Mollin Fundamental Number Theory with Applications, Second Edition

2. Auflage 2011
ISBN: 978-1-4200-6661-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 384 Seiten

Reihe: Discrete Mathematics and Its Applications

An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.

Zielgruppe

Undergraduates in number theory.

Autoren/Hrsg.

Mollin, Richard A.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik EDV | Informatik Betriebssysteme

Inhaltsverzeichnis

Preface

Arithmetic of the Integers

Induction

Division

Primes

The Chinese Remainder Theorem

Thue’s Theorem

Combinatorial Number Theory

Partitions and Generating Functions

True Primality Tests

Distribution of Primes

Modular Arithmetic

Basic Properties

Modular Perspective

Arithmetic Functions: Euler, Carmichael, and Möbius

Number and Sums of Divisors

The Floor and the Ceiling

Polynomial Congruences

Primality Testing

Cryptology

Primitive Roots

Order

Existence

Indices

Random Number Generation

Public-Key Cryptography

Quadratic Residues

The Legendre Symbol

The Quadratic Reciprocity Law

Factoring

Simple Continued Fractions and Diophantine Approximation

Infinite Simple Continued Fractions

Periodic Simple Continued Fractions

Pell’s Equation and Surds

Continued Fractions and Factoring

Additivity—Sums of Powers

Sums of Two Squares

Sums of Three Squares

Sums of Four Squares

Sums of Cubes

Diophantine Equations

Norm-Form Equations

The Equation ax2 + by2 + cz2 = 0

Bachet’s Equation

Fermat’s Last Theorem

Appendix A: Fundamental Facts

Appendix B: Complexity

Appendix C: Primes = 9547 and Least Primitive Roots

Appendix D: Indices

Appendix E: The ABC Conjecture

Appendix F: Primes Is in P

Solutions to Odd-Numbered Exercises

Bibliography

List of Symbols

Index