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Friendly Introduction to Number Theory, A, 2/E
Joseph H Silverman, Brown University

ISBN-10: 0130309540
ISBN-13: 9780130309549

Publisher: Pearson
Copyright: 2001
Format: Cloth; 400 pp
Published: 01/05/2001

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Description

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

This is an introductory undergraduate text designed to entice non-math 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. The emphasis is on the methods used for proving theorems rather than on specific results.

Features

NEW - 8 new chapters—1) Number Theory and Imaginary Numbers; 2) Gaussian Integers and Unique Factorization; 3) Irrational Numbers and Transcendental Numbers; 4) Fibonacci's Rabbits and Linear Recurrence Sequences; 5) Generating Functions; 6) Sums of Powers; 7) Binomial Coefficients and Pascal's Triangle; and 8) Primality Testing and Carmichael Numbers.

NEW - Many new problems and computer exercises—Over 250 new problems. Problems relocated to the end of each chapter.
- This provides students with more logical flow of information. Ex.___

Low key introduction to Number Theory.
- Allows students to explore an area of math different from standard calculus sequences. Ex.___

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.
- Enables students to see real-life applications of mathematics. Ex.___

Proof of Fermat's Last theorem by Andrew Wiles—Overview provided.
- Gives students an introduction to one of the most significant mathematical achievements of the 20th century. Ex.___

New To This Edition

8 new chapters—1) Number Theory and Imaginary Numbers; 2) Gaussian Integers and Unique Factorization; 3) Irrational Numbers and Transcendental Numbers; 4) Fibonacci's Rabbits and Linear Recurrence Sequences; 5) Generating Functions; 6) Sums of Powers; 7) Binomial Coefficients and Pascal's Triangle; and 8) Primality Testing and Carmichael Numbers.

Many new problems and computer exercises—Over 250 new problems. Problems relocated to the end of each chapter.
- This provides students with more logical flow of information. Ex.___

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.

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. Euler's Phi Function and Sums of Divisors.

20. Powers Modulo p and Primitive Roots.

21. Primitive Roots and Indices.

22. Squares Modulo p.

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

24. Quadratic Reciprocity.

25. Which Primes Are Sums of Two Squares?

26. Which Numbers Are Sums of Two Squares?

27. The Equation X⁴ + Y⁴ = Z⁴.

28. Square-Triangular Numbers Revisited.

29. Pell's Equation.

30. Diophantine Approximation.

31. Diophantine Approximation and Pell's Equation.

32. Primality Testing and Carmichael Numbers

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. Generating Functions.

39. Sums of Powers.

40. Cubic Curves and Elliptic Curves.

41. Elliptic Curves with Few Rational Points.

42. Points on Elliptic Curves Modulo p.

43. Torsion Collections Modulo p and Bad Primes.

44. Defect Bounds and Modularity Patterns.

45. Elliptic Curves and Fermat's Last Theorem.

Further Reading.

Appendix A: Factorization of Small Composite Integers.

Appendix B: List of Primes.

Index.

Courses

Number Theory (Mathematics)

Next Edition(s)

Friendly Introduction to Number Theory, A, 4/E
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©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.
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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.
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Friendly Introduction to Number Theory, A, 2/E