A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic (Undergraduate Texts in Mathematics) - Tapa blanda

Takloo-Bighash, Ramin

 
9783030805296: A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic (Undergraduate Texts in Mathematics)
Tapa blanda
ISBN 10: 3030805298 ISBN 13: 9783030805296
Editorial: Springer, 2021

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.

"Sinopsis" puede pertenecer a otra edición de este libro.

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2021
Idioma
Inglés
ISBN 10 
3030805298
ISBN 13 
9783030805296
Encuadernación
Tapa blanda
Número de edición
1
Número de páginas
300
Contacto del fabricante
no disponible
Persona responsable
CMN Printpool Inh. Mathis Neumann
https://www.also.com/ec/cms5/en_6000/6000/index.jsp

Friedrich-Karl-Str. 9
Hamburg
Alemania

Otras ediciones populares con el mismo título

9783030026035: A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic (Undergraduate Texts in Mathematics)

Edición Destacada

ISBN 10:  3030026035 ISBN 13:  9783030026035
Editorial: Springer-Verlag GmbH, 2018
Tapa dura