New research in neuro-engineering is beginning to suggest how the nervous system may perform the basic computations of calculus: Differentiation and Integration to facilitate the control of body movement. Computer models of cerebral and cerebellar control that solve large numbers of differential equations simultaneously enable lifelike simulation of sensorimotor neural control. Subsequent analysis by engineers using, for example, Laplace Transform techniques can suggest how important "long loop" reflexes are stabilized with respect to time delays. These compensated reflexes appear to enable the brain to control dynamically challenging tasks such as human walking much more simply than thought previously. Mathematical models of central nervous system function may soon enable us to construct artificial humanoids.

The basal ganglia and frontal cortex interact intimately to facilitate adaptive action plans while suppressing those that are less adaptive. The dynamics of this circuitry in reinforcement learning and decision making have been explored via a series of inter-related computational models. The models suggest distinct neurobiological mechanisms associated with (a) action selection; (b) learning the probability of an action leading to reward; (c) holding in mind graded values of reinforcement magnitude in working memory; and (d) dynamic modulation of decision thresholds. I will present novel predictions arising from these models that have been confirmed in experiments with multiple patient populations, pharmacological manipulation, neuroimaging and genetics.

Social scientists have long struggled to account for sex differences in test scores on test of mathematical ability. Social psychologists have argued that these performance differences can be at least partly explained by a phenomenon called stereotype threat, whereby women feel an added pressure to perform well to avoid confirming negative stereotypes about their gender group's math abilities. Paradoxically, this added pressure impairs performance on cognitively complex tasks. The first part of this talk will provide a summary of the current state of research on stereotype threat documenting the processes that underlie this phenomenon. Having identified some of the key mechanisms of these effects, the second part of the talk will examine strategies that might be effective at reducing stereotype threat. Implications will be discussed for narrowing the gap in performance and participation of women in math and science.