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Mathematical Models for Society and Biology
- 1st Edition - December 27, 2001
- Author: Edward Beltrami
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 0 8 5 5 6 1 - 2
- Paperback ISBN:9 7 8 - 0 - 1 2 - 3 9 1 0 8 9 - 9
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 5 1 1 2 5 - 2
Mathematical Modeling for Society and Biology engagingly relates mathematics to compelling real-life problems in biology and contemporary society. It shows how mathematical tools… Read more
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Request a sales quoteMathematical 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.
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.
Preface ix
1 Crabs and Criminals
1.1 Background
1.2 Absorbing Markov Chains
1.3 Social Mobility
1.4 Recidivism
1.5 Exercises
1.6 Further Readings
2 It Isn't Fair: Municipal Workers, Congressional Seats, and the Talmud
2.1 Background
2.2 Manpower Scheduling
2.3 Apportionment
2.4 An Inheritance
2.5 Exercises
2.6 Further Readings
3 While the City Burns
3.1 Background
3.2 Poisson Processes
3.3 The Inverse Square Root Law
3.4 How Busy Are the Fire Companies?
3.5 Optimal Deployment of Fire Companies
3.6 Exercises
3.7 Further Readings
4 Clean Streets
4.1 Background
4.2 Euler Tour
4.3 Street Sweeping
4.4 Vehicle Scheduling
4.5 Exercises
4.6 Further Readings
5 The Coil of Life
5.1 Background
5.2 The Gauss Linking Number
5.3 Twisting and Writhing of DNA
5.4 Exercises
5.5 Further Readings
6 Measles and Blood Clots
6.1 Background
6.2 Equilibria and Stability
6.3 Linearization
6.4 Measles Epidemics
6.5 Chaotic Dynamics or Randomness?
6.6 Blood Clotting
6.7 Exercises
6.8 Further Readings
7 Sardines and Algae Blooms
7.1 Background
7.2 A Catastrophe Model of Fishing
7.3 Unusual Blooms
7.4 Cycles
7.5 Another View of Fish Harvesting
7.6 Exercises
7.7 Further Readings
8 Red Tides and What Ever Happened to the Red Squirrel?
8.1 Background
8.2 Diffusion
8.3 Algal Patches
8.4 Traveling Waves
8.5 The Spread of the Gray Squirrel
8.6 Exercises
8.7 Further Readings
9 Submarines and Trawlers
9.1 Background
9.2 A Variational Lemma
9.3 Hide and Seek
9.4 A Restricted Access Fishery
9.5 A Comment about Strategy
9.6 Exercises
9.7 Further Readings
Afterthoughts on Modeling
Appendix. Conditional Probability
References
Solutions to Select Exercises
Index
1 Crabs and Criminals
1.1 Background
1.2 Absorbing Markov Chains
1.3 Social Mobility
1.4 Recidivism
1.5 Exercises
1.6 Further Readings
2 It Isn't Fair: Municipal Workers, Congressional Seats, and the Talmud
2.1 Background
2.2 Manpower Scheduling
2.3 Apportionment
2.4 An Inheritance
2.5 Exercises
2.6 Further Readings
3 While the City Burns
3.1 Background
3.2 Poisson Processes
3.3 The Inverse Square Root Law
3.4 How Busy Are the Fire Companies?
3.5 Optimal Deployment of Fire Companies
3.6 Exercises
3.7 Further Readings
4 Clean Streets
4.1 Background
4.2 Euler Tour
4.3 Street Sweeping
4.4 Vehicle Scheduling
4.5 Exercises
4.6 Further Readings
5 The Coil of Life
5.1 Background
5.2 The Gauss Linking Number
5.3 Twisting and Writhing of DNA
5.4 Exercises
5.5 Further Readings
6 Measles and Blood Clots
6.1 Background
6.2 Equilibria and Stability
6.3 Linearization
6.4 Measles Epidemics
6.5 Chaotic Dynamics or Randomness?
6.6 Blood Clotting
6.7 Exercises
6.8 Further Readings
7 Sardines and Algae Blooms
7.1 Background
7.2 A Catastrophe Model of Fishing
7.3 Unusual Blooms
7.4 Cycles
7.5 Another View of Fish Harvesting
7.6 Exercises
7.7 Further Readings
8 Red Tides and What Ever Happened to the Red Squirrel?
8.1 Background
8.2 Diffusion
8.3 Algal Patches
8.4 Traveling Waves
8.5 The Spread of the Gray Squirrel
8.6 Exercises
8.7 Further Readings
9 Submarines and Trawlers
9.1 Background
9.2 A Variational Lemma
9.3 Hide and Seek
9.4 A Restricted Access Fishery
9.5 A Comment about Strategy
9.6 Exercises
9.7 Further Readings
Afterthoughts on Modeling
Appendix. Conditional Probability
References
Solutions to Select Exercises
Index
- No. of pages: 199
- Language: English
- Edition: 1
- Published: December 27, 2001
- Imprint: Academic Press
- Hardback ISBN: 9780120855612
- Paperback ISBN: 9780123910899
- eBook ISBN: 9780080511252
EB
Edward Beltrami
Affiliations and expertise
State University of New York, Stony Brook, U.S.A.