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

Takloo-Bighash, Ramin

ISBN 10: 3030805298 / ISBN 13: 9783030805296

Verlag: Springer, 2021

Beschreibung

PRINT ON DEMAND. Bestandsnummer des Verkäufers 18387760128

Bibliografische Details

Titel: A Pythagorean Introduction to Number Theory:...

Verlag: Springer

Erscheinungsdatum: 2021

Einband: Softcover

Zustand: New

Über diesen Titel

Inhaltsangabe:

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.

Über die Autorin bzw. den 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.