We propose the spectrum allocation and resource scheduling algorithms in cognitive point to multipoint (PMP)networks with rapid changes of spectrum opportunities and present a media access control (MAC) protocol based on these algorithms. The objective of spectrum allocation is to make efficient use of the spectrum while maintaining the transceiver synchronization on frequency and time in the network. The objective of resource scheduling is to guarantee the quality of service (QoS)requirements of different kinds of connections and to minimize the total energy consumption in the network as well. By sensing only a small set of possible channels in each slot based on the state transition probability of each channel, our spectrum allocation algorithm achieves high spectrum efficiency in the network. The resource scheduling problem is divided into three sub problems and we derive optimal solutions to these problems by greedy algorithm and convex optimization. The simulation results show that our algorithm can make efficient use of the spectrum and the network resources at a cost of low computational complexity.