The Resource A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic, by Ramin Takloo-Bighash, (electronic resource)

A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic, by Ramin Takloo-Bighash, (electronic resource)

Label
A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic
Title
A Pythagorean Introduction to Number Theory
Title remainder
Right Triangles, Sums of Squares, and Arithmetic
Statement of responsibility
by Ramin Takloo-Bighash
Creator
Contributor
Author
Author
Provider
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Takloo-Bighash, Ramin
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
G4f8LwTBtZI
Image bit depth
0
LC call number
QA241-247.5
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Undergraduate Texts in Mathematics,
http://library.link/vocab/subjectName
  • Number theory
  • Number Theory
Label
A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic, by Ramin Takloo-Bighash, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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? -- Part III Appendices -- A. Background -- B. Algebraic integers -- C. SageMath -- References -- Index
Dimensions
unknown
Extent
XVIII, 279 p. 24 illus., 9 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783030026042
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-030-02604-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-030-02604-2
Label
A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic, by Ramin Takloo-Bighash, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
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? -- Part III Appendices -- A. Background -- B. Algebraic integers -- C. SageMath -- References -- Index
Dimensions
unknown
Extent
XVIII, 279 p. 24 illus., 9 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9783030026042
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-030-02604-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-030-02604-2

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