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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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Let me preface this by saying I think this question might be a bit too open ended for the site, but to give you a head start... Well, don't be embarrassed you haven't taken calculus, everyone has to start somewhere. However, I would say that a solid course in differential equations is a prereq for anything "dynamical", and that normally requires a couple of semesters of single variable, and usually a semester of multivariable calculus to stomach it all. Of course, you could just start studying the dynamical systems and fill in whatever math you run across, which will give you a –  Chuck Sherrington Nov 2 '12 at 1:49
    
more intuitive grasp of things, but might be more painful in the short-term. –  Chuck Sherrington Nov 2 '12 at 1:50
    
I've taken advanced calculus and have a few classes on state space and control systems, and still, can barely understand even the simplest state space equations. If I remember correctly, a lot of them involve matrices and linear algebra to be able to understand what's happening with the states. –  Alex Stone Nov 2 '12 at 6:38
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Tyler, you have posted this question on seven different Stack Exchange sites: here, 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? –  Josh Gitlin Nov 3 '12 at 13:16
    
Sorry Tyler, I never heard back from you and so I cast the final close vote on this question. Please comment back if you'd like to discuss this with me. I'd be happy to help explain what went wrong here and help you out! –  Josh Gitlin Nov 9 '12 at 15:15
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closed as not constructive by Chuck Sherrington, Artem Kaznatcheev, Ben Brocka, Jeff, Josh Gitlin Nov 9 '12 at 15:09

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1 Answer

Unfortunately, in psychology and cognitive sciences (and some parts of neuroscience) absolutely no mathematical training is given beyond the highschool level (intro stats, basics of linear algebra in $\mathbb{R}^2$ and $\mathbb{R}^3$, and intro calc; see also this answer). To make this relatable, I will compare understanding dynamics sytems to literature, where you have 3 levels: (1) being able to read, (2) being able to assess, (3) being able to write.

  1. Reading level: a basic course in dynamic systems should be enough. If you understand math at the level of Strogatz's "Nonlinear dynamics and chaos" (usually used in a first undergrad course on dynamic systems), then you know how to read a paper on dynamic systems in cognitive science.

  2. Assessment level: you need to achieve the basics of math that everybody in the 'hard' sciences or (non-software) engineering has: linear algebra, ordinary differential equations, introductory PDEs (at the level of calc 3 or 4), logic, and introductory discrete math. More importantly, you would need the extremely vague notion of mathematical maturity. Unfortunately, it is hard to explain how to achieve this. I don't know of any equivalent concept in the cognitive sciences. There is no shortcut to achieving mathematical maturity, and it is not domain specific. Mathematical maturity is something you reach from doing lots of different kinds of basic math and proofs.

  3. Writing level: the step from (2) to (3) is not as big as from (1) to (2), all you need is creativity and breadth of reading in the relevant domain: i.e. cognitive science. The lack of a large gap from (2) to (3) is why you often see mathematicians and theoretical physicists cross domains and start contributing to the theory branches of various fields (biology, neuroscience, psychology, etc).

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