Author: Kira ScheibelhutPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Polynomials that are Integer-Valued on the Fibonacci Numbers
Author: Kira ScheibelhutThe INTEGER-VALUED POLYNOMIALS ON LUCAS NUMBERS.
Author: Amitabh Kumer HalderPublisher:
ISBN:
Category :
Languages : en
Pages : 0
Book Description
An integer-valued polynomial on a subset, S, of the set of integers, Z, is a polynomial f(x) 2 Q[x] such that f(S) Z. The collection, Int(S;Z), of such integer-valued polynomials forms a ring with many interesting properties. The concept of p-ordering and the associated p-sequence due to Bhargava [2] is used for nding integer-valued polynomials on any subset, S, of Z. In this thesis, we concentrate on extending the work of Keith Johnson and Kira Scheibelhut [14] for the case S = L, the Lucas numbers, where they work on integervalued polynomials on S = F, Fibonacci numbers. We also study integer-valued polynomials on the general 3 term recursion sequence, G, of integers for a given pair of initial values with some interesting properties. The results are well-agreed with those of [14].
Integer-valued Polynomials
Author: Paul-Jean CahenPublisher: American Mathematical Soc.
ISBN: 0821803883
Category : Mathematics
Languages : en
Pages : 345
Book Description
Integer-valued polynomials on the ring of integers have been known for a long time and have been used in calculus. Polya and Ostrowski generalized this notion to rings of integers of number fields. More generally still, one may consider a domain $D$ and the polynomials (with coefficients in its quotient field) mapping $D$ into itself. They form a $D$-algebra - that is, a $D$-module with a ring structure. Appearing in a very natural fashion, this ring possesses quite a rich structure, and the very numerous questions it raises allow a thorough exploration of commutative algebra. Here is the first book devoted entirely to this topic. This book features: thorough reviews of many published works; self-contained text with complete proofs; and numerous exercises.
Fibonacci and Lucas Numbers with Applications, Volume 2
Author: Thomas KoshyPublisher: John Wiley & Sons
ISBN: 1118742141
Category : Mathematics
Languages : en
Pages : 755
Book Description
Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshev polynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and professional mathematicians. As in Volume I, Volume II focuses on problem-solving techniques such as pattern recognition; conjecturing; proof-techniques, and applications. It offers a wealth of delightful opportunities to explore and experiment, as well as plentiful material for group discussions, seminars, presentations, and collaboration. In addition, the material covered in this book promotes intellectual curiosity, creativity, and ingenuity. Volume II features: A wealth of examples, applications, and exercises of varying degrees of difficulty and sophistication. Numerous combinatorial and graph-theoretic proofs and techniques. A uniquely thorough discussion of gibonacci subfamilies, and the fascinating relationships that link them. Examples of the beauty, power, and ubiquity of the extended gibonacci family. An introduction to tribonacci polynomials and numbers, and their combinatorial and graph-theoretic models. Abbreviated solutions provided for all odd-numbered exercises. Extensive references for further study. This volume will be a valuable resource for upper-level undergraduates and graduate students, as well as for independent study projects, undergraduate and graduate theses. It is the most comprehensive work available, a welcome addition for gibonacci enthusiasts in computer science, electrical engineering, and physics, as well as for creative and curious amateurs.
Applications of Fibonacci Numbers
Author: G.E. BergumPublisher: Springer Science & Business Media
ISBN: 9401150206
Category : Mathematics
Languages : en
Pages : 500
Book Description
Proceedings of `The Seventh International Research Conference on Fibonacci Numbers and Their Applications', Technische Universität, Graz, Austria, July 15-19, 1996
Commutative Algebra
Author: Marco FontanaPublisher: Springer
ISBN: 1493909258
Category : Mathematics
Languages : en
Pages : 372
Book Description
This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non- Noetherian ring theory as well as integer-valued polynomials and functions. Specific topics include: · Homological dimensions of Prüfer-like rings · Quasi complete rings · Total graphs of rings · Properties of prime ideals over various rings · Bases for integer-valued polynomials · Boolean subrings · The portable property of domains · Probabilistic topics in Intn(D) · Closure operations in Zariski-Riemann spaces of valuation domains · Stability of domains · Non-Noetherian grade · Homotopy in integer-valued polynomials · Localizations of global properties of rings · Topics in integral closure · Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees of the conference in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Graz conference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere.
Fibonacci and Lucas Numbers with Applications, Volume 2
Author: Thomas KoshyPublisher: John Wiley & Sons
ISBN: 1118742087
Category : Mathematics
Languages : en
Pages : 752
Book Description
Volume II provides an advanced approach to the extended gibonacci family, which includes Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Vieta, Vieta-Lucas, and Chebyshev polynomials of both kinds. This volume offers a uniquely unified, extensive, and historical approach that will appeal to both students and professional mathematicians. As in Volume I, Volume II focuses on problem-solving techniques such as pattern recognition; conjecturing; proof-techniques, and applications. It offers a wealth of delightful opportunities to explore and experiment, as well as plentiful material for group discussions, seminars, presentations, and collaboration. In addition, the material covered in this book promotes intellectual curiosity, creativity, and ingenuity. Volume II features: A wealth of examples, applications, and exercises of varying degrees of difficulty and sophistication. Numerous combinatorial and graph-theoretic proofs and techniques. A uniquely thorough discussion of gibonacci subfamilies, and the fascinating relationships that link them. Examples of the beauty, power, and ubiquity of the extended gibonacci family. An introduction to tribonacci polynomials and numbers, and their combinatorial and graph-theoretic models. Abbreviated solutions provided for all odd-numbered exercises. Extensive references for further study. This volume will be a valuable resource for upper-level undergraduates and graduate students, as well as for independent study projects, undergraduate and graduate theses. It is the most comprehensive work available, a welcome addition for gibonacci enthusiasts in computer science, electrical engineering, and physics, as well as for creative and curious amateurs.
Fibonacci’s Liber Abaci
Author: Laurence SiglerPublisher: Springer Science & Business Media
ISBN: 1461300797
Category : Mathematics
Languages : en
Pages : 736
Book Description
First published in 1202, Fibonacci’s Liber Abaci was one of the most important books on mathematics in the Middle Ages, introducing Arabic numerals and methods throughout Europe. This is the first translation into a modern European language, of interest not only to historians of science but also to all mathematicians and mathematics teachers interested in the origins of their methods.
Biscuits of Number Theory
Author: Arthur T. BenjaminPublisher: American Mathematical Soc.
ISBN: 088385340X
Category : Mathematics
Languages : en
Pages : 311
Book Description
In Biscuits of Number Theory, the editors have chosen articles that are exceptionally well-written and that can be appreciated by anyone who has taken (or is taking) a first course in number theory. This book could be used as a textbook supplement for a number theory course, especially one that requires students to write papers or do outside reading. The editors give examples of some of the possibilities. The collection is divided into seven chapters: Arithmetic; Primes; Irrationality and Continued Fractions; Sums of Squares and Polygonal Numbers; Fibonacci Numbers; Number-Theoretic Functions; and Elliptic Curves, Cubes and Fermat's Last Theorem. As with any anthology, you don't have to read the Biscuits in order. Dip into them anywhere: pick something from the table of contents that strikes your fancy, and have at it. If the end of an article leaves you wondering what happens next, then by all means dive in and do some research. You just might discover something new!
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