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Titlebook: Explorations in Number Theory; Commuting through th Cam McLeman,Erin McNicholas,Colin Starr Textbook 2022 Springer Nature Switzerland AG 20

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書目名稱Explorations in Number Theory
副標(biāo)題Commuting through th
編輯Cam McLeman,Erin McNicholas,Colin Starr
視頻videohttp://file.papertrans.cn/321/320209/320209.mp4
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
叢書名稱Undergraduate Texts in Mathematics
圖書封面Titlebook: Explorations in Number Theory; Commuting through th Cam McLeman,Erin McNicholas,Colin Starr Textbook 2022 Springer Nature Switzerland AG 20
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
關(guān)鍵詞Elementary Number theory; Diophantine equations; Abstract Algebra; Gaussian Integers; Eisenstein Integer
版次1
doihttps://doi.org/10.1007/978-3-030-98931-6
isbn_softcover978-3-030-98933-0
isbn_ebook978-3-030-98931-6Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer Nature Switzerland AG 2022
The information of publication is updating

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Markenst?rke von Arbeitgebermarkennteenth-century French mathematician Pierre de Fermat,?has all the hallmarks of an epic tale: an arduous quest spanning centuries and continents taken on by a legion of mathematicians; a resilient foe that bested many of the greatest minds for 300 years; and the classic template of human anguish, redemption, and then ultimate triumph.
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Markentransfers im Dienstleistungsbereich of something deeper, let us choose to focus for the time being on the Diophantine equations . for various integers ., asking which numbers . can be written as the sum of two integer squares (and how to do so).
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Gaussian Number Theory: , of the Storm, of something deeper, let us choose to focus for the time being on the Diophantine equations . for various integers ., asking which numbers . can be written as the sum of two integer squares (and how to do so).
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https://doi.org/10.1007/978-3-8350-9232-7t a closely related problem in a different number system. A flipped, and equally valuable, version of this perspective is that we understand arithmetic in . well enough that we should attempt to export this mastery to other systems.
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Number Theory in , Beginning,t a closely related problem in a different number system. A flipped, and equally valuable, version of this perspective is that we understand arithmetic in . well enough that we should attempt to export this mastery to other systems.
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