An Introduction to Infectious Disease Modelling

Author: Emilia Vynnycky,Richard White

Publisher: Oxford University Press

ISBN: 0198565763

Category: Mathematics

Page: 370

View: 8396

Mathematical models are increasingly being used to examine questions in infectious disease control. Applications include predicting the impact of vaccination strategies against common infections and determining optimal control strategies against HIV and pandemic influenza. This book introduces individuals interested in infectious diseases to this exciting and expanding area. The mathematical level of the book is kept as simple as possible, which makes the book accessible to those who have not studied mathematics to university level. Understanding is further enhanced by models that can be accessed online, which will allow readers to explore the impact of different factors and control strategies, and further adapt and develop the models themselves. The book is based on successful courses developed by the authors at the London School of Hygiene and Tropical Medicine. It will be of interest to epidemiologists, public health researchers, policy makers, veterinary scientists, medical statisticians and infectious disease researchers.

An Introduction to Mathematical Modeling of Infectious Diseases

Author: Michael Y. Li

Publisher: Springer

ISBN: 3319721224

Category: Mathematics

Page: 156

View: 7875

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies. The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis. Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases. Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

Modeling Infectious Diseases in Humans and Animals

Author: Matt J. Keeling,Pejman Rohani

Publisher: Princeton University Press

ISBN: 1400841038

Category: Science

Page: 408

View: 1432

For epidemiologists, evolutionary biologists, and health-care professionals, real-time and predictive modeling of infectious disease is of growing importance. This book provides a timely and comprehensive introduction to the modeling of infectious diseases in humans and animals, focusing on recent developments as well as more traditional approaches. Matt Keeling and Pejman Rohani move from modeling with simple differential equations to more recent, complex models, where spatial structure, seasonal "forcing," or stochasticity influence the dynamics, and where computer simulation needs to be used to generate theory. In each of the eight chapters, they deal with a specific modeling approach or set of techniques designed to capture a particular biological factor. They illustrate the methodology used with examples from recent research literature on human and infectious disease modeling, showing how such techniques can be used in practice. Diseases considered include BSE, foot-and-mouth, HIV, measles, rubella, smallpox, and West Nile virus, among others. Particular attention is given throughout the book to the development of practical models, useful both as predictive tools and as a means to understand fundamental epidemiological processes. To emphasize this approach, the last chapter is dedicated to modeling and understanding the control of diseases through vaccination, quarantine, or culling. Comprehensive, practical introduction to infectious disease modeling Builds from simple to complex predictive models Models and methodology fully supported by examples drawn from research literature Practical models aid students' understanding of fundamental epidemiological processes For many of the models presented, the authors provide accompanying programs written in Java, C, Fortran, and MATLAB In-depth treatment of role of modeling in understanding disease control

An Introduction to Mathematical Epidemiology

Author: Maia Martcheva

Publisher: Springer

ISBN: 1489976124

Category: Mathematics

Page: 453

View: 7883

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of infectious diseases. It includes model building, fitting to data, local and global analysis techniques. Various types of deterministic dynamical models are considered: ordinary differential equation models, delay-differential equation models, difference equation models, age-structured PDE models and diffusion models. It includes various techniques for the computation of the basic reproduction number as well as approaches to the epidemiological interpretation of the reproduction number. MATLAB code is included to facilitate the data fitting and the simulation with age-structured models.

Mathematical Epidemiology

Author: Fred Brauer,Pauline van den Driessche,J. Wu

Publisher: Springer Science & Business Media

ISBN: 3540789103

Category: Medical

Page: 414

View: 2104

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).

Infectious Disease Epidemiology

Author: Ibrahim Abubakar,Helen R. Stagg,Ted Cohen,Laura C. Rodrigues

Publisher: Oxford University Press

ISBN: 0191030546

Category: Medical

Page: 416

View: 9072

Infectious Disease Epidemiology is a concise reference guide which provides trainees and practicing epidemiologists with the information that they need to understand the basic concepts necessary for working in this specialist area. Divided into two sections, part one comprehensively covers the basic principles and methods relevant to the study of infectious disease epidemiology. It is organised in order of increasing complexity, ranging from a general introduction to subjects such as mathematical modelling and sero-epidemiology. Part two examines key major infectious diseases that are of global significance. Grouped by their route of transmission for ease of reference, they include diseases that present a particular burden or a high potential for causing mortality. This practical guide will be essential reading for postgraduate students in infectious disease epidemiology, health protection trainees, and practicing epidemiologists.

Modeling Paradigms and Analysis of Disease Transmission Models

Author: Abba B. Gumel,Suzanne Lenhart

Publisher: American Mathematical Soc.

ISBN: 0821843842

Category: Mathematics

Page: 268

View: 3823

This volume stems from two DIMACS activities, the U.S.-Africa Advanced Study Institute and the DIMACS Workshop, both on Mathematical Modeling of Infectious Diseases in Africa, held in South Africa in the summer of 2007. It contains both tutorial papers and research papers. Students and researchers should find the papers on modeling and analyzing certain diseases currently affecting Africa very informative. In particular, they can learn basic principles of disease modeling and stability from the tutorial papers where continuous and discrete time models, optimal control, and stochastic features are introduced.

Epidemic Modelling

An Introduction

Author: D. J. Daley,J. Gani

Publisher: Cambridge University Press

ISBN: 9780521014670

Category: Mathematics

Page: 213

View: 2207

This is a general introduction to the mathematical modelling of diseases.

An Introduction to Mathematical Modeling in Physiology, Cell Biology, and Immunology

American Mathematical Society, Short Course, January 8-9, 2001, New Orleans, Louisiana

Author: James Sneyd

Publisher: American Mathematical Soc.

ISBN: 0821828169

Category: Medical

Page: 177

View: 8932

In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach. This book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done, what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief historical survey of each topic, putting current research into perspective. The book is suitable for mathematicians and biologists interested in mathematical methods in biology.

Mathematical Modelling of Immune Response in Infectious Diseases

Author: Guri I. Marchuk

Publisher: Springer Science & Business Media

ISBN: 9780792345282

Category: Mathematics

Page: 350

View: 7285

Beginning his work on the monograph to be published in English, this author tried to present more or less general notions of the possibilities of mathematics in the new and rapidly developing science of infectious immunology, describing the processes of an organism's defence against antigen invasions. The results presented in this monograph are based on the construc tion and application of closed models of immune response to infections which makes it possible to approach problems of optimizing the treat ment of chronic and hypertoxic forms of diseases. The author, being a mathematician, had creative long-Iasting con tacts with immunologists, geneticist, biologists, and clinicians. As far back as 1976 it resulted in the organization of a special seminar in the Computing Center of Siberian Branch of the USSR Academy of Sci ences on mathematical models in immunology. The seminar attracted the attention of a wide circle of leading specialists in various fields of science. All these made it possible to approach, from a more or less united stand point, the construction of models of immune response, the mathematical description of the models, and interpretation of results.

Models for Life

An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel

Author: Jeffrey T. Barton

Publisher: John Wiley & Sons

ISBN: 1119039762

Category: Mathematics

Page: 488

View: 9942

Features an authentic and engaging approach to mathematical modeling driven by real-world applications With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® guides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques. The book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next. Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in Excel. The book examines single-compartment models in contexts such as population growth, personal finance, and body weight and provides an introduction to more advanced, multi-compartment models via applications in many areas, including military combat, infectious disease epidemics, and ranking methods. Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® also features: A modular organization that, after the first chapter, allows readers to explore chapters in any order Numerous practical examples and exercises that enable readers to personalize the presented models by using their own data Carefully selected real-world applications that motivate the mathematical material such as predicting blood alcohol concentration, ranking sports teams, and tracking credit card debt References throughout the book to disciplinary research on which the presented models and model parameters are based in order to provide authenticity and resources for further study Relevant Excel concepts with step-by-step guidance, including screenshots to help readers better understand the presented material Both mathematical and graphical techniques for understanding concepts such as equilibrium values, fixed points, disease endemicity, maximum sustainable yield, and a drug’s therapeutic window A companion website that includes the referenced Excel spreadsheets, select solutions to homework problems, and an instructor’s manual with solutions to all homework problems, project ideas, and a test bank The book is ideal for undergraduate non-mathematics majors enrolled in mathematics or quantitative reasoning courses such as introductory mathematical modeling, applications of mathematics, survey of mathematics, discrete mathematical modeling, and mathematics for liberal arts. The book is also an appropriate supplement and project source for honors and/or independent study courses in mathematical modeling and mathematical biology. Jeffrey T. Barton, PhD, is Professor of Mathematics in the Mathematics Department at Birmingham-Southern College. A member of the American Mathematical Society and Mathematical Association of America, his mathematical interests include approximation theory, analytic number theory, mathematical biology, mathematical modeling, and the history of mathematics.

The Economics of Epidemiology

Author: Troy Tassier

Publisher: Springer Science & Business Media

ISBN: 3642381200

Category: Business & Economics

Page: 94

View: 1146

The book presents a basic introduction to epidemiology from the perspective of economics, using economic modeling to better understand and describe how infectious disease spreads. Three main elements are introduced: epidemiology, social network analysis, and the economics needed to model the behavior of individuals in the presence of infectious disease. The book aims to provide a starting point for discussion between medical professionals, social scientists and public health officials, the three groups interested in the spread of disease.

Modeling and Dynamics of Infectious Diseases

Author: Zhien Ma,Yicang Zhou,Jianhong Wu

Publisher: World Scientific

ISBN: 9814261254

Category: Medical

Page: 343

View: 8081

This book provides a systematic introduction to the fundamental methods and techniques and the frontiers of ? along with many new ideas and results on ? infectious disease modeling, parameter estimation and transmission dynamics. It provides complementary approaches, from deterministic to statistical to network modeling; and it seeks viewpoints of the same issues from different angles, from mathematical modeling to statistical analysis to computer simulations and finally to concrete applications.

Medizinische Mikrobiologie

Author: Ernest Jawetz,Joseph L. Melnick,Edward A. Adelberg

Publisher: Springer-Verlag

ISBN: 3662001551

Category: Science

Page: N.A

View: 2352

Die Autoren haben beabsichtigt, diejenigen Gebiete der medizinischen Mikrobiologie kurz, exakt und in ihrem gegenwärtigen Stand darzustellen, die für die Infektionskrankheiten und ihre Chemotherapie von besonderer Bedeutung sind. Das Buch wendet sich in erster Linie an Medizinstudenten, außerdem an alle Ärzte in Krankenhaus und Praxis. Die Notwendigkeit für ein klares Verständnis der mlkrobiologischen Grundtatsachen ist in den letzten Jahren stärker geworden, da in Biochemie, Virologie und Chemotherapie so wie auf weiteren, die Medizin beeinflussenden Gebieten bedeutende Entwicklungen statt gefunden haben. Ein wesendicher Teil dieses Lehrbuches ist deswegen der Darstellung der Grundlagen gewidmet, wodurch sich das Buch auch für die Einführung des Studenten in den mikrobiologischen Kurs als brauchbar erweisen wird. Für die neue Auflage wurde ein Kapitel über Virus und Krebs neu geschrieben, und das Kapitel über antimikrobielle Chemotherapie wurde von Grund auf neu bearbeitet. Die Autoren freuen sich, bei dem Erscheinen der 7. amerikanischen Ausgabe von einer spanischen, deutschen, italienischen und griechischen Ausgabe, sowie von der Vorbereitung für eine serbokroatische Übersetzung berichten zu können. Die Autoren möchten nochmals allen danken, die ihnen bei der Bearbeitung dieser Auf lage behilflich waren, und die es ihnen durch ihre Kommentare und ihre Kritik ermöglicht haben, die in 2jährigen Abständen erscheinenden Revisionen dieses Buches auf dem neu esten Stand zu halten. ERNEsr JAWETZ JOSEPH L MELNICK San Frandsco, August 1966 EnWARD A AnELBERG III Inhaltsverzeichnis 1 Kapitell Die ~lt der Mikroben 8 Kapitel 2 Cytologie der Bakterien Optische Methoden 8 9 Eukaryote Zellstrukturen Prokaryote Zellstrukturen . 12 14 Cytoplasmatische Strukturen. 27 Färbeverfahren .

Einführung in die Geometrie und Topologie

Author: Werner Ballmann

Publisher: Springer-Verlag

ISBN: 3034809018

Category: Mathematics

Page: 162

View: 2736

Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.

Die Kunst des Heilens

eine medizinische Geschichte der Menschheit von der Antike bis heute

Author: Roy Porter

Publisher: N.A

ISBN: 9783827414540

Category: Medicine

Page: 818

View: 5196

Zwischen Leben und Tod Ein faszinierender Aoeberblick A1/4ber fA1/4nf Jahrtausende Medizingeschichte -- von der Steinzeit bis zum New Age, von der Magie zur Molekularbiologie, begeisternd geschrieben und begeistert aufgenommen: ”Roy Porter ist ein brillanter Triumph gelungen.Evening Standard" ”Eine erstklassige EinfA1/4hrung in die Geschichte der Medizin.The Times" ”Roy Porters Mammut-Medizingeschichte ist eine auAerordentliche Leistung ... lebhaft und voller faszinierender Information.Observer" ”Lehrbuch-Geschichte der Spitzenklasse.Nature" ”Eine immens unterhaltsame Erkundung von Medizin und Geschichte. Von den JAgern und Sammlern bis zur Herztransplantation wird ein Geflecht von Ideen und Ereignissen gewoben, das nahtlos Medizin, Philosophie, Wissenschaft und Geschichte integriert. Ein verfA1/4hrerischer Sog entsteht ... Die Prosa flieAt mA1/4helos, das Material ist wohlorganisiert und in den Anekdoten faszinierend ... Eine groAartige LektA1/4re.British Journal of General Practice" ”Im Zentrum des nun deutsch vorliegenden Werkes stehen das Denken, Wissen und Handeln der A"rzte oder im weiteren Sinne Heiler; durchgAngig wird die Aufmerksamkeit auf den Kranken und die soziale Welt gelenkt, wird die Geschichte der Krankheit mit der Geschichte des Kranken verbunden ... Fachliches Wissen verbindet sich bei Porter mit einem Schreibstil, der auch den Laien zu fesseln vermag und den Fachmann A1/4berzeugt. Substanz und Humor mA1/4ssen sich, das lAsst sich hier einmal wieder eindrucksvoll nachvollziehen, keineswegs widersprechen. Abbildungen ergAnzen und vertiefen auf einleuchtende Weise den Text ... Das ebenso gehaltreiche wie stimulierende Werk von Roy Porter mAge viele Leser finden -- in der medizinhistorischen Zunft wie in der allgemeinen A-ffentlichkeit, auch unter Patienten und ihren AngehArigen.Aus dem Geleitwort von Prof. Dr. Dietrich von Engelhardt, Institut fA1/4r Medizin- und Wissenschaftsgeschichte, Medizinische UniversitAt zu LA1/4beck" Porters monumentales Buch verknA1/4pft in geschickter Weise zwei AnsAtze der Medizingeschichte miteinander. Zum einen stellen kurze, prAgnante Portraits jene vielfAltigen PersAnlichkeiten vor, deren Leistungen fA1/4r die stetige Entwicklung der Medizin von entscheidender Bedeutung waren. Zum anderen gelingt es dem Autor zugleich, jede Phase dieser komplexen Geschichte in ihren politischen, sozialen und demographischen Rahmen zu stellen. Dieser duale Ansatz spannt sich von den Berichten A1/4ber die medizinische Praxis im alten Griechenland, in China und in Indien A1/4ber die arabisch-islamische Periode und das Mittelalter hinweg bis zur Medizin der Gegenwart. Trotz aller FaktenfA1/4lle ist dieses gewichtige Werk aber so eloquent geschrieben, mit so viel Stil, Einsicht und Humor, dass man es kaum aus der Hand legen mag. Porter erweist den heutigen (und den zukA1/4nftigen) A"rzten wie der Fachgemeinschaft insgesamt einen groAen Dienst, indem er die aktuelle medizinische Landschaft in eine breite historische Perspektive stellt. Sein Buch ist spannendste Unterhaltung fA1/4r alle (medizin)historisch Interessierten und PflichtlektA1/4re fA1/4r all jene, die sich der schweren Aufgabe gewidmet haben, die Ziele der medizinischen TAtigkeit fA1/4r die Zukunft neu zu definieren.

The Geographic Spread of Infectious Diseases

Models and Applications

Author: Lisa Sattenspiel

Publisher: Princeton University Press

ISBN: 069112132X

Category: Mathematics

Page: 286

View: 1665

The 1918-19 influenza epidemic killed more than fifty million people worldwide. The SARS epidemic of 2002-3, by comparison, killed fewer than a thousand. The success in containing the spread of SARS was due largely to the rapid global response of public health authorities, which was aided by insights resulting from mathematical models. Models enabled authorities to better understand how the disease spread and to assess the relative effectiveness of different control strategies. In this book, Lisa Sattenspiel and Alun Lloyd provide a comprehensive introduction to mathematical models in epidemiology and show how they can be used to predict and control the geographic spread of major infectious diseases. Key concepts in infectious disease modeling are explained, readers are guided from simple mathematical models to more complex ones, and the strengths and weaknesses of these models are explored. The book highlights the breadth of techniques available to modelers today, such as population-based and individual-based models, and covers specific applications as well. Sattenspiel and Lloyd examine the powerful mathematical models that health authorities have developed to understand the spatial distribution and geographic spread of influenza, measles, foot-and-mouth disease, and SARS. Analytic methods geographers use to study human infectious diseases and the dynamics of epidemics are also discussed. A must-read for students, researchers, and practitioners, no other book provides such an accessible introduction to this exciting and fast-evolving field.

Solutions Manual to Accompany Models for Life

An Introduction to Discrete Mathematical Modeling with Microsoft Office Excel

Author: Jeffrey T. Barton

Publisher: John Wiley & Sons

ISBN: 1119040027

Category: Mathematics

Page: 182

View: 6269

A solutions manual to accompany An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® With a focus on mathematical models based on real and current data, Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® guides readers in the solution of relevant, practical problems by introducing both mathematical and Excel techniques. The book begins with a step-by-step introduction to discrete dynamical systems, which are mathematical models that describe how a quantity changes from one point in time to the next. Readers are taken through the process, language, and notation required for the construction of such models as well as their implementation in Excel. The book examines single-compartment models in contexts such as population growth, personal finance, and body weight and provides an introduction to more advanced, multi-compartment models via applications in many areas, including military combat, infectious disease epidemics, and ranking methods. Models for Life: An Introduction to Discrete Mathematical Modeling with Microsoft® Office Excel® also features: A modular organization that, after the first chapter, allows readers to explore chapters in any order Numerous practical examples and exercises that enable readers to personalize the presented models by using their own data Carefully selected real-world applications that motivate the mathematical material such as predicting blood alcohol concentration, ranking sports teams, and tracking credit card debt References throughout the book to disciplinary research on which the presented models and model parameters are based in order to provide authenticity and resources for further study Relevant Excel concepts with step-by-step guidance, including screenshots to help readers better understand the presented material Both mathematical and graphical techniques for understanding concepts such as equilibrium values, fixed points, disease endemicity, maximum sustainable yield, and a drug’s therapeutic window A companion website that includes the referenced Excel spreadsheets, select solutions to homework problems, and an instructor’s manual with solutions to all homework problems, project ideas, and a test bank

Digitale Werkzeuge, Simulationen und mathematisches Modellieren

Didaktische Hintergründe und Erfahrungen aus der Praxis

Author: Gilbert Greefrath,Hans-Stefan Siller

Publisher: Springer-Verlag

ISBN: 3658219408

Category: Computers

Page: 262

View: 6654

Dieses Buch widmet sich dem Einsatz digitaler Medien und Werkzeuge im Zusammenhang mit Modellierungsprozessen im Mathematikunterricht. Gerade bei der Bearbeitung realitätsbezogener Probleme können digitale Werkzeuge eine sinnvolle Unterstützung für Lernende darstellen, aber auch für Lehrende können sie eine sinnvolle Ergänzung sein. Dabei kommt insbesondere Simulationen, in allen Variationen, eine besondere Aufgabe zu. Diese können durch den Einsatz digitaler Werkzeuge umfassend um- und eingesetzt werden. So gelingt es realitätsnahe Problemstellungen aus unterschiedlichen Perspektiven zu bearbeiten. In einem ersten Teil werden theoretische und empirische Beiträge zu diesem Thema zusammengefasst. Im zweiten Teil des Bandes liegt der Schwerpunkt auf Erfahrungen aus der Praxis des Simulierens und des mathematischen Modellierens mit digitalen Werkzeugen. Die vorgestellten Ansätze sind in die aktuelle Modellierungsdiskussion eingebunden und wurden alle in der Praxis erprobt. Modellierung mit digitalen Werkzeugen und Simulation sind auch für die aktuelle mathematikdidaktische Diskussion und die Lehrerbildung im Fach Mathematik von großem Interesse.