Friendly Introduction to Number Theory

ISBN-10: 0131861379
ISBN-13: 9780131861374
Edition: 3rd 2006 (Revised)
Authors: Joseph Silverman
List price: $126.67
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Description: Starting with nothing more than basic high school algebra, this volume leads readers gradually from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. Features an  More...

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Book details

List price: $126.67
Edition: 3rd
Copyright year: 2006
Publisher: Prentice Hall PTR
Publication date: 3/21/2005
Binding: Hardcover
Pages: 448
Size: 6.00" wide x 9.00" long x 0.75" tall
Weight: 1.496
Language: English

Starting with nothing more than basic high school algebra, this volume leads readers gradually from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. Features an informal writing style and includes many numerical examples. Emphasizes the methods used for proving theorems rather than specific results. Includes a 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. Provides a new chapter that introduces the theory of continued fractions. Includes a new chapter on ldquo;Continued Fractions, Square Roots and Pellrsquo;s Equation.rdquo; Contains additional historical material, including material on Pellrsquo;s equation and the Chinese Remainder Theorem. A useful reference for mathematics teachers.

What Is Number Theory?
Pythagorean Triples
Pythagorean Triples and the Unit Circle
Sums of Higher Powers and Fermat's Last Theorem
Divisibility and the Greatest Common Divisor
Linear Equations and the Greatest Common Divisor
Factorization and the Fundamental Theorem of Arithmetic
Congruences
Congruences, Powers, and Fermat's Little Theorem
Congruences, Powers, and Euler's Formula
Euler's Phi Function and the Chinese Remainder Theorem
Prime Numbers
Counting Primes
Mersenne Primes
Mersenne Primes and Perfect Numbers8
Powers Modulo m and Successive Squaring
Computing kth Roots Modulo m
Powers, Roots, and "Unbreakable" Codes
Primality Testing and Carmichael Numbers
Euler's Phi Function and Sums of Divisors
Powers Modulo p and Primitive Roots
Primitive Roots and Indices
Squares Modulo p
Is -1 a Square Modulo p? Is 2?
Quadratic Reciprocity
Which Primes Are Sums of Two Squares?
Which Numbers Are Sums of Two Squares?
The Equation X4 + Y 4 = Z4
Square-Triangular Numbers Revisited
Pell's Equation
Diophantine Approximation
Diophantine Approximation and Pell's Equation
Number Theory and Imaginary Numbers
The Gaussian Integers and Unique Factorization
Irrational Numbers and Transcendental Numbers
Binomial Coefficients and Pascal's Triangle
Fibonacci's Rabbits and Linear Recurrence Sequences
Oh, What a Beautiful Function
The Topsy-Turvy World of Continued Fractions
Continued Fractions, Square Roots and Pell's Equation
Generating Functions
Sums of Powers
Cubic Curves and Elliptic Curves
Elliptic Curves with Few Rational Points
Points on Elliptic Curves Modulo p
Torsion Collections Modulo p and Bad Primes
Defect Bounds and Modularity Patterns
Elliptic Curves and Fermat's Last Theorem
Further Reading
Factorization of Small Composite Integers
A List of Primes

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