Applied Number Theory

Mehr zum Buch

This textbook bridges basic number theory and recent advances in applied number theory, providing a unified account of four major application areas: cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation. It highlights the connections between these fields. Number theory, often referred to as the queen of mathematics by Carl-Friedrich Gauss, is celebrated for its beauty, elegant results, and proofs. While historically limited in real-life applications, it is now integral to everyday technologies such as supermarket bar code scanners, GPS systems, and online banking. The book begins with an introductory course on number theory in Chapter 1, making it accessible for undergraduates. Chapters 2-5 delve into the four main application areas and present advanced results without proofs, requiring more sophisticated mathematical skills. The final chapter reviews additional applications, including check-digit systems, quantum computation, and raster-graphics memory organization. This resource is valuable for upper-level undergraduates, graduates, and researchers in number theory.