{"title":"Pascal's Triangle Identities","authors":"M. Radin","doi":"10.1201/9781003089469-5","DOIUrl":"https://doi.org/10.1201/9781003089469-5","url":null,"abstract":"","PeriodicalId":401390,"journal":{"name":"Introduction to Math Olympiad Problems","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123254458","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}
{"title":"Proofs","authors":"M. Radin","doi":"10.1201/9781003089469-3","DOIUrl":"https://doi.org/10.1201/9781003089469-3","url":null,"abstract":"","PeriodicalId":401390,"journal":{"name":"Introduction to Math Olympiad Problems","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117108528","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}
{"title":"Geometry","authors":"M. Radin","doi":"10.1201/9781003089469-6","DOIUrl":"https://doi.org/10.1201/9781003089469-6","url":null,"abstract":"An efficient geometric formulation of the problem of parameter estimation is developed, based on Hilbert space geometry. This theory, which allows for a transparent transition between classical and quantum statistical inference, is then applied to the analysis of exponential families of distributions (of relevance to statistical mechanics) and quantum mechanical evolutions. The extension to quantum theory is achieved by the introduction of a complex structure on the given real Hilbert space. We find a set of higher order corrections to the parameter estimation variance lower bound, which are potentially important in quantum mechanics, where these corrections appear as modifications to Heisenberg uncertainty relations for the determination of the parameter. [S0031-9007(96)01153-2]","PeriodicalId":401390,"journal":{"name":"Introduction to Math Olympiad Problems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124529304","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}
{"title":"Integers' Characteristics","authors":"M. Radin","doi":"10.1201/9781003089469-4","DOIUrl":"https://doi.org/10.1201/9781003089469-4","url":null,"abstract":"","PeriodicalId":401390,"journal":{"name":"Introduction to Math Olympiad Problems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121336877","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}
{"title":"Graph Theory","authors":"M. Radin","doi":"10.1201/9781003089469-7","DOIUrl":"https://doi.org/10.1201/9781003089469-7","url":null,"abstract":"INTRODUCTION A picture is worth a thousand words is a commonly used adage meaning that complex and sometimes multiple ideas can be conveyed by a single still image(wiki). So does the graph through the visual representation of data. Visual representation provides better insights and helps us make better data-driven decisions based on them. A better understanding of the \"Graph Theory\" concept can aid our data visualization to the next level. Though the graph theory is important, it is often hidden under the concept of many ML algorithms. Understanding the graph theory concepts and application of it to data science can benefit us by speeding up our code dramatically, reducing functions with plenty of looping to sweet one-liners, making possible certain tasks that were previously practically unsolvable.","PeriodicalId":401390,"journal":{"name":"Introduction to Math Olympiad Problems","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134589580","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}
{"title":"Sequences and Summations","authors":"M. Radin","doi":"10.1201/9780367808747-3","DOIUrl":"https://doi.org/10.1201/9780367808747-3","url":null,"abstract":"A sequence is a function from a subset of Z, typically Z + or N, to some other set. Can be denoted by f (n) = y or a n = y. A summation sums the terms in a sequence.","PeriodicalId":401390,"journal":{"name":"Introduction to Math Olympiad Problems","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127867738","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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