Friendly Introduction to Number Theory

ISBN-10: 0321816196
ISBN-13: 9780321816191
Edition: 4th 2013 (Revised)
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Description: A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce readers to the overall themes and methodology of mathematics through the detailed study of one particular facet number theory. Starting with nothing more than basic  More...

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Book details

List price: $99.99
Edition: 4th
Copyright year: 2013
Publisher: Pearson Education, Limited
Publication date: 1/18/2012
Binding: Hardcover
Pages: 432
Size: 6.50" wide x 9.50" long x 1.25" tall
Weight: 2.464

A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce readers 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, readers 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.

Preface
Flowchart of Chapter Dependencies
Introduction
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 Numbers
Powers Modulo m and Successive Squaring
Computing k<sup>th</sup> Roots Modulo m
Powers, Roots, and "Unbreakable" Codes
Primality Testing and Carmichael Numbers
Squares Modulo p
Is-1 a Square Modulo p? Is 2?
Quadratic Reciprocity
Proof of Quadratic Reciprocity
Which Primes Are Sums of Two Squares?
Which Numbers Are Sums of Two Squares?
As Easy as One, Two, Three
Euler's Phi Function and Sums of Divisors
Powers Modulo p and Primitive Roots
Primitive Roots and Indices
The Equation X<sup>4</sup>+Y<sup>4</sup>=Z<sup>4</sup>
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
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
Index
The Topsy-Turvy World of Continued Fractions [online]
Continued Fractions and Pell's Equation [online]
Generating Functions [online]
Sums of Powers [online]
Factorization of Small Composite Integers [online]
A List of Primes [online]

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