The central challenge in progressing from petascale to exascale supercomputing is the same as that in progressing from gigascale to terascale personal computing: strong scaling within shared memory on a single node of up to 1K simultaneously active computational threads. Many issues in algorithmic design and implementation are identical in these two simultaneous quests; however, the exascale quest has additional challenges due to practical limits on total power consumption (which come at the expense of resilience and node performance uniformity), to system-scale reliability (due to more points of failure), and to the need to merge the on-node programming environment with a million others (a weak scaling that is not in itself difficult, but will lead to challenges of coordination). This lecture series presents the issues, as digested from recent US Department of Energy roadmapping exercises, and focuses attention on some new issues that require mathematical attention. It is intended to provide those new to exascale computing with a working background for the week ahead, and motivation for the GPU scientific programming unit of the tutorial.