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A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic (Undergraduate Texts in Mathematics) - Tapa blanda
Sinopsis
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.
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Acerca del autor
Ramin Takloo-Bighash is a Professor of Mathematics at the University of Illinois at Chicago, where his research is centered on Diophantine geometry and automorphic forms. His enthusiasm for research inspires his teaching at all levels.
De la contraportada
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 of which 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.
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- EditorialSpringer
- Año de publicación2021
- ISBN 10 3030805298
- ISBN 13 9783030805296
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de edición1
- Número de páginas300
- Contacto del fabricanteno disponible
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A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic (Undergraduate Texts in Mathematics)
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A Pythagorean Introduction to Number Theory
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ISBN 10: 3030805298
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 of which 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. 300 pp. Englisch. Nº de ref. del artículo: 9783030805296
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Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic
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A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Nº de ref. del artículo: 9783030805296
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A Pythagorean Introduction to Number Theory
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ISBN 10: 3030805298
ISBN 13: 9783030805296
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Kartoniert / Broschiert. Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Offers an innovative approach to elementary number theory motivated by right trianglesInspires students to explore number theory through investigation of concrete examplesProvides historical context throughout, showing how ideas developed i. Nº de ref. del artículo: 477957107
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A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic (Paperback or Softback)
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A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic (Undergraduate Texts in Mathematics)
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