LEADER 04135nam 2200625 450 001 9910683357003321 005 20240116130356.0 010 $a9783031130175$b(electronic bk.) 010 $z9783031130168 024 7 $a10.1007/978-3-031-13017-5 035 $a(MiAaPQ)EBC7220673 035 $a(Au-PeEL)EBL7220673 035 $a(OCoLC)1374429230 035 $a(DE-He213)978-3-031-13017-5 035 $a(PPN)269093265 035 $a(EXLCZ)9926347414500041 100 $a20230604d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aExcursions in Number Theory, Algebra, and Analysis /$fKenneth Ireland and Al Cuoco 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer Nature Switzerland AG,$d[2023] 210 4$d©2023 215 $a1 online resource (199 pages) 225 1 $aUndergraduate Texts in Mathematics Series 311 08$aPrint version: Ireland, Kenneth Excursions in Number Theory, Algebra, and Analysis Cham : Springer International Publishing AG,c2023 9783031130168 320 $aIncludes bibliographical references and index. 327 $aPreface -- 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. 330 $aThis textbook originates from a course taught by the late Ken Ireland in 1972. Designed to explore the theoretical underpinnings of undergraduate mathematics, the course focused on interrelationships and hands-on experience. Readers of this textbook will be taken on a modern rendering of Ireland?s path of discovery, consisting of excursions into number theory, algebra, and analysis. Replete with surprising connections, deep insights, and brilliantly curated invitations to try problems at just the right moment, this journey weaves a rich body of knowledge that is ideal for those going on to study or teach mathematics. A pool of 200 ?Dialing In? problems opens the book, providing fuel for active enquiry throughout a course. The following chapters develop theory to illuminate the observations and roadblocks encountered in the problems, situating them in the broader mathematical landscape. Topics cover polygons and modular arithmetic; the fundamental theorems of arithmetic and algebra; irrational, algebraic and transcendental numbers; and Fourier series and Gauss sums. A lively accompaniment of examples, exercises, historical anecdotes, and asides adds motivation and context to the theory. Return trips to the Dialing In problems are encouraged, offering opportunities to put theory into practice and make lasting connections along the way. Excursions in Number Theory, Algebra, and Analysis invites readers on a journey as important as the destination. Suitable for a senior capstone, professional development for practicing teachers, or independent reading, this textbook offers insights and skills valuable to math majors and high school teachers alike. A background in real analysis and abstract algebra is assumed, though the most important prerequisite is a willingness to put pen to paper and do some mathematics. 410 0$aUndergraduate texts in mathematics. 606 $aAlgebra 606 $aMathematical analysis 606 $aNumber theory 606 $aTeoria de nombres$2thub 606 $aÀlgebra$2thub 606 $aAnàlisi matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aAlgebra. 615 0$aMathematical analysis. 615 0$aNumber theory. 615 7$aTeoria de nombres 615 7$aÀlgebra 615 7$aAnàlisi matemàtica 676 $a512.9 700 $aIreland$b Kenneth$057618 702 $aCuoco$b Albert 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910683357003321 996 $aExcursions in Number Theory, Algebra, and Analysis$93087075 997 $aUNINA