"For things separated from matter according to being and notion pertain to metaphysics; things separated according to notion and not according to being pertain to mathematics; last, things that in their notion refer to sensible matter pertain to natural sciences." St Thomas Aquinas, OP, Commentary on the Sentences 1, lect. 1
The first question that everybody asks, after hearing that I am getting my PhD in mathematical behavioral sciences, is what is it? In short, the mathematical social and behavioral sciences concern formulating precise theories of human social behavior. The goal of researchers in the field is to create a relationship between the social and behavioral sciences and mathematics that is analogous to the one that has been enjoyed between the natural sciences and mathematics for several millenia. There are various sub-fields of mathematical behavioral science, some of which are the following: game and decision theory, measurement theory, statistical modeling, and cognitive modeling. The mathematical tools used are as disparate as the fields themselves: non-linear dynamics, mathematical logic, probability, statistics, algebra, and geometry. For details click here.
My own research is presently in mathematical psychology. In particular, I am using formal language theory (as is found in mathematical logic, computer science, and mathematical linguistics) to investigate the formal properties of statistical models that are cognitively relevant. My other research interests within the field of mathematical psychology concern measurement theory and game theory. I am also very interested in philosophy, in particular "scientific philosophy" as well as certain areas of pure mathematics. Details on my research interests can be found under 'Research'.
I also have a background in philosophy and so I like to think of my work as being in the same vein as a philosopher of science. I am here to clarify the murkiness that surrounds the use of cognitively relevant statistical models using the tools of analysis and logic. But since I purport to be a scientist, or at the very least an applied epistemologist, I also want to create my own models and offer my own modifications to them. For example, for my master's thesis i quantitatively described neural networks using measure theory.