Applied Number Theory by Harald Niederreiter (PDF)

Description

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas.Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc.Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory.Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Beautifully written, well motivated, rigorous and discusses number theory. The quality of the paper, printing and composition of the book is great as well. H. Niederreiter is a world-class researcher in random number generators / numerical distributions, and finite fields, and all of those areas are discussed. Each chapter begins with an amusing limerick. Overall, a perfect book. Rigorous, beautiful subject matter explained by a top authority, motivation and humor. One cannot ask for more.Few books possess the quality this one does. It is an example of lovely exposition. Relative to that, I put it in the same category as “Foundations of Constructive Analysis” by Errett Bishop, “The Art of Computer Programming” by Don Knuth, “Enumerative Combinatorics” by Richard P. Stanley, “Mathematical Logic” by S.C. Kleene, “Principles of Mathematical Analysis” by Walter Rudin, and “Analysis I and II” / “Analytic Function Theory, vol. I and II” by Einar Hille. Possibly a few other books, notably ones by John E. Hopcroft, Al Aho, Robert W Floyd, and Jeffrey D. Ullman.I hope this book becomes more well known, because it is an absolute gem!

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