I am currently a junior. I need to decide whether to take complex analysis or cryptology this semester. Complex analysis seems to be a recommended course for people considering graduate school, but cryptology is strongly recommended by my advisor because 1. I will be exposed to many different fields of math in crypto so it is better for my overall mathematical maturity and 2. my current research interest is in probability and may want to study probability in grad school, and I will see lots of applicaitons of probability in cryptology and possibly find a new research idea. Besides these two classes, by the time I graduate I will have taken calc, linear, modeling, diffeq, probability, math stats, sets and proofs, topology, graph theory, abstract algebra, real analysis, stochastic process, abstract algebra II, combinotorics, and numerical analysis/dynamical systems. Any suggestions on whether I should take complex analysis or cryptology?

If cryptology is pertinent to your research now, then you should take it to hopefully progress your research experience. Since you are only a junior you have time to take complex analysis senior year and, even though it may not be your focus for grad school, it is a pretty standard course that grad schools like to see the applicant has taken. That would be my two cents - though there is certainly no wrong answer.

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