| Hardcover ISBN: | 978-1-4704-4348-1 |
| Product Code: | TEXT/39 |
| List Price: | $75.00 |
| MAA Member Price: | $56.25 |
| AMS Member Price: | $56.25 |
| eBook ISBN: | 978-1-4704-4684-0 |
| Product Code: | TEXT/39.E |
| List Price: | $69.00 |
| MAA Member Price: | $51.75 |
| AMS Member Price: | $51.75 |
| Hardcover ISBN: | 978-1-4704-4348-1 |
| eBook: ISBN: | 978-1-4704-4684-0 |
| Product Code: | TEXT/39.B |
| List Price: | $144.00 $109.50 |
| MAA Member Price: | $108.00 $82.13 |
| AMS Member Price: | $108.00 $82.13 |
| Hardcover ISBN: | 978-1-4704-4348-1 |
| Product Code: | TEXT/39 |
| List Price: | $75.00 |
| MAA Member Price: | $56.25 |
| AMS Member Price: | $56.25 |
| eBook ISBN: | 978-1-4704-4684-0 |
| Product Code: | TEXT/39.E |
| List Price: | $69.00 |
| MAA Member Price: | $51.75 |
| AMS Member Price: | $51.75 |
| Hardcover ISBN: | 978-1-4704-4348-1 |
| eBook ISBN: | 978-1-4704-4684-0 |
| Product Code: | TEXT/39.B |
| List Price: | $144.00 $109.50 |
| MAA Member Price: | $108.00 $82.13 |
| AMS Member Price: | $108.00 $82.13 |
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Book DetailsAMS/MAA TextbooksVolume: 39; 2018; 283 ppMSC: Primary 11
A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well prepared by this text for a second-semester course focusing on algebraic number theory. The approach throughout is geometric and intuitive; there are over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. There are also nine substantial student projects on topics not usually covered in a first-semester course, including Bernoulli numbers and polynomials, geometric approaches to number theory, the \(p\)-adic numbers, quadratic extensions of the integers, and arithmetic generating functions.
Ancillaries:
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Table of Contents
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Chapters
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Chapter 1. The integers, $\mathbb {Z}$
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Chapter 2. Modular arithmetic in $\mathbb {Z}/m\mathbb {Z}$
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Chapter 3. Quadratic extensions of the integers, $\mathbb {Z}[\sqrt {d}]$
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Chapter 4. An interlude of analytic number theory
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Chapter 5. Quadratic residues
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Chapter 6. Further topics
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Appendix A. Tables
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Appendix B. Projects
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Additional Material
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Reviews
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[The book] weaves a path through various interesting topics and shows how they are connected and can be extended.
Allen Stenger, MAA Reviews
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseInstructor's Solutions Manual – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a courseAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
A well-written, inviting textbook designed for a one-semester, junior-level course in elementary number theory. The intended audience will have had exposure to proof writing, but not necessarily to abstract algebra. That audience will be well prepared by this text for a second-semester course focusing on algebraic number theory. The approach throughout is geometric and intuitive; there are over 400 carefully designed exercises, which include a balance of calculations, conjectures, and proofs. There are also nine substantial student projects on topics not usually covered in a first-semester course, including Bernoulli numbers and polynomials, geometric approaches to number theory, the \(p\)-adic numbers, quadratic extensions of the integers, and arithmetic generating functions.
Ancillaries:
-
Chapters
-
Chapter 1. The integers, $\mathbb {Z}$
-
Chapter 2. Modular arithmetic in $\mathbb {Z}/m\mathbb {Z}$
-
Chapter 3. Quadratic extensions of the integers, $\mathbb {Z}[\sqrt {d}]$
-
Chapter 4. An interlude of analytic number theory
-
Chapter 5. Quadratic residues
-
Chapter 6. Further topics
-
Appendix A. Tables
-
Appendix B. Projects
-
[The book] weaves a path through various interesting topics and shows how they are connected and can be extended.
Allen Stenger, MAA Reviews
