The emphasis of this book lies on the teaching of mathematical modeling rather than simply presenting models. To this end the book starts with the simple discrete exponential growth model as a building block, and successively refines it. This involves adding variable growth rates, multiple variables, fitting growth rates to data, including random elements, testing exactness of fit, using computer simulations and moving to a continuous setting. No advanced knowledge is assumed of the reader, making this book suitable for elementary modeling courses. The book can also be used to supplement courses in linear algebra, differential equations, probability theory and statistics.
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Book Description
The aim of this book is the teaching of mathematical modeling. No advanced knowledge is assumed of the reader, making this book suitable for elementary modeling courses, or to supplement courses in linear algebra, differential equations, probability theory and statistics.
From the Publisher
Students taking a course based on this book should have some mathematical maturity, but will need little advanced knowledge. The book presents more advanced topics on an as-needed basis and serves to show how the different topics of undergraduate mathematics can be used together to solve problems. The course presents elements of discrete dynamical systems, basic probability theory, differential equations, matrix algebra, stochastic processes, curve fitting, statistical testing, and regression analysis. Computer analysis is extensively used in conjunction with these topics. You can also use this book if you are seeking applications to supplement a course in linear algebra, differential equations, difference equations, probability theory, or statistics.
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Most Helpful Customer Reviews
28 of 29 people found the following review helpful:
5.0 out of 5 stars
Superb.,
By A Customer
This review is from: A Course in Mathematical Modeling (Mathematical Association of America Textbooks) (Paperback)
To break it down.
1. The authors write with a clarity and elegance that is almost universally absent in math/science texts. The book is beautifully paced. Anybody thinking about writing a technical book would do well to read this before starting out. 2. The mathematics is second to the modelling. They move from simple examples towards the formal mathematics, nothing is introduced without explanation. This is a vast improvement over so many other texts that are happy to derive the math first and then show an example, which is no way to engage the mind. It is the only text I have come across that presents differential equations and continuous stochastic processes in a palatable manner. 3. The exercises have been well thought out, and not just thrown in at the end of each chapter, reflecting the authors' teaching experience, and leave you with any number of directions in which to take your own steps in modelling. It is simply one of the best written and engaging technical books I have read this or any other year. This books shows that one can write clearly about mathematics. If you really want to understand and ground yourself in math modelling and simulation, this is where to start.
3 of 3 people found the following review helpful:
5.0 out of 5 stars
easy to understand,
By Grad Student "Monika" (FL USA) - See all my reviews
Amazon Verified Purchase(What's this?)
This review is from: A Course in Mathematical Modeling (Mathematical Association of America Textbooks) (Paperback)
Clear explanations. Models are from biology. Does not elaborate on the math and solving the differential equations, but a good overview.
11 of 22 people found the following review helpful:
1.0 out of 5 stars
Simply Awful,
By A Customer
Amazon Verified Purchase(What's this?)
This review is from: A Course in Mathematical Modeling (Mathematical Association of America Textbooks) (Paperback)
Incredibly poorly written book. This is NOT a general introduction to M&S. A more appropriate title for this book would be "A Course in Biological Modeling". If you are looking for an introduction to numerous biological modeling systems then this is your book. If you want a book that overviews the wonderfully complex world of modeling then look elsewhere. (I'm still looking - any help out there). Point is that modeling is much more than understanding birth and death rates of Sand Hill Cranes. Modeling encompasses all fields of Engineering and Physics of which this book hardly mentions. (As you may detect I am particularly annoyed about the misleading title of this book. ) Also, take the authors math expectation in the forward seriously. Make sure you math skills are current before tackling this book. There is a lot of assumption and little equation development. If your skills are rusty you'll find yourself frequently bewildered by how they got from A to B. I am completing a class on M&S using this book and I can honestly say that I do not know of one student in a class of 25 that is happy with this text.
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Inside This Book
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First Sentence:
If we were to ask seceral people for examples of models, we would get a variety of responses which might include mathematical equations, toy trains, prototype cars, or fashion models. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
maximum safe traffic flow, phase line analysis, compartmental diagram, exponential differential equation, crane model, crane population, lynx data, pure death process, pure birth process, logistic differential equation, environmental stochasticity, average queue size, fur returns, demographic stochasticity, fear model, season model, average population size, affine equation, current population size, dominant eigenvalue, curvilinear regression, squirrel populations, phase plane analysis, differential equation solver, season data Key Phrases - Capitalized Phrases (CAPs): (learn more)
The X-files, United States, New York, Mean Square F-ratio Regression, Source Sum of Squares, Variable Coefficient, Lake Erie, Lake Ontario, John Wiley, Forestry Commission, Projects Project, Data Desk, Ecological Modelling, Great Britain, Income Model, Modeling Basics, Primer of Matrix Algebra, Spruce Budworm Phase Line Analysis, Week Number, Year Population Size, Addison-Wesley Publishing Company, Advertising Expenditures, Blackwell Science Inc, Harvesting Scot Pines, Leah Edelstein-Keshet New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
If we were to ask seceral people for examples of models, we would get a variety of responses which might include mathematical equations, toy trains, prototype cars, or fashion models. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
maximum safe traffic flow, phase line analysis, compartmental diagram, exponential differential equation, crane model, crane population, lynx data, pure death process, pure birth process, logistic differential equation, environmental stochasticity, average queue size, fur returns, demographic stochasticity, fear model, season model, average population size, affine equation, current population size, dominant eigenvalue, curvilinear regression, squirrel populations, phase plane analysis, differential equation solver, season data Key Phrases - Capitalized Phrases (CAPs): (learn more)
The X-files, United States, New York, Mean Square F-ratio Regression, Source Sum of Squares, Variable Coefficient, Lake Erie, Lake Ontario, John Wiley, Forestry Commission, Projects Project, Data Desk, Ecological Modelling, Great Britain, Income Model, Modeling Basics, Primer of Matrix Algebra, Spruce Budworm Phase Line Analysis, Week Number, Year Population Size, Addison-Wesley Publishing Company, Advertising Expenditures, Blackwell Science Inc, Harvesting Scot Pines, Leah Edelstein-Keshet New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 42
books:
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32
books
cite this book:
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- Mathematical Models in Biology (Classics in Applied Mathematics) by Leah Edelstein-Keshet on 8 pages
- Fort Worth by Rh Value Publishing on page 306, Back Matter (1), and Back Matter (2)
- Career Skills Library: Problem Solving, Second Edition by Facts on File on page 6, and Back Matter
- Environmental Modeling: Fate and Transport of Pollutants in Water, Air, and Soil (Environmental Science and Technology: A Wiley-Interscience Series of Texts and Monographs) by Jerald L. Schnoor on page 314, and Back Matter
- Differential Equations (with CD-ROM) by Paul Blanchard on page 306, and Back Matter
See all 42 books this book cites
- Innovative Approaches to Undergraduate Mathematics Courses Beyond Calculus by Richard J. Maher on page 127, and page 131
- Applied Mathematics by J. David Logan on page 83, and page 336
- Identification Numbers and Check Digit Schemes (Classroom Resource Materials) by Joseph Kirtland in Front Matter
- Proofs without Words: Exercises in Visual Thinking (Classroom Resource Materials) (v. 1) by Roger B. Nelsen in Front Matter
- Combinatorics: A Problem Oriented Approach (Mathematical Association of America Textbooks) by Daniel A. Marcus in Front Matter
See all 32 books citing this book
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