Mathematics and Statistics for Sustainability
Edition: 1
Copyright: 2023
Pages: 300
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Mathematics and Statistics for Sustainability addresses problems arising in sustainability through the lens of mathematical models and statistical methods. A mathematical analysis of such problems raises awareness of sustainability issues while making learning the corresponding topics in mathematics a more relevant endeavor.
The primary aim of the book is to expose students to the ways in which mathematics and statistics can be applied to model phenomena pertaining to sustainability and subsequently, solve problems in such areas as climate change, natural building, green transportation, wealth inequality, and organic agriculture. The first three chapters deal primarily with continuous mathematics, following a natural flow from algebra, to trigonometry, to calculus. The next three chapters follow the development of set theory into the fundamentals of probability and subsequently, into statistics. The final two chapters cover discrete mathematics topics from the fields of network theory and game theory. Each of the eight chapters pairs a field of mathematics or statistics with a field from sustainability studies:
- Algebra and Population Growth
- Geometry/Trigonometry and Natural Building
- Calculus and Wealth Inequality
- Set Theory and Renewable Energy
- Probability and Organic Agriculture
- Statistics and Climate Change
- Network Theory and Green Transportation
- Game Theory and Water Security
Each chapter contains a project module outlining a hands-on, expanded application of the mathematical concepts and models covered in the chapter. Some example projects include growing living yeast cell colonies for students to practice population growth modeling, measuring solar altitude for passive solar building design using trigonometry, and assessing the connectivity of bicycle infrastructure using graph theory.
Each chapter also contains a short biographical section highlighting the life, achievements, and contributions to the mathematical sciences of a mathematician/statistician from a racial, ethnic, or gender identity group that has historically been underrepresented in science, technology, mathematics, and engineering fields. The purpose of these sections is to raise awareness of such individuals and their contributions to mathematics with the aim of building confidence and inspiring students of such groups to pursue a path in the mathematical sciences or other STEM field.
Mathematics and Statistics for Sustainability is designed for introductory level college mathematics courses or junior/senior level high school courses. Parts of the textbook may be adapted for an introductory mathematical modeling course as well. A minimal exposure to algebra (e.g., 1–2 years high school algebra) is assumed.
Introduction
Algebra and Population Growth
1.1 Linear Equations and Functions
1.2 Exponential Functions and the Malthusian Growth Model
1.3 The Logistic Growth Model
1.4 Project: Yeast Population Growth Lab
1.5 Spotlight on Mathematicians from Underrepresented Groups: Hypatia
1.6 Exercises
2 Geometry, Trigonometry, and Natural Building 29
2.1 Geometry
2.2 Trigonometry
2.3 Project: Modeling Solar Altitude for Passive Solar Design
2.4 Spotlight on Mathematicians from Underrepresented Groups: Shakuntala Devi
2.5 Exercises
3 Calculus and Wealth Inequality
3.1 Differentiation
3.2 Integration
3.3 Project: The Game of Wealth: Privilege and Lorenz Curves
3.4 Spotlight on Mathematicians from Underrepresented Groups: Talitha Washington
3.5 Exercises
4 Set Theory and Renewable Energy
4.1 Sets
4.2 Set Operations
4.3 Venn Diagrams
4.4 Project: World Energy Sources
4.5 Spotlight on Mathematicians from Underrepresented Groups: Benjamin Banneker
4.6 Exercises
5 Probability and Organic Agriculture
5.1 Probability Preliminaries
5.2 General Probability Theory
5.3 Random Variables
5.4 Project: Seed Germination Lab and Harvest Profit
5.5 Spotlight on Mathematicians from Underrepresented Groups: Maria Agnesi
5.6 Exercises
6 Statistics and Climate Change
6.1 Descriptive Statistics
6.2 Bivariate Data and Correlation
6.3 Normal Distribution
6.4 Distribution of a Sample Mean
6.5 Confidence Intervals
6.6 Hypothesis Testing
6.7 Project: Effects of Biochar on Seed Germination
6.8 Spotlight on Mathematicians from Underrepresented Groups: David Blackwell
6.9 Exercises
7 Graph Theory and Green Transportation
7.1 Graph Theory Preliminaries
7.2 Eulerian Circuits
7.3 Graph Connectivity
7.4 Project: Assessing the Connectivity of Bikeway Systems
7.5 Spotlight on Mathematicians from Underrepresented Groups: Katherine Johnson
7.6 Exercises
8 Game Theory and Water Security
8.1 Two-Player Zero-Sum and Constant-Sum Games
8.2 Project: Shared Freshwater Source Game
8.3 Spotlight on Mathematicians from Underrepresented Groups: C. Bryan Dawson
8.4 Exercises
Jacob Duncan received his PhD in mathematics from Utah State University with a focus on applied math and mathematical modeling in the biological sciences. He is currently an associate professor of mathematics at Winona State University where he has developed and taught several mathematical modeling courses including a Math for Sustainability course for which this textbook was developed. He also teaches a variety of other undergraduate mathematics courses ranging from introductory algebra and statistics, through the calculus sequence and, ultimately, to differential equations and numerical analysis. Along with his teaching responsibilities in the Department of Mathematics and Statistics at Winona State, Dr. Duncan also teaches courses in the Sustainability department.