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A Friendly Introduction to Number Theory
ISBN: 9780132637992 | 0132637995
Edition: 1stFormat: Hardcover
Publisher: Prentice Hall Professional Technical Reference
Pub. Date: 10/1/1996
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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. Pr... MORE
| 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 ... MORE | |
| 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 | |
| Table of Contents provided by Publisher. All Rights Reserved. |
