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Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior.
Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced.
- Offers 40% more content – 5 new chapters in addition to revisions to existing chapters
- Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general
- Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book
Life science researchers, professionals, post-docs, and graduate students interested in how mathematics can be used to gain and convey a greater understanding of biology and society as well as applied mathematics professionals and students interested in exploring mathematical modeling in biology.
Preface to the Second Edition
Chapter 1. Crabs and Criminals
1.2 Transitions Between States
1.3 Social Mobility
1.4 Absorbing Chains
1.6 Concluding Thoughts
Chapter 2. It Isn’t Fair
2.2 Manpower Scheduling
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
3.2 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
4.2 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
5.2 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?
6.2 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
6.7 Stock Funds and Baseball Streaks, Redux
6.8 Concluding Thoughts
Chapter 7. It’s Normal Not to Be Normal
7.2 The One-Percenters
7.3 Market Volatility
7.4 A Few Mathematical Details
7.5 Concluding Thoughts
Chapter 8. Boom and Bust
8.2 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
9.2 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?
10.2 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
11.2 Stripes or Splotches?
11.3 Slime Molds
Chapter 12. The Coil of Life
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
- No. of pages:
- © Academic Press 2013
- 19th June 2013
- Academic Press
- eBook ISBN:
- Hardcover ISBN:
State University of New York, Stony Brook, U.S.A.
"…this is a very good introduction to mathematical modeling, one of the best that I have seen…he presents his book as a reference or a tool for self-study by mathematically prepared undergraduates who wish to see interesting and unusual applications in the biological and social sciences…This is a delightful book. By design it is not a textbook, but it would be a wonderful accompaniment to any course in modeling."--MMA.org, February 17, 2014
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