ISBN 9789332535237,A Friendly Introduction to Number Theory

A Friendly Introduction to Number Theory



Pearson Education

Publication Year 2014

ISBN 9789332535237

ISBN-10 933253523X

Paper Back

Number of Pages 480 Pages
Language (English)

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.
Flowchart of Chapter Dependencies
1. What Is Number Theory?
2. Pythagorean Triples
3. Pythagorean Triples and the Unit Circle
4. Sums of Higher Powers and Fermats 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 Fermats Little Theorem
10. Congruences, Powers, and Eulers Formula
11. Eulers 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. Quadratic Reciprocity
22. Proof of Quadratic Reciprocity
23. Which Primes Are Sums of Two Squares?
24. Which Numbers Are Sums of Two Squares?
25. Eulers Phi Function and Sums of Divisors
26. Powers Modulo p and Primitive Roots
27. Primitive Roots and Indices
28. The Equation X4 + Y4 = Z4
29. Square-Triangular Numbers Revisited
30. Pells Equation
31. Diophantine Approximation
32. Diophantine Approximation and Pells Equation
33. Number Theory and Imaginary Numbers
34. The Gaussian Integers and Unique Factorization
35. Irrational Numbers and Transcendental Numbers
36. Binomial Coefficients and Pascals Triangle
37. Fibonaccis Rabbits and Linear Recurrence Sequences
38. Cubic Curves and Elliptic Curves
39. Elliptic Curves with Few Rational Points
40. Points on Elliptic Curves Modulo p
41. Torsion Collections Modulo p and Bad Primes
42. Defect Bounds and Modularity Patterns
43. Elliptic Curves and Fermats Last Theorem