Applied Number Theory (PDF)
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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 fourmain 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.
Arne Winterhof: Edmund and Rosa Hlawka Prize 2004; Advancement Award of the Austrian Mathematical Society 2010
- Autoren: Harald Niederreiter , Arne Winterhof
- 2015, 1st ed. 2015, 442 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319223216
- ISBN-13: 9783319223216
- Erscheinungsdatum: 01.09.2015
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- Größe: 4.80 MB
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“The book is intended to be usable as a text … . It would also be useful for those of us who received our training in number theory in the days before it had any applications and wanted to find out about them. … The writing is clear and lively. … The book is pleasant to the eyes, and in the hands. … It is an estimable book that I hope is successful.” (Underwood Dudley, MAA Reviews, maa.org, January, 2016)
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