Compute resource management involves requesting a compute resource like a GPU, checking if it is available, allocating it if free, running the workload, and then releasing the resource after the job completes. If the resource is not available, the request waits or triggers scaling up additional resources. The execution table traces these steps showing resource state changes and job status. Key moments include understanding when the resource is allocated and released, and what happens if the resource is busy. The visual quiz tests understanding of resource state at different steps and the flow of allocation and release.