Periodic Character and Patterns of Recursive Sequences PDF Download

Author: Michael A. Radin
Publisher: Springer
ISBN: 303001780X
Category : Mathematics
Languages : en
Pages : 226

View

Book Description
This textbook on periodic character and patterns of recursive sequences focuses on discrete periodic patterns of first order, second order and higher order difference equations. Aimed toward advanced undergraduate students and graduate students who have taken a basic course in Calculus I and Discrete Mathematics, this book serves as a core text for a course in Difference Equations and Discrete Dynamical Systems. The text contains over 200 exercises to provide readers with a hands-on experience working with the material; the exercises include computations of specific examples and proofs of general results. Readers will receive a first-hand introduction to patterns of periodic cycles and patterns of transient terms with exercises for most sections of the text, preparing them for significant research work in the area.

Author: Michael A. Radin
Publisher: CRC Press
ISBN: 1000078531
Category : Mathematics
Languages : en
Pages : 195

View

Book Description
Introduction to Recognition and Deciphering of Patterns is meant to acquaint STEM and non-STEM students with different patterns, as well as to where and when specific patterns arise. In addition, the book teaches students how to recognize patterns and distinguish the similarities and differences between them. Patterns, such as weather patterns, traffic patterns, behavioral patterns, geometric patterns, linguistic patterns, structural patterns, digital patterns, and the like, emerge on an everyday basis, . Recognizing patterns and studying their unique traits are essential for the development and enhancement of our intuitive skills and for strengthening our analytical skills. Mathematicians often apply patterns to get acquainted with new concepts--a technique that can be applied across many disciplines. Throughout this book we explore assorted patterns that emerge from various geometrical configurations of squares, circles, right triangles, and equilateral triangles that either repeat at the same scale or at different scales. The book also analytically examines linear patterns, geometric patterns, alternating patterns, piecewise patterns, summation-type patterns and factorial-type patterns. Deciphering the details of these distinct patterns leads to the proof by induction method, and the book will also render properties of Pascal’s triangle and provide supplemental practice in deciphering specific patterns and verifying them. This book concludes with first-order recursive relations: describing sequences as recursive relations, obtaining the general solution by solving an initial value problem, and determining the periodic traits. Features • Readily accessible to a broad audience, including those with limited mathematical background • Especially useful for students in non-STEM disciplines, such as psychology, sociology, economics and business, as well as for liberal arts disciplines and art students.

Author: Michael A Radin
Publisher: World Scientific
ISBN: 9811202982
Category : Mathematics
Languages : en
Pages : 330

View

Book Description
'Radlin has done a nice job in producing a textbook which provides a learner friendly introduction to difference equations. It would suit as a core text for a first year course in the topic, aimed, as the title suggests, at physical science or engineering undergraduates. The student who is prepared to work through the book will get a good grounding in basic techniques and gain a feel for the possible behaviours of standard equations. He will also be given some indication of the usefulness and potential complexity of discrete systems in modern science and engineering.'London Mathematical SocietyWe introduce interdisciplinary research and get students and the audience familiarized with the difference equations; solving them explicitly, determining the long-term behavior of solutions (convergence, boundedness and periodicity). We help to develop intuition in analyzing convergence of solutions in terms of subsequences and analyzing patterns of periodic cycles. Our book helps you learn applications in biology, economics and business, computer science and engineering.

Author: Michael A. Radin
Publisher: CRC Press
ISBN: 0429855257
Category : Mathematics
Languages : en
Pages : 108

View

Book Description
Piece-wise and Max-Type Difference Equations: Periodic and Eventually Periodic Solutions is intended for lower-level undergraduate students studying discrete mathematics. The book focuses on sequences as recursive relations and then transitions to periodic recursive patterns and eventually periodic recursive patterns. In addition to this, it will also focus on determining the patterns of periodic and eventually periodic solutions inductively. The aim of the author, throughout this book, is to get students to understand the significance of pattern recognition as a mathematical tool. Key Features Can provide possible topics for undergraduate research and for bachelor’s thesis Provides supplementary practice problems and some open-ended research problems at the end of each chapter Focusses on determining the patterns of periodic and eventually periodic solutions inductively Enhances students’ algebra skills before moving forward to upper level courses Familiarize students with the topics before they start undergraduate research by providing applications.

Author: Michael A Radin
Publisher: World Scientific
ISBN: 9811261067
Category : Mathematics
Languages : en
Pages : 252

View

Book Description
The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.

Author: R. Uday Kiran
Publisher: Springer Nature
ISBN: 9811639647
Category : Computers
Languages : en
Pages : 263

View

Book Description
This book provides an introduction to the field of periodic pattern mining, reviews state-of-the-art techniques, discusses recent advances, and reviews open-source software. Periodic pattern mining is a popular and emerging research area in the field of data mining. It involves discovering all regularly occurring patterns in temporal databases. One of the major applications of periodic pattern mining is the analysis of customer transaction databases to discover sets of items that have been regularly purchased by customers. Discovering such patterns has several implications for understanding the behavior of customers. Since the first work on periodic pattern mining, numerous studies have been published and great advances have been made in this field. The book consists of three main parts: introduction, algorithms, and applications. The first chapter is an introduction to pattern mining and periodic pattern mining. The concepts of periodicity, periodic support, search space exploration techniques, and pruning strategies are discussed. The main types of algorithms are also presented such as periodic-frequent pattern growth, partial periodic pattern-growth, and periodic high-utility itemset mining algorithm. Challenges and research opportunities are reviewed. The chapters that follow present state-of-the-art techniques for discovering periodic patterns in (1) transactional databases, (2) temporal databases, (3) quantitative temporal databases, and (4) big data. Then, the theory on concise representations of periodic patterns is presented, as well as hiding sensitive information using privacy-preserving data mining techniques. The book concludes with several applications of periodic pattern mining, including applications in air pollution data analytics, accident data analytics, and traffic congestion analytics.

Author: Jay Bonner
Publisher: Springer
ISBN: 1441902171
Category : Mathematics
Languages : en
Pages : 616

View

Book Description
The main focus of this unique book is an in-depth examination of the polygonal technique; the primary method used by master artists of the past in creating Islamic geometric patterns. The author details the design methodology responsible for this all-but-lost art form and presents evidence for its use from the historical record, both of which are vital contributions to the understanding of this ornamental tradition. Additionally, the author examines the historical development of Islamic geometric patterns, the significance of geometric design within the broader context of Islamic ornament as a whole, the formative role that geometry plays throughout the Islamic ornamental arts (including calligraphy, the floral idiom, dome decoration, geometric patterns, and more), and the underexamined question of pattern classification. Featuring over 600 beautiful color images, Islamic Geometric Patterns: Their Historical Development and Traditional Methods of Con struction is a valuable addition to the literature of Islamic art, architecture and geometric patterns. This book is ideal for students and scholars of geometry, the history of mathematics, and the history of Islamic art, architecture, and culture. In addition, artists, designers, craftspeople, and architects will all find this book an exceptionally informative and useful asset in their fields. Jay Bonner is an architectural ornamentalist and unaffiliated scholar of Islamic geometric design. He received his MDes from the Royal College of Art in London (1983). He has contributed ornamental designs for many international architectural projects, including the expansion of both the al-Masjid al-Haram (Grand Mosque) in Mecca, and the al-Masjid an Nawabi (Prophet’s Mosque) in Medina, as well the Tomb of Sheikh Hujwiri in Lahore, and the Ismaili Centre in London – to name but a few. He is committed to the revitalization of Islamic geometric design through the teaching of traditional methodological practices. To this end, in addition to publishing, Jay Bonner has lectured and taught design seminars at many universities and conferences in North America, Europe, North Africa and Asia.

Author: Wei Wang
Publisher: Springer Science & Business Media
ISBN: 0387242473
Category : Computers
Languages : en
Pages : 174

View

Book Description
In many applications, e.g., bioinformatics, web access traces, system u- lization logs, etc., the data is naturally in the form of sequences. It has been of great interests to analyze the sequential data to find their inherent char- teristics. The sequential pattern is one of the most widely studied models to capture such characteristics. Examples of sequential patterns include but are not limited to protein sequence motifs and web page navigation traces. In this book, we focus on sequential pattern mining. To meet different needs of various applications, several models of sequential patterns have been proposed. We do not only study the mathematical definitions and application domains of these models, but also the algorithms on how to effectively and efficiently find these patterns. The objective of this book is to provide computer scientists and domain - perts such as life scientists with a set of tools in analyzing and understanding the nature of various sequences by : (1) identifying the specific model(s) of - quential patterns that are most suitable, and (2) providing an efficient algorithm for mining these patterns. Chapter 1 INTRODUCTION Data Mining is the process of extracting implicit knowledge and discovery of interesting characteristics and patterns that are not explicitly represented in the databases. The techniques can play an important role in understanding data and in capturing intrinsic relationships among data instances. Data mining has been an active research area in the past decade and has been proved to be very useful.

Author: Jung-Chao Ban
Publisher: American Mathematical Soc.
ISBN: 0821872907
Category : Mathematics
Languages : en
Pages : 72

View

Book Description
This work is concerned with zeta functions of two-dimensional shifts of finite type. A two-dimensional zeta function $\zeta^{0}(s)$, which generalizes the Artin-Mazur zeta function, was given by Lind for $\mathbb{Z}^{2}$-action $\phi$. In this paper, the $n$th-order zeta function $\zeta_{n}$ of $\phi$ on $\mathbb{Z}_{n\times \infty}$, $n\geq 1$, is studied first. The trace operator $\mathbf{T}_{n}$, which is the transition matrix for $x$-periodic patterns with period $n$ and height $2$, is rotationally symmetric. The rotational symmetry of $\mathbf{T}_{n}$ induces the reduced trace operator $\tau_{n}$ and $\zeta_{n}=\left(\det\left(I-s^{n}\tau_{n}\right)\right)^{-1}$. The zeta function $\zeta=\prod_{n=1}^{\infty} \left(\det\left(I-s^{n}\tau_{n}\right)\right)^{-1}$ in the $x$-direction is now a reciprocal of an infinite product of polynomials. The zeta function can be presented in the $y$-direction and in the coordinates of any unimodular transformation in $GL_{2}(\mathbb{Z})$. Therefore, there exists a family of zeta functions that are meromorphic extensions of the same analytic function $\zeta^{0}(s)$. The natural boundary of zeta functions is studied. The Taylor series for these zeta functions at the origin are equal with integer coefficients, yielding a family of identities, which are of interest in number theory. The method applies to thermodynamic zeta functions for the Ising model with finite range interactions.

Author: Graham Everest
Publisher: American Mathematical Soc.
ISBN: 1470423154
Category : Mathematics
Languages : en
Pages : 338

View

Book Description
Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.