Intuition in Science and Mathematics An Educational Approach

Mathematics

Intuition in Science and Mathematics: An Educational Approach By Efraim Fischbein
Face Processing And Applications To Distance Learning
Crafts Of Simulation Programming
Elastic Shape Analysis of Three-Dimensional Objects
Introduction To Evolutionary Informatics
Intuition in Science and Mathematics: An Educational Approach By Efraim Fischbein

English | PDF | 2002 | 234 Pages | ISBN : 9027725063 | 1.86 MB
In writing the present book I have had in mind the following objectives: – To propose a theoretical, comprehensive view of the domain of intuition. – To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. – To reveal the educational implications of the idea, developed for science and mathematics education.
Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates – definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge (1 962) and of Noddings and Shore (1 984).) A notable exception is the book by Westcott (1968), which combines theoretical analyses with the author’s own experimental studies. But, so far, no attempt has been made to identify systematically those findings, spread throughout the research literature, which could contribute to the deciphering of the mechanisms of intuition. Very often the relevant studies do not refer explicitly to intuition. Even when this term is used it occurs, usually, as a self-evident, common sense term.

Face Processing And Applications To Distance Learning

World Scientific | English | 2016 | ISBN-10: 9814733024 | 136 pages | PDF | 23.21 mb
by Vuong Le (Author), Usman Tariq (Author), Hao Tang (Author)
This special compendium provides a concise and unified vision of facial image processing. It addresses a collection of state-of-the-art techniques, covering the most important areas for facial biometrics and behavior analysis. These techniques also converge to serve an emerging practical application of interactive distance learning.Readers will get a broad picture of the fundamental science of the field and technical details that make the research interesting. Moreover, the intellectual investigation motivated by the demand of real-life application will make this volume an inspiring read for current and prospective researchers and engineers in the fields of computer vision, machine learning and image processing.

Crafts Of Simulation Programming

World Scientific | English | 2016 | ISBN-10: 9814740179 | 304 pages | PDF | 7.74 mb
by E Jack Chen (Author)
Crafts of Simulation Programs is a collection of tools, techniques and theories required to develop and implement simulation models on a computer. This timely book provides the various skills and techniques needed in simulation programming with general-purpose languages. The topics range in difficulty, and several latest fields in simulation output analysis are covered such as samples sizes, order statistics, ranking and selection, comparison with a control, selection with constraints, etc.Presented in the format of research project reports, detailed descriptions, important concepts and techniques are introduced and developed. Each chapter is relatively self-contained and can be used as a study unit. Algorithms have detailed implementations in C and are readable by anyone who has done a little programming. Many chapters include simulation results. It is designed to impart to the readers the statistical techniques used in simulation. This book will prove to be invaluable not only to students and researchers in the fields of simulation programming, but also to teachers of this subject who will find this text useful as a supplement.

Elastic Shape Analysis of Three-Dimensional Objects

Morgan & Claypool | English | Sep 2017 | ISBN-10: 1681730278 | 185 pages | PDF | 6.04 mb
by Ian H Jermyn (Author)
Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations.
We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in ℝ, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations.
The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities.
These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis.
This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.

Introduction To Evolutionary Informatics

World Scientific | English | 2017 | ISBN-10: 9813142138 | 332 pages | PDF | 22.57 mb
by Robert J Marks Ii (Author), William A Dembski (Author), Winston Ewert (Author)
Science has made great strides in modeling space, time, mass and energy. Yet little attention has been paid to the precise representation of the information ubiquitous in nature.Introduction to Evolutionary Informatics fuses results from complexity modeling and information theory that allow both meaning and design difficulty in nature to be measured in bits. Built on the foundation of a series of peer-reviewed papers published by the authors, the book is written at a level easily understandable to readers with knowledge of rudimentary high school math. Those seeking a quick first read or those not interested in mathematical detail can skip marked sections in the monograph and still experience the impact of this new and exciting model of nature’s information.This book is written for enthusiasts in science, engineering and mathematics interested in understanding the essential role of information in closely examined evolution theory.