2019;
323 pp;
Hardcover

MSC: Primary 92; 39; 62;
Secondary 00

**Print ISBN: 978-1-4704-4869-1
Product Code: MBK/120**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

**Electronic ISBN: 978-1-4704-5200-1
Product Code: MBK/120.E**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

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#### Supplemental Materials

# Modeling and Data Analysis: An Introduction with Environmental Applications

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*John B. Little*

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 society's 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
consequences 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 \({\tt R}\) statistical package.

Exercises and solutions for this title are available
electronically to those instructors who have adopted the textbook for
classroom use. Please send email to textbooks@ams.org for more
information.

#### Readership

Undergraduate and graduate students and researchers interested in math modeling and data analysis with environmental applications.

#### Reviews & Endorsements

This book on elementary topics in mathematical modeling and data analysis is intended for an undergraduate liberal arts mathematics course with a specific focus on environmental applications. A great variety of exercises extends the discussions of the main text to new situations and/or introduces new real-world examples.

-- Tom Schulte, MAA Reviews

It is great that mathematics is finally taught as a tool to understand the challenges that the planet will be facing and to participate in the debate. The book aims at developing skills in mathematical modeling and data analysis, with a focus on the environment. The projects encourage active learning. A wonderful book!

-- Christiane Rousseau, Initiator of Mathematics of Planet Earth (MPE2013) and Professor of Mathematics, Université de Montréal

Using diverse examples with environmental science data, this text provides a lively review of high school math. Ideal for a quantitative literacy course, it offers an excellent alternative to the typical math rehash.

-- Louis J. Gross, Chancellor's Professor of Ecology and Evolutionary Biology and Mathematics, University of Tennessee, Knoxville

#### Table of Contents

# Table of Contents

## Modeling and Data Analysis: An Introduction with Environmental Applications

- Cover Cover11
- Title page iii4
- Preface ix10
- I. Basic Quantitative Concepts 118
- II. Elementary Modeling 5572
- Chapter 4. Linear Functions as Models 5774
- References for Chapter 4 7895
- Chapter 5. Exponential Functions as Models 7996
- References for Chapter 5 101118
- Chapter 6. Power Functions as Models 103120
- References for Chapter 6 125142
- Chapter 7. Discrete Time Dynamic Modeling and Difference Equations 127144
- 7.1. Introduction 127144
- 7.2. Difference Equations 129146
- 7.3. Modeling with Difference Equations 131148
- 7.4. Equilibria and Stability of Solutions 134151
- 7.5. Logistic Growth Models 138155
- 7.6. Some Higher Order Difference Equations (Optional) 145162
- 7.7. Some Technical Notes (Optional) 149166
- 7.8. Project 151168
- Exercises 153170

- References for Chapter 7 159176
- Chapter 8. Modeling with Systems of Difference Equations 161178
- References for Chapter 8 189206

- III. Data Analysis and Statistics 191208
- Chapter 9. Descriptive Statistics 193210
- References for Chapter 9 220237
- Chapter 10. Probability Distributions and Random Variables 221238
- 10.1. Introduction 221238
- 10.2. Conditional Probabilities and Independence 222239
- 10.3. Probability Mass Functions and Discrete Distributions 227244
- 10.4. Expected Value and Variance 236253
- 10.5. Probability Density Functions and Continuous Distributions 241258
- 10.6. Normal Distributions 246263
- 10.7. ๐-Scores and Computing Normal Probabilities 247264
- 10.8. Some Technical Notes (Optional) 251268
- 10.9. Project 254271
- Exercises 259276

- Chapter 11. Statistics of Sampling 263280
- Reference for Chapter 11 284301
- Chapter 12. Hypothesis Testing and Statistical Inference 285302
- 12.1. Introduction 285302
- 12.2. The Logic of Hypothesis Tests 286303
- 12.3. Tests for Means and Proportions 290307
- 12.4. ๐-Values and Hypothesis Tests 296313
- 12.5. Small-Sample Test for Differences of Means 297314
- 12.6. ๐ยฒ Tests for Model Fit and Independence 300317
- 12.7. Hypothesis Tests on Regression Coefficients 305322
- 12.8. Project 308325
- Exercises 311328

- References for Chapter 12 317334
- Index 319336

- Back Cover Back Cover1342