Fundamental Number Theory with Applications

This update presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. This edition removes all advanced material to be even more accessible in scope; adds new fundamental material, including partition theory, generating functions, and combinatorial number theory; and expands coverage of random number generation, Diophantine analysis, and additive number theory. It also includes more applications to cryptography, primality testing, and factoring as well as nearly 70 biographies of major contributors to the field. Appendices of background material and almost 400 exercises supplement the coverage.

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.

Autorentext
Mollin, Richard A.

Zusammenfassung

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.

Inhalt
Preface. Arithmetic of the Integers. Modular Arithmetic. Primitive Roots. Quadratic Residues. Simple Continued Fractions and Diophantine Approximation. AdditivitySums of Powers. Diophantine Equations. Appendices. Solutions to Odd-Numbered Exercises. Bibliography. List of Symbols. Index.