| Hardcover ISBN: | 978-0-88385-347-4 |
| Product Code: | DOL/41 |
| List Price: | $65.00 |
| MAA Member Price: | $48.75 |
| AMS Member Price: | $48.75 |
| eBook ISBN: | 978-0-88385-918-6 |
| Product Code: | DOL/41.E |
| List Price: | $60.00 |
| MAA Member Price: | $45.00 |
| AMS Member Price: | $45.00 |
| Hardcover ISBN: | 978-0-88385-347-4 |
| eBook: ISBN: | 978-0-88385-918-6 |
| Product Code: | DOL/41.B |
| List Price: | $125.00 $95.00 |
| MAA Member Price: | $93.75 $71.25 |
| AMS Member Price: | $93.75 $71.25 |
| Hardcover ISBN: | 978-0-88385-347-4 |
| Product Code: | DOL/41 |
| List Price: | $65.00 |
| MAA Member Price: | $48.75 |
| AMS Member Price: | $48.75 |
| eBook ISBN: | 978-0-88385-918-6 |
| Product Code: | DOL/41.E |
| List Price: | $60.00 |
| MAA Member Price: | $45.00 |
| AMS Member Price: | $45.00 |
| Hardcover ISBN: | 978-0-88385-347-4 |
| eBook ISBN: | 978-0-88385-918-6 |
| Product Code: | DOL/41.B |
| List Price: | $125.00 $95.00 |
| MAA Member Price: | $93.75 $71.25 |
| AMS Member Price: | $93.75 $71.25 |
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Book DetailsDolciani Mathematical ExpositionsVolume: 41; 2009; 141 pp
A Guide to Elementary Number Theory is a 140- page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through a traditional text, some of which approach 500 pages in length. It will be especially useful to graduate students preparing for the qualifying exams. Though Plato did not quite say, “He is unworthy of the name of man who does not know which integers are the sums of two squares”, he came close. This guide can make everyone more worthy.
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Table of Contents
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Chapters
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Chapter 1. Greatest Common Divisors
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Chapter 2. Unique Factorization
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Chapter 3. Linear Diophantine Equations
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Chapter 4. Congruences
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Chapter 5. Linear Congruences
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Chapter 6. The Chinese Remainder Theorem
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Chapter 7. Fermat’s Theorem
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Chapter 8. Wilson’s Theorem
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Chapter 9. The Number of Divisors of an Integer
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Chapter 10. The Sum of the Divisors of an Integer
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Chapter 11. Amicable Numbers
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Chapter 12. Perfect Numbers
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Chapter 13. Euler’s Theorem and Function
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Chapter 14. Primitive Roots and Orders
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Chapter 15. Decimals
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Chapter 16. Quadratic Congruences
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Chapter 17. Gauss’s Lemma
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Chapter 18. The Quadratic Reciprocity Theorem
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Chapter 19. The Jacobi Symbol
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Chapter 20. Pythagorean Triangles
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Chapter 21. $x^4+y^4\neq z^4$
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Chapter 22. Sums of Two Squares
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Chapter 23. Sums of Three Squares
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Chapter 24. Sums of Four Squares
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Chapter 25. Waring’s Problem
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Chapter 26. Pell’s Equation
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Chapter 27. Continued Fractions
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Chapter 28. Multigrades
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Chapter 29. Carmichael Numbers
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Chapter 30. Sophie Germain Primes
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Chapter 31. The Group of Multiplicative Functions
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Chapter 32. Bounds for $\pi (x)$
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Chapter 33. The Sum of the Reciprocals of the Primes
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Chapter 34. The Riemann Hypothesis
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Chapter 35. The Prime Number Theorem
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Chapter 36. The abc Conjecture
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Chapter 37. Factorization and Testing for Primes
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Chapter 38. Algebraic and Transcendental Numbers
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Chapter 39. Unsolved Problems
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Additional Material
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Reviews
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Anyone who wishes to learn what elementary number theory is about and some of its important, yet open, questions will not find a better resource.The author provides the basic pertinent definitions and theorems in elementary number theory, ranging from greatest common divisors to quadratic recipocity to Waring's problems. A valuable resource for any student especially graduate students preparing for qualifying exams.
J. T. Zerger, Choice Magazine -
This is one of the books in the MAA Guides series, others include A Guide to Complex Variables, Real Variables, and Topology, etc. Since this is a small book, the book review must be short. What we would like to say is that this is a very nice book for anyone interested in number theory. However, if you want to know more about number theory you can read this book first, make yourself familiar with the basic concepts and ideas of number theory, then read Baker's introductory book or Hardy's comprehensive book.
Song Yan, Sigact News
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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
A Guide to Elementary Number Theory is a 140- page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through a traditional text, some of which approach 500 pages in length. It will be especially useful to graduate students preparing for the qualifying exams. Though Plato did not quite say, “He is unworthy of the name of man who does not know which integers are the sums of two squares”, he came close. This guide can make everyone more worthy.
-
Chapters
-
Chapter 1. Greatest Common Divisors
-
Chapter 2. Unique Factorization
-
Chapter 3. Linear Diophantine Equations
-
Chapter 4. Congruences
-
Chapter 5. Linear Congruences
-
Chapter 6. The Chinese Remainder Theorem
-
Chapter 7. Fermat’s Theorem
-
Chapter 8. Wilson’s Theorem
-
Chapter 9. The Number of Divisors of an Integer
-
Chapter 10. The Sum of the Divisors of an Integer
-
Chapter 11. Amicable Numbers
-
Chapter 12. Perfect Numbers
-
Chapter 13. Euler’s Theorem and Function
-
Chapter 14. Primitive Roots and Orders
-
Chapter 15. Decimals
-
Chapter 16. Quadratic Congruences
-
Chapter 17. Gauss’s Lemma
-
Chapter 18. The Quadratic Reciprocity Theorem
-
Chapter 19. The Jacobi Symbol
-
Chapter 20. Pythagorean Triangles
-
Chapter 21. $x^4+y^4\neq z^4$
-
Chapter 22. Sums of Two Squares
-
Chapter 23. Sums of Three Squares
-
Chapter 24. Sums of Four Squares
-
Chapter 25. Waring’s Problem
-
Chapter 26. Pell’s Equation
-
Chapter 27. Continued Fractions
-
Chapter 28. Multigrades
-
Chapter 29. Carmichael Numbers
-
Chapter 30. Sophie Germain Primes
-
Chapter 31. The Group of Multiplicative Functions
-
Chapter 32. Bounds for $\pi (x)$
-
Chapter 33. The Sum of the Reciprocals of the Primes
-
Chapter 34. The Riemann Hypothesis
-
Chapter 35. The Prime Number Theorem
-
Chapter 36. The abc Conjecture
-
Chapter 37. Factorization and Testing for Primes
-
Chapter 38. Algebraic and Transcendental Numbers
-
Chapter 39. Unsolved Problems
-
Anyone who wishes to learn what elementary number theory is about and some of its important, yet open, questions will not find a better resource.The author provides the basic pertinent definitions and theorems in elementary number theory, ranging from greatest common divisors to quadratic recipocity to Waring's problems. A valuable resource for any student especially graduate students preparing for qualifying exams.
J. T. Zerger, Choice Magazine -
This is one of the books in the MAA Guides series, others include A Guide to Complex Variables, Real Variables, and Topology, etc. Since this is a small book, the book review must be short. What we would like to say is that this is a very nice book for anyone interested in number theory. However, if you want to know more about number theory you can read this book first, make yourself familiar with the basic concepts and ideas of number theory, then read Baker's introductory book or Hardy's comprehensive book.
Song Yan, Sigact News
