| Softcover ISBN: | 978-1-4704-4398-6 |
| Product Code: | CLRM/55 |
| List Price: | $59.00 |
| MAA Member Price: | $44.25 |
| AMS Member Price: | $44.25 |
| eBook ISBN: | 978-1-4704-4846-2 |
| Product Code: | CLRM/55.E |
| List Price: | $55.00 |
| MAA Member Price: | $41.25 |
| AMS Member Price: | $41.25 |
| Softcover ISBN: | 978-1-4704-4398-6 |
| eBook: ISBN: | 978-1-4704-4846-2 |
| Product Code: | CLRM/55.B |
| List Price: | $114.00 $86.50 |
| MAA Member Price: | $85.50 $64.88 |
| AMS Member Price: | $85.50 $64.88 |
| Softcover ISBN: | 978-1-4704-4398-6 |
| Product Code: | CLRM/55 |
| List Price: | $59.00 |
| MAA Member Price: | $44.25 |
| AMS Member Price: | $44.25 |
| eBook ISBN: | 978-1-4704-4846-2 |
| Product Code: | CLRM/55.E |
| List Price: | $55.00 |
| MAA Member Price: | $41.25 |
| AMS Member Price: | $41.25 |
| Softcover ISBN: | 978-1-4704-4398-6 |
| eBook ISBN: | 978-1-4704-4846-2 |
| Product Code: | CLRM/55.B |
| List Price: | $114.00 $86.50 |
| MAA Member Price: | $85.50 $64.88 |
| AMS Member Price: | $85.50 $64.88 |
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Book DetailsClassroom Resource MaterialsVolume: 55; 2018; 153 ppMSC: Primary 11
Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. Author Roger Nelsen is a long-time contributor of “Proofs Without Words” in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press.
ReadershipUndergraduate students, high school students, and teachers interested in number theory and visualization.
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Table of Contents
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Chapters
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Chapter 1. Figurate numbers
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Chapter 2. Congruence
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Chapter 3. Diophantine equations
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Chapter 4, Pythagorean triples
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Chapter 5. Irrational numbers
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Chapter 6. Fibonacci and Lucas numbers
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Chapter 7. Perfect numbers
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Solutions to the exercises
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Additional Material
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Reviews
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The starting point for this book was the author's observation that many number theory texts contain few figures. He wrote an article for Math Horizons in 2008 that showed ways to use figures (the article was reprinted in the book "Biscuits of Number Theory"), and eventually expanded it to the present book. The book starts out with figurate numbers (squares, triangular numbers, etc.) that have an obvious picture, but quickly moves to other areas that we usually don't think of visually. This is not a complete introduction to number theory, but it does cover a good sampling, with something about congruences, Diophantine equations, irrational numbers, perfect numbers, and Fibonacci numbers.
Allen Stenger, MAA Reviews
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. Author Roger Nelsen is a long-time contributor of “Proofs Without Words” in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press.
Undergraduate students, high school students, and teachers interested in number theory and visualization.
-
Chapters
-
Chapter 1. Figurate numbers
-
Chapter 2. Congruence
-
Chapter 3. Diophantine equations
-
Chapter 4, Pythagorean triples
-
Chapter 5. Irrational numbers
-
Chapter 6. Fibonacci and Lucas numbers
-
Chapter 7. Perfect numbers
-
Solutions to the exercises
-
The starting point for this book was the author's observation that many number theory texts contain few figures. He wrote an article for Math Horizons in 2008 that showed ways to use figures (the article was reprinted in the book "Biscuits of Number Theory"), and eventually expanded it to the present book. The book starts out with figurate numbers (squares, triangular numbers, etc.) that have an obvious picture, but quickly moves to other areas that we usually don't think of visually. This is not a complete introduction to number theory, but it does cover a good sampling, with something about congruences, Diophantine equations, irrational numbers, perfect numbers, and Fibonacci numbers.
Allen Stenger, MAA Reviews
