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The Resource A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic, by Ramin TaklooBighash, (electronic resource)
A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic, by Ramin TaklooBighash, (electronic resource)
Resource Information
The item A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic, by Ramin TaklooBighash, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic, by Ramin TaklooBighash, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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 higherlevel 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
 Language
 eng
 Extent
 XVIII, 279 p. 24 illus., 9 illus. in color.
 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
 Isbn
 9783030026042
 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 TaklooBighash
 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 higherlevel 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
 http://library.link/vocab/creatorName
 TaklooBighash, Ramin
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 G4f8LwTBtZI
 Image bit depth
 0
 LC call number
 QA241247.5
 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 TaklooBighash, (electronic resource)
 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
 10.1007/9783030026042
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783030026042
 Label
 A Pythagorean Introduction to Number Theory : Right Triangles, Sums of Squares, and Arithmetic, by Ramin TaklooBighash, (electronic resource)
 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
 10.1007/9783030026042
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783030026042
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