Integer Sequences
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Integer Sequences
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Author : Masum Billal
language : en
Publisher: Springer Nature
Release Date : 2021-06-18
Integer Sequences written by Masum Billal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Mathematics categories.
This book discusses special properties of integer sequences from a unique point of view. It generalizes common, well-known properties and connects them with sequences such as divisible sequences, Lucas sequences, Lehmer sequences, periods of sequences, lifting properties, and so on. The book presents theories derived by using elementary means and includes results not usually found in common number theory books. Considering the impact and usefulness of these theorems, the book also aims at being valuable for Olympiad level problem solving as well as regular research. This book will be of interest to students, researchers and faculty members alike.
A Handbook Of Integer Sequences
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Author : N.J.A. Sloane
language : en
Publisher: Academic Press
Release Date : 2014-05-10
A Handbook Of Integer Sequences written by N.J.A. Sloane and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
A Handbook of Integer Sequences contains a main table of 2300 sequences of integers that are collected from all branches of mathematics and science. This handbook describes how to use the main table and provides methods for analyzing and describing unknown and important sequences. This compilation also serves as an index to the literature for locating references on a particular problem and quickly finds numbers such as 712, number of partitions of 30, 18th Catalan number, or expansion of ? to 60 decimal places. Other topics include the method of differences, self-generating sequences, polyominoes, permutations, and puzzle sequences. This publication is a good source for students and researchers who are confronted with strange and important sequences.
Sequences
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Author : H. Halberstam
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sequences written by H. Halberstam and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
THIS volume is concerned with a substantial branch of number theory of which no connected account appears to exist; we describe the general nature of the constituent topics in the introduction. Although some excellent surveys dealing with limited aspects of the subject under con sideration have been published, the literature as a whole is far from easy to study. This is due in part to the extent of the literature; it is necessary to thread one's way through a maze of results, a complicated structure of inter-relationships, and many conflicting notations. In addition, however, not all the original papers are free from obscurities, and consequently some of these papers are difficult (a few even exceed ingly difficult) to master. We try to give a readable and coherent account of the subject, con taining a cross-section of the more interesting results. We felt that it would have been neither practicable nor desirable to attempt a compre hensive account; we treat each aspect of the subject from some special point of view, and select results accordingly. Needless to say, this approach entails the omission of many interesting and important results (quite apart from defects in the selection due to errors of judgement on our part). Those results selected for inclusion are, however, proved in complete detail and without the assumption of any prior knowledge on the part of the reader.
A Handbook Of Integer Sequences
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Author : Neil James Alexander Sloane
language : en
Publisher:
Release Date : 1973
A Handbook Of Integer Sequences written by Neil James Alexander Sloane and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.
Sequences And Their Applications
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Author : C. Ding
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sequences And Their Applications written by C. Ding and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
This book contains survey papers and research papers by leading experts on sequences and their applications. It discusses both the theory of sequences and their applications in cryptography, coding theory, communications systems, numerical computation and computer simulation. Sequences have important applications in ranging systems, spread spectrum communication systems, multi-terminal system identification, code division multiply access communications systems, global positioning systems, software testing, circuit testing, computer simulation, and stream ciphers. The papers contained in this volume bring together experts from discrete mathematics, computer science and communications engineering, and help to bridge advances in these different areas.
Recurrent Sequences
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Author : Dorin Andrica
language : en
Publisher: Springer Nature
Release Date : 2020-09-23
Recurrent Sequences written by Dorin Andrica and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Mathematics categories.
This self-contained text presents state-of-the-art results on recurrent sequences and their applications in algebra, number theory, geometry of the complex plane and discrete mathematics. It is designed to appeal to a wide readership, ranging from scholars and academics, to undergraduate students, or advanced high school and college students training for competitions. The content of the book is very recent, and focuses on areas where significant research is currently taking place. Among the new approaches promoted in this book, the authors highlight the visualization of some recurrences in the complex plane, the concurrent use of algebraic, arithmetic, and trigonometric perspectives on classical number sequences, and links to many applications. It contains techniques which are fundamental in other areas of math and encourages further research on the topic. The introductory chapters only require good understanding of college algebra, complex numbers, analysis and basic combinatorics. For Chapters 3, 4 and 6 the prerequisites include number theory, linear algebra and complex analysis. The first part of the book presents key theoretical elements required for a good understanding of the topic. The exposition moves on to to fundamental results and key examples of recurrences and their properties. The geometry of linear recurrences in the complex plane is presented in detail through numerous diagrams, which lead to often unexpected connections to combinatorics, number theory, integer sequences, and random number generation. The second part of the book presents a collection of 123 problems with full solutions, illustrating the wide range of topics where recurrent sequences can be found. This material is ideal for consolidating the theoretical knowledge and for preparing students for Olympiads.
The Encyclopedia Of Integer Sequences
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Author : N. J. A. Sloane
language : en
Publisher: Academic Press
Release Date : 1995-04
The Encyclopedia Of Integer Sequences written by N. J. A. Sloane and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04 with Computers categories.
This encyclopedia contains more than 5000 integer sequences, over half of which have never before been catalogued. Because the sequences are presented in the most natural form, and arranged for easy reference, this book is easier to use than the authors earlier classic "A Handbook of Integer Sequences. The Encyclopedia gives the name, mathematical description, and citations to literature for each sequence. Following sequences of particular interest, thereare essays on their origins, uses, and connections to related sequences (all cross-referenced). A valuable new feature to this text is the inclusion of a number of interesting diagrams and illustrations related to selected sequences. The initial chapters are both amusing and enlightening. They serve as a delightful introduction to the subject and a short course on how to identify and work with integer sequences. This encyclopedia brings Sloanes ground-breaking "Handbook up to date, more than doubling its size, and linking both the old and the new material to an extensive bibliography (over 25 pages long), of current and classic references. An index to all the sequences in the book is also available separately on disk in Macintosh and IBM formats. Key Features * Contains more than 5000 integer sequences * Gives the name and mathematical description of each sequence * Provides citations to literature for each sequence * Extensively cross-referenced * Lists a bibliography of more than 25 pages
Automated Theory Formation In Pure Mathematics
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Author : Simon Colton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Automated Theory Formation In Pure Mathematics written by Simon Colton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.
Another Set Of Sequences Sub Sequences And Sequences Of Sequences
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
Another Set Of Sequences Sub Sequences And Sequences Of Sequences written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
New sequences in number theory are showed below with definitions, examples, solved or open questions and references for each case.
New National Framework Mathematics
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Author : M. J. Tipler
language : en
Publisher: Nelson Thornes
Release Date : 2003
New National Framework Mathematics written by M. J. Tipler and has been published by Nelson Thornes this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Juvenile Nonfiction categories.
New National Framework Mathematics features extensive teacher support materials which include dedicated resources to support each Core and Plus Book. The 7 Plus Teacher Planning Pack contains Teacher Notes for every chapter with a 'Self-contained lesson plan' for each of the units in the pupil books.