Kategoria BISAC: Mathematics >> Number Theory

In Single Digits, Marc Chamberland takes readers on a fascinating exploration of small numbers, from one to nine, looking at their history, applications, and connections to various areas of mathematics, including number theory, geometry, chaos theory, numerical analysis, and mathematical physics. For instance, why do eight perfect card shuffles leave a standard deck of cards unchanged? And, are there really "six degrees of separation" between all pairs of people? Chamberland explores these questions and covers vast numerical territory, such as illustrating the ways that the number...

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.

Throughout Geometry, Complex Dimensions and Zeta Functions, Second Edition, new results are examined and a new definition of fractality as the presence of nonreal complex dimensions with positive real parts is presented. The new final chapter discusses several new topics and results obtained since the publication of the first edition.

To date, the theoretical development of q-calculus has rested on a non-uniform basis. Generally, the bulky Gasper-Rahman notation was used, but the published works on q-calculus looked different depending on where and by whom they were written. This confusion of tongues not only complicated the theoretical development but also contributed to q-calculus remaining a neglected mathematical field. This book overcomes these problems by introducing a new and interesting notation for q-calculus based on logarithms.For instance, q-hypergeometric functions are now visually clear and easy to trace...

A highly successful presentation of the fundamental concepts of number theory and computer programming

Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced...

Dieses Buch bietet einen historisch orientierten Einstieg in die elementare Zahlentheorie. Es stellt eine solide Basis fur vielfaltige Ausbaumoglichkeiten dar. Besondere Zielsetzungen sind: Elementaritat und Anschaulichkeit, die Berucksichtigung der historischen Entwicklung, Motivation der Begriffe und Verfahren anhand konkreter, aussagekraftiger Beispiele unter Einbezug moderner Werkzeuge (Computeralgebra Systeme, Internet). Als Zusatzmedien werden Computer- und Internet-spezifische Interaktions- und Visualisierungsmoglichkeiten (kostenlos) zur Verfugung gestellt. Das Werk wendet sich an...

The ease of use of the programs in the application to ever more complex cases of disease and pestilence. The lack of need on the part of the student or modelers of mathematics beyond algebra and the lack of need of any prior computer programming experience. The surprising insights that can be gained from initially simple systems models.