書目名稱 | Excursions in Number Theory, Algebra, and Analysis | 編輯 | Kenneth Ireland,Al Cuoco | 視頻video | http://file.papertrans.cn/319/318434/318434.mp4 | 概述 | Explores the rich theory and interconnections that underlie undergraduate mathematics.Invites readers to actively explore problems before concepts are formalized.Offers a lively accompaniment of obser | 叢書名稱 | Undergraduate Texts in Mathematics | 圖書封面 |  | 描述 | .This textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate mathematics, the course focused on interrelationships and hands-on experience. Readers of this textbook will be taken on a modern rendering of Ireland’s path of discovery, consisting of excursions into number theory, algebra, and analysis. Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on to study or teach mathematics...A pool of 200 ‘Dialing In’ problems opens the book, providing fuel for active enquiry throughout a course. The following chapters develop theory to illuminate the observations and roadblocks encountered in the problems, situating them in the broader mathematical landscape. Topics cover polygons and modular arithmetic; the fundamental theorems of arithmetic and algebra; irrational, algebraic and transcendental numbers; and Fourier series and Gauss sums. A lively accompaniment of examples, exercises, historical anecdotes, and asides adds motivation and context to the t | 出版日期 | Textbook 2023 | 關(guān)鍵詞 | polygons and modular arithmetic; Fundamental Theorem of Arithmetic; Fundamental Theorem of Algebra; irr | 版次 | 1 | doi | https://doi.org/10.1007/978-3-031-13017-5 | isbn_softcover | 978-3-031-13019-9 | isbn_ebook | 978-3-031-13017-5Series ISSN 0172-6056 Series E-ISSN 2197-5604 | issn_series | 0172-6056 | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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