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