About
These lecture notes were prepared by Stefano Allesina (sallesina@uchicago.edu) for the ICTP-ICTS Winter School on Quantitative Systems Biology, held at NCBS, Bengaluru, India.
Call-out sections contain special material:
This type of call-out contains brief reviews of important mathematical concepts.
R
This type of call-out contains information about coding dynamical systems in R.
Resources
These are good introductions to theoretical ecology:
Case, An Illustrated Guide to Theoretical Ecology, 1999
May and McLean, Theoretical Ecology: Principles and Applications, 2007
Gotelli, A primer of ecology, 2008
Hofbauer and Sigmund Evolutionary Games and Population Dynamics, 1998
Mathematical background
Following the material requires basic notions in calculus, linear algebra and dynamical systems. Students should be familiar with:
- Functions, exponential function, logarithm
- Limits
- Derivatives and chain rule
- Integration of functions in one and several variables
- Taylor series
- Vectors, dot product, cross product
- Matrix product, transpose, determinant, eigenvalue decomposition
- Positive and negative definiteness of a matrix
These are good websites offering a brief review of these materials, and cheat sheets reporting the main formulas:
Paul’s Online Notes covering calculus I, II and III as well as dynamical systems; the cheat sheets are excellent.
The legendary Linear Algebra class by Gilbert Strang, who has written popular books on the subject, and taught legions of students at MIT.
Ziko Kolter has published a brief review of linear algebra concepts.
Linear algebra in four pages by Ivan Savov.
Linear algebra visualized by 3Blue1Brown.
Steve Brunton’s (U. Washington) YouTube channel contains extremely well-done lectures on dynamical systems; for example, here are reviews of derivatives, Taylor series, simulating the logistic map, integrating ODEs in a computer.