A Pythagorean Introduction to Number Theory

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.

A Pythagorean Introduction to Number Theory

A Pythagorean Introduction to Number Theory

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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A Pythagorean Introduction to Number Theory
Language: en
Pages: 279
Authors: Ramin Takloo-Bighash
Categories: Mathematics
Type: BOOK - Published: 2018-11-26 - Publisher: Springer

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
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Language: en
Pages: 376
Authors: Benjamin Hutz
Categories: Number theory
Type: BOOK - Published: 2018-04-17 - Publisher: American Mathematical Soc.

This book presents material suitable for an undergraduate course in elementary number theory from a computational perspective. It seeks to not only introduce students to the standard topics in elementary number theory, such as prime factorization and modular arithmetic, but also to develop their ability to formulate and test precise
A Friendly Introduction to Number Theory
Language: en
Pages: 434
Authors: Joseph H. Silverman
Categories: Mathematics
Type: BOOK - Published: 2006 - Publisher: Prentice Hall

Starting with nothing more than basic high school algebra, this volume leads readers gradually from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. Features an informal writing style and includes many numerical examples. Emphasizes the methods used for proving theorems
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Language: en
Pages: 536
Authors: Anthony Vazzana, Martin Erickson, David Garth
Categories: Mathematics
Type: BOOK - Published: 2007-10-30 - Publisher: CRC Press

One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array
Friendly Introduction to Number Theory, A,
Language: en
Pages: 432
Authors: Joseph H. Silverman
Categories: Education
Type: BOOK - Published: 2014-01-14 - Publisher: Pearson Higher Ed

This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce readers to the overall themes and methodology of mathematics through