Pearson - Friendly Introduction to Number Theory, A, 3/E

Pearson

Always Learning

Browse by discipline

Humanities & Social Sciences

Math & Science

Professional & Career

Friendly Introduction to Number Theory, A, 3/E
Joseph H. Silverman

ISBN-10: 0131861379
ISBN-13: 9780131861374

Publisher: Pearson
Copyright: 2006
Format: Cloth; 448 pp
Published: 03/21/2005

Customers outside the U.S., click here.

Request a printed exam copy

Email this page to a colleague
Prepare for the First Day of Class
Learn about customization options
Print this page

Print this content

In this section:

Description

For courses in Elementary Number Theory for math majors, for mathematics education students, and for Computer Science students.

This introductory undergraduate text is designed to entice a wide variety of majors into learning some mathematics, while teaching them to think mathematically at the same time. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal 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.

Features

• A low-key introduction to Number Theory – Enables students to explore an area of math different from standard calculus sequences.

• Five basic steps emphasized – Experimentation, pattern recognition, hypothesis formation, hypothesis testing, and formal proof.

– Encourages students to make mathematical discovers on their own through use of open-ended problems. Ex.___

• RSA cryptosystem, elliptic curves, and Fermat's Last Theorem are featured, enabling students to see real-life applications of mathematics.

• Proof of Fermat's Last theorem by Andrew Wiles – Provides overview, introducing students to one of the most significant mathematical achievements of the 20th century.

New To This Edition

• A new chapter that introduces the theory of continued fractions – Includes the recursion formula for convergents and the difference of successive convergents (Ch. 39, “The Topsy-Turvy World of Continued Fractions”)

• New chapter on big-Oh notation and how it is used to describe the growth rate of number theoretic functions and to describe the complexity of algorithms (Ch. 38, “Oh, What a Beautiful Function”).

• A new chapter on “Continued Fractions, Square Roots and Pell’s Equation” (Ch. 40) – A continuation of the previous chapter, inlcuding a discussion of periodicity of continued fractions for quadratic irrationalities and the relationship between such continued fraction and solutions to Pell’s equation.

• Additional historical material – Includes material on Pell’s equation and the Chinese Remainder Theorem.

• New exercises added to existing chapters.

• Some proofs have been rewritten for added clarity.

Table of Contents

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 Numbers8

16. Powers Modulo m and Successive Squaring

17. Computing k^th Roots Modulo m

18. Powers, Roots, and “Unbreakable” Codes

19. Primality Testing and Carmichael Numbers

20. Euler’s Phi Function and Sums of Divisors

21. Powers Modulo p and Primitive Roots

22. Primitive Roots and Indices

23. Squares Modulo p

24. Is —1 a Square Modulo p? Is 2?

25. Quadratic Reciprocity

26. Which Primes Are Sums of Two Squares?

27. Which Numbers Are Sums of Two Squares?

28. The Equation X⁴ + Y ⁴ = Z⁴

29. Square-Triangular Numbers Revisited

30. Pell’s Equation

31. Diophantine Approximation

32. Diophantine Approximation and Pell’s Equation

33. Number Theory and Imaginary Numbers

34. The Gaussian Integers and Unique Factorization

35. Irrational Numbers and Transcendental Numbers

36. Binomial Coefficients and Pascal’s Triangle

37. Fibonacci’s Rabbits and Linear Recurrence Sequences

38. Oh, What a Beautiful Function

39. The Topsy-Turvy World of Continued Fractions

40. Continued Fractions, Square Roots and Pell’s Equation

41. Generating Functions

42. Sums of Powers

43. Cubic Curves and Elliptic Curves

44. Elliptic Curves with Few Rational Points

45. Points on Elliptic Curves Modulo p

46. Torsion Collections Modulo p and Bad Primes

47. Defect Bounds and Modularity Patterns

48. Elliptic Curves and Fermat’s Last Theorem

Further Reading

A. Factorization of Small Composite Integers

B. A List of Primes

Courses

Number Theory (Mathematics)

Next Edition(s)

Friendly Introduction to Number Theory, A, 4/E
Silverman
©2013 | Pearson | Cloth; 432 pp | Instock
ISBN-10: 0321816196 | ISBN-13: 9780321816191
Net price: $95.00 (What's this?)Brief Description |

For one-semester undergraduate courses in Elementary Number Theory.

A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students 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, students 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.
More Info

Print this content

In this section:

Instructor Resources

Downloadable Instructor Resources
Other Instructor Resources

Course & Discipline Resources

For the Mathematics Discipline

Instructor's Solutions Manual (Download only) for Friendly Introduction to Number Theory, A
Silverman
©2007 | Pearson | On-line Supplement | Live
ISBN-10: 0132335506 | ISBN-13: 9780132335508

Show Downloadable Files

More Info

For the Mathematics Discipline

Allied Health Study Card, 2/E
Forshier
©2006 | Pearson | Study Card | Instock
ISBN-10: 0321394747 | ISBN-13: 9780321394743
Net price: $3.00 (What's this?)More Info

Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Pearson | Study Card; 6 pp | Instock
ISBN-10: 0321394763 | ISBN-13: 9780321394767
Net price: $3.00 (What's this?)More Info

Center for Excellence Sticker
Addison Wesley Higher Education Group
©2000 | Pearson | Unknown / Other | Instock
ISBN-10: 0201716275 | ISBN-13: 9780201716276
Suggested retail price: $0.00Net price: $0.00 (What's this?)More Info

Concept Videos: Algebra
Addison-Wesley
©2008 | Pearson | Multiple Media Package | Instock
ISBN-10: 0321517199 | ISBN-13: 9780321517197
Suggested retail price: $36.67Net price: $27.50 (What's this?)More Info

Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008 | Pearson | Multiple Media Package | Instock
ISBN-10: 032151758X | ISBN-13: 9780321517586
Suggested retail price: $36.67Net price: $27.50 (What's this?)More Info

Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997 | Pearson | Paper; 195 pp | Instock
ISBN-10: 0136492037 | ISBN-13: 9780136492030
Net price: $35.85 (What's this?)More Info

Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
Net price: $10.00 (What's this?)More Info

Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000 | Pearson | Paper | Instock
ISBN-10: 0321069188 | ISBN-13: 9780321069184
Net price: $27.50 (What's this?)More Info

Prealgebra Review Workbook
Wheel
©2006 | Pearson | Paper; 300 pp | Instock
ISBN-10: 0321473329 | ISBN-13: 9780321473325
Net price: $27.50 (What's this?)More Info

Review of Algebra, A
Howard
©2002 | Pearson | Paper; 224 pp | Instock
ISBN-10: 0201773473 | ISBN-13: 9780201773477
Net price: $27.50 (What's this?)More Info

Spanish Basic Math Study Card
Leonarte
©2007 | Pearson | Study Card | Instock
ISBN-10: 0321438582 | ISBN-13: 9780321438584
Net price: $3.00 (What's this?)More Info

TestGen All-in-One 2005 Package
Addison-Wesley
©2005 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321334469 | ISBN-13: 9780321334466
Suggested retail price: $0.00Net price: $0.00 (What's this?)More Info

Password:

Forgot login/password? | Need to redeem an access code?

We're sorry!

We don't recognize your login or password. Please try again.

If you continue to have problems, try retrieving your login name password or contacting Customer Technical Support.

We're sorry!

The account you used to log in on the previous website does not contain IRC access.
If you have a separate IRC count, please log in using that login name and password.
If you do not have an IRC account, you canrequest access here

close window

Your access will expire soon.

To ensure uninterrupted service, you should renew your access for this site soon.

Renew now or proceed without renewing.

close window

We're sorry!

Your access to the Instructor Resource Center has expired.

To continue using the IRC, renew your access now.

An internal error has occurred. Please try again.

Instructor Resource Center File Download

This work is protected by local and international copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from this site should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

Cancel

I accept, proceed with download

Print this content

Pearson Higher Education offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students contact your Pearson Higher Education representative.

Friendly Introduction to Number Theory, A, 3/E