The scenario described is indicative of a port scanning attack. Port scanning is a method used by attackers to discover open ports on network devices. A single SYN packet sent to each port is a technique known as SYN scanning or half-open scanning, where the attacker sends a SYN message (as if they are going to initiate a TCP connection) to every port on the server, looking for positive responses which indicate an open port. This type of scanning is less intrusive and harder to detect because it never completes the TCP three-way handshake1.
Cisco community resources on Denial of Service (DoS) attacks