Elementary number theory with applications
著者
書誌事項
Elementary number theory with applications
Harcourt/Academic Press, c2002
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
The advent of modern technology has brought a new dimension to the power of number theory: constant practical use. Once considered the purest of pure mathematics, it is used increasingly now in the rapid development of technology in a number of areas, such as art, coding theory, cryptology, computer science, and other necessities of modern life.
Elementary Number Theory with Applications is the fruit of years of dreams and the author's fascination with the subject, encapsulating the beauty, elegance, historical development, and opportunities provided for experimentation and application. This is the only number theory book to show how modular systems can be employed to create beautiful designs, thus linking number theory with both geometry and art. It is also the only number theory book to deal with bar codes, Zip codes, International Standard Book Numbers (ISBN), and European Article Numbers (EAN). Emphasis is on problem-solving strategies (doing experiments, collecting and organizing data, recognizing patterns, and making conjectures). Each section provides a wealth of carefully prepared, well-graded examples and exercises to enhance the readers' understanding and problem-solving skills.
目次
- Fundamentals
- Divisibility Theory
- Canonical Decompositions
- Linear Diophantine Equations and Congruences
- Congruences Applications
- Systems of Linear Congruences
- Three Classical Milestones
- Multiplicative Functions
- Cryptology
- Primitive Roots and Indices
- Quadratic Residues
- Nonlinear Diophantine Equations
- Appendix
- Tables
- References
- Solutions to Odd-Numbered Exercises
- Index
- Credits
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