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An Elementary Transition to Abstract Mathematics最新文献

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Matrices and Sets with Algebraic Structure 具有代数结构的矩阵和集合
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-12
Gove Effinger, G. Mullen
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引用次数: 0
Divisibility in Z and Number Theory Z和数论中的可整除性
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-13
Gove Effinger, G. Mullen
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引用次数: 0
Subspaces of Vector Spaces 向量空间的子空间
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-32
Gove Effinger, G. Mullen
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引用次数: 0
The Well-Ordering Principle 有序原则
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-5
Gove Effinger, G. Mullen
{"title":"The Well-Ordering Principle","authors":"Gove Effinger, G. Mullen","doi":"10.1201/9780429324819-5","DOIUrl":"https://doi.org/10.1201/9780429324819-5","url":null,"abstract":"The well-ordering principle is a concept which is equivalent to mathematical induction. In your textbook, there is a proof for how the well-ordering principle implies the validity of mathematical induction. However, because of the very way in which we constructed the set of natural numbers and its arithmetic, we deduced, in class, the validity of mathematical induction directly from the axioms of set theory. In this note, we show how mathematical induction, in turn, implies the well-ordering principle.","PeriodicalId":383229,"journal":{"name":"An Elementary Transition to Abstract Mathematics","volume":"756 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116409701","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
Primes and Unique Factorization 素数与唯一分解
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-14
Gove Effinger, G. Mullen
{"title":"Primes and Unique Factorization","authors":"Gove Effinger, G. Mullen","doi":"10.1201/9780429324819-14","DOIUrl":"https://doi.org/10.1201/9780429324819-14","url":null,"abstract":"","PeriodicalId":383229,"journal":{"name":"An Elementary Transition to Abstract Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129108640","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
Polynomials over the Rational, Real and Complex Numbers 有理数、实数和复数上的多项式
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-35
G. Mullen
{"title":"Polynomials over the Rational, Real and Complex Numbers","authors":"G. Mullen","doi":"10.1201/9780429324819-35","DOIUrl":"https://doi.org/10.1201/9780429324819-35","url":null,"abstract":"","PeriodicalId":383229,"journal":{"name":"An Elementary Transition to Abstract Mathematics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127695347","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
Diffie-Hellman Key Exchange 迪菲-赫尔曼密钥交换
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-18
A. Biryukov, Christophe De Cannière, W. Winkler, C. Aggarwal, Markus G. Kuhn, Luc Bouganim, Yanli Guo, B. Preneel, G. Bleumer, T. Helleseth, R. Canetti, Mayank Varia, C. Peters, B. Kaliski, Y. Desmedt, G. Kesidis, Marijke De Soete, Berry Schoenmakers, C. Adams, E. Biham, T. Caddy, C. Dwork, Mike Just, M. Finiasz, N. Sendrier, Kazue Sako, P. Gaborit, D. Boneh, C. Cachin, D. Gordon, Ninghui Li, S. Vimercati, M. Videau, S. Yanushkevich, D. Popel, Brent Byunghoon Kang, John Ioannidis, Mihai Christodorescu, V. Ganapathy, A. Srivastava, Sean W. Smith
{"title":"Diffie-Hellman Key Exchange","authors":"A. Biryukov, Christophe De Cannière, W. Winkler, C. Aggarwal, Markus G. Kuhn, Luc Bouganim, Yanli Guo, B. Preneel, G. Bleumer, T. Helleseth, R. Canetti, Mayank Varia, C. Peters, B. Kaliski, Y. Desmedt, G. Kesidis, Marijke De Soete, Berry Schoenmakers, C. Adams, E. Biham, T. Caddy, C. Dwork, Mike Just, M. Finiasz, N. Sendrier, Kazue Sako, P. Gaborit, D. Boneh, C. Cachin, D. Gordon, Ninghui Li, S. Vimercati, M. Videau, S. Yanushkevich, D. Popel, Brent Byunghoon Kang, John Ioannidis, Mihai Christodorescu, V. Ganapathy, A. Srivastava, Sean W. Smith","doi":"10.1201/9780429324819-18","DOIUrl":"https://doi.org/10.1201/9780429324819-18","url":null,"abstract":"","PeriodicalId":383229,"journal":{"name":"An Elementary Transition to Abstract Mathematics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121461444","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: 23
About Proofs and Proof Strategies 关于证明和证明策略
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-3
Gove Effinger, G. Mullen
{"title":"About Proofs and Proof Strategies","authors":"Gove Effinger, G. Mullen","doi":"10.1201/9780429324819-3","DOIUrl":"https://doi.org/10.1201/9780429324819-3","url":null,"abstract":"","PeriodicalId":383229,"journal":{"name":"An Elementary Transition to Abstract Mathematics","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123026286","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
Groups - Basic Properties 组-基本属性
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-22
Gove Effinger, G. Mullen
{"title":"Groups - Basic Properties","authors":"Gove Effinger, G. Mullen","doi":"10.1201/9780429324819-22","DOIUrl":"https://doi.org/10.1201/9780429324819-22","url":null,"abstract":"","PeriodicalId":383229,"journal":{"name":"An Elementary Transition to Abstract Mathematics","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115452403","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
Subrings and Ideals 子带与理想
An Elementary Transition to Abstract Mathematics Pub Date : 2019-11-05 DOI: 10.1201/9780429324819-27
Gove Effinger, G. Mullen
{"title":"Subrings and Ideals","authors":"Gove Effinger, G. Mullen","doi":"10.1201/9780429324819-27","DOIUrl":"https://doi.org/10.1201/9780429324819-27","url":null,"abstract":"","PeriodicalId":383229,"journal":{"name":"An Elementary Transition to Abstract Mathematics","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128622559","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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