Final answer:
The NMDA receptor is critical for the induction of hippocampal LTP by allowing calcium entry into the postsynaptic cell. This triggers a cascade that leads to the insertion of more AMPA receptors, enhancing the responsiveness to glutamate.
Step-by-step explanation:
The type of receptor critical for the induction of hippocampal LTP, by admitting calcium into the postsynaptic cell, is the NMDA receptor.
When a synapse is repeatedly stimulated, calcium entry through the NMDA receptor triggers a cellular cascade that leads to the insertion of more AMPA receptors into the postsynaptic membrane. The increased number of AMPA receptors enhances the depolarization of the membrane, making it more responsive to glutamate.