
Friendly Introduction to Number Theory, A (Classic Version), 4th edition
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Overview
Hallmark features of this title
- 50 short chapters provide flexibility and options for instructors and students. A flowchart of chapter dependencies is included.
- 5 basic steps are emphasized throughout the text to help readers develop a robust thought process: Experimentation, pattern recognition, hypothesis formation, hypothesis testing, and formal proof.
- RSA cryptosystem, elliptic curves, and Fermat's Last Theorem are featured, showing the real-life applications of mathematics.
Published by Pearson (May 24th 2023) - Copyright © 2023
ISBN-13: 9780137981175
Subject: Advanced Math
Category: Number Theory
Table of contents
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 kth 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 X4 + Y4 = 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
- 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
- The Topsy-Turvey World of Continued Fractions [online]
- Continued Fractions, Square Roots, and Pell’s Equation [online]
- Generating Functions [online]
- Sums of Powers [online]
Further Reading
Index
A. Factorization of Small Composite Integers [online]
B. A List of Primes [online]
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