Patients with Alzheimer's disease (AD) can have seizures in addition to losing their memory and other mental functions (referred to as cognitive functions). The seizures, and other examples of overactive electrical activity in the brain that is not noticeable, contribute to the loss of cognitive function. Studies in animal models of AD suggest that a drug that prevents seizures called levetiracetam may reduce neuronal over-excitation and improve cognition. Based on this evidence, the investigators propose to determine if levetiracetam can be used to treat patients with AD. The investigators developed novel instruments for this population that will also be used in future large-scale clinical trials.