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Graph Mining

How the Quest for the Biggest, Fewest and Weirdest Makes Maths

Reaching for the Extreme

From the author of the award-winning Which One Doesn't Belong? and How Many? comes How Did You Count?, the latest title in Christopher Danielson's collection that is sure to spark conversation, questioning and wondering amongst both younger and older students alike.

From the author of the award-winning Which One Doesn’t Belong? and How Many? comes How Did You Count?, the latest title in Christopher Danielson’s collection that is sure to spark conversation, questioning and wondering amongst both younger and older students alike.

Picture Book

How Did You Count?

Vladimir I. Arnold - Collected Works

This volume 7 of the “Collected Works" includes papers written by V.I. Arnold, one of the most outstanding mathematicians of all times, &nbsp;during the period from 1996 to 1999. At that time Arnold was focusing on the description of various spaces of curves, higher-dimensional continued fractions, pseudoperiodic topology, and unifying ideas related to symplectization, complexification and mathematical trinities in topology and mathematics in general. The “Arnoldfest" conference celebrating 60th anniversary of V.Arnold took place at the Fields Institute and University of Toronto, Canada, in 1997, &nbsp;and Arnold's lectures at that conference are included in this volume. In the 1990s Arnold got increasingly concerned with the decay of science and math education in many Western countries, and his publications fighting “the victorious march of the antiscientific revolution" (as he phrased it in one of his papers) are collected in this volume as well. Some of Arnold's writings stimulated others to write supplements with more detail, and the volume also includes the notes of A.M.Vershik, J.K.Moser, and B.A.Khesin. Finally, a glimpse of Arnold's personality can also be appreciated in a little gem, his short article devoted to resolving the mystery of the origin of the epigraph to “Eugene Onegin" by A.S. Pushkin, a famous XIXth century Russian poet. &nbsp; 
The book will be of interest to the wide audience &nbsp;from college students to professionals in mathematics or physics and in the history of science. This volume completes the seven-volume project of “Collected Works of Vladimir Arnold", the first volume of which was published in 2009. Arnold's publications in the 2000s were also abundant, he turned to new topics, wrote several books, he gave numerous lectures, both research and educational. But what has already been published in these seven volumes is a treasure trove, an ocean of ideas, methods, and results, and this is now before the reader to explore. Happy voyage!

Spaces and Singularities of Curves, Mathematical Trinities, and Mathematical Education 1996–1999

The robot “concept” was clearly established by those many creative historical realizations, such as those recalled above. Nonetheless, the emergence of the “physical” robot had to await the advent of its underlying technologies of mechanics, controls, computers, electronics and sensors ―in one word, mechatronics― during the course of the twentieth century. As always, new designs motivate new research and discoveries which, in turn, lead to enhanced solutions and thus to novel concepts. This virtuous circle over time produced that knowledge and understanding which gave birth to the field of Robotics, properly referred to as the science and technology of robots.To make robots and intelligent machines useful to humans it is necessary to have a broad and tight intersection between Robotics and AI. Sophisticated mathematical models are needed that enable the robot from a physical point of view, as well as intelligent algorithms capable of correlating all the information coming from the use of technologically advanced sensors with the data available from experience. It is expected that the synergy of model-based techniques with data-driven approaches will contribute to increasing the level of autonomy of robots and intelligent machines in the near future.The first book of the Robotics Goes MOOC project starts with the journey of robotics in the introductory chapter by Khatib, who has pioneered our field of robotics and has ferried it to the third millennium. Sensing is crucial for the development of intelligent and autonomous robots, as covered in Chapter 2 by Nüchter et al. Model-based control is dealt with in Chapter 3 by Kröeger et al along with motion planning, as well as in Chapter 4 by Villani and Chapter 5 by Chaumette to handle force and visual feedback, respectively, when interacting with the environment. Resorting to AI techniques is the focus of the last part of the book, namely, Chapter 6 by Peters et al on Learning, Chapter 7 by Beetzet al on knowledge representation and reasoning, and Chapter 8 by Burgard et al on graph-based SLAM.&nbsp;The image on the cover metaphorically illustrates the&nbsp;knowledge&nbsp;paradigm of robotics through a hand trying to catch an apple.&nbsp;The content published here are linked to a series of MOOCs on Robotics specifically created and hosted by Federica Web Learning. You can access the related content via our app: download the SN More Media app for free, scan the link and access directly to the online courses on your smartphone or tablet.

This book is part of the Springer MOOC &amp; BOOK project, providing both a MOOC – offered through Federica Web Learning – and a Springer reference book based on the online course, combining the quality of a scientific essay with the communicative power of an online educational product.&nbsp;It provides a state-of-the-art overview of various aspects of the rapidly developing field of robotics, which is vigorously engaged in the growing challenges of emerging new domains.Interacting, exploring and working with humans, the new generation of robots will increasingly touch people and their lives.&nbsp;The book is strictly linked to the MOOC, and includes numerous examples and exercises in addition to those offered in the MOOC. Moreover, it features multimedia content, such as videos and augmented reality, which can be accessed via PC, tablet or any other mobile device. Students who buy the print book can easily access this content through the Springer Multimedia App,optimized for cell phones and tablets. Readers simply scan the image with their cell phone or tablet and they are taken directly to the video, figure, photo, table, PowerPoint slide, etc. Moreover, this content can be shared via other apps, email, messengers, and more.The book, edited by an outstanding, internationally respected expert in the field, includes valuable contributions from more than 30 authors, making this innovative project an authoritative reference resource for senior graduate and PhD level students, as well as for robotics researchers and scientists from related disciplines.This book focuses on&nbsp;Knowledge.

Knowledge

Robotics Goes MOOC

Math Survival Guide: Tips for Science Student, 3E

Dieses Buch deckt alle relevanten mathematischen Themen eines Grundstudiums der Natur- oder Ingenieurwissenschaften ab, von der Analysis (inklusive einer ausführlichen Behandlung gewöhnlicher Differentialgleichungen mitsamt Modellierungsaspekten) und der linearen Algebra bis hin zu den wichtigsten Lösungsmethoden für partielle Differentialgleichungen. Das selbstständige Erlernen der Inhalte wird durch zahlreiche anwendungs- und praxisrelevante Beispiele motiviert und durch interaktive Aufgaben, verlinkte Videos und Repetitionsfragen gefördert. 
 Außerdem werden die Studierenden durch direkt in den entsprechenden Programmen bearbeitbare Dateien befähigt, mit den gängigsten Computer-Algebra-Systemen zu arbeiten, wodurch die eigene Auseinandersetzung mit der Materie weiter unterstützt wird.
 Insgesamt wird hier nicht nur eine äußerst geschickte didaktische Herangehensweise an die Mathematik umgesetzt, sondern die Themen werden zudem mit modernsten multimedialen Mitteln aufbereitet.&nbsp;&nbsp;Die AutorinDr. Laura Keller
 ist Senior Scientist an der ETH Zürich, also einerseits als Dozentin und andererseits als Forscherin tätig. Insbesondere hält sie seit mehreren Jahren Grundstudium-Mathematik-Vorlesungen für Studierende, die Mathematik nicht als Hauptfach belegen. Diese Vorlesungen sind bei den Studierenden nicht zuletzt wegen des großen didaktischen Geschicks der Dozentin und den vielen Praxisbezügen sehr geschätzt.

Dieses Buch deckt alle relevanten mathematischen Themen eines Grundstudiums der Natur- oder Ingenieurwissenschaften ab, von der Analysis (inklusive einer ausführlichen Behandlung gewöhnlicher Differentialgleichungen mitsamt Modellierungsaspekten) und der linearen Algebra bis hin zu den wichtigsten Lösungsmethoden für partielle Differentialgleichungen. Das selbstständige Erlernen der Inhalte wird durch zahlreiche anwendungs- und praxisrelevante Beispiele motiviert und durch interaktive Aufgaben, verlinkte Videos und Repetitionsfragen gefördert. 
 Außerdem werden die Studierenden durch direkt in den entsprechenden Programmen bearbeitbare Dateien befähigt, mit den gängigsten Computer-Algebra-Systemen zu arbeiten, wodurch die eigene Auseinandersetzung mit der Materie weiter unterstützt wird.
 Insgesamt wird hier nicht nur eine äußerst geschickte didaktische Herangehensweise an die Mathematik umgesetzt, sondern die Themen werden zudem mit modernstenmultimedialen Mitteln aufbereitet.&nbsp;&nbsp;

für Naturwissenschaftler, Ingenieure und Mediziner

Mathematik interaktiv und verständlich

Tauche ein in die Elektrodynamik mit einem Lehrbuch, welches die Maxwellschen Gleichungen als Ausgangspunkt nutzt, wodurch Schritt für Schritt ein tiefes Verständnis vermittelt wird.&nbsp;Besonderheiten:Dieses Buch beginnt jedes Kapitel mit einer der Maxwellschen Gleichungen und erklärt dann schrittweise die einzelnen Bestandteile.&nbsp;Anfänger/innen haben so ein konkretes Lernziel vor Augen.&nbsp;Sowohl die vorkommenden physikalischen Größen als auch mathematischen Grundlagen werden in ihrem natürlichen Kontext erklärt. Grundlegende Prinzipien und komplexe Konzepte werden für verschiedene Fälle betrachtet und mit einfachen Beispielen verdeutlicht. Mithilfe von Aufgaben und Lösungen – sowohl klassisch im Buch als auch als digitale Karteikarten für unterwegs – kann das erworbene Wissen eingeübt und vertieft werden.&nbsp;Inhalt:1. Das Gaußsche Gesetz für elektrische Felder – 2. Das Gaußsche Gesetz für magnetische Felder –&nbsp;3. Das Faradaysche Induktionsgesetz&nbsp;– 4. Das Ampère-Maxwellsche Gesetz – 5. Weiterführende Themen der Elektrodynamik – 6. Wechselwirkung von elektrischen und magnetischen Feldern mit Materie&nbsp;Zielgruppe:Studierende der Ingenieurwissenschaften und Naturwissenschaften, wie z.B. Elektrotechnik, Physik, Medizinphysik, etc. als auch Interessierte bzw. Berufstätige, die ein tieferes Verständnis für die Grundlagen der Elektrodynamik entwickeln möchten.&nbsp;Vorkenntnisse: Hilfreich sind physikalische Grundkenntnisse wie sie z.B. im Buch Vorkurs Physik fürs MINT-Studium vermittelt werden.&nbsp;Der Autor:Dr. Patrick Steglich&nbsp;promovierte 2017 an der Universität Rom ‚Tor Vergata‘ und habilitierte 2023 an der Brandenburgischen Technischen Universität Cottbus-Senftenberg.&nbsp;Seit 2018 ist er Dozent mit Lehrauftrag an der Technischen Hochschule Wildau&nbsp;für das Fach Elektrodynamik und forscht am Leibniz-Institut für innovative Mikroelektronik.

Tauche ein in die Elektrodynamik mit einem Lehrbuch, welches die Maxwellschen Gleichungen als Ausgangspunkt nutzt, wodurch Schritt für Schritt ein tiefes Verständnis vermittelt wird.&nbsp;Besonderheiten:Dieses Buch beginnt jedes Kapitel mit einer der Maxwellschen Gleichungen und erklärt dann schrittweise die einzelnen Bestandteile.&nbsp;Anfänger/innen haben so ein konkretes Lernziel vor Augen.&nbsp;Sowohl die vorkommenden physikalischen Größen als auch mathematischen Grundlagen werden in ihrem natürlichen Kontext erklärt. Grundlegende Prinzipien und komplexe Konzepte werden für verschiedene Fälle betrachtet und mit einfachen Beispielen verdeutlicht. Mithilfe von Aufgaben und Lösungen – sowohl klassisch im Buch als auch als digitale Karteikarten für unterwegs – kann das erworbene Wissen eingeübt und vertieft werden.&nbsp;Inhalt:1. Das Gaußsche Gesetz für elektrische Felder – 2. Das Gaußsche Gesetz für magnetische Felder –&nbsp;3. Das Faradaysche Induktionsgesetz&nbsp;– 4. Das Ampère-Maxwellsche Gesetz – 5. Weiterführende Themen der Elektrodynamik – 6. Wechselwirkung von elektrischen und magnetischen Feldern mit Materie&nbsp;Zielgruppe:Studierende der Ingenieurwissenschaften und Naturwissenschaften, wie z.B. Elektrotechnik, Physik, Medizinphysik, etc. als auch Interessierte bzw. Berufstätige, die ein tieferes Verständnis für die Grundlagen der Elektrodynamik entwickeln möchten.&nbsp;Vorkenntnisse: Hilfreich sind physikalische Grundkenntnisse wie sie z.B. im Buch Vorkurs Physik fürs MINT-Studium vermittelt werden.&nbsp;

Eine schrittweise Reise durch Maxwells Gleichungen

Klassische Elektrodynamik

This book combines theory and practice to enable successful mathematical education for children from birth to twelve years. It considers how students, academics, parents and professionals can develop their mathematical thinking practice whilst acknowledging we will always be practising the craft of teaching mathematics.

Supporting Early Mathematical Development is an essential text, combining theory and practice to enable successful mathematical education for children from birth to 12 years. This text considers how students, academics, parents and professionals can develop their mathematical thinking practice whilst acknowledging there will always be a road yet to travel; we will always be practising the craft of teaching mathematics. Charting the delivery of mathematical development in playgroups, children’s centres, nurseries and primary schools, the book promotes an effective pedagogy for mathematics.This new edition provides a conceptualisation of mathematics and places a fresh emphasis on mathematical literacy to empower children. New chapters include the following:■ Mediators of Mathematical Thinking■ Understanding Pattern, Pre-Algebraic and Algebraic Thinking■ Naming, Renaming and Processing Numbers■ Statistics, Statistical Diagrams and Probability■ Measure■ GeometryThroughout the book, Caroline McGrath navigates the complexity of teaching and learning mathematics, through careful thought and consideration of mediators of mathematical thinking. This supportive book is designed for educators who want to know how to reconstruct mathematical ideas with children and respond in the moment. Returning to the root of understanding, using the adaptive pedagogical style recommended in this text, you can create satisfying mathematical experiences for children.

Practical Approaches to Play-Based Learning

Supporting Early Mathematical Development

Essays in Developmental Psychology

Perspectives from Developmental Psychology

Attitudes and Emotions Towards Mathematics

Selected Chapters Of Number Theory: Special Numbers

Catalan numbers, named after the French-Belgian mathematician Eugène Charles Catalan (1814-1894), arise in a variety of combinatorial problems. They have many interesting properties, a rich history, and numerous arithmetic, number-theoretical, analytical, and combinatorial connections, as well as a variety of classical and modern applications. Considering the long list of open problems and questions related to the classical case, its relatives (Bell numbers, Motzkin numbers, Narayana numbers, etc.) and its generalizations, this book provides a broad perspective on the theory of this class of special numbers that will be of interest to professionals, students, and a general audience.

The book begins with the history of the problem, before defining the considered numerical sets. The recurrence equation, closed formula, and generating function are then presented, followed by the simplest properties and number-theoretical properties. Later chapters discuss the relationships between Catalan numbers and other special numbers, as well as their applications and open problems.

Catalan Numbers

UNITEXT

La Matematica per il 3+2

L'obiettivo principale di questo libro è presentare un trattamento unificato della termomeccanica dei continui utilizzando l'approccio assiomatico tipico della meccanica razionale. Mentre molti testi di meccanica dei continui si concentrano su tipi specifici di corpi continui, come i corpi solidi deformabili o i fluidi, questo libro adotta una prospettiva generale. Viene presentata la struttura matematica delle leggi di bilancio e delle equazioni costitutive come un insieme coeso, con particolare attenzione alla moderna teoria delle equazioni costitutive. Si sottolineano principi importanti, come il principio di indifferenza materiale e l'interpretazione contemporanea del principio di entropia. Per garantire la coerenza interna, la prima parte del libro affronta questioni relative all'algebra lineare, con particolare attenzione agli operatori lineari all'interno degli spazi vettoriali a dimensione finita. Successivamente, il libro offre un'esplorazione dettagliata delle deformazioni finite dei continui, seguita da una panoramica sulla cinematica. Vengono caratterizzate le varie forze che possono esistere in un continuo, introdotto il tensore degli sforzi e presentate le leggi di bilancio sia in forma euleriana che lagrangiana. Successivamente viene definita la moderna teoria delle equazioni costitutive, sottolineando il ruolo dei principi generali di indifferenza materiale e di entropia come criteri per la selezione delle classi fisicamente accettabili di equazioni costitutive. Le equazioni di campo risultanti sono specializzate per vari casi, tra cui la termoelasticità, i fluidi euleriani, i fluidi di Fourier-Navier‒Stokes e i conduttori rigidi di calore. Nell'ultima parte del libro vengono discussi i sistemi di equazioni alle derivate parziali nella meccanica dei continui, con particolare attenzione ai sistemi iperbolici. Il metodo delle caratteristiche viene introdotto sia nei casi lineari che non lineari, e si discute la necessità di ampliare la classe delle soluzioni introducendo le soluzioni deboli, con le onde d'urto come caso significativo. Come esempio illustrativo di soluzione debole, viene presentato il problema di Riemann per il modello fluidodinamico del traffico veicolare, in cui le automobili sono inizialmente ferme a un semaforo rosso e poi iniziano a muoversi quando il semaforo diventa verde.Questo libro sarà utile non solo per gli studenti di ingegneria, ma anche per gli studenti di altre discipline scientifiche in cui si studiano aspetti della meccanica dei continui. Fornisce l'opportunità di considerare argomenti tradizionalmente distinti in un contesto più ampio e interconnesso.

Introduzione alla termomeccanica dei sistemi continui ed ai sistemi iperbolici

This work, designed for clinicians, adopts a coordinated multidisciplinary approach to a range of topics central to complexity in medicine, with the aim of offering an integrated, unitary perspective that stands in contrast to the traditional simplification inherent in the subdivision into single specialties. It recognizes that medicine today has to face emerging issues that current knowledge cannot accommodate because the properties to be addressed do not simply equate to the sum of&nbsp;the properties of single components but rather are the product of interactions among them or among different environments. Examples include the interactions among genetic, environmental, pathological, psychological, and ethical aspects. This new model, represented by so-called systems medicine, entails a different approach, already reflected in, for instance, the view of cancer as a cellular ecosystem in evolution rather than a unique&nbsp;disease and the acknowledgment that future guidelines for cardiovascular prevention will have to consider many factors beyond blood pressure or cholesterol levels. It also recognizes the impact of other fields upon medicine, as in the crucial contributions of CERN to projects of great medical importance and of grid computing to genomics research. The Handbook of Complexity in Medicine offers stimulating insights into this new reality; it will provide readers with a tool for deepening their understanding of topics that even today remain somewhat unclear and will hopefully assist in decision making that takes into account this uncertainty.

Handbook of Complexity in Medicine

Graph Mining

Bibliografische Angaben

Schlagworte

Bibliografische Angaben

Schlagworte

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