A variety of measurements using a differential scanning calorimeter were used to probe how single-walled carbon nanotubes (SWCNTs) affect polymer dynamics associated with the glass transition. Tubes were dispersed in N,N-dimethylformamide containing dissolved polystyrene, and precipitation was quickly forced by the addition to large amounts of water. The percolation threshold was found to be less than 0.5 wt %, indicating good dispersion of the tubes. The glass transition temperature (T-g) increased at low nanotube fractions to a constant value about 6-7 degrees C higher than the T-g. of pure polystyrene, and did not change further as the nanotube amount changed from 1 to 30 wt %. The heat capacity change at the glass transition decreased with increasing nanotube concentration, except at very high SWCNT contents ( > 10 wt %), where the heat capacity change began to increase. The decrease of heat capacity at low nanotube contents indicates that a fraction of the polymer is made immobile via the addition of SWCNTs; while the large increase at high contents suggests that nanotubes are participating in the molecular motion that is the glass transition. The relaxation rate as determined by the change in limiting fictive temperature with annealing time showed the same qualitative behavior as the glass transition, a decrease in polymer mobility at very low nanotube fractions followed by a constant value. Surprisingly, one measure of the activation energy increased at low nanotube contents (< 0.5 wt %) and dropped at high nanotube contents to an energy that looks to be slightly higher than that for pure polystyrene. In other words, in the region where the formation of a continuous network occurs the activation energy is highest.