| 书目名称 | Explorations in Number Theory | | 副标题 | Commuting through th | | 编辑 | Cam McLeman,Erin McNicholas,Colin Starr | | 视频video | | | 概述 | Integrates abstract algebra into elementary number theory to enhance students‘ understanding.Offer numerous IBL explorations that allow students develop insights for forthcoming material.Written in an | | 丛书名称 | Undergraduate Texts in Mathematics | | 图书封面 |  | | 描述 | This innovative undergraduate textbook approaches number theory through the lens of abstract algebra. Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory. Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics.. .The text is organized around three core themes: the notion of what a “number” is, and the premise that it takes familiarity with a large variety of number systems to fully explore number theory; the use of Diophantine equations as catalysts for introducing and developing structural ideas; and the role of abstract algebra in number theory, in particular the extent to which it provides the Fundamental Theorem of Arithmetic for various new number systems. Other aspects of modern number theory – including the study of elliptic curves, the analogs between integer and polynomial arithmetic, .p.-adic arithmetic, and relationships between the spectra of primes in various rings – are inc | | 出版日期 | Textbook 2022 | | 关键词 | Elementary Number theory; Diophantine equations; Abstract Algebra; Gaussian Integers; Eisenstein Integer | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-98931-6 | | isbn_softcover | 978-3-030-98933-0 | | isbn_ebook | 978-3-030-98931-6Series ISSN 0172-6056 Series E-ISSN 2197-5604 | | issn_series | 0172-6056 | | copyright | Springer Nature Switzerland AG 2022 |
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发表于 2025-3-21 17:30:07
