A Biologist's Guide to Mathematical Modeling in Ecology and Evolution

Author: Sarah P. Otto,Troy Day

Publisher: Princeton University Press

ISBN: 1400840910

Category: Science

Page: 744

View: 510

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Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available
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Guide to Mathematical Modelling

Author: Dilwyn Edwards,Mike Hamson

Publisher: Macmillan International Higher Education

ISBN: 1349100420

Category: Applied mathematics

Page: 277

View: 9164

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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.
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Exam Prep for: A Biologists Guide to Mathematical Modeling ...

Author: David Mason

Publisher: Rico Publications

ISBN: N.A

Category: Education

Page: 800

View: 6707

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5,600 Exam Prep questions and answers. Ebooks, Textbooks, Courses, Books Simplified as questions and answers by Rico Publications. Very effective study tools especially when you only have a limited amount of time. They work with your textbook or without a textbook and can help you to review and learn essential terms, people, places, events, and key concepts.
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Computer Algebra Recipes

An Introductory Guide to the Mathematical Models of Science

Author: Richard H. Enns,George C. McGuire

Publisher: Springer Science & Business Media

ISBN: 0387257675

Category: Mathematics

Page: 430

View: 7382

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* Contains computer algebra worksheets or "recipes" designed using MAPLE (System 10); no prior knowledge of MAPLE is assumed * Effective computational science text for first- and second-year undergraduates in mathematics, physics, engineering, chemistry, economics, biology, and pre-medicine * Examples and problems provide basis for both self-study and on-line course
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Mathematical Modeling

Applications with GeoGebra

Author: Jonas Hall,Thomas Lingefjärd

Publisher: John Wiley & Sons

ISBN: N.A

Category: Mathematics

Page: 550

View: 1886

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This book is a logical, well-organized guide to various mathematical modeling techniques and applications for evaluating and solving problems in the diverse field of mathematics. A highly-qualified lecturer in the area of mathematics education and modeling, the author provides a unique pedagogical approach to using GeoGebra and WolframAlpha in courses that require problem solving and evaluation through mathematical modeling. The main software presented in the book is GeoGebra, which is a fast-growing, free program and can be used within numerous areas of mathematics such as algebra, geometry, geometry 3D, functions, statistics, spreadsheet calculations, and symbolic algebra. The book provides detailed information on how to use GeoGebra to teach mathematics, as well as a technical guide to using GeoGebra for mathematical modeling. Beginning with the basics of GeoGebra, the book introduces specific GeoGebra exercises and additional resources for further study. The book then moves on to comprehensive modeling examples that correspond to different levels of mathematics experience. Each chapter builds on the previous chapter’s level, and includes numerous examples of solved modeling tasks with at least one, sometimes several, solution suggestions. These solutions are detailed both mathematically and in a GeoGebra sense to engage readers with the necessary skills for future problem solving and mathematical modeling. Subsequently, the book addresses how to organize practical work and gives examples of various approaches to teaching modeling in the classroom. Finally, the book illustrates the methods for evaluating models, including relative error, correlation, square sum of errors, regression, and confidence interval.
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Mathematical Modeling of Pharmacokinetic Data

Author: DavidW.A. Bourne

Publisher: Routledge

ISBN: 1351433245

Category: Medical

Page: 152

View: 2420

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A concise guide to mathematical modeling and analysis of pharmacokinetic data, this book contains valuable methods for maximizing the information obtained from given data. It is an ideal resource for scientists, scholars, and advanced students.
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Mathematical Modeling

Models, Analysis and Applications

Author: Sandip Banerjee

Publisher: CRC Press

ISBN: 1439854513

Category: Mathematics

Page: 276

View: 7191

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Almost every year, a new book on mathematical modeling is published, so, why another? The answer springs directly from the fact that it is very rare to find a book that covers modeling with all types of differential equations in one volume. Until now. Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differential equations, namely ordinary, partial, delay, and stochastic. The book also contains a chapter on discrete modeling, consisting of differential equations, making it a complete textbook on this important skill needed for the study of science, engineering, and social sciences. More than just a textbook, this how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial, delayed, and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB® and Mathematica® are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project. Since mathematical modeling involves a diverse range of skills and tools, the author focuses on techniques that will be of particular interest to engineers, scientists, and others who use models of discrete and continuous systems. He gives students a foundation for understanding and using the mathematics that is the basis of computers, and therefore a foundation for success in engineering and science streams.
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A Concrete Approach to Mathematical Modelling

Author: Mike Mesterton-Gibbons

Publisher: John Wiley & Sons

ISBN: 1118030648

Category: Mathematics

Page: 620

View: 6305

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WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists ofselected books that have been made more accessible to consumers inan effort to increase global appeal and general circulation. Withthese new unabridged softcover volumes, Wiley hopes to extend thelives of these works by making them available to future generationsof statisticians, mathematicians, and scientists. " . . . [a] treasure house of material for students and teachersalike . . . 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 theundergraduate population who want to see mathematics in action, andthe mathematics used is extensive and provoking." —SIAM Review "Each chapter discusses a wealth of examples ranging from oldstandards . . . to novelty . . . each model is developedcritically, analyzed critically, and assessed critically." —Mathematical Reviews A Concrete Approach to Mathematical Modelling providesin-depth and systematic coverage of the art and science ofmathematical modelling. Dr. Mesterton-Gibbons shows how themodelling process works and includes fascinating examples fromvirtually every realm of human, machine, natural, and cosmicactivity. Various models are found throughout the book, includinghow to determine how fast cars drive through a tunnel, how manyworkers industry should employ, the length of a supermarketcheckout line, and more. With detailed explanations, exercises, andexamples demonstrating real-life applications in diverse fields,this book is the ultimate guide for students and professionals inthe social sciences, life sciences, engineering, statistics,economics, politics, business and management sciences, and everyother discipline in which mathematical modelling plays a role.
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Mathematical Modeling

Author: Mark M. Meerschaert

Publisher: Academic Press

ISBN: 012386996X

Category: Technology & Engineering

Page: 384

View: 7003

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The new edition of Mathematical Modeling, the survey text of choice for mathematical modeling courses, adds ample instructor support and online delivery for solutions manuals and software ancillaries. From genetic engineering to hurricane prediction, mathematical models guide much of the decision making in our society. If the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor. With mathematical modeling growing rapidly in so many scientific and technical disciplines, Mathematical Modeling, Fourth Edition provides a rigorous treatment of the subject. The book explores a range of approaches including optimization models, dynamic models and probability models. Offers increased support for instructors, including MATLAB material as well as other on-line resources Features new sections on time series analysis and diffusion models Provides additional problems with international focus such as whale and dolphin populations, plus updated optimization problems
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Mathematical Modelling for Teachers

A Practical Guide to Applicable Mathematics Education

Author: Jürgen Maaß,Niamh O’Meara,Patrick Johnson,John O’Donoghue

Publisher: Springer

ISBN: 3030004317

Category: Education

Page: 159

View: 8771

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While there are many areas of focus in mathematics education, there are many good reasons for offering applicable mathematics education in schools. Let us just mention two of the most important reasons. On the one hand, a focus on the practical side of mathematics presents a convincing and motivating answer to the typical student question: ‘Why study mathematics?’ On the other hand, education policy seems inclined to move in this direction by implementing international testing, curricula and catalogues of skills. The most important feature of this book is that the authors speak directly to you, the mathematics teachers. The authors attempt to draw you into a continuous dialogue about activities you are asked to engage in as learners. You are asked to do something, and through doing and reflecting you will gain first-hand experience of new approaches and materials. In this way, you can learn to teach applicable mathematics to your students using your own experience as learners of applicable mathematics, motivated and supported by the book. Here applicable mathematics education is the phrase we use to describe reality-based mathematics education. Reality-based mathematics relies heavily on problem solving and a positive disposition to engage with mathematics. Modelling reality and simulating selected aspects of reality are other pillars of reality-based mathematics education.
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