Notes & Resources

General resources for the related subjects that I am interested in or working on [constantly being updated]:
  1. Dynamical Systems
    • Books
      • From Calculus to Chaos by D. Acheson - A very good introduction to the subject requiring very minimal background
      • Chaos: An Introduction to Dynamical Systems by K. T. Alligood, T. D. Sauer, J. A. Yorke - Mathematically rigorous, step by step derivations; involves a lot of paper-pen as well as computer exercises
      • Introduction to Modern Dynamics by D. D. Nolte - Very modern and original account of dynamical systems by treating up-to-date applications such as network theory, evolutionary dynamics etc..
      • Dynamics : Geometry of Behaviour by R. H. Abraham and C. D. Shaw - A must read for geometric intuition of dynamical systems with full of wonderful illustrations
      • Chaos Book - Original book of the MOOC Nonlinear Dynamics: Geometry of Chaos(see below) 
    • Online Course  - MOOC
  2. Differential Equations
    • Books
      • Ordinary Differential Equations by V. I. Arnold
      • Differential Equations and Dynamical Systems by Lawrance Perko
  3. Numerical Techniques & Scientific Computing
  4. Statistical Mechanics
  5. Evolutionary Dynamics & Theoretical Ecology
    • Books
      • Evolutionary Dynamics by M. A. Nowak - Standard textbook which covers the very basics of evolutionary dynamics with interesting applications
      • Stability and Complexity in Model Ecosystems by Robert M. May - A classical book which defined the field of theoretical ecology from the very founder R. May - must read
      • Theoretical Ecology - Principles and Applications by Robert M. May - A collection of theoretical ecology chapters written by key figures in the field; great overview for the major problems and perspectives
      • Evolutionary Games and Population Dynamics by Josef Hofbauer and Karl Sigmund - Extensive treatment of Lotka-Volterra and Replicator Equations in relation with game theoretical approach to ecology and dynamical systems analysis
      • Models in Ecology by John Maynard Smith - General and compact treatment of mathematical models touching key ideas of ecological modeling
      • Evolution and Theory of Games by  John Maynard Smith - Introduction to game theoretical concepts in evolution and ecology with a lot of valuable insight
    • Online Course - MOOC
  6. Game Theory
    • Online Course - MOOC
    • Books
      • Two-Person Game Theory by Anatol Rapaport (Dover Pub.)
      • Games and Decisions by R. D. Luce and H. Raiffa
    • Papers
  7. Mathematics related
    • Books
      • Mathematics Applied to Deterministic Problems in the Natural Sciences by C. C. Lin and L. A. Segel - A very detailed and extensive collection of applied mathematical tools presented for a 'beginner' audience
      • Naive Set Theory by Paul Halmos - Undergraduate beginner level set theory which provides the foundations to build up mathematical rigor in a 'naive' way