Applying mathematical tools to criminology is a relatively new but promising and exciting avenue of research. In this talk we present several case study models that are meant to mathematically frame and analyze basic sociological findings such as the broken windows effect and repeat victimization theories. We introduce agent based and PDE models to study burglary and the spread of opportunistic crime, game theories to investigate the role of informants within a criminal society, stochastic simulations to model recidivism and rehabilitation efforts, network modes to study growth and containment of hierarchical criminal organizations. Where available we have used actual criminological data to guide our modeling efforts. Finally, we will discuss how some of our models were used to design behavioral experiments conducted on actual human subjects, allowing us to compare analytical results and experimental outcomes
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