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Visualizing Mathematics with 3D Printing
by Henry SegermanWouldn;€™t it be great to experience three-dimensional ideas in three dimensions? In this book;¢;‚¬;€?the first of its kind;¢;‚¬;€?mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book;€™s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.
Visualizing Mathematics with 3D Printing
by Henry SegermanWouldn;€™t it be great to experience three-dimensional ideas in three dimensions? In this book;¢;‚¬;€?the first of its kind;¢;‚¬;€?mathematician and mathematical artist Henry Segerman takes readers on a fascinating tour of two-, three-, and four-dimensional mathematics, exploring Euclidean and non-Euclidean geometries, symmetry, knots, tilings, and soap films. Visualizing Mathematics with 3D Printing includes more than 100 color photographs of 3D printed models. Readers can take the book;€™s insights to a new level by visiting its sister website, 3dprintmath.com, which features virtual three-dimensional versions of the models for readers to explore. These models can also be ordered online or downloaded to print on a 3D printer. Combining the strengths of book and website, this volume pulls higher geometry and topology out of the realm of the abstract and puts it into the hands of anyone fascinated by mathematical relationships of shape. With the book in one hand and a 3D printed model in the other, readers can find deeper meaning while holding a hyperbolic honeycomb, touching the twists of a torus knot, or caressing the curves of a Klein quartic.
Visualizing Mortality Dynamics in the Lexis Diagram (The Springer Series on Demographic Methods and Population Analysis #44)
by Roland Rau Christina Bohk-Ewald Magdalena M. Muszyńska James W. VaupelThis book visualizes mortality dynamics in the Lexis diagram. While the standard approach of plotting death rates is also covered, the focus in this book is on the depiction of rates of mortality improvement over age and time. This rather novel approach offers a more intuitive understanding of the underlying dynamics, enabling readers to better understand whether period- or cohort-effects were instrumental for the development of mortality in a particular country. Besides maps for single countries, the book includes maps on the dynamics of selected causes of death in the United States, such as cardiovascular diseases or lung cancer. The book also features maps for age-specific contributions to the change in life expectancy, for cancer survival and for seasonality in mortality for selected causes of death in the United States. The book is accompanied by instructions on how to use the freely available R Software to produce these types of surface maps. Readers are encouraged to use the presented tools to visualize other demographic data or any event that can be measured by age and calendar time, allowing them to adapt the methods to their respective research interests. The intended audience is anyone who is interested in visualizing data by age and calendar time; no specialist knowledge is required.This book is open access under a CC BY license.
Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
by Andrew J. HansonIntroduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions.Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing.Covers both non-mathematical and mathematical approaches to quaternions.
Visualizing Surveys in R
by Teppo ValtonenVisualizing Surveys in R is about creating static, print quality figures from survey data using R. The focus is not, for example, on statistical analysis of survey data, but rather on giving concrete solutions for typical problems in visualizing survey data. While there are many excellent books on data visualization, surveys and R, the aim of this book is to bring these topics together, and offer practical instructions for visualizing surveys in R. Features • Introduction to survey data: variables, categories, and scales • Description of a process for visualizing survey data • Recommendations for reading survey data into R • Advice on building a survey dataset in R to facilitate versatile plotting • Step-by-step recipes in R for creating useful plots from survey data The book is intended for researchers who regularly use surveys and are interested in learning how to seize the vast possibilities and the flexibility of R in survey analysis and visualizations. The book is also valuable for psychologists, marketeers, HR personnel, managers, and other professionals who wish to standardize and automate the process for visualizing survey data. Finally, the book is suitable as a course textbook, either more widely on survey studies, or more strictly on visualizing survey data in R.
Visualizing Surveys in R
by Teppo ValtonenVisualizing Surveys in R is about creating static, print quality figures from survey data using R. The focus is not, for example, on statistical analysis of survey data, but rather on giving concrete solutions for typical problems in visualizing survey data. While there are many excellent books on data visualization, surveys and R, the aim of this book is to bring these topics together, and offer practical instructions for visualizing surveys in R. Features • Introduction to survey data: variables, categories, and scales • Description of a process for visualizing survey data • Recommendations for reading survey data into R • Advice on building a survey dataset in R to facilitate versatile plotting • Step-by-step recipes in R for creating useful plots from survey data The book is intended for researchers who regularly use surveys and are interested in learning how to seize the vast possibilities and the flexibility of R in survey analysis and visualizations. The book is also valuable for psychologists, marketeers, HR personnel, managers, and other professionals who wish to standardize and automate the process for visualizing survey data. Finally, the book is suitable as a course textbook, either more widely on survey studies, or more strictly on visualizing survey data in R.
Visualizing Time: Designing Graphical Representations for Statistical Data (Statistics and Computing)
by Graham WillsArt, or Science? Which of these is the right way to think of the field of visualization? This is not an easy question to answer, even for those who have many years experience in making graphical depictions of data with a view to help people understand it and take action. In this book, Graham Wills bridges the gap between the art and the science of visually representing data. He does not simply give rules and advice, but bases these on general principles and provide a clear path between them This book is concerned with the graphical representation of time data and is written to cover a range of different users. A visualization expert designing tools for displaying time will find it valuable, but so also should a financier assembling a report in a spreadsheet, or a medical researcher trying to display gene sequences using a commercial statistical package.
Visuelle Kryptographie (Springer-Lehrbuch)
by Andreas KleinMit Erfindung der Schrift entstand gleichzeitig der Bedarf, Geschriebenes vor unbefugten Lesern zu verbergen. Als Wissenschaft im modernen Sinne ist die Kryptographie jedoch noch sehr jung. 1994 erfanden Naor und Shamir folgendes Verfahren: Sie verteilten ein Bild so auf zwei Folien, dass auf jeder einzelnen Folie nur ein zufälliges Punktmuster zu sehen ist, aber beide Folien übereinander gelegt ein geheimes Bild ergeben. Das Buch gibt einen Einblick in die aktuelle Forschung, verzichtet aber bewusst auf Höhere Mathematik. Daher eine ideale Grundlage für Proseminare und Mathematik-AGs der Sekundarstufe. Plus: Aufgaben mit Musterlösungen.
Visuospatial Reasoning: An Ecocultural Perspective for Space, Geometry and Measurement Education (Mathematics Education Library #111)
by Kay OwensThis book develops the theoretical perspective on visuospatial reasoning in ecocultural contexts, granting insights on how the language, gestures, and representations of different cultures reflect visuospatial reasoning in context. For a number of years, two themes in the field of mathematics education have run parallel with each other with only a passing acquaintance. These two areas are the psychological perspective on visuospatial reasoning and ecocultural perspectives on mathematics education. This volume examines both areas of research and explores the intersection of these powerful ideas. In addition, there has been a growing interest in sociocultural aspects of education and in particular that of Indigenous education in the field of mathematics education. There has not, however, been a sound analysis of how environmental and cultural contexts impact visuospatial reasoning, although it was noted as far back as the 1980s when Alan Bishop developed his duality of visual processing and interpreting visual information. This book provides this analysis and in so doing not only articulates new and worthwhile lines of research, but also uncovers and makes real a variety of useful professional approaches in teaching school mathematics. With a renewed interest in visuospatial reasoning in the mathematics education community, this volume is extremely timely and adds significantly to current literature on the topic.
Vital Directions for Mathematics Education Research
by Keith R LeathamThis book provides a collection of chapters from prominent mathematics educators in which they each discuss vital issues in mathematics education and what they see as viable directions research in mathematics education could take to address these issues. All of these issues are related to learning and teaching mathematics. The book consists of nine chapters, seven from each of seven scholars who participated in an invited lecture series (Scholars in Mathematics Education) at Brigham Young University, and two chapters from two other scholars who are writing reaction papers that look across the first seven chapters. The recommendations take the form of broad, overarching principles and ideas that cut across the field. In this sense, this book differs from classical “research agenda projects,” which seek to outline specific research questions that the field should address around a central topic.
Vite matematiche: Protagonisti del '900, da Hilbert a Wiles (I blu)
by C. Bartocci R. Betti A. Guerraggio R. LucchettiLo scibile matematico si espande a un ritmo vertiginoso. Nel corso degli ultimi cinquant'anni sono stati dimostrati più teoremi che nei precedenti millenni della storia umana. Per illustrare la ricchezza della matematica del Novecento, il presente volume porta sulla ribalta alcuni dei protagonisti di questa straordinaria impresa intellettuale, che ha messo a nostra disposizione nuovi e potenti strumenti per indagare la realtà che ci circonda. Presentando matematici famosi accanto ad altri meno noti al grande pubblico – da Hilbert a Gödel, da Turing a Nash, da De Giorgi a Wiles – i ritratti raccolti in questo volume ci presentano personaggi dal forte carisma personale, dai vasti interessi culturali, appassionati nel difendere l’importanza delle proprie ricerche, sensibili alla bellezza, attenti ai problemi sociali e politici del loro tempo. Ne risulta un affresco che documenta la centralità della matematica nella cultura, non solo scientifica ma anche filosofica, artistica e letteraria, del nostro tempo, in un continuo gioco di scambi e di rimandi, di corrispondenze e di suggestioni.
Vito Volterra
by Angelo Guerraggio Giovanni PaoloniVito Volterra (1860-1940) was one of the most famous representatives of Italian science in his day. Angelo Guerragio and Giovanni Paolini analyze Volterra’s most important contributions to mathematics and their applications, as well as his outstanding organizational achievements in scientific policy. Volterra was one of the founding fathers of functional analysis and the author of fundamental contributions in the field of integral equations, elasticity theory and population dynamics (Lotka-Volterra model). He delivered keynote lectures on the occasion of the International Congresses of Mathematicians held in Paris (1900), Rome (1908), Strasbourg (1920) and Bologna (1928). He became involved in the scientific development in united Italy and was appointed senator of the kingdom in 1905. One of his numerous non-mathematical activities was founding the National Research Council (Consiglio Nazionale delle Ricerche, CNR). During the First World War he was active in military research. After the war he took a clear stand against fascism, which was the starting point for his exclusion. In 1926 he resigned as president of the world famous Accademia Nazionale dei Lincei and was later on excluded from the academy. In 1931 he was one of the few university lecturers who denied to swear an oath of allegiance to the fascistic regime. In 1938 he suffered from the impact of the racial laws. The authors draw a comprehensive picture of Vito Volterra, both as a great mathematician and an organizer of science.
Vito Volterra (Vita Mathematica #15)
by Angelo Guerraggio Giovanni PaoloniDer Mathematiker Vito Volterra (1860 – 1940) war nicht nur ein großer Mathematiker, sondern auch ein guter Wissenschaftsorganisator. Über Jahrzehnte galt er als der bedeutendste Repräsentant der Wissenschaft in Italien. Die Autoren rekonstruieren seine wichtigsten Beiträge zur Wissenschaft und zur Entwicklung der wissenschaftlichen Institutionen in Italien und der Welt: von der Entwicklung der Funktionalanalysis über die Untersuchung der Populationsdynamik bis zu seiner Lehrtätigkeit und der Gründung des staatlichen italienischen Forschungsrates.
Vito Volterra Symposium on Mathematical Models in Biology: Proceedings of a Conference Held at the Centro Linceo Interdisciplinare, Accademia Nazionale dei Lincei, Rome December 17 – 21, 1979 (Lecture Notes in Biomathematics #39)
by Claudio BarigozziThe idea of organizing a symposium on mathematical models in biology came to some colleagues, members of the Accademia dei Lincei, in order to point out the importance of mathematics not only for supplying instruments for the elaboration and the evaluation of experimental data, but also for discussing the possibility of developing mathematical formulations of biological problems. This appeared particularly appropriate for genetics, where mathematical models have been of historical importance. When the organizing work had started, it became clear to us that the classic studies of Vito Volterra (who was also a Member of the Academy and its President from 1923 to 1926) might be con sidered a further reason to have the meeting in Rome at the Accademia dei Lincei; thus the meeting is dedicated to his memory. Biology, in its manifold aspects proved to Se ~ difficult object for an exhaustive approach; thus it became necessary for practical reasons to make a choice of problems. Therefore not all branches of biology have been represented. The proceedings of the symposium, as a whole, assume a knowledge of mathematics on the part of the reader; however the problem of teaching mathematics to biologists was the subject of a round table discussion, not recorded in these proceedings. On this were brought up some basic points to be recommended to teachers on an international basis, and a statement was prepared for circulation. The Organizing Committee TABLE OF CONTENTS TOPIC I MODELS OF NATUPAL SELECTION . . . . . . . • . . . .
Vitushkin’s Conjecture for Removable Sets (Universitext)
by James DudziakVitushkin's conjecture, a special case of Painlevé's problem, states that a compact subset of the complex plane with finite linear Hausdorff measure is removable for bounded analytic functions if and only if it intersects every rectifiable curve in a set of zero arclength measure. Chapters 1-5 of the book provide important background material on removability, analytic capacity, Hausdorff measure, arclength measure, and Garabedian duality that will appeal to many analysts with interests independent of Vitushkin's conjecture. The fourth chapter contains a proof of Denjoy's conjecture that employs Melnikov curvature. A brief postscript reports on a deep theorem of Tolsa and its relevance to going beyond Vitushkin's conjecture. This text can be used for a topics course or seminar in complex analysis. To understand it, the reader should have a firm grasp of basic real and complex analysis.
VIVO: A Semantic Portal for Scholarly Networking Across Disciplinary Boundaries (Synthesis Lectures on Data, Semantics, and Knowledge)
by Katy Borner Ying Ding Mike Conlon Jon Corson-RikertThe world of scholarship is changing rapidly. Increasing demands on scholars, the growing size and complexity of questions and problems to be addressed, and advances in sophistication of data collection, analysis, and presentation require new approaches to scholarship. A ubiquitous, open information infrastructure for scholarship, consisting of linked open data, open-source software tools, and a community committed to sustainability are emerging to meet the needs of scholars today. This book provides an introduction to VIVO, http://vivoweb.org/, a tool for representing information about research and researchers -- their scholarly works, research interests, and organizational relationships. VIVO provides an expressive ontology, tools for managing the ontology, and a platform for using the ontology to create and manage linked open data for scholarship and discovery. Begun as a project at Cornell and further developed by an NIH funded consortium, VIVO is now being established as an open-source project with community participation from around the world. By the end of 2012, over 20 countries and 50 organizations will provide information in VIVO format on more than one million researchers and research staff, including publications, research resources, events, funding, courses taught, and other scholarly activity. The rapid growth of VIVO and of VIVO-compatible data sources speaks to the fundamental need to transform scholarship for the 21st century. Table of Contents: Scholarly Networking Needs and Desires / The VIVO Ontology / Implementing VIVO and Filling It with Life / Case Study: University of Colorado at Boulder / Case Study: Weill Cornell Medical College / Extending VIVO / Analyzing and Visualizing VIVO Data / The Future of VIVO: Growing the Community
VizSEC 2007: Proceedings of the Workshop on Visualization for Computer Security (Mathematics and Visualization)
by John R. Goodall Gregory Conti Kwan-Liu MaNetworked computers are ubiquitous, and are subject to attack, misuse, and abuse. One method to counteracting this cyber threat is to provide security analysts with better tools to discover patterns, detect anomalies, identify correlations, and communicate their findings. Visualization for computer security (VizSec) researchers and developers are doing just that. VizSec is about putting robust information visualization tools into the hands of human analysts to take advantage of the power of the human perceptual and cognitive processes in solving computer security problems. This volume collects the papers presented at the 4th International Workshop on Computer Security - VizSec 2007.
Vladimir I. Arnold - Collected Works: Hydrodynamics, Bifurcation Theory, and Algebraic Geometry 1965-1972 (Vladimir I. Arnold - Collected Works)
by Vladimir I. ArnoldVladimir Arnold was one of the great mathematical scientists of our time. He is famous for both the breadth and the depth of his work. At the same time he is one of the most prolific and outstanding mathematical authors. This second volume of his Collected Works focuses on hydrodynamics, bifurcation theory, and algebraic geometry.
Vladimir I. Arnold - Collected Works: Representations of Functions, Celestial Mechanics, and KAM Theory 1957-1965 (Vladimir I. Arnold - Collected Works #1)
by Vladimir I. Arnold
VLSI — Compatible Implementations for Artificial Neural Networks (The Springer International Series in Engineering and Computer Science #382)
by Sied Mehdi Fakhraie Kenneth C. SmithThis book introduces several state-of-the-art VLSI implementations of artificial neural networks (ANNs). It reviews various hardware approaches to ANN implementations: analog, digital and pulse-coded. The analog approach is emphasized as the main one taken in the later chapters of the book. The area of VLSI implementation of ANNs has been progressing for the last 15 years, but not at the fast pace originally predicted. Several reasons have contributed to the slow progress, with the main one being that VLSI implementation of ANNs is an interdisciplinaly area where only a few researchers, academics and graduate students are willing to venture. The work of Professors Fakhraie and Smith, presented in this book, is a welcome addition to the state-of-the-art and will greatly benefit researchers and students working in this area. Of particular value is the use of experimental results to backup extensive simulations and in-depth modeling. The introduction of a synapse-MOS device is novel. The book applies the concept to a number of applications and guides the reader through more possible applications for future work. I am confident that the book will benefit a potentially wide readership. M. I. Elmasry University of Waterloo Waterloo, Ontario Canada Preface Neural Networks (NNs), generally defined as parallel networks that employ a large number of simple processing elements to perform computation in a distributed fashion, have attracted a lot of attention in the past fifty years. As the result. many new discoveries have been made.
VLSI Analog Filters: Active RC, OTA-C, and SC (Modeling and Simulation in Science, Engineering and Technology #0)
by P.V. Ananda MohanGreat strides have been made in the development of analog filters over the past few decades. The first book to treat these recent advances in depth, "VLSI Analog Filters" provides a comprehensive guide for researchers and upper-level graduate students, which fully prepares readers for professional work. In particular, the work covers active R filters, OTA-C filters, and switched-capacitor filters, including topics such as differential output opamps, sensitivity analysis for passive components, multiple-feedback techniques, double-sampling, and N-path filters. Throughout the book, exercises are included to reinforce understanding of concepts, and simulations are used to enhance connections to practical applications. This advanced textbook is suitable for engineering graduate students studying analog filter design, offering a full course that can feed seamlessly to employment industry. At the same time, it serves as an extremely valuable reference for researchers and engineers looking to gain a deeper understanding of the field.
VLSI Artificial Neural Networks Engineering
by Mohamed I. ElmasryEngineers have long been fascinated by how efficient and how fast biological neural networks are capable of performing such complex tasks as recognition. Such networks are capable of recognizing input data from any of the five senses with the necessary accuracy and speed to allow living creatures to survive. Machines which perform such complex tasks as recognition, with similar ac curacy and speed, were difficult to implement until the technological advances of VLSI circuits and systems in the late 1980's. Since then, the field of VLSI Artificial Neural Networks (ANNs) have witnessed an exponential growth and a new engineering discipline was born. Today, many engineering curriculums have included a course or more on the subject at the graduate or senior under graduate levels. Since the pioneering book by Carver Mead; "Analog VLSI and Neural Sys tems", Addison-Wesley, 1989; there were a number of excellent text and ref erence books on the subject, each dealing with one or two topics. This book attempts to present an integrated approach of a single research team to VLSI ANNs Engineering.
VLSI Design and Test: 23rd International Symposium, VDAT 2019, Indore, India, July 4–6, 2019, Revised Selected Papers (Communications in Computer and Information Science #1066)
by Anirban Sengupta Sudeb Dasgupta Virendra Singh Rohit Sharma Santosh Kumar VishvakarmaThis book constitutes the refereed proceedings of the 23st International Symposium on VLSI Design and Test, VDAT 2019, held in Indore, India, in July 2019. The 63 full papers were carefully reviewed and selected from 199 submissions. The papers are organized in topical sections named: analog and mixed signal design; computing architecture and security; hardware design and optimization; low power VLSI and memory design; device modelling; and hardware implementation.
Volkswirtschaftslehre – mathematisch gedacht
by Mark SellenthinDieses Lehrbuch stellt die theoretischen Konzepte der Volkswirtschaftslehre durch grundlegende mathematische Konzepte dar. Während eine wirtschaftswissenschaftliche akademische Karriere ohne fundierte Methodenkenntnisse undenkbar erscheint, sind in der akademischen Lehre die theoretischen Inhalte und die quantitativen Methoden zumeist relativ streng voneinander getrennt. Dieses Lehrbuch geht einen anderen Weg. Die Mathematik wird als lebendiger, integraler Bestandteil des wirtschaftswissenschaftlichen Studiums verstanden, ohne den weder ein tieferes theoretisches Verständnis noch eine empirische Anwendung möglich ist. Der Autor analysiert wesentliche Konzepte aus der Mikro- und der Makroökonomik mit Hilfe mathematischer Ansätze. Der Anwendungsnutzen mathematischer Methoden steht dabei im Vordergrund und soll daher anhand von Musteraufgaben illustriert werden. Das vorliegende Lehrbuch richtet sich an Bachelorstudierende, die eine Einführung in die mathematische Modellierung grundlegender Modelle der Mikro- und Makroökonomik wünschen.
Volkswirtschaftslehre – mathematisch gedacht
by Mark SellenthinDieses Lehrbuch stellt die theoretischen Modelle der Volkswirtschaftslehre durch grundlegende mathematische Konzepte dar. Während eine wirtschaftswissenschaftliche akademische Karriere ohne fundierte Methodenkenntnisse undenkbar erscheint, sind in der akademischen Lehre die theoretischen Inhalte und die quantitativen Methoden zumeist relativ streng voneinander getrennt. Dieses Lehrbuch geht einen anderen Weg. Die Mathematik wird als lebendiger, integraler Bestandteil des wirtschaftswissenschaftlichen Studiums verstanden, ohne den weder ein tieferes theoretisches Verständnis noch eine empirische Anwendung möglich ist. Der Autor analysiert wesentliche Modelle aus der Mikro- und der Makroökonomik mit Hilfe mathematischer Ansätze. Der Anwendungsnutzen mathematischer Methoden steht dabei im Vordergrund und soll daher anhand von Musteraufgaben illustriert werden. Das vorliegende Lehrbuch richtet sich an Bachelorstudierende, die eine Einführung in die mathematische Modellierung grundlegender Modelle der Mikro- und Makroökonomik wünschen.Für die 2. Auflage wurde ein neues Kapitel zu den mathematischen Grundlagen ergänzt, das gebündelt alle benötigten Methoden für ein wirtschaftswissenschaftliches Studium vorstellt. Im Kapitel zur Makroökonomik wurde zudem die Makroökonomik offener Volkswirtschaften neu aufgenommen.