Table of Contents

Cover image

Title page

Copyright

Dedication

Preface to the Second Edition

Acknowledgments

Chapter 1. Crabs and Criminals

1.1 Background

1.2 Transitions Between States

1.3 Social Mobility

1.4 Absorbing Chains

1.5 Recidivism

1.6 Concluding Thoughts

Chapter 2. It Isn’t Fair

2.1 Background

2.2 Manpower Scheduling

2.3 Apportionment

2.4 An Inheritance in the Talmud and Madoff’s Scheme

2.5 A Few Mathematical Details

2.6 Concluding Thoughts

Chapter 3. While the City Burns

3.1 Background

3.2 Poisson Events

3.3 The Inverse Square-Root Law

3.4 The Encumbrance of an Urban Grid

3.5 Equilibrium States

3.6 How Busy are the Fire Companies?

3.7 Optimal Deployment of Fire Companies

3.8 Concluding Thoughts

Chapter 4. Clean Streets

4.1 Background

4.2 Euler Tours

4.3 Street Sweeping

4.4 Vehicle Scheduling

4.5 Concluding Thoughts

Chapter 5. A Bayesian Take on Colorectal Screening, Baseball, Fund Managers, and a Murder

5.1 Background

5.2 Bayes’ Theorem

5.3 Colorectal Screening

5.4 Murder and OJ Simpson

5.5 Skeptical Bayesians

5.6 Batting Averages and a Paradox

5.7 A Few Mathematical Details

5.8 Comparing Apples and Oranges

5.9 Concluding Thoughts

Chapter 6. What Are the Odds of That?

6.1 Background

6.2 Coincidence and Near-Coincidence

6.3 A Few Mathematical Details

6.4 Fire Alarms, Bomb Hits, and Baseball Streaks

6.5 Not a Designer but a Gardener

6.6 Chi-Squared

6.7 Stock Funds and Baseball Streaks, Redux

6.8 Concluding Thoughts

Chapter 7. It’s Normal Not to Be Normal

7.1 Background

7.2 The One-Percenters

7.3 Market Volatility

7.4 A Few Mathematical Details

7.5 Concluding Thoughts

Chapter 8. Boom and Bust

8.1 Background

8.2 A Fishery Model

8.3 Unstable Equilibria and Cyclic Behavior

8.4 A Second Look at the Fishery Model

8.5 A Restricted-Access Fishery

8.6 Concluding Thoughts

Chapter 9. Viral Outbreaks and Blood Clots

9.1 Background

9.2 Measles Epidemics

9.3 Chaotic Dynamics or Randomness?

9.4 Predator-Mediated Coexistence

9.5 An Unusual Bloom

9.6 Viral Contamination of Algae

9.7 Blood Clotting

9.8 Concluding Thoughts

Chapter 10. Red Tides and Whatever Happened to the Red Squirrel?

10.1 Background

10.2 Reaction and Diffusion

10.3 Algal Patches

10.4 Traveling Waves

10.5 The Spread of the Gray Squirrel

10.6 Rabid Foxes and Traffic Congestion

10.7 Concluding Thoughts

Chapter 11. Spatial Patterns: The Cat’s Tail and Spreading Slime

11.1 Background

11.2 Stripes or Splotches?

11.3 Slime Molds

Chapter 12. The Coil of Life

12.1 Background

12.2 Link, Twist, and Writhe

12.3 Loopy DNA

12.4 The Gauss Linking Number

12.5 Concluding Thoughts

Afterthoughts on Modeling

Appendix A. The Normal Density

Appendix B. Poisson Events

Appendix C. Nonlinear Differential Equations and Oscillations

Appendix D. Conditional Probability

References

Index

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