**Incorporating a formal modeling approach is similar to incorporating a neuroscience-based approach**

Around the 1990s fMRI research really took off. I think one reason for this is that many researchers had abandoned a mathematical modeling approach that was popular in the 50s and 60s, but they wanted to look at more than behavior. So, many researchers turned to examining what brain structures or networks were responsible for various cognitive tasks. They wanted to study more than just behavior, and learning what brain regions mediate behavior is a great place to start. I think mathematical modeling offers a similar alternative to examining only behavior, but it can also inform fMRI research. Mathematical modeling makes behavioral research truly scientific and theory-driven; it allows us to examine theories as well as behavior.

An early goal of mathematical modeling efforts by people like W.K. Estes, R.R. Bush, Frederick Mosteller, Roger Shepard, and Patrick Suppes was to try to mold Psychology into a formal science like Physics. If you think about the theory of gravity, physicists don’t just talk in words and say things like “objects tend to fall” or “gravity pulls objects together” – and leave it at that. They go a step further and specify the precise rate that objects fall on earth (9.8 m/s^2). Physicists would not get very far at all if they only worked in verbal theories, and I think the same holds true for Psychologists.

Taking a behavioral effect and developing a formal model that could simulate such an effect, or taking a verbal theory and translating it into a mathematical theory are things researchers can do to go beyond mere analysis of behavior. To me this is similar to turning to neuroscientific methods like fMRI to learn more about behavioral phenomena. Yet, working at the theoretical or formal modeling level can also inform fMRI research. This approach is called model-based fMRI. Thus, there are multiple reasons to go beyond behavioral and fMRI analysis and develop mathematical theories of cognition.

**Courses to take to develop skills for mathematical modeling and data analysis**

Our lab is interested in developing and using mathematical models as formal theories of cognitive processes. These models can be used to make specific predictions about how people will behave in laboratory tasks. We can then see if human behavior aligns with one model’s predictions more than others. These models are also useful for fMRI or mixed effects analyses. Formal mathematical theories are more tractable and falsifiable than verbal theories.

I have had to teach myself much of the methods for how to do this type of work because the current psychology undergraduate degree does not properly prepare students in this domain. There is no programming course required for the Psyc degree, and a student can get by taking only relatively easy math courses that are not as difficult as Calculus 1. I think math and programming courses are invaluable skills for any college graduate to have. Most importantly, these courses teach students how to think in a rationally sound and mechanistic way. This type of thinking is needed to develop formal models of cognition.

I have put together a short list that a Psychology undergraduate student could try to incorporate into their degree plan. This is a list I wish someone had shown me many years ago. The skills and ways of thinking that are learned from taking these courses will help prepare students for research using mathematical modeling approaches. These are also the type of skills used in data mining jobs at places like Google, Facebook, etc., and are an incredible supplement to the soft, but very important skills learned from the Psychology degree.

Math for university required courses:

Math 147 (Calculus 1 for Biological sciences)

Math 172 (Calculus)

Other Math courses:

Math 304 (Linear Algebra) and/or Math 323 (Linear Algebra) – more demanding

Math 411 (Mathematical Probability)

Math 442 (Mathematical Modeling)

CSCE 110 (Programming I) – 4 credits

CSCE 121 (Introduction to Program Design and Concepts) – 4 credits

CSCE 221 (Data Structures and Algorithms) – 4 credits

CSCE 420 (Artificial Intelligence) – 3 credits

CSCE 442 (Scientific Programming) – 3 credit hours