Step 1: Identify the subject structure.
The sentence joins two subjects using "neither...nor": "the mathematics department" and "the economics department".
Step 2: Recall the agreement rule for neither...nor.
When two subjects are joined by "neither...nor", the verb does not agree with the first subject, it agrees with the subject placed closer to it, which is the second one.
Step 3: Apply the rule to this sentence.
Here the subject closer to the verb is "the economics department", which is singular. So the verb must take the singular form "requires", not the plural form "require" that is actually used.
Step 4: Confirm the rest of the sentence is fine.
"Neither...nor" is the right conjunction pair for this structure, "must" correctly shows obligation, and "a Master's Degree" is a correctly used noun phrase. None of these carry an error.
Final Answer:
The verb "require" should be "requires" to agree with the nearer singular subject, so option (b) is correct.