04135nam 2200625 450 991068335700332120240116130356.09783031130175(electronic bk.)978303113016810.1007/978-3-031-13017-5(MiAaPQ)EBC7220673(Au-PeEL)EBL7220673(OCoLC)1374429230(DE-He213)978-3-031-13017-5(PPN)269093265(EXLCZ)992634741450004120230604d2023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierExcursions in Number Theory, Algebra, and Analysis /Kenneth Ireland and Al Cuoco1st ed. 2023.Cham, Switzerland :Springer Nature Switzerland AG,[2023]©20231 online resource (199 pages)Undergraduate Texts in Mathematics SeriesPrint version: Ireland, Kenneth Excursions in Number Theory, Algebra, and Analysis Cham : Springer International Publishing AG,c2023 9783031130168 Includes bibliographical references and index.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.Undergraduate texts in mathematics.AlgebraMathematical analysisNumber theoryTeoria de nombresthubÀlgebrathubAnàlisi matemàticathubLlibres electrònicsthubAlgebra.Mathematical analysis.Number theory.Teoria de nombresÀlgebraAnàlisi matemàtica512.9Ireland Kenneth57618Cuoco AlbertMiAaPQMiAaPQMiAaPQ9910683357003321Excursions in Number Theory, Algebra, and Analysis3087075UNINA