Analyzing Mathematical Patterns - Detection & Formulation: Inductive Approach To Recognition, Analysis And Formulations Of Patterns PDF Download
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Author: Michael A Radin
Publisher: World Scientific
ISBN: 9811261067
Category : Mathematics
Languages : en
Pages : 252
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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: Michael A Radin
Publisher: World Scientific
ISBN: 9811261067
Category : Mathematics
Languages : en
Pages : 252
Get Book Here
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: Michael A. Radin
Publisher: CRC Press
ISBN: 1000078531
Category : Mathematics
Languages : en
Pages : 195
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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: Satosi Watanabe
Publisher: Academic Press
ISBN: 1483268985
Category : Reference
Languages : en
Pages : 591
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Book Description
Methodologies of Pattern Recognition is a collection of papers that deals with the two approaches to pattern recognition (geometrical and structural), the Robbins-Monro procedures, and the implications of interactive graphic computers for pattern recognition methodology. Some papers describe non-supervised learning in statistical pattern recognition, parallel computation in pattern recognition, and statistical analysis as a tool to make patterns emerge from data. One paper points out the importance of cluster processing in visual perception in which proximate points of similar brightness values form clusters. At higher levels of mental activity humans are efficient in clumping complex items into clusters. Another paper suggests a recognition method which combines versatility and an efficient noise-proofness in dealing with the two main problems in the field of recognition. These difficulties are the presence of a large variety of observed signals and the presence of interference. One paper reports on a possible feature selection for pattern recognition systems employing the minimization of population entropy. Electronic engineers, physicists, physiologists, psychologists, logicians, mathematicians, and philosophers will find great rewards in reading the above collection.
Author: Jack Bryant
Publisher:
ISBN:
Category :
Languages : en
Pages : 74
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Book Description
Author: Luc Devroye
Publisher: Springer Science & Business Media
ISBN: 0387946187
Category : Mathematics
Languages : en
Pages : 658
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Book Description
A self-contained and coherent account of probabilistic techniques, covering: distance measures, kernel rules, nearest neighbour rules, Vapnik-Chervonenkis theory, parametric classification, and feature extraction. Each chapter concludes with problems and exercises to further the readers understanding. Both research workers and graduate students will benefit from this wide-ranging and up-to-date account of a fast- moving field.
Author: Diane Wolff
Publisher: Springer
ISBN:
Category : Computers
Languages : en
Pages : 248
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Book Description
An attempt is made in this book to give scientists a detailed working knowledge of the powerful mathematical tools available to aid in data interpretation, especially when con fronted with large data sets incorporating many parameters. A minimal amount of com puter knowledge is necessary for successful applications, and we have tried conscien tiously to provide this in the appropriate sections and references. Scientific data are now being produced at rates not believed possible ten years ago. A major goal in any sci entific investigation should be to obtain a critical evaluation of the data generated in a set of experiments in order to extract whatever useful scientific information may be present. Very often, the large number of measurements present in the data set does not make this an easy task. The goals of this book are thus fourfold. The first is to create a useful reference on the applications of these statistical pattern recognition methods to the sciences. The majority of our discussions center around the fields of chemistry, geology, environmen tal sciences, physics, and the biological and medical sciences. In Chapter IV a section is devoted to each of these fields. Since the applications of pattern recognition tech niques are essentially unlimited, restricted only by the outer limitations of.
Author: NASA. Johnson Space Center. Earth Resources Research Division
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Heinrich Niemann
Publisher:
ISBN:
Category : Pattern perception
Languages : en
Pages : 400
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Book Description
Author: Y. Kharin
Publisher: Springer
ISBN: 9789401586313
Category : Mathematics
Languages : en
Pages : 302
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Book Description
This book is concerned with important problems of robust (stable) statistical pat tern recognition when hypothetical model assumptions about experimental data are violated (disturbed). Pattern recognition theory is the field of applied mathematics in which prin ciples and methods are constructed for classification and identification of objects, phenomena, processes, situations, and signals, i. e. , of objects that can be specified by a finite set of features, or properties characterizing the objects (Mathematical Encyclopedia (1984)). Two stages in development of the mathematical theory of pattern recognition may be observed. At the first stage, until the middle of the 1970s, pattern recogni tion theory was replenished mainly from adjacent mathematical disciplines: mathe matical statistics, functional analysis, discrete mathematics, and information theory. This development stage is characterized by successful solution of pattern recognition problems of different physical nature, but of the simplest form in the sense of used mathematical models. One of the main approaches to solve pattern recognition problems is the statisti cal approach, which uses stochastic models of feature variables. Under the statistical approach, the first stage of pattern recognition theory development is characterized by the assumption that the probability data model is known exactly or it is esti mated from a representative sample of large size with negligible estimation errors (Das Gupta, 1973, 1977), (Rey, 1978), (Vasiljev, 1983)).
Author: Christopher M. Bishop
Publisher: Springer
ISBN: 9781493938438
Category : Computers
Languages : en
Pages : 0
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Book Description
This is the first textbook on pattern recognition to present the Bayesian viewpoint. The book presents approximate inference algorithms that permit fast approximate answers in situations where exact answers are not feasible. It uses graphical models to describe probability distributions when no other books apply graphical models to machine learning. No previous knowledge of pattern recognition or machine learning concepts is assumed. Familiarity with multivariate calculus and basic linear algebra is required, and some experience in the use of probabilities would be helpful though not essential as the book includes a self-contained introduction to basic probability theory.
