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Modeling and data analysis. An introduction with environmental applications. (English) Zbl 1419.00010

Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4869-1/hbk; 978-1-4704-5200-1/ebook). xv, 323 p. (2019).
From the cover of the book: “Can we coexist with the other life forms that have evolved on this planet? Are there realistic alternatives to fossil fuels that would sustainably provide for human societys energy needs and have fewer harmful effects? How do we deal with threats such as emergent diseases?
Mathematical models equations of various sorts capturing relationships between variables involved in a complex situation are fundamental for understanding the potential consequence of choices we make. Extracting insights from the vast amounts of data we are able to collect requires analysis methods and statistical reasoning.
This book on elementary topics in mathematical modeling and data analysis is intended for an undergraduate liberal arts mathematics-type course but with a specific focus on environmental applications. It is suitable for introductory courses with no prerequisites beyond high school mathematics. A great variety of exercises extends the discussions of the main text to new situations and/or introduces new real-world examples. Every chapter ends with a section of problems, as well as with an extended chapter project which often involves substantial computing work either in spreadsheet software or in the R statistical package”.
The book is very large structured in a Preface with Acknowledgments, 3 Parts (divided in 12 Chapters with 77 subchapters), Index:
Part I. Basic Quantitative Concepts (Chapter 1. Scales of Measurement, Chapter 2. Ratios, Percents, Proportions, Chapter. Part I Summary Project).
Part II. Elementary Modeling (Chapter 4. Linear Functions as Models, Chapter 5. Exponential Functions as Models, Chapter 6. Power Functions as Models, Chapter 7. Discrete Time Dynamic Modeling and Difference Equations, Chapter 8. Modeling with Systems of Difference Equations).
Part III. Data Analysis and Statistics (Chapter 9. Descriptive Statistics, Chapter 10. Probability Distributions and Random Variables, Chapter 11. Statistics of Sampling, Chapter 12. Hypothesis Testings and Statistical Interference).
Every chapter finished with Exercises (except chapter 3) and with References (except chapter 10). The Bibliography contains 55 references and the Index more than 370 items. For some references see: Zbl 0361.62037, Zbl 0593.62040, Zbl 0681.62001 (7th ed. 2008), JFM 32.0697.05 (6th ed. 1937), JFM 53.0517.01, Zbl 0712.90018, Zbl 1369.37088, Zbl 0706.58002. Zbl 1025.37001, Zbl 0102.00703.
Many references are Internet addresses related to environmental data.
The book can be recommend all readers, who are interested in this field.

MSC:

00A71 General theory of mathematical modeling
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62-07 Data analysis (statistics) (MSC2010)
39A06 Linear difference equations
62P12 Applications of statistics to environmental and related topics
97-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education
97A40 Mathematics education and society
26A06 One-variable calculus
54C30 Real-valued functions in general topology

Software:

R
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