<p>What would be better? Criminology / sociology?</p>
<p>Math could be helpful for field agents. It’ll give you an edge over colleagues when it comes to… ummm… like, deciding how far somebody could have gotten in a certain amount of time, like they do on TV. You know… “he can drive at 50 MPH, been gone for 5 hours, etc…” Could also help in setting up roadblocks… probability and that kind of stuff. You know, … he wants to get from A to B, and there are 18 intersections he could travel through, which intersection is most likely to be crossed, etc…</p>
<p>Game theory could be useful for interrogations… cutting deals the guy will take, you know. Logic - formal logic - could be used to find inconsistencies in testimony, etc. As a math major, you probably know some programming, too. You could model evacuation scenarios at high-risk locations to help prepare for terrorist attacks. Hell, you could even write a program that implements an expert system and some AI to do basic profiling automatically.</p>
<p>You could talk intelligently about encryption schemes and break codes. You can find statistical irregularities in suspects’ bank account records and finance records. You could probably also better understand the strengths and limitations of polygraphs.</p>
<p>These are just some ideas I’m throwing around. You should decide for yourself whether these are plausible or not.</p>