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A current trend in cognitive science is to view the mind as a dynamical system (e.g., Continuity of Mind by Spivey, in which cognition is understood as a "continuous and often recurrent trajectory through a state space"). Although I'd like to critically evaluate this trend, I'm embarresed to admit that I've never taken even a basic calculus course.

Yet since I don't intend to build dynamical systems models myself, what is the bare minimum of maths learning that I need to accomplish in order to understand dynamical systems in the context of psychology? Remember, I'm a total novice!

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    $\begingroup$ Hi @TylerAlterman, and welcome to scicomp! There are many good introductions to dynamical systems stemming from non-traditional fields such as biology and social sciences. However, the ones that I'm aware of require at bare minimum an understanding of both calculus and differential equations. $\endgroup$ – Paul♦ Nov 2 '12 at 0:47
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    $\begingroup$ Tyler, you have posted this question on seven different Stack Exchange sites: Cog Sci, Linguistics, Computational Science, Mathematics, Computer Science, CS Theory, and Philosophy. Cross posting once is frowned upon, let alone six times! Which site do you want this question on? $\endgroup$ – Josh Nov 3 '12 at 13:18
  • $\begingroup$ @TylerAlterman: Josh is right. We strongly discourage posting the exact same question on multiple stack exchange sites. We suggest one of two possible courses of action. You can edit your current question on scicomp in a way that makes it unique to computational science alone or remove all your other duplicate posts. $\endgroup$ – Paul♦ Nov 3 '12 at 13:37
  • $\begingroup$ I agree with Paul, and I am closing the question, pending edits. $\endgroup$ – Geoff Oxberry Nov 4 '12 at 2:47
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That all depends.

Not having read the psychology literature at all, the minimum you probably need is 2-3 semesters of calculus and 1 semester of differential equations, and that's to understand something on the level of Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity) by Steven Strogatz. Even then, you'd probably understand the big picture, but not any of the subtleties. You could try reading that book without the math background and see how far you get.

To really start getting into the maths of dynamical systems, you'd need 1-2 semesters of real analysis on top of that (at the level of Rudin's Principles of Mathematical Analysis and, say, Munkres' Analysis on Manifolds) to be able to tackle something like Nonlinear Systems (3rd Edition) by Hassan Khalil, which would delve into much more advanced ways of quantifying and proving properties of dynamical systems. It is probably not worth you getting that much background to study dynamical systems, but maybe it is of interest to other people.

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  • $\begingroup$ Strogatz's book is really good for beginners... Way back in the day when I was an undergraduate student, we used that book and I found it a very easy read (of course, I was a math major back then) $\endgroup$ – Paul♦ Nov 2 '12 at 16:46

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