Some thought-provoking mathematical theoretical biology books. Currently incomplete and under construction.

• Elements of Mathematical Ecology, by Mark Kot, 2000. or

• An Introduction to Population Ecology, by G. E. Hutchinson, 1978. or

• Mathematical Biology volumes 1 and 2, by James D. Murray, 2004. or , or

• Theoretical Ecology: Principles and Applications, edited by R. M. May, 1976. (the 1976 version is my favorite)

• Theoretical Evolutionary Genetics, by Joe Felsenstein, 2003+ FREE!

• Mathematical Bioeconomics by Colin W. Clark, 1976. or

• Mathematical Epidemiology, Lecture Notes in Mathematics, edited by Fred Brauer, Pauline van den Driessche, and Jianhong Wu, 2008. or

• Matrix Population Models, by Hal Caswell, 2006. or

• Theoretical Evolutionary Ecology by Michael Bulmer, 1994. or

• The Evolution of Life Histories by Stephen C. Stearns, 2004. or

• Stochastic Models in Biology, by Narendra S. Goel and Nira Richter-Dyn, 1974. or

• Stochastic Population Models, by James H. Matis and Thomas R. Kiffe, 2000. or

• Modelling Biological Populations in Space and Time, by Eric Renshaw, 1991. or

• The Natural Selection of Populations and Communities by David Sloan Wilson, 1980.

• Evolutionary Games and Population Dynamics by Josef Hofbauer and Karl Sigmund, 1998. or

• Mathematical Ecology of Populations and Ecosystems by John Pastor, 2008. or

• Encyclopedia of Theoretical Ecology, edited by Alan Hastings and Louis Gross, 2012. or

• Encyclopedia of Theoretical Ecology, edited by Alan Hastings and Louis Gross, 2012. or

• Foundations of Mathematical Neuroscience by Bard Ermentrout and David Terman FREE

In addition, there are a number of books in other fields I have found valuable.

• 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. or

• The Feynman lectures on physics, by Richard Feynman, 1970. or

• Governing the Commons: The Evolution of Institutions for Collective Action by Elinor Ostrom, 1990. or

• Dynamic Programming and Markov Processes, Ronald A. Howard, 1960. The first book and my preferred introduction to Markov decision processes.

• 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. or

• 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., or

• Interacting Particle Systems, by Thomas M. Liggett, 1985. or

• Networks: An Introduction, by Mark Newman, 2010. or

For introductory textbooks at the calculus level,

• Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, by Fred Adler, 2004. or

• A Biologist's Guide to Mathematical Modeling in Ecology and Evolution, by Sarah P. Otto and Troy Day, 2007. or

• Mark Ridley's Evolution website has an interesting collection of free classic texts on evolutionary biology.

Miscellaneous:

• The prevention of malaria in the Federated Malay States : a record of twenty years' progress 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 does of pragmatism about the role of theory in practice.

• Ecological dynamics data on tribolium experiments.