Mathematics for the Environment shows how to employ simple mathematical tools, such as arithmetic, to uncover fundamental conflicts between the logic of human civilization and the logic of Nature. These tools can then be used to understand and effectively deal with economic, environmental, and social issues. With elementary mathematics, the book seeks answers to a host of real-life questions, including: How safe is our food and will it be affordable in the future? What are the simple lessons to be learned from the economic meltdown of 2008--2009? Is global climate change happening? Were some humans really doing serious mathematical thinking 50,000 years ago? What does the second law of thermodynamics have to do with economics? How can identity theft be prevented? What does a mathematical proof prove?

A truly interdisciplinary, concrete study of mathematics, this classroom-tested text discusses the importance of certain mathematical principles and concepts, such as fuzzy logic, feedback, deductive systems, fractions, and logarithms, in various areas other than pure mathematics. It teaches students how to make informed choices using fundamental mathematical tools, encouraging them to find solutions to critical real-world problems.

The book is heavily referenced ! there are many detailed exercises designed to highlight how mathematics can be used to explain natural phenomena and human behavior and its consequences. ! this book could serve as a text for courses in applied mathematics and a resource for study material in many other subject areas ! --MAA Reviews, July 2011

MATHEMATICS IS CONNECTED TO EVERYTHING ELSE Earth's Climate and Some Basic Principles One of the Greatest Crimes of the 20th Century Feedback Edison's Algorithm: Listening to Nature's Feedback Fuzzy Logic, Filters, the Bigger Picture Principle Consequences of the Crime: Suburbia's Topology A Toxic Consequence of the Crime Hubbert's Peak and the End of Cheap Oil Resource Wars: Oil and Water The CO2 Greenhouse Law of Svante Arrhenius Economic Instability: Ongoing Causes Necessary Conditions for Economic Success The Mathematical Structure of Ponzi Schemes Dishonest Assessment of Risk One Reason Why Usury Should Again Be Illegal What Is Mathematics? More Basics The Definition of Mathematics Used in This Book The Logic of Nature and the Logic of Civilization Box-Flow Models Cycles and Scales in Nature and Mathematics The Art of Estimating We All Soak in a Synthetic Chemical Soup Thomas Latimer's Unfortunate Experience What's in the Synthetic Chemical Soup? Synthetic Flows and Assumptions The Flow of Information about Synthetic Flows You Cannot Do Just One Thing: Two Examples Mathematics: Food, Soil, Water, Air, Free Speech The "Hour Glass" Industrial Agriculture Machine Industrial Agriculture Logic vs. the Logic of Life Fast Foods, Few Foods, and Fossil Fuels Genetic Engineering: One Mathematical Perspective Toxic Sludge Is Good for You! Media Concentration Oceans: Rising Acidity and Disappearing Life Stocks, Flows and Distributions of Food My Definition of Food Choices: Central vs. Diverse Decision Making Correlations Mathematics and Energy How Much Solar Energy Is There? Solar Energy Is There, Do We Know How to Get It? Four Falsehoods Nuclear Power: Is It Too Cheap to Meter? Net Primary Productivity and Ecological Footprints NPP, Soil, Biofuels, and the Super Grid The Brower--Cousteau Model of the Earth How Heavily Do We Weigh upon the Earth? Mining and Damming: Massive Rearrangements Fish, Forests, Deserts, and Soil: Revisited The Cousteau--Brower Earth Model Fuzzy Logic, Sharp Logic, Frames, and Bigger Pictures Sharp (Aristotelian) Logic: A Standard Syllogism Measuring Truth Values: Fuzzy/Measured Logic Definitions, Assumptions and the Frame of Debate Humans in Denial -- Nature Cannot Be Fooled -- Gravity Exists The Bigger Picture Principle The Dunbar Number The Sustainability Hypothesis: Is It True? The Dunbar Number Public Relations, Political Power, and the Organization of Society Political Uses of Fear Confronting Fear (and Apathy): Organizing Your Community for Self-Preservation and Sustainability MATH AND NATURE: THE NATURE OF MATH One Pattern Viewed via Geometry and Numbers: Mathese The Square Numbers of Pythagoras The Language of Mathematics: Mathese A General Expression in Mathese: A Formula for Odd Numbers An Important Word in Mathese: IGBP Sentences in Mathese: Equations with IGBP and a Dummy Variable Induction, Deduction, Mathematical Research, and Mathematical Proofs What Is a Mathematical Proof? What Is a Deductive System? Originalidad es volver al Origen Axioms and Atoms Molecules and Atoms; the Atomic Number and the Atomic Mass Number of an Atom Scaling and Our First Two Axioms for Numbers Our First Axiom for Numbers Number 1: Its Definition, Properties, Uniqueness The Definition of Multiplicative Inverse Our Second Axiom for Numbers If ! , Then ! . Our First Proofs Return to the Problem: How Many Protons in One Gram of Protons? What Is a Mole? Scaling Up from the Atomic to the Human Scale Five More Axioms for Numbers Associativity, Identity, and Inverses for + Commutativity of + and * Distributivity What Patterns Can Be Deduced in Our Deductive System? Playing the Mathematics Game Rules for Playing the Mathematics Game The Usual Rules for Fractions Are Part of Our Deductive System Can You Tell the Difference between True and False Patterns? More Exercises ONE OF THE OLDEST MATHEMATICAL PATTERNS A Short Story and Some Numberless Mathematics Relations Defined as Collections of Ordered Pairs Symmetric Relations Transitive and Reflexive Relations Equivalence Relations Relations That Are Functions A Set of Social Rules for the Warlpiri People The Section Rule The Mother Relation Rules The Marriage Rules The Father Relation Rules Cultural Contexts in Which Mathematics Is Done COUNTING Counting Exactly Numeracy Counting Social Security Numbers among Other Things Permutations: Order Matters There Are n! Permutations of n Distinct Objects Counting Connections: Order Does Not Matter Equivalence Relations and Counting Using Equivalence Relations to Count Combinations: Order Does Not Matter Additional Counting Problems DNA Computing More Exercises BOX MODELS: POPULATION, MONEY, RECYCLING Some Population Numbers Counting People in the World A Fundamental Axiom of Population Ecology Counting People in the United States Basic Mathematical Patterns in Population Growth Schwartz Charts Are Box-Flow Models Our First Population Model: Simple Boxes and Flows Three Basic Operations: Addition, Multiplication, and Exponentiation Defining Logarithm Functions Computing Formulas for Doubling Times Natural Logarithms Logarithms to Any Base Further Study: More Complicated Models and Chaos Theory The World's Human Population: One Box Box Models: Money, Recycling, Epidemics Some Obvious Laws Humans Continue to Ignore A Linear Multiplier Effect: Some Mathematics of Money Multiplier Effects Arising from Cycles: The Mathematics of Recycling A Simple Model of an Influenza Epidemic CHANCE: HEALTH, SURVEILLANCE, SPIES, AND VOTING Chance: Health and News If You Test HIV Positive, Are You Infected? Chance and the "News Surveillance, Spies, Snitches, Loss of Privacy, and Life Is Someone Watching You? Why? Living with a Police Escort? I'm Not Worried, I've Done Nothing Wrong Identity Theft, Encryption, Torture, Planespotting Encryption Mathematics and Identity Protection Extraordinary Rendition = Kidnapping and Torture Planespotting: A Self-Organizing Countermeasure the CIA Did Not Anticipate Bigger Pictures and the CIA Voting in the 21st Century Stealing Elections Is a Time Honored Tradition A Simple Solution Exists Two Modest Proposals ECONOMICS What Exactly Is Economics? It Takes the Longest Time to Think of the Simplest Things A Preview of Two Laws of Nature Three Kinds of Economists The Human Economy Depends on Nature's Flows of Energy and Entropy Nature's Services and Human Wealth: Important Calculations How We Treat Each Other: How We Treat Nature -- The Tragedy of the Commons Mathematical Concepts and Economics Misapplied Mathematics New Mathematical Patterns: Self-Organizing Systems Finding a Niche: Habits and Habitats The Concept of Money Financial Wealth and Real Wealth Is Financial Collapse Possible Now? Follow the Money Are You Paying More or Less Than Your Fair Share of Taxes? Financial Growth vs. Fish Growth Fractional Reserve Banking: An Amazing Mathematical Trick Distributed vs. Centralized Control and Decision Making Farms: To Be Run by Few or by Many? Utilities: MUNI or Investor-Owned? Linux vs. Microsoft Medicine for People or for Profit or Both? A Little History An Example of the Need for Fuzzy Logic: The Definition of Poverty Energy and Thermodynamics Energy and the First Law of Thermodynamics The First Law of Thermodynamics Entropy and the Second Law of Thermodynamics Early Statements of the Second Law of Thermodynamics Algebraic Statement of the Second Law of Thermodynamics So What Is Entropy and Can We Measure It? Some Applications of the Second Law of Thermodynamics: Power Plants and Hurricanes Hiking up a Mountain Understanding Entropy with a Little Mathematics The Financial Mathematics of Loans, Debts, and Compound Interest Simple and Compound Interest: A Review How Much Does a Debt Really Cost You? Buying on Time and/or Installment Plans. Amortization. The Four Important Numbers: P, R, r, n Examples of Individual Debt: Rent-to-Own, Credit Cards, and Loans MEDIA LITERACY Information Flow in the 21st Century Investigative Journalism Requires Cash Thesis: The Range of Debate is Too Narrow Now Time Series Test and Multiple Source Test Measuring the Range of Debate Distractions and Illusions Media Literacy: Censorship and Propaganda Filters and Censors Censorship: External and Internal Conclusion and Epilog: Where Are the Adults? References Index

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Martin Walter is a professor in the Department of Mathematics at the University of Colorado at Boulder. Dr. Walter is a Sloan, Woodrow Wilson, and National Science Foundation Fellow as well as a member of the American Mathematical Society and Mathematical Association of America. He has lectured or taught in various countries, including Japan, China, Poland, Romania, Australia, Belgium, Norway, Sweden, Denmark, England, Germany, India, Italy, Mexico, Puerto Rico, Canada, and Brazil.