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Titlebook: Excursions in Number Theory, Algebra, and Analysis; Kenneth Ireland,Al Cuoco Textbook 2023 The Editor(s) (if applicable) and The Author(s)

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发表于 2025-3-21 18:28:53 | 显示全部楼层 |阅读模式
书目名称Excursions in Number Theory, Algebra, and Analysis
编辑Kenneth Ireland,Al Cuoco
视频video
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
丛书名称Undergraduate Texts in Mathematics
图书封面Titlebook: Excursions in Number Theory, Algebra, and Analysis;  Kenneth Ireland,Al Cuoco Textbook 2023 The Editor(s) (if applicable) and The Author(s)
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
关键词polygons and modular arithmetic; Fundamental Theorem of Arithmetic; Fundamental Theorem of Algebra; irr
版次1
doihttps://doi.org/10.1007/978-3-031-13017-5
isbn_softcover978-3-031-13019-9
isbn_ebook978-3-031-13017-5Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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The Fundamental Theorem of Arithmetic, where students spend much of elementary school working with integers, using this . property as if it were a law of nature. For example, young children build “factor trees” for whole numbers, and it is usually taken for granted that two different trees, like those in Figure ., end up with the same set of prime factors.
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Identifying Basic Dimensions of Personality,er theory and a little group theory, all bound up in a delightful package. Here we go ...One of the richest mathematical structures is the field of complex numbers. With its wonderful balance of algebraic, analytic, and topological properties, it has played a major role in the development of classical and modern mathematics.
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Bioavailability and Bioequivalence, where students spend much of elementary school working with integers, using this . property as if it were a law of nature. For example, young children build “factor trees” for whole numbers, and it is usually taken for granted that two different trees, like those in Figure ., end up with the same set of prime factors.
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Fourier Series and Gauss Sums,The basic functions that we will be concerned with in this chapter are for .. The elements of the vector spaces over . spanned by these functions are called Thus a finite trigonometric series of degree at most . is a function of the form.
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