Best path to Non-Linear Dynamics/Chaos theory for non-science major?

[Dods]

Hi,

I think some background is necessary:

I'm a Psychology undergraduate student. I also really love math. I've incorporated some pure math into my studies - next semester I'll have room for a course on "Foundational Mathematics" (I'm not sure if that's exactly what they call it outside my country but it's basically logic, set theory, and some extra topics), and hopefully will be accepted into the rigorous calculus course sequence they offer to students in the hard sciences rather than the hand-wavy stuff they give to everyone else. I think I'm preparing well for these courses - I've been learning set theory from a book and from these forums (thanks, micromass :) ) and I've started going through Spivak's Calculus to prepare for the calculus sequence.

That is going quite well. However, I would love to learn non linear dynamics or chaos theory as well - I'm planning to interdisciplinary graduate work and feel that knowing something about this branch of math would be a bonus - but I have no idea what the prerequisites are, what books are considered standard/very good, etc.

Mostly, I'd like to know more about which math courses you guys think I should take before a non-linear dynamics course, but also, because my studies are so far removed from the hard sciences, if there are any other relevant courses I should take before this kind of course - for instance courses that are foundational for science students but I may not have taken.

Thanks in advance! I'd very much appreciate any advice.

Dods.

 

[Number Nine]

That depends strongly on the rigour of the course. Courses in multivariable calculus, linear algebra, and differential equations should serve well enough as prerequisites for a good introduction to non-linear dynamics (in fact, they're more or less a bare minimum).

That said, non-linear dynamics is the language of an enormous portion of modern cognitive/computational neuroscience; knowing some of the basics will open up a great deal of the literature to you. As a side note, knowing some calculus and linear algebra will make it possible for you to study statistics properly. I have never seen a discipline that prepares students so poorly for research as psychology; the statistics courses you take in the psych department will be grossly insufficient for the kind of research that actually psychologists do. Study as much math as you can.

 

[symbolipoint]

That depends strongly on the rigour of the course. Courses in multivariable calculus, linear algebra, and differential equations should serve well enough as prerequisites for a good introduction to non-linear dynamics (in fact, they're more or less a bare minimum).

That said, non-linear dynamics is the language of an enormous portion of modern cognitive/computational neuroscience; knowing some of the basics will open up a great deal of the literature to you. As a side note, knowing some calculus and linear algebra will make it possible for you to study statistics properly. I have never seen a discipline that prepares students so poorly for research as psychology; the statistics courses you take in the psych department will be grossly insufficient for the kind of research that actually psychologists do. Study as much math as you can.

Sometimes, people from other educational background, including so many professionals, will say, "Statistics is very hard". These are people whose backgrounds were not in any physical sciences. They did not go through two or three semesters of Calculus with Analytic Geometry; they did not develop critical analytical use of Intermediate Algebra and mostly did not analyze physical problems, to solve them. They usually went through courses of Intermediate Algebra, and then because their chosen subject field was different, had a different set of mathematical requirements. They often went through some Elementary Statistics course. No Calculus, Differential Equations, Linear Algebra.

Just be aware, their minds are different. Engineers and physical scientists want to attach numbers to things; while the sociologists, journalists, art historians, public administrators, retail managers, ... want to understand the present and past human conditions, and are interested in how other people think, behave, and how people can be served and influenced.

Just wanted to comment about what Number Nine said.

 

[Dods]

Thanks for the replies!

Number Nine, I found your comments on statistics especially helpful and illuminating, because I didn't realize that the statistics courses offered to psych majors were all that different - thanks for giving me an idea of what I can expect from them. And yeah, I will study as much math as I can! :)

Do you think I should have a physics course under my belt before taking the non-linear dynamics course, or is that less relevant?

Thanks again,

Dods.

 

[micromass]

As far as I know, a lot of examples of non-linear dynamics come from physics. So yes, a physics course would be either immediately helpful, or it should broaden your perspective on things.

Things like ODE and PDE are crucial. So don't limit yourself to cookbook classes on solve differential equations, but take classes that get into the theory as well.

 

[Number Nine]

Thanks for the replies!

Number Nine, I found your comments on statistics especially helpful and illuminating, because I didn't realize that the statistics courses offered to psych majors were all that different - thanks for giving me an idea of what I can expect from them. And yeah, I will study as much math as I can! :)

Do you think I should have a physics course under my belt before taking the non-linear dynamics course, or is that less relevant?

Thanks again,

Dods.

Physics isn't necessary in order to understand NLD, but someone who doesn't have much experience with (or love for) pure mathematics would probably find one helpful, if only because it would motivate some of the concepts; though, don't feel that you need to take a physics course if it's difficult to fit into your schedule.

Statistics in psychology departments is a bit weird. Experimental psychology (particularly in areas like cognitive psychology) tends to be a fairly math heavy discipline (ranging all the way from vanilla statistical procedures like ANOVA to computational modelling with ODE's and neural networks, all the way to differential geometry and algebraic topology).

Psychology as a major, on the other hand, is very profitable for most Universities (being an extremely popular major) and tends to attract lots of people who's only exposure to psychology is from shows like criminal minds and Dr. Phil. You can't expect all of these people to study math, so psychology departments generally organize their own statistics courses. These courses explain some of the basics well enough (and some not; about 80% of psychology undergraduates can't properly explain what a p-value is, for instance), but they're more or less terminal (i.e. you can't really build upon them in order to study anything more advanced). The result is that lots of students are shocked at just how much they have to learn once they start reading the literature. A a few good courses in linear algebra and calculus (and maybe statistics in the STATS department?) will put you in a better position that 99% of psychology students.

 

[Dods]

Thank you both very much!

I'm definitely going to take all your advice on board, thank you for the help :)

I think I will try to take a physics course - either it helps me ground or prepare for other areas of study (probably), or, in the worst case scenario, I fulfill part of the requirements for credits outside my major with an interesting course. :)

 

[craig_241]

If you have the prerequisites, which are, "multivariable calculus and introductory physics," then this is a good book to read. We used it for our course on nonlinear dynamics.

http://www.amazon.com/dp/0738204536/?tag=pfamazon01-20

 

[Dods]

Thanks!

Once I do the courses I need I'll have a look at that book. :)

 

[Number Nine]

If you have the prerequisites, which are, "multivariable calculus and introductory physics," then this is a good book to read. We used it for our course on nonlinear dynamics.

http://www.amazon.com/dp/0738204536/?tag=pfamazon01-20

I'll second this. Probably the best written introduction to the subject.

 

[atyy]

If you have the prerequisites, which are, "multivariable calculus and introductory physics," then this is a good book to read. We used it for our course on nonlinear dynamics.

http://www.amazon.com/dp/0738204536/?tag=pfamazon01-20

Strogatz is great for eg. Neurobiology, but I'm a bit surprised it's used in physics - don't they usually talk lots about Hamiltonian chaos and the KAM theorem?