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＜電子ブック＞
Excursions in Number Theory, Algebra, and Analysis / by Kenneth Ireland, Al Cuoco
(Readings in Mathematics. ISSN:29455847)

版	1st ed. 2023.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2023
本文言語	英語
大きさ	XXV, 177 p. 34 illus., 2 illus. in color : online resource
著者標目	*Ireland, Kenneth author Cuoco, Al author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Group theory LCSH:Functions of real variables FREE:Number Theory FREE:Group Theory and Generalizations FREE:Real Functions
一般注記	Preface -- 1. Dialing In Problems -- 2. Polygons and Modular Arithmetic -- 3. The Fundamental Theorem of Arithmetic -- 4. The Fundamental Theorem of Algebra -- 5. Irrational, Algebraic and Transcendental Numbers -- 6. Fourier Series and Gauss Sums -- Epilogue -- Notation -- Bibliography -- Index 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 theory. Return trips to the Dialing In problems are encouraged, offering opportunities to put theory into practice and make lasting connections along the way. Excursions in Number Theory, Algebra, and Analysis invites readers on a journey as important as the destination. Suitable for a senior capstone, professional development for practicing teachers, or independent reading, this textbook offers insights and skills valuable to math majors and high school teachers alike. A background in real analysis and abstract algebra is assumed, though the most important prerequisite is a willingness to put pen to paper and do some mathematics HTTP:URL=https://doi.org/10.1007/978-3-031-13017-5

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