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Friendly Introduction to Number Theory, A

ISBN: 9780130309549 | 0130309540
Edition: 2nd
Format: Hardcover
Publisher: Prentice Hall
Pub. Date: 1/1/2001

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SummaryTable of Contents
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.
Prefacev
Introduction1(6)
What Is Number Theory?
7(6)
Pythagorean Triples
... MORE(6)
Pythagorean Triples and the Unit Circle
19(4)
Sums of Higher Powers and Fermat's Last Theorem
23(4)
Divisibility and the Greatest Common Divisor
27(7)
Linear Equations and the Greatest Common Divisor
34(9)
Factorization and the Fundamental Theorem of Arithmetic
43(9)
Congruences
52(6)
Congruences, Powers, and Fermat's Little Theorem
58(6)
Congruences, Powers, and Euler's Formula
64(4)
Euler's Phi Function
68(7)
Prime Numbers
75(7)
Counting Primes
82(6)
Mersenne Primes
88(4)
Mersenne Primes and Perfect Numbers
92(10)
Powers Modulo m and Successive Squaring
102(7)
Computing kth Roots Modulo m
109(4)
Powers, Roots, and ``Unbreakable'' Codes
113(7)
Euler's Phi Function and Sums of Divisors
120(5)
Powers Modulo p and Primitive Roots
125(10)
Primitive Roots and Indices
135(7)
Squares Modulo p
142(8)
Is -- 1 a Square Modulo p? Is 2?
150(11)
Quadratic Reciprocity
161(11)
Which Primes Are Sums of Two Squares?
172(12)
Which Numbers Are Sums of Two Squares?
184(6)
The Equation X4 + Y4 = Z4
190(3)
Square-Triangular Numbers Revisited
193(10)
Pell's Equation
203(5)
Diophantine Approximation
208(9)
Diophantine Approximation and Pell's Equation
217(8)
Primality Testing and Carmichael Numbers
225(11)
Number Theory and Imaginary Numbers
236(14)
The Gaussian Integers and Unique Factorization
250(17)
Irrational Numbers and Transcendental Numbers
267(16)
Binomial Coefficients and Pascal's Triangle
283(11)
Fibonacci's Rabbits and Linear Recurrence Sequences
294(12)
Generating Functions
306(11)
Sums of Powers
317(11)
Cubic Curves and Elliptic Curves
328(13)
Elliptic Curves with Few Rational Points
341(6)
Points on Elliptic Curves Modulo p
347(12)
Torsion Collections Modulo p and Bad Primes
359(4)
Defect Bounds and Modularity Patterns
363(6)
Elliptic Curves and Fermat's Last Theorem
369(2)
Further Reading371(1)
Appendix A. Factorization of Small Composite Integers372(2)
Appendix B. A List of Primes374(3)
Index377

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