A Friendly Introduction To Number Theory

Hardcover | January 18, 2012

byJoseph H. Silverman

not yet rated|write a review

A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce readers to the overall themes and methodology of mathematics through the detailed study of one particular facet—number theory. Starting with nothing more than basic high school algebra, readers are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.

Pricing and Purchase Info

$199.95

Ships within 1-2 weeks
Ships free on orders over $25

From the Publisher

A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce readers to the overall themes and methodology of mathematics through the detailed study of one particular facet—number theory. Starting with nothing more than basic high school algebra, readers are gradually led to the point of actively performing mat...

Joseph H. Silverman is a Professor of Mathematics at Brown University. He received his Sc.B. at Brown and his Ph.D. at Harvard, after which he held positions at MIT and Boston University before joining the Brown faculty in 1988. He has published more than 100 peer-reviewed research articles and seven books in the fields of number theor...

other books by Joseph H. Silverman

Advanced Topics in the Arithmetic of Elliptic Curves
Advanced Topics in the Arithmetic of Elliptic Curves

Kobo ebook|Dec 1 2013

$45.59 online$59.13list price(save 22%)
The Arithmetic of Elliptic Curves
The Arithmetic of Elliptic Curves

Kobo ebook|Apr 20 2009

$50.59 online$65.71list price(save 23%)
An Introduction to Mathematical Cryptography
An Introduction to Mathematical Cryptography

Kobo ebook|Sep 11 2014

$67.59 online$87.76list price(save 22%)
see all books by Joseph H. Silverman
Format:HardcoverDimensions:432 pages, 9.1 × 6.2 × 1.1 inPublished:January 18, 2012Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0321816196

ISBN - 13:9780321816191

Look for similar items by category:

Customer Reviews of A Friendly Introduction To Number Theory

Reviews

Extra Content

Table of Contents

Preface

Flowchart of Chapter Dependencies

Introduction

1. What Is Number Theory?

2. Pythagorean Triples

3. Pythagorean Triples and the Unit Circle

4. Sums of Higher Powers and Fermat’s Last Theorem

5. Divisibility and the Greatest Common Divisor

6. Linear Equations and the Greatest Common Divisor

7. Factorization and the Fundamental Theorem of Arithmetic

8. Congruences

9. Congruences, Powers, and Fermat’s Little Theorem

10. Congruences, Powers, and Euler’s Formula

11. Euler’s Phi Function and the Chinese Remainder Theorem

12. Prime Numbers

13. Counting Primes

14. Mersenne Primes

15. Mersenne Primes and Perfect Numbers

16. Powers Modulo m and Successive Squaring

17. Computing kth Roots Modulo m

18. Powers, Roots, and “Unbreakable” Codes

19. Primality Testing and Carmichael Numbers

20. Squares Modulo p

21. Is -1 a Square Modulo p? Is 2?

22. Quadratic Reciprocity

23. Proof of Quadratic Reciprocity

24. Which Primes Are Sums of Two Squares?

25. Which Numbers Are Sums of Two Squares?

26. As Easy as One, Two, Three

27. Euler’s Phi Function and Sums of Divisors

28. Powers Modulo p and Primitive Roots

29. Primitive Roots and Indices

30. The Equation X 4 + Y 4 = Z 4

31. Square–Triangular Numbers Revisited

32. Pell’s Equation

33. Diophantine Approximation

34. Diophantine Approximation and Pell’s Equation

35. Number Theory and Imaginary Numbers

36. The Gaussian Integers and Unique Factorization

37. Irrational Numbers and Transcendental Numbers

38. Binomial Coefficients and Pascal’s Triangle

39. Fibonacci’s Rabbits and Linear Recurrence Sequences

40. Oh, What a Beautiful Function

41. Cubic Curves and Elliptic Curves

42. Elliptic Curves with Few Rational Points

43. Points on Elliptic Curves Modulo p

44. Torsion Collections Modulo p and Bad Primes

45. Defect Bounds and Modularity Patterns

46. Elliptic Curves and Fermat’s Last Theorem

 

Further Reading

Index

 

*47. The Topsy-Turvey World of Continued Fractions [online]

*48. Continued Fractions, Square Roots, and Pell’s Equation [online]

*49. Generating Functions [online]

*50. Sums of Powers [online]

*A. Factorization of Small Composite Integers [online]

*B. A List of Primes [online]

 

*These chapters are available online.