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A Pythagorean Introduction to Number Theory - Right Triangles, Sums of Squares, and Arithmetic (Paperback, 1st ed. 2018)
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A Pythagorean Introduction to Number Theory - Right Triangles, Sums of Squares, and Arithmetic (Paperback, 1st ed. 2018)
Series: Undergraduate Texts in Mathematics
Expected to ship within 10 - 15 working days
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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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