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Mathematical Modelling Skills

Author: Dilwyn Edwards,Michael Hamson

Publisher: Macmillan International Higher Education

ISBN: 1349132500

Category: Applied mathematics

Page: 164

The aim of this book is to assist the reader to build up the necessary range of skills needed to be able to solve problems by mathematical modelling. After an introduction to the general principles and advantages of mathematical modelling, chapters 1 to 4 concentrate on the development of basic modelling skills. Each of chapters 5 to 11 isolates a particular modelling concept and provides exercises aimed at developing skills in the use of that concept. The later chapters may be conveniently read in any order as they are self contained. In keeping with the Work Out approach, each chapter contains a large number of examples and exercises, taken from a variety of subject areas and covering a broad range of difficulty. Answers are provided wherever appropriate.

Guide to Mathematical Modelling

Author: Dilwyn Edwards,Mike Hamson

Publisher: Macmillan International Higher Education

ISBN: 1349100420

Category: Applied mathematics

Page: 277

The authors' enthusiasm for their subject is eloquently conveyed in this book, and draws the reader very quickly into active investigation of the problems posed. By providing plenty of modelling examples from a wide variety of fields - most of which are familiar from everyday life - the book shows how to apply mathematical ideas to situations which would not previously have been considered to be 'mathematical' in character.

Teaching Mathematical Modelling: Connecting to Research and Practice

Author: Gloria Ann Stillman,Gabriele Kaiser,Werner Blum,Jill P. Brown

Publisher: Springer Science & Business Media

ISBN: 9400765401

Category: Education

Page: 627

This book provides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy.

Trends in Teaching and Learning of Mathematical Modelling

ICTMA14

Author: Gabriele Kaiser,Werner Blum,Rita Borromeo Ferri,Gloria Stillman

Publisher: Springer Science & Business Media

ISBN: 9789400709102

Category: Education

Page: 734

This book contains suggestions for and reflections on the teaching, learning and assessing of mathematical modelling and applications in a rapidly changing world, including teaching and learning environments. It addresses all levels of education from universities and technical colleges to secondary and primary schools. Sponsored by the International Community of Teachers of Mathematical Modelling and Applications (ICTMA), it reflects recent ideas and methods contributed by specialists from 30 countries in Africa, the Americas, Asia, Australia and Europe. Inspired by contributions to the Fourteenth Conference on the Teaching of Mathematical Modelling and Applications (ICTMA14) in Hamburg, 2009, the book describes the latest trends in the teaching and learning of mathematical modelling at school and university including teacher education. The broad and versatile range of topics will stress the international state-of-the-art on the following issues: Theoretical reflections on the teaching and learning of modelling Modelling competencies Cognitive perspectives on modelling Modelling examples for all educational levels Practice of modelling in school and at university level Practices in Engineering and Applications

Mathematical Modelling

Author: John Stephen Berry,Ken Houston

Publisher: Gulf Professional Publishing

ISBN: 0340614048

Category: Mathematics

Page: 142

Assuming virtually no prior knowledge, Modular Mathematics encourages the reader to develop and solve real models, as well as looking at traditional examples. Accessible and concise, it contains tutorial problems, case studies and exercises.

Mathematical Modelling

A Way of Life - ICTMA 11

Author: S J Lamon,W A Parker,S K Houston

Publisher: Elsevier

ISBN: 085709954X

Category: Mathematics

Page: 288

Mathematical modelling is often spoken of as a way of life, referring to habits of mind and to dependence on the power of mathematics to describe, explain, predict and control real phenomena. This book aims to encourage teachers to provide opportunities for students to model a variety of real phenomena appropriately matched to students’ mathematical backgrounds and interests from early stages of mathematical education. Habits, misconceptions, and mindsets about mathematics can present obstacles to university students’ acceptance of a ‘‘models-and-modelling perspective’’ at this stage of mathematics education. Without prior experience in building, interpreting and applying mathematical models, many students may never come to view and regard modelling as a way of life. The book records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003. Examines mathematical modelling as a way of life, referring to habits of mind and dependence on the power of mathematics to describe, explain, predict and control real phenomena Encourages teachers to provide students with opportunities to model a variety of real phenomena appropriately matched to students’ mathematical backgrounds and interests from early stages of mathematical education Records presentations at the ICTMA 11 conference held in Milwaukee, Wisconsin in 2003

Mathematical Modelling Techniques

Author: Rutherford Aris

Publisher: Courier Corporation

ISBN: 0486138895

Category: Technology & Engineering

Page: 288

Highly useful volume discusses the types of models, how to formulate and manipulate them for best results. Numerous examples.

Mathematical Modelling in Education and Culture

ICTMA 10

Author: Q-X Ye,W Blum,S K Houston,Q-Y Jiang

Publisher: Elsevier

ISBN: 0857099558

Category: Mathematics

Page: 342

The mathematical modelling movement in mathematics education at school and university level has been influencing curricula for about 25 years. Lecturers will find material to enhance their teaching and extracurricular activities and educators will find innovative ideas to inform their course design and focus their research, while students will find interesting problems to explore. Helps lecturers enhance their teaching and extracurricular activities Provides educators with innovative ideas to inform their course design and focus their research Students will find interesting problems to explore

Mathematical Modelling

Case Studies and Projects

Author: J. Caldwell,Douglas K.S. Ng

Publisher: Springer Science & Business Media

ISBN: 1402019939

Category: Mathematics

Page: 253

Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science, engineering, business and management. Recent developments in computer technology and related software have provided the necessary tools of increasing power and sophistication which have significant implications for the use and role of mathematical modelling in the above disciplines. In the past, traditional methods have relied heavily on expensive experimentation and the building of scaled models, but now a more flexible and cost effective approach is available through greater use of mathematical modelling and computer simulation. In particular, developments in computer algebra, symbolic manipulation packages and user friendly software packages for large scale problems, all have important implications in both the teaching of mathematical modelling and, more importantly, its use in the solution of real world problems. Many textbooks have been published which cover the art and techniques of modelling as well as specific mathematical modelling techniques in specialist areas within science and business. In most of these books the mathematical material tends to be rather tailor made to fit in with a one or two semester course for teaching students at the undergraduate or postgraduate level, usually the former. This textbook is quite different in that it is intended to build on and enhance students’ modelling skills using a combination of case studies and projects.

An Introduction to Mathematical Modeling

Author: Edward A. Bender

Publisher: Courier Corporation

ISBN: 0486137120

Category: Mathematics

Page: 272

Accessible text features over 100 reality-based examples pulled from the science, engineering, and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

Mathematical Modelling

Education, Engineering and Economics - ICTMA 12

Author: C Haines,P Galbraith,W Blum,S Khan

Publisher: Elsevier

ISBN: 0857099418

Category: Mathematics

Page: 510

This book continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling. Each chapter shows how real life problems can be discussed during university lectures, in school classrooms and industrial research. International experts contribute their knowledge and experience by providing analysis, insight and comment whilst tackling large and complex problems by applying mathematical modelling. This book covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications. Covers the proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications Continues the ICTMA tradition of influencing teaching and learning in the application of mathematical modelling Shows how real life problems can be discussed during university lectures, in school classrooms and industrial research

Modelling and Applications in Mathematics Education

The 14th ICMI Study

Author: Peter L. Galbraith,Hans-Wolfgang Henn,Mogens Niss

Publisher: Springer Science & Business Media

ISBN: 9780387298221

Category: Education

Page: 524

The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.

Mathematical Modelling with Case Studies

Using Maple and MATLAB, Third Edition

Author: B. Barnes,G..R. Fulford

Publisher: CRC Press

ISBN: 1482247755

Category: Mathematics

Page: 388

Mathematical Modelling with Case Studies: Using MapleTM and MATLAB®, Third Edition provides students with hands-on modelling skills for a wide variety of problems involving differential equations that describe rates of change. While the book focuses on growth and decay processes, interacting populations, and heating/cooling problems, the mathematical techniques presented can be applied to many other areas. The text carefully details the process of constructing a model, including the conversion of a seemingly complex problem into a much simpler one. It uses flow diagrams and word equations to aid in the model-building process and to develop the mathematical equations. Employing theoretical, graphical, and computational tools, the authors analyze the behavior of the models under changing conditions. The authors often examine a model numerically before solving it analytically. They also discuss the validation of the models and suggest extensions to the models with an emphasis on recognizing the strengths and limitations of each model. The highly recommended second edition was praised for its lucid writing style and numerous real-world examples. With updated MapleTM and MATLAB® code as well as new case studies and exercises, this third edition continues to give students a clear, practical understanding of the development and interpretation of mathematical models.

Mathematical Modelling

A Case Studies Approach

Author: Reinhard Illner

Publisher: American Mathematical Soc.

ISBN: 0821836501

Category: Mathematics

Page: 196

Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects.Some projects are extensive, as with the explorations of the predator-prey model; others are more modest. The text was designed to be suitable for a one-term course for advanced undergraduates. The selection of topics and the style of exposition reflect this choice. The authors have also succeeded in demonstrating just how enjoyable the subject can be. This is an ideal text for classes on modelling. It can also be used in seminars or as preparation for mathematical modelling competitions.

Mathematical Modelling of Zombies

Author: Robert Smith?

Publisher: University of Ottawa Press

ISBN: 0776621688

Category: Mathematics

Page: 468

You’re outnumbered, in fear for your life, surrounded by flesheating zombies. What can save you now? Mathematics, of course. Mathematical Modelling of Zombies engages the imagination to illustrate the power of mathematical modelling. Using zombies as a “hook,” you’ll learn how mathematics can predict the unpredictable. In order to be prepared for the apocalypse, you’ll need mathematical models, differential equations, statistical estimations, discretetime models, and adaptive strategies for zombie attacks—as well as baseball bats and Dire Straits records (latter two items not included). In Mathematical Modelling of Zombies, Robert Smith? brings together a highly skilled team of contributors to fend off a zombie uprising. You’ll also learn how modelling can advise government policy, how theoretical results can be communicated to a nonmathematical audience and how models can be formulated with only limited information. A forward by Andrew Cartmel—former script editor of Doctor Who, author, zombie fan and all-round famous person in science-fiction circles—even provides a genealogy of the undead. By understanding how to combat zombies, readers will be introduced to a wide variety of modelling techniques that are applicable to other real-world issues (biology, epidemiology, medicine, public health, etc.). So if the zombies turn up, reach for this book. The future of the human race may depend on it.

Mathematical Modelling with Case Studies

Using Maple and MATLAB, Third Edition

Author: B. Barnes,G..R. Fulford

Publisher: CRC Press

ISBN: 1482247755

Category: Mathematics

Page: 388

Mathematical Modelling with Case Studies: Using MapleTM and MATLAB®, Third Edition provides students with hands-on modelling skills for a wide variety of problems involving differential equations that describe rates of change. While the book focuses on growth and decay processes, interacting populations, and heating/cooling problems, the mathematical techniques presented can be applied to many other areas. The text carefully details the process of constructing a model, including the conversion of a seemingly complex problem into a much simpler one. It uses flow diagrams and word equations to aid in the model-building process and to develop the mathematical equations. Employing theoretical, graphical, and computational tools, the authors analyze the behavior of the models under changing conditions. The authors often examine a model numerically before solving it analytically. They also discuss the validation of the models and suggest extensions to the models with an emphasis on recognizing the strengths and limitations of each model. The highly recommended second edition was praised for its lucid writing style and numerous real-world examples. With updated MapleTM and MATLAB® code as well as new case studies and exercises, this third edition continues to give students a clear, practical understanding of the development and interpretation of mathematical models.

Model Building in Mathematical Programming

Author: H. Paul Williams

Publisher: John Wiley & Sons

ISBN: 1118506189

Category: Business & Economics

Page: 432

The 5th edition of Model Building in Mathematical Programming discusses the general principles of model building in mathematical programming and demonstrates how they can be applied by using several simplified but practical problems from widely different contexts. Suggested formulations and solutions are given together with some computational experience to give the reader a feel for the computational difficulty of solving that particular type of model. Furthermore, this book illustrates the scope and limitations of mathematical programming, and shows how it can be applied to real situations. By emphasizing the importance of the building and interpreting of models rather than the solution process, the author attempts to fill a gap left by the many works which concentrate on the algorithmic side of the subject. In this article, H.P. Williams explains his original motivation and objectives in writing the book, how it has been modified and updated over the years, what is new in this edition and why it has maintained its relevance and popularity over the years: http://www.statisticsviews.com/details/feature/4566481/Model-Building-in-Mathematical-Programming-published-in-fifth-edition.html

Effective Learning and Teaching in Mathematics and Its Applications

Author: Peter Kahn,Joseph Kyle

Publisher: Routledge

ISBN: 1135726906

Category: Education

Page: 240

The Effective Learning and Teaching in Higher Education series is packed with up-to-date advice, guidance and expert opinion on teaching in the key subjects in higher education today, and is backed up by the authority of the Institute for Learning and Teaching. This book covers all of the key issues surrounding the effective teaching of maths- a key subject in its own right, and one that forms an important part of many other disciplines. The book includes contributions from a wide range of experts in the field, and has a broad and international perspective.

Mathematical Epidemiology of Infectious Diseases

Model Building, Analysis and Interpretation

Author: O. Diekmann,J. A. P. Heesterbeek

Publisher: John Wiley & Sons

ISBN: 9780471492412

Category: Mathematics

Page: 303

Mathematical Epidemiology of Infectious Diseases Model Building, Analysis and Interpretation O. Diekmann University of Utrecht, The Netherlands J. A. P. Heesterbeek Centre for Biometry Wageningen, The Netherlands The mathematical modelling of epidemics in populations is a vast and important area of study. It is about translating biological assumptions into mathematics, about mathematical analysis aided by interpretation and about obtaining insight into epidemic phenomena when translating mathematical results back into population biology. Model assumptions are formulated in terms of, usually stochastic, behaviour of individuals and then the resulting phenomena, at the population level, are unravelled. Conceptual clarity is attained, assumptions are stated clearly, hidden working hypotheses are attained and mechanistic links between different observables are exposed. Features: * Model construction, analysis and interpretation receive detailed attention * Uniquely covers both deterministic and stochastic viewpoints * Examples of applications given throughout * Extensive coverage of the latest research into the mathematical modelling of epidemics of infectious diseases * Provides a solid foundation of modelling skills The reader will learn to translate, model, analyse and interpret, with the help of the numerous exercises. In literally working through this text, the reader acquires modelling skills that are also valuable outside of epidemiology, certainly within population dynamics, but even beyond that. In addition, the reader receives training in mathematical argumentation. The text is aimed at applied mathematicians with an interest in population biology and epidemiology, at theoretical biologists and epidemiologists. Previous exposure to epidemic concepts is not required, as all background information is given. The book is primarily aimed at self-study and ideally suited for small discussion groups, or for use as a course text.

A Concrete Approach to Mathematical Modelling

Author: Mike Mesterton-Gibbons

Publisher: John Wiley & Sons

ISBN: 1118030648

Category: Mathematics

Page: 620

WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. " . . . [a] treasure house of material for students and teachers alike . . . can be dipped into regularly for inspiration and ideas. It deserves to become a classic." —London Times Higher Education Supplement "The author succeeds in his goal of serving the needs of the undergraduate population who want to see mathematics in action, and the mathematics used is extensive and provoking." —SIAM Review "Each chapter discusses a wealth of examples ranging from old standards . . . to novelty . . . each model is developed critically, analyzed critically, and assessed critically." —Mathematical Reviews A Concrete Approach to Mathematical Modelling provides in-depth and systematic coverage of the art and science of mathematical modelling. Dr. Mesterton-Gibbons shows how the modelling process works and includes fascinating examples from virtually every realm of human, machine, natural, and cosmic activity. Various models are found throughout the book, including how to determine how fast cars drive through a tunnel, how many workers industry should employ, the length of a supermarket checkout line, and more. With detailed explanations, exercises, and examples demonstrating real-life applications in diverse fields, this book is the ultimate guide for students and professionals in the social sciences, life sciences, engineering, statistics, economics, politics, business and management sciences, and every other discipline in which mathematical modelling plays a role.