Ramin Takloo-Bighash
A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic
A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic
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Excellent- More about A Pythagorean Introduction to Number Theory: Right Triangles, Sums of Squares, and Arithmetic
This textbook introduces elementary number theory through the study of right triangles, inspiring students to ask questions, work through exercises, use technology, and learn about the broader context. It progresses from fundamentals to advanced topics and includes exercises for SageMath. The active process of inquiry and investigation empowers students to understand the foundations of number theory and its ongoing development.
Format: Paperback / softback
Length: 279 pages
Publication date: 24 July 2021
Publisher: Springer Nature Switzerland AG
Right triangles play a central role in this textbook's innovative approach to elementary number theory. Drawing inspiration from the well-known Pythagorean theorem, the author encourages readers to explore natural arithmetic questions related to right triangles. Subsequently, the theory is developed to provide answers to these inquiries. Throughout the text, students are actively engaged through the posing of questions, the completion of exercises, the utilization of technology, and the exploration of the broader context in which these ideas emerged. The first part of the textbook serves as an innovative introduction to elementary number theory, progressing from the fundamentals to advanced topics such as Gauss sums and quadratic reciprocity. The subsequent advanced topics, including counting lattice points and the four squares theorem, offer opportunities for extension or can be used as the foundation for a higher-level course. Numerous exercises are included, many of which are designed for SageMath.
By engaging students in the active process of inquiry and investigation, this textbook imparts valuable insights into the dynamic mathematical process that continues to drive progress in the field of number theory. While a formal prerequisite for the book is experience writing proofs, a background in basic real analysis will enhance the readers' appreciation of the final chapters.
Weight: 462g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030805296
Edition number: 1st ed. 2018
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