophe Vignat","doi":"10.1080/00029890.2024.2309099","DOIUrl":"https://doi.org/10.1080/00029890.2024.2309099","url":null,"abstract":"We contribute to the zoo of dubious identities established by J.M. and P.B. Borwein in their 1992 paper, “Strange Series and High Precision Fraud” with five new entries, each of a different variety...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139952107","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 : 2024-02-14DOI: 10.1080/00029890.2024.2309126
Edited by Vadim Ponomarenko
Published in The American Mathematical Monthly (Ahead of Print, 2024)
发表于《美国数学月刊》（2024 年提前出版）
{"title":"100 Years Ago This Month in The American Mathematical Monthly","authors":"Edited by Vadim Ponomarenko","doi":"10.1080/00029890.2024.2309126","DOIUrl":"https://doi.org/10.1080/00029890.2024.2309126","url":null,"abstract":"Published in The American Mathematical Monthly (Ahead of Print, 2024)","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765344","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 : 2024-02-14DOI: 10.1080/00029890.2024.2309123
Christian Axler
Let Nk denote the kth primorial and let K(x) be the primorial counting function, the function that counts the number of primorials not exceeding x. In this note, we examine the sign of the function...
让 Nk 表示第 k 个基元，让 K(x) 表示基元计数函数，即计算不超过 x 的基元数的函数。在本说明中，我们将研究函数的符号。
{"title":"On the Primorial Counting Function","authors":"Christian Axler","doi":"10.1080/00029890.2024.2309123","DOIUrl":"https://doi.org/10.1080/00029890.2024.2309123","url":null,"abstract":"Let Nk denote the kth primorial and let K(x) be the primorial counting function, the function that counts the number of primorials not exceeding x. In this note, we examine the sign of the function...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765789","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 : 2024-02-14DOI: 10.1080/00029890.2024.2309118
Vincent Vatter
Published in The American Mathematical Monthly (Ahead of Print, 2024)
发表于《美国数学月刊》（2024 年提前出版）
{"title":"Counting Parity Palindrome Compositions","authors":"Vincent Vatter","doi":"10.1080/00029890.2024.2309118","DOIUrl":"https://doi.org/10.1080/00029890.2024.2309118","url":null,"abstract":"Published in The American Mathematical Monthly (Ahead of Print, 2024)","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139765420","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 : 2024-02-08DOI: 10.1080/00029890.2023.2298656
Matthew Macauley
In this paper, we will take the classic dihedral and quaternion groups and explore questions like “what if we replace i=e2πi/4 in Q8 with a larger root of unity?” and “what if we add a reflection...
{"title":"Dihedralizing the Quaternions","authors":"Matthew Macauley","doi":"10.1080/00029890.2023.2298656","DOIUrl":"https://doi.org/10.1080/00029890.2023.2298656","url":null,"abstract":"In this paper, we will take the classic dihedral and quaternion groups and explore questions like “what if we replace i=e2πi/4 in Q8 with a larger root of unity?” and “what if we add a reflection...","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312799","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 : 2024-02-05DOI: 10.1080/00029890.2024.2305019
Edited by Daniel H. Ullman, Daniel J. Velleman, Stan Wagon, Douglas B. West
Published in The American Mathematical Monthly (Vol. 131, No. 4, 2024)
发表于《美国数学月刊》（第 131 卷第 4 期，2024 年）
{"title":"Problems and Solutions","authors":"Edited by Daniel H. Ullman, Daniel J. Velleman, Stan Wagon, Douglas B. West","doi":"10.1080/00029890.2024.2305019","DOIUrl":"https://doi.org/10.1080/00029890.2024.2305019","url":null,"abstract":"Published in The American Mathematical Monthly (Vol. 131, No. 4, 2024)","PeriodicalId":501497,"journal":{"name":"The American Mathematical Monthly","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312834","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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