عنوان

A Pythagorean introduction to number theory :

شابک

3030026035

شابک

9783030026035

شابک اشتباه

9783030026042

شماره

b623795

عنوان اصلي

A Pythagorean introduction to number theory :

نام عام مواد

[Book]

ساير اطلاعات عنواني

right triangles, sums of squares, and arithmetic /

نام نخستين پديدآور

Ramin Takloo-Bighash.

نام خاص و کميت اثر

xviii, 279 pages :

ساير جزييات

illustrations (some color) ;

ابعاد

25 cm

عنوان فروست

Undergraduate texts in mathematics,

شاپا ي ISSN فروست

0172-6056

متن يادداشت

Includes bibliographical references (pages 271-275) and index.

متن يادداشت

Part I Foundational Material -- 1. Introduction -- 2. Basic number theory -- 3. Integral solutions to the Pythagorean Equation -- 4. What integers are areas of right triangles? -- 5. What numbers are the edges of a right triangle? -- 6. Primes of the form 4k+1 -- 7. Gauss sums, Quadratic Reciprocity, and the Jacobi symbol -- Part II Advanced Topics -- 8. Counting Pythagorean triples modulo an integer -- 9. How many lattice points are there on a circle or a sphere? -- 10. What about geometry? -- 11. Another proof of the four squares theorem -- 12. Quadratic forms and sums of squares -- 13. How many Pythagorean triples are there? -- 14. How are rational points distributed, really? -- Appendix A. Background -- Appendix B. Algebraic integers -- Appendix C. SageMath.

بدون عنوان

0

متن يادداشت

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.--

عنوان

Pythagorean introduction to number theory.

شماره استاندارد بين المللي کتاب و موسيقي

9783030026042

موضوع مستند نشده

Number theory.

موضوع مستند نشده

Pythagorean theorem.

موضوع مستند نشده

Number theory.

موضوع مستند نشده

Pythagorean theorem.

موضوع مستند نشده

QA

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Takloo-Bighash, Ramin

تاريخ عمليات

20201221082914.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

کد کاربرگه

270410

تكميل شده

Y