Mathematical Models for Society and Biology


  • Edward Beltrami, State University of New York, Stony Brook, U.S.A.

Mathematical Modeling for Society and Biology engagingly relates mathematics to compelling real-life problems in biology and contemporary society. It shows how mathematical tools can be used to gain insight into these modern, common problems to provide effective, real solutions. Beltrami's creative, non-threatening approach draws on a wealth of interesting examples pertaining to current social and biological issues. Central ideas appear again in different contexts throughout the book, showing the general unity of the modeling process. The models are strikingly novel and based on issues of real concern. Most have never appeared in book form. Through the relevance of these models mathematics becomes not just figures and numbers, but a means to a more refined understanding of the world.
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Beltrami is appropriate for readers interested in biology, sociology, public policy, political science, and mathematics as well as anyone interested in how mathematics can be used to gain, and convey, a greater understanding of biology and society.


Book information

  • Published: December 2001
  • ISBN: 978-0-12-085561-2


Reviews "One has here a wealth of interesting applications -- selected to motivate the large group of readers outside engineering and the physical sciences who can benefit from mathematical modeling but are seldom shown how it can be useful for their own areas." - Thomas Seidman, University of Maryland "This is a delightful collection of essays that take the reader from the specific application to the more general mathematical methods...I enjoyed reading the author's style that draws the reader into the subject and motivates the mathematical methods that follow." - Daniel Zelterman, Yale University "This is one of the best texts I have seen for undergraduate modeling courses. It is less formal and much more engaged than most in real questions from the very start. Yet the material is accessible and does not require an excessive amount of background." -Bruce N. Lundberg, University of Southern Colorado

Table of Contents

Preface ix1 Crabs and Criminals 1.1 Background1.2 Absorbing Markov Chains1.3 Social Mobility1.4 Recidivism1.5 Exercises1.6 Further Readings 2 It Isn't Fair: Municipal Workers, Congressional Seats, and the Talmud 2.1 Background2.2 Manpower Scheduling2.3 Apportionment2.4 An Inheritance2.5 Exercises2.6 Further Readings 3 While the City Burns 3.1 Background3.2 Poisson Processes3.3 The Inverse Square Root Law3.4 How Busy Are the Fire Companies?3.5 Optimal Deployment of Fire Companies3.6 Exercises3.7 Further Readings 4 Clean Streets 4.1 Background4.2 Euler Tour4.3 Street Sweeping4.4 Vehicle Scheduling4.5 Exercises4.6 Further Readings 5 The Coil of Life 5.1 Background5.2 The Gauss Linking Number5.3 Twisting and Writhing of DNA5.4 Exercises5.5 Further Readings 6 Measles and Blood Clots 6.1 Background6.2 Equilibria and Stability6.3 Linearization6.4 Measles Epidemics6.5 Chaotic Dynamics or Randomness?6.6 Blood Clotting6.7 Exercises6.8 Further Readings 7 Sardines and Algae Blooms 7.1 Background7.2 A Catastrophe Model of Fishing7.3 Unusual Blooms7.4 Cycles7.5 Another View of Fish Harvesting7.6 Exercises7.7 Further Readings 8 Red Tides and What Ever Happened to the Red Squirrel? 8.1 Background8.2 Diffusion8.3 Algal Patches8.4 Traveling Waves8.5 The Spread of the Gray Squirrel8.6 Exercises8.7 Further Readings 9 Submarines and Trawlers 9.1 Background9.2 A Variational Lemma 9.3 Hide and Seek 9.4 A Restricted Access Fishery9.5 A Comment about Strategy9.6 Exercises9.7 Further Readings Afterthoughts on Modeling Appendix. Conditional Probability References Solutions to Select Exercises Index