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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Arithmetik & Algebra A Pythagorean Introduction to Number Theory
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A Pythagorean Introduction to Number Theory
Ramin Takloo-Bighash (Broschiert, Englisch)
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Beschreibung
Right triangles are at the heart of this textbook’s vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through… exercises, using technology, and learning about the broader context in which ideas developed. Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course; the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many ofwhich are designed for SageMath. By involving students in the active process of inquiry and investigation, this textbook imbues the foundations of number theory with insights into the lively mathematical process that continues to advance the field today. Experience writing proofs is the only formal prerequisite for the book, while a background in basic real analysis will enrich the reader’s appreciation of the final chapters. 53,49 €
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Technische Daten
Erscheinungsdatum
24.07.2021
Sprache
Englisch
EAN
9783030805296
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Undergraduate Texts in Mathematics
Sonderedition
Nein
Autor
Ramin Takloo-Bighash
Seitenanzahl
279
Einbandart
Broschiert
Buch Untertitel
Right Triangles, Sums of Squares, and Arithmetic
Schlagwörter
Pythagorean theorem, Elementary number theory, Fermat's theorem, Diophantine equation, Primes of the form 4k+1, Quadratic reciprocity, Pythagorean triples, Counting lattice points, Gauss sums, Four squares theorem, Quadratic forms and sums of squares, Number theory with SageMath
Thema-Inhalt
PBH - Zahlentheorie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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