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I am a sophomore Mathematics major w/ concentration in applied math. My secondary interests are in biology and psychology. I plan to go on to graduate study, but I'm not exactly sure what I want to specialize in yet. I've got a few questions.

My understanding is that there are two types of modeling - deterministic (i.e. dynamical systems) and stochastic. The prior generally uses differential equations and the latter uses statistical methods such as linear regression. It seems like most of the faculty here specialize in one domain or the other. Is that usually the case or do researchers usually just look at a real-world problem and apply whichever they feel like? I don't really have a preference to studying one or the other at the moment.

Also, are there some fields of application (i.e. biological, physical, social, financial) for which deterministic models are more useful and others where stochastic models are? If so, which are most applicable to biology (medical) and psychology? What courses should I take and what skills do I need to develop to be successful in graduate school?

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    Can't offer a comprehensive answer but in my understanding, medical and psychology research predominantly use statistical methods. I would definitely take mathematical statistics and regression/ANOVA courses. For financial, time series statistics and machine learning are a good idea. Physical / physically oriented biology often use stochastic models but of a different flavor than regression, somewhat more like deterministic (and sometimes even deterministic). For this, stochastic processes and stat mech. Don't worry too much about learning it all now. That's what grad school is for. – 2017-01-05
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    I agree with @spaceisdarkgreen just wanted to add that the classification you used is not precise. It happens very often that a deterministic model is derived using statistical methods and vice versa. I mean, being deterministic or stochastic is mostly in the nature of the phenomena and how we want to use/treat it – 2017-01-06

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