Final answer:
The WLAN security threat using mathematical algorithms to determine a pre-shared key is WEP cracking. It exploits cryptographic weaknesses in the WEP protocol to reveal the key and gain unauthorized network access.
Step-by-step explanation:
The wireless LAN (WLAN) security threat that involves mathematical algorithms to determine a pre-shared key value is c) WEP cracking. WEP, which stands for Wired Equivalent Privacy, was a security protocol that was found to have significant vulnerabilities. Cryptographic weaknesses in WEP allow attackers to use algorithms that can crack the encryption, revealing the pre-shared key used to protect the network. WEP cracking relies on the mathematical analysis of the protocol's use of static encryption keys, which once compromised, can allow an unauthorized user to gain access to a protected WLAN network.