Hardcover ISBN:  9780883853474 
Product Code:  DOL/41 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9780883859186 
Product Code:  DOL/41.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853474 
eBook: ISBN:  9780883859186 
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:  9780883853474 
Product Code:  DOL/41 
List Price:  $65.00 
MAA Member Price:  $48.75 
AMS Member Price:  $48.75 
eBook ISBN:  9780883859186 
Product Code:  DOL/41.E 
List Price:  $60.00 
MAA Member Price:  $45.00 
AMS Member Price:  $45.00 
Hardcover ISBN:  9780883853474 
eBook ISBN:  9780883859186 
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 

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 halfforgotten 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.

Table of Contents

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


Additional Material

Reviews

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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 Book Details
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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 halfforgotten 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