Some thought-provoking mathematical theoretical biology books.
Currently incomplete and under construction.
- Mathematical Biology volumes 1 and 2, by James D. Murray,
- Elements of Mathematical Ecology, by Mark Kot, 2000.
- An Introduction to Population Ecology, by G. E. Hutchinson,
- Theoretical Ecology: Principles and Applications, edited by
R. M. May, 1976. (the 1976 version is my favorite)
- Theoretical Evolutionary Genetics, by Joe Felsenstein, 2003+
- Mathematical Bioeconomics by Colin W. Clark, 1976.
- Mathematical Epidemiology, Lecture Notes in Mathematics,
edited by Fred Brauer, Pauline van den Driessche, and
Jianhong Wu, 2008.
- Matrix Population Models, by Hal Caswell, 2006.
- Theoretical Evolutionary Ecology by Michael Bulmer, 1994.
- The Evolution of Life Histories by Stephen C. Stearns, 2004.
- Stochastic Models in Biology, by Narendra S. Goel and Nira
- Stochastic Population Models, by James H. Matis and Thomas
R. Kiffe, 2000.
- Modelling Biological Populations in Space and Time, by
Eric Renshaw, 1991.
- The Natural Selection of Populations and Communities by
David Sloan Wilson, 1980.
- Evolutionary Games and Population Dynamics by Josef Hofbauer
and Karl Sigmund, 1998.
- Mathematical Ecology of Populations and Ecosystems
by John Pastor, 2008.
- Encyclopedia of Theoretical Ecology,
edited by Alan Hastings and Louis Gross, 2012.
- Foundations of Mathematical Neuroscience
by Bard Ermentrout and David Terman
- Mathematical Physiology: I and II by James Keener and James Sneyd, 2008.
- Modeling and Simulation in Medicine and the Life Sciences by
Frank C. Hoppensteadt and Charles Peskin, 2004.
There are a few books that are older, and were outside the
scope of my education until my perspective was already
formed. Some of these rarely mentioned
these days but good and interesting for both their content
and the historical perspective that content provides.
- Models in Biology, by D. Brown and P. Rothery, 1993.
(A great book with a unique fusion of modelling and
statistics - should have been a classic in the field.)
- Mathematical Models in Biology by Leah Edelstein-Keshet, 1988.
(This was one of the first books to synthesize a dynamical-systems
perspective on mathematical biology. A classic, as SIAM points out.)
- Modelling Fluctuating Populations by Nisbet and Gurney, 1982.
- Mathematical Biophysics by N. Rashevsky, 1948.
(An ambitious analysis of cells, nerves, locomotion, scaling
laws, and boolean networks before the discovery of DNA)
In addition, there are a number of books in other fields I have found valuable.
For introductory textbooks at the calculus level,
- Public Investment, the Rate of Return, and Optimal Fiscal Policy,
by Kenneth J. Arrow and Mordecai Kurz, 1970.
This is an economics book, but the techniques inspire a number of
connections to mathbio.
- The Feynman lectures on physics, by Richard Feynman, 1970.
- Governing the Commons: The Evolution of Institutions for Collective Action
by Elinor Ostrom, 1990.
- Dynamic Programming and Markov Processes,
Ronald A. Howard,
1960. The first book and my preferred introduction to Markov decision
- The Theory of Branching Processes, by Theodore E. Harris, 1963.
This is a mathematics book, but a good historical starting point
for the study of stochastic, density-independent growth processes.
- Branching Processes by K. B. Athreya and P. E. Ney, 1972.
An in-depth study of multi-type processes.
- Multitype Branching Processes: Theory and Applications,
by Charles J. Mode, 1971.
This has some results that are missing from Harris and Athreya
having to do with spatial models.
- An introduction to probability theory and its applications,
William Feller, 1968.
- Introduction to the Mathematical Theory of Control,
by Alberto Bressan and Benedetto Piccoli, 2007.,
- Interacting Particle Systems,
by Thomas M. Liggett, 1985.
- Networks: An Introduction,
by Mark Newman, 2010.
- Modeling the Dynamics of Life: Calculus and Probability for Life Scientists,
by Fred Adler, 2004.
- A Biologist's Guide to Mathematical Modeling in Ecology and Evolution,
by Sarah P. Otto and Troy Day, 2007.
- Mark Ridley's
website has an interesting collection of free classic texts on evolutionary
- The prevention of malaria in the
Federated Malay States : a record of twenty years'
by Sir Malcolm Watson, 1921, is a phenomenal case study of
the challenges of learning and managing a complex system (In this case,
namely, malaria transmission). While the material itself is
a interesting historical tail for anybody interested in
public health management, the tome also offers a healthy
dose of pragmatism about the role of theory in practice.
- Ecological dynamics
on tribolium experiments.