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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra Excursions in Number Theory, Algebra, and Analysis
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Excursions in Number Theory, Algebra, and Analysis
Kenneth Ireland, Al Cuoco (Broschiert, Englisch)
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Beschreibung
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 . Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
30.03.2024
Sprache
Englisch
EAN
9783031130199
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Undergraduate Texts in Mathematics
Sonderedition
Nein
Autor
Kenneth Ireland, Al Cuoco
Seitenanzahl
177
Einbandart
Broschiert
Schlagwörter
polygons and modular arithmetic, Fundamental Theorem of Arithmetic, Fundamental Theorem of Algebra, irrational numbers textbook, algebraic numbers textbook, transcendental numbers textbook, Fourier series textbook, Gauss sums, senior capstone mathematics, undergraduate mathematics reading course, high school mathematics teacher preparation, Ken Ireland textbook
Thema-Inhalt
PBH - Zahlentheorie
PBG - Gruppen und Gruppentheorie
PBKB - Reelle Analysis, Real-Variablen
Höhe
254 mm
Breite
17.8 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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