{"title":"对极小极大定理的再认识","authors":"M. I. Schlesinger, V. Krygin","doi":"10.1080/00029890.2022.2144085","DOIUrl":null,"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":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Minimax Theorem Revisited\",\"authors\":\"M. I. Schlesinger, V. Krygin\",\"doi\":\"10.1080/00029890.2022.2144085\",\"DOIUrl\":null,\"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\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"American Mathematical Monthly\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/00029890.2022.2144085\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Mathematical Monthly","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00029890.2022.2144085","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
期刊介绍：
The Monthly''s readers expect a high standard of exposition; they look for articles that inform, stimulate, challenge, enlighten, and even entertain. Monthly articles are meant to be read, enjoyed, and discussed, rather than just archived. Articles may be expositions of old or new results, historical or biographical essays, speculations or definitive treatments, broad developments, or explorations of a single application. Novelty and generality are far less important than clarity of exposition and broad appeal. Appropriate figures, diagrams, and photographs are encouraged.
Notes are short, sharply focused, and possibly informal. They are often gems that provide a new proof of an old theorem, a novel presentation of a familiar theme, or a lively discussion of a single issue.
Abstracts for articles or notes should entice the prospective reader into exploring the subject of the paper and should make it clear to the reader why this paper is interesting and important. The abstract should highlight the concepts of the paper rather than summarize the mechanics. The abstract is the first impression of the paper, not a technical summary of the paper. Excessive use of notation is discouraged as it can limit the interest of the broad readership of the MAA, and can limit search-ability of the article.
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