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Undergraduate Texts in Mathematics

A Pythagorean Introduction to Number Theory

Right Triangles, Sums of Squares, and Arithmetic

Authors: Takloo-Bighash, Ramin

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  • Offers an innovative approach to elementary number theory motivated by right triangles
  • Inspires students to explore number theory through investigation of concrete examples
  • Provides historical context throughout, showing how ideas developed in the field
  • Features numerous engaging exercises, including many designed for SageMath
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Buy this book

eBook 35,69 €
price for Spain (gross)
  • ISBN 978-3-030-02604-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 46,79 €
price for Spain (gross)
  • ISBN 978-3-030-02603-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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.

About the authors

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.

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Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook 35,69 €
price for Spain (gross)
  • ISBN 978-3-030-02604-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 46,79 €
price for Spain (gross)
  • ISBN 978-3-030-02603-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
A Pythagorean Introduction to Number Theory
Book Subtitle
Right Triangles, Sums of Squares, and Arithmetic
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-02604-2
DOI
10.1007/978-3-030-02604-2
Hardcover ISBN
978-3-030-02603-5
Series ISSN
0172-6056
Edition Number
1
Number of Pages
XVIII, 279
Number of Illustrations
15 b/w illustrations, 9 illustrations in colour
Topics